From 1249a1b47c9f760ac92e64a441b8c6581e2b6247 Mon Sep 17 00:00:00 2001 From: Max Freedom Pollard Date: Thu, 3 Sep 2026 21:37:45 -0400 Subject: [PATCH] Run the ampoule in real photon transport: budget, gate, synapse, boundary and dose MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit ampoule/ builds the sealed machine of transistor/SEALED.md and transistor/EMBODIMENT.md shell by shell in OpenMC 0.16 with the official ENDF/B-VIII.0 photoatomic library, drives it with the ⁹⁰Sr and ⁹⁰Y beta spectra of its own core through the thick target bremsstrahlung treatment, and calibrates the instrument first against NIST XCOM attenuation, exponential slab transmission and the thick target rule. Measured: 43.9 M photons per second leave the core at a mean 252 keV (0.057 per decay); the vessel deposits 183 µW against the 181 µW ledger; the 64 sites see 32.9 k/s in plastic and 1.02 M/s in CsI against a proposal budget of 10⁶; the boundary counts 3.25 M/s against the assumed 10⁷; the collar's ON/OFF contrast is 6.3 (11.9 with CsI); the 64 × 64 Green's function has nearest neighbour weights of 3×10⁻⁵ and a fan out of 0.1 percent; a 1 mm lead septum halves the coupling it sits across; the ambient dose is 68 µSv/h at the wall and 0.26 µSv/h at a metre. The notes are amended in place: the cells must be CsI, the mouth is a factor three narrower than priced, the aperture and the septum are analog knobs, and the dose figure the build note deferred is on the table. neutron/data.py now fetches the photoatomic files and the natural isotopes of the vessel's elements. Closes #14 Co-Authored-By: Claude Fable 5.1 --- .gitignore | 1 + README.md | 20 +- ampoule/README.md | 61 + ampoule/beta.py | 72 + ampoule/calibrate.py | 178 + ampoule/calibration.json | 213 + ampoule/model.py | 609 + ampoule/report.py | 466 + ampoule/results.md | 147 + ampoule/tallies.json | 30862 ++++++++++++++++++++++++++++++++++++ figures/fig17_ampoule.png | Bin 0 -> 236627 bytes figures/fig17_ampoule.svg | 5912 +++++++ index.html | 19 +- neutron/data.py | 26 +- transistor/EMBODIMENT.md | 4 + transistor/SEALED.md | 2 + 16 files changed, 38585 insertions(+), 7 deletions(-) create mode 100644 ampoule/README.md create mode 100644 ampoule/beta.py create mode 100644 ampoule/calibrate.py create mode 100644 ampoule/calibration.json create mode 100644 ampoule/model.py create mode 100644 ampoule/report.py create mode 100644 ampoule/results.md create mode 100644 ampoule/tallies.json create mode 100644 figures/fig17_ampoule.png create mode 100644 figures/fig17_ampoule.svg diff --git a/.gitignore b/.gitignore index 760e148..9d91966 100644 --- a/.gitignore +++ b/.gitignore @@ -4,3 +4,4 @@ __pycache__/ neutron/data/ neutron/work/ photon/cache/ +ampoule/work/ diff --git a/README.md b/README.md index ee91ee4..a13eeed 100644 --- a/README.md +++ b/README.md @@ -309,6 +309,7 @@ Every component except one is either routine nuclear physics or recently demonst | [simulator/](simulator/) | the digital twin: a Tier 1 machine run decay by decay, validated against exact enumeration, with decays per sample and energy per sample measured | | [neutron/](neutron/) | the keystone at reactor scale, computed: the two region subcritical gate in OpenMC with the official ENDF/B-VIII.0 library, calibrated against three ICSBEP handbook criticals; gain, the fission matrix and its eigenvalue check, transfer curves under two absorbers, the truth tables, the superposition check, level restoration spectra, the clock and gain bandwidth product, and the temperature coefficient that prices the veto | | [photon/](photon/) | the photon keystone searched for in ENSDF: every gateway of every isomer that holds a bit for a second, in observed and allowed classes, with its release cascade; every level restoring coincidence within rotor reach and the areal density wall each one meets; every isomer with a signal gateway and a veto gateway; the NEEC class ranked | +| [ampoule/](ampoule/) | the sealed machine in real photon transport: the vessel of the build note in OpenMC with ENDF/B-VIII.0 photoatomic data and its own beta spectra, calibrated against XCOM and the thick target rule; the photon budget, site rates in plastic and in CsI, pile up, the collar's transfer curve, the 64 × 64 Green's function and what the septum does to it, the boundary count rate, the energy budget, and the dose outside | | [transistor/](transistor/) | the reference transistor: one pinout at three scales, the valve, the datasheet with characteristic curves and maximum ratings; with four accompanying notes: [SEALED.md](transistor/SEALED.md) (the machine), [EMBODIMENT.md](transistor/EMBODIMENT.md) (the build, at assembly grade), [VALVE.md](transistor/VALVE.md) (the logic), [COMPONENTS.md](transistor/COMPONENTS.md) (the full inventory of a working computer, missing pieces simulated), [POWER.md](transistor/POWER.md) (the metabolism), and [SCALING.md](transistor/SCALING.md) (the trajectory) | --- @@ -403,15 +404,30 @@ Two lines of the theory change as a result. The convertible class of Section 2 i --- +## The ampoule, transported + +The sealed machine of the two notes above was a design at assembly grade whose every number, beyond the decay constants, was an assumption. [ampoule/](ampoule/) builds the vessel shell by shell in OpenMC with the official ENDF/B-VIII.0 photoatomic library, drives it with the beta spectra of its own ⁹⁰Sr/⁹⁰Y core through a thick target bremsstrahlung treatment, calibrates the instrument first (attenuation to 0.4 percent of NIST XCOM, slab transmission to 1.0 percent of the exponential, thick target yields within the rule's own tolerance), and replaces the assumptions with tallies. + +- **The light is scarce and hard.** A gigabecquerel of each nuclide makes 0.0569 bremsstrahlung photons per decay, and its own pellet and capsule absorb the soft majority of them: **43.9 M/s** leave the core, at a mean energy of 252 keV, while the vessel deposits 183 µW against the ledger's 181 µW per GBq. Everything the compute shell, the boundary and the shield do, they do with that. +- **The budget closes only where the cells are dense.** The boundary ring counts **3.25 M/s**, 7% of the photons leaving the core but 0.33× the note's 10⁷ per second, so the precision law gives 50 eight bit reads per second where the note priced 153. The 64 sites, as 2 mm plastic cells, see 32.9 k/s of interactions together, 0.033× the proposal budget the sampler was priced at; the same cells in CsI, the note's other option, see **1.02 M/s**, 31× more, which meets the budget. The build note is amended: the cells are CsI, and the mouth is a factor 3.0 narrower than it was priced. +- **The weights are small and the controls are knobs.** The Green's function between sites, measured 64 × 64, puts a nearest neighbour coupling at 3×10⁻⁵ per photon and the whole fan out of a site to its 63 neighbours at 0.1%: the fan out tax of theory Section 1.3 for a real shell, three orders below the compiler's toy fabric, and an attenuation of 3×10⁴ per hop. The tungsten collar, the reference transistor's GATE terminal, has an ON/OFF contrast of 6.34 with plastic cells and 11.94 with CsI, and the lead septum, the build note's inhibitory blocking, leaves the coupling it sits across at 0.49 of its open value against 1.00 on the unshielded side. Both are filters for a hard spectrum, not barriers: the same finding as the cadmium sheet of the neutron gate, for the same reason. +- **The wall is thinner than the spectrum.** 3.4 M/s escape the shield, 7.7% of what left the core at a mean 565 keV, and the ambient dose rate is **67.8 µSv/h** at the titanium wall and **0.261 µSv/h** at one metre (ICRP 116). The build note deferred this figure to the builder; it is now on the table, and it says a gigabecquerel ⁹⁰Sr ampoule behind 4 mm of lead is an instrument for a lead pot, which is the licence class the note already gave it. + +![The ampoule in photon transport](figures/fig17_ampoule.svg) + +The machine the theory can seal today is therefore a rate coded sampler whose photons are hard, whose weights are small, whose mouth is narrower than it was priced, and whose two mechanical controls are analog. Every one of those adjectives was an adjective; each is now a number, and the notes are corrected where the numbers say so. + +--- + ## Open problems and how to contribute 1. **Keystone:** propose or measure a compact state meeting the leak condition with β>1 *in a level restoring or convertible class* (theory, Section 2). *This is problem number one.* A concrete, computable subproblem: search ENSDF for heterogeneous pairs of isomers whose cascade lines and gateway lines are mutually resonant (gate A's output pumps gate B and vice versa); the search space is already tabulated in `/gates`. The computed neutron gate ([neutron/](neutron/)) adds a second requirement that the photon sector had not been asked for: the state must also supply a *signal controlled inhibition*, because the only one the neutron sector has is heat and it is worth a fraction of the gain. A gate with gain but no inversion is a linear amplifier with a comparator bolted to its boundary, and the machine it builds is the Bernstein machine of Section 6 with better numbers, not a logic family. 2. Tighten the throughput law for fan out reuse: when is a count "spent"? 3. A learning rule: aperture update Δα ∝ coincidence(pre,post) is Hebbian or STDP using the *same* coincidence primitive as the AND gate (Appendix B.4); formalize and simulate. -4. Transport level 𝒢 for a real geometry that implements a target weight matrix (signed weights via complementary channels). +4. Transport level 𝒢 for a real geometry that implements a target weight matrix (signed weights via complementary channels). *The measurement half is done:* [ampoule/](ampoule/) has the 64 × 64 Green's function of the build note's compute shell, nearest neighbour weights of 3×10⁻⁵ per photon with 0.1% total fan out; what remains is to run the compiler of theory Section 11 on that geometry rather than on the toy fabric. 5. Tier 2: a concrete two qubit gate on nuclear spin or Mössbauer DOF with a room temperature error budget. 6. **The addressed long retention write.** The broadband route to self written memory is dead by a bandwidth ratio of 10¹⁸, and the narrowline route is now open in principle (nuclear lamps, radiogenic feeding, resonance addressing: theory Section 9); what remains is a state that is simultaneously *parent fed, gradient addressable, and long lived*. A concrete, computable search: scan the catalog in `/gates` for isomers with lifetime above seconds whose feeding parents emit Mössbauer class lines, and rank by the addressing sensitivity Γ/(dE/dB). -7. Measure realized bits per detected quantum for a pixelated spectroscopic boundary against the log_2(N_E N_x N_τ) ceiling of the boundary theory. +7. Measure realized bits per detected quantum for a pixelated spectroscopic boundary against the log_2(N_E N_x N_τ) ceiling of the boundary theory. The boundary's raw budget is now computed, 3.25 M/s detected in the build note's ring, 0.33× what it was priced at ([ampoule/](ampoule/)); the ceiling is still to be measured against it. Open an Issue stating the claim and the test; pair every Pull Request with the Issue it closes. diff --git a/ampoule/README.md b/ampoule/README.md new file mode 100644 index 0000000..218723a --- /dev/null +++ b/ampoule/README.md @@ -0,0 +1,61 @@ +# /ampoule: the sealed machine in real photon transport + +The ampoule of [transistor/SEALED.md](../transistor/SEALED.md) is the one machine the theory says it can seal today, and [transistor/EMBODIMENT.md](../transistor/EMBODIMENT.md) specifies it at assembly grade. Every number in those two notes that is not a decay constant was an assumption: the photons a gigabecquerel of ⁹⁰Sr/⁹⁰Y actually sends into the compute shell, the rate at which the boundary counts them, the pile up in a 2 mm site, the coupling between sites through a real glass plate, what a tungsten aperture and a lead septum actually do to a hard bremsstrahlung spectrum, and the dose outside a wall the build note said the builder must certify. This directory builds the vessel in OpenMC with the official ENDF/B-VIII.0 photoatomic library, drives it with the beta spectra of its own core, calibrates the instrument first, and replaces every one of those assumptions with a tally. + +| file | what it is | +|---|---| +| [`beta.py`](beta.py) | the ⁹⁰Sr and ⁹⁰Y beta spectra (unique first forbidden shape, Fermi function), checked against the ICRP 107 mean energies | +| [`calibrate.py`](calibrate.py) | the instrument against references that are not OpenMC: attenuation against NIST XCOM, slab transmission against the exponential, thick target bremsstrahlung against the textbook rule; writes `calibration.json` | +| [`model.py`](model.py) | the vessel, shell by shell, its sources and tallies, and the stages below; writes `tallies.json` (needs OpenMC and the data) | +| [`report.py`](report.py) | every derived number, `results.md`, and figure 17, from the two JSON files (numpy and matplotlib only) | +| [`results.md`](results.md) | the numbers, regenerated by `report.py` | +| `tallies.json`, `calibration.json` | the committed run, with uncertainties | + +## The vessel as built + +Nested cylinders on one axis, dimensions from the build note where it gives them and stated where it does not: + +- **core**: an 8 mm × 10 mm SrTiO₃ pellet in a 1 mm 316L capsule at the centre of a 30 mm × 40 mm krypton cell at 5 bar with 2 mm aluminium walls; +- **collar**: a 2 mm tungsten sleeve around the lamp cell with one opening per site, ±10° by 6 mm at nominal, the mechanical GATE terminal of the reference transistor; +- **compute shell**: borosilicate glass from 19 to 25 mm radius carrying 64 sites, 2 mm scintillator cells on a lattice of 8 heights by 8 azimuths at 22 mm radius, plastic throughout and CsI in one variant run (the build note offers either), with an optional 1 mm lead septum between two sectors, the build note's inhibitory blocking; +- **boundary**: a 6 mm plastic scintillator ring with end caps (the 24 SiPM paddles), 1 mm of silicon behind it, and four 5 mm CZT pixels in the ring; +- **shield**: 8 mm PMMA, 4 mm lead, 3 mm titanium, outer radius 4.9 cm and half length 6.6 cm, then air to a metre. + +The betas are handled by OpenMC's thick target bremsstrahlung treatment: an electron born in the pellet deposits its energy there and emits the bremsstrahlung a thick target of that material would. For a ceramic pellet whose radius exceeds the range of most of the spectrum this is the right approximation and it is stated wherever a number descends from it. + +## The stages + +1. **Calibration.** The library's total attenuation for lead, iron, tungsten and water at 100 keV to 2 MeV against NIST XCOM; uncollided transmission through slabs of up to three mean free paths against exp(−μx); the energy an electron radiates stopping in water and iron at 0.5, 1 and 2 MeV against the thick target rule. The last is the source term of everything and the least certain link, and the report says so. +2. **The source.** An emission stage first: the betas at their real activities in the pellet ceramic, and the bremsstrahlung they make, per second. Then the nominal vessel driven by that spectrum: photons leaving the capsule, the field in every site, the boundary counts and their spectra, the energy deposited in every cell, the dose in air at contact, ten centimetres and a metre, and the leakage through the shield. The same stage is run once more with CsI cells in place of plastic. +3. **The gate.** The collar opening at 0, 25, 50, 75 and 100 percent of nominal: the transfer curve. +4. **The septum.** The nominal vessel with the lead sheet in place. +5. **The synapse.** Photons born in each site in turn, with the spectrum the source stage found there, tallied in every site: the 64 × 64 Green's function, open and with the septum. + +## What came out + +| what | assumed in the notes | computed | where it lands | +|---|---|---|---| +| photons leaving the core | not given | 43.9 M/s, mean 252 keV, 0.0569 per decay | the whole budget, a few percent of the beta energy | +| deposited power | 181 µW per GBq | 183 µW for the pair | the ledger holds | +| site interactions, all 64 | proposal budget 10⁶/s | 32.9 k/s in plastic, 1.02 M/s in CsI | plastic is 30× short; CsI meets the budget | +| pile up per site | n ≳ λ τ_d | 0.16 percent of events overlap at 100 ns in CsI | the floor plan holds | +| accidental coincidences, two mean sites | the coincidence multiplier's raw material | 51 /s in CsI (0.2 four bit readings per second) | enough for a slow four bit AND gate | +| boundary events | 10⁷/s at percent level collection | 3.25 M/s, from 7% of core photons | 0.33× the assumption; 50 eight bit reads per second, not 153 | +| collar contrast | the GATE terminal | 6.34 in plastic, 11.94 in CsI | a knob, not a switch | +| synapse weights | written by geometry | nearest neighbour 3×10⁻⁵, fan out 0.1% | the fan out tax, three orders below the toy fabric | +| septum blocking | inhibitory | coupling left at 0.49 (unshielded side 1.00) | a filter, not a wall | +| dose | to be certified | 67.8 µSv/h at the wall, 0.261 µSv/h at 1 m; 7.7% of core photons escape | a lead pot instrument, as the licence class said | + +The design's power ledger holds; its proposal budget holds only with CsI cells; its boundary budget is a factor 3.0 optimistic; its two mechanical controls are analog because its light is hard; and its wall is a filter for the same reason. The ampoule is a rate coded sampler with small weights and a narrower mouth than it was priced with, and each of those words is now a number. + +## Running it + +``` +python3 calibrate.py # a minute +python3 model.py # about ten minutes on a laptop; --quick for a tenth of the particles +python3 report.py # seconds; numpy and matplotlib only +``` + +Requires OpenMC 0.16 and the data that [`neutron/data.py`](../neutron/data.py) fetches, which now includes the photoatomic files and the natural isotopes of every element in the vessel. + +*The theory's sealed machine was a design; it is now a transport calculation, and the calculation says what the design could not: how many photons there are, where they go, how much of each site's traffic is another site's, what the two mechanical controls are worth, and what the wall lets through.* diff --git a/ampoule/beta.py b/ampoule/beta.py new file mode 100644 index 0000000..9b77fd6 --- /dev/null +++ b/ampoule/beta.py @@ -0,0 +1,72 @@ +#!/usr/bin/env python3 +# Copyright 2026 Max Freedom Pollard +# SPDX-License-Identifier: Apache-2.0 +""" +The beta spectra of the ampoule's core, ⁹⁰Sr and its daughter ⁹⁰Y, from the +Fermi theory with the shape factor both decays require. + +Both are unique first forbidden transitions (0⁺ → 2⁻ and 2⁻ → 0⁺), whose +spectrum is the allowed one times the shape factor p² + q² (electron and +neutrino momenta). The Fermi function is the standard nonrelativistic +Coulomb correction with the relativistic exponent, adequate here to about +a percent, which is far below what the bremsstrahlung yield needs. The +check is the mean energy: the tabulated values are 195.8 keV for ⁹⁰Sr and +933.6 keV for ⁹⁰Y (ICRP 107), and the spectra built here must reproduce +them. + +Used by model.py as tabular source distributions; run directly to print +the check. +""" +import math + +import numpy as np + +ME_KEV = 510.99895 # electron rest energy, keV +ALPHA = 1.0 / 137.035999 # fine structure constant + +# endpoint kinetic energy (keV), daughter Z, tabulated mean (keV, ICRP 107) +BRANCHES = { + "90Sr": dict(Q=546.0, Z=39, mean_ref=195.8), + "90Y": dict(Q=2280.1, Z=40, mean_ref=933.6), +} + + +def fermi_simple(Z, T): + """The nonrelativistic Fermi function 2πη/(1 − e^(−2πη)) with a first + order relativistic correction (p/W)^(2(γ−1)); accurate to a percent for + Z near 40, which is all the yield calculation can use.""" + W = 1.0 + T / ME_KEV + p = math.sqrt(W * W - 1.0) + eta = ALPHA * Z * W / p + gamma = math.sqrt(1.0 - (ALPHA * Z) ** 2) + f = 2.0 * math.pi * eta / (1.0 - math.exp(-2.0 * math.pi * eta)) + return f * (2.0 * p) ** (2.0 * (gamma - 1.0)) + + +def spectrum(name, n=400): + """Kinetic energy grid (keV) and normalised probability per bin for the + named branch, on a linear grid from 0 to the endpoint.""" + b = BRANCHES[name] + Q, Z = b["Q"], b["Z"] + T = np.linspace(0.0, Q, n + 1) + Tm = 0.5 * (T[1:] + T[:-1]) + W = 1.0 + Tm / ME_KEV + p = np.sqrt(W * W - 1.0) # electron momentum, m_e c + q = (Q - Tm) / ME_KEV # neutrino momentum, m_e c + F = np.array([fermi_simple(Z, t) for t in Tm]) + shape = p * p + q * q # unique first forbidden + N = F * p * W * q * q * shape + N /= N.sum() + return T, Tm, N + + +def mean_energy(name): + T, Tm, N = spectrum(name) + return float((Tm * N).sum()) + + +if __name__ == "__main__": + for name, b in BRANCHES.items(): + m = mean_energy(name) + print(f"{name}: endpoint {b['Q']:.1f} keV, mean {m:.1f} keV, tabulated {b['mean_ref']:.1f} keV, " + f"difference {100*(m/b['mean_ref']-1):+.2f} percent") diff --git a/ampoule/calibrate.py b/ampoule/calibrate.py new file mode 100644 index 0000000..1381d87 --- /dev/null +++ b/ampoule/calibrate.py @@ -0,0 +1,178 @@ +#!/usr/bin/env python3 +# Copyright 2026 Max Freedom Pollard +# SPDX-License-Identifier: Apache-2.0 +""" +Calibration of the photon instrument before it is pointed at the ampoule. + +Three checks, cheapest first, each against a reference that is not OpenMC: + + attenuation the total mass attenuation coefficient of lead, iron, + tungsten and water at 100, 500, 1000 and 2000 keV, read + from the library files the model uses, against the NIST + XCOM values (Hubbell and Seltzer): the data + transmission the fraction of a pencil beam that crosses a slab without + a single collision and at its own energy, Monte Carlo + against exp(-mu x) with the XCOM coefficient: the transport + bremsstrahlung the energy an electron stopped in a thick target radiates, + in water and iron at 0.5, 1 and 2 MeV, against the + textbook thick target rule Y = 6e-4 Z T / (1 + 6e-4 Z T), + which is good to a few tens of percent and known to run + high at low Z; OpenMC's thick + target bremsstrahlung treatment was validated by its + authors against ESTAR and Geant4 (Lund and Romano 2018), + and this is only the check that the version and data in + hand behave as published: the source term + +Writes calibration.json, read by report.py. +""" +import json +import math +import os +import shutil +import sys + +import numpy as np + +HERE = os.path.dirname(os.path.abspath(__file__)) +ROOT = os.path.dirname(HERE) +sys.path.insert(0, os.path.join(ROOT, "neutron")) +from data import ensure_data # noqa: E402 +sys.path.insert(0, HERE) +from model import add_natural # noqa: E402 + +NA = 6.02214076e23 +# NIST XCOM total attenuation with coherent scattering, cm2/g +XCOM = { + "Pb": {"M": 207.2, "rho": 11.35, "mu": {100e3: 5.549, 500e3: 0.1614, 1e6: 0.07102, 2e6: 0.04606}}, + "Fe": {"M": 55.845, "rho": 7.874, "mu": {100e3: 0.3717, 500e3: 0.08414, 1e6: 0.05995, 2e6: 0.04265}}, + "W": {"M": 183.84, "rho": 19.3, "mu": {100e3: 4.438, 500e3: 0.1378, 1e6: 0.06618, 2e6: 0.04433}}, +} +WATER = {"rho": 1.0, "mu": {100e3: 0.1707, 500e3: 0.09687, 1e6: 0.07072, 2e6: 0.04942}} +Z_EFF = {"water": 7.42, "iron": 26.0} + + +def attenuation(xs_path): + import openmc.data + root = os.path.dirname(xs_path) + rows = [] + for el, d in XCOM.items(): + ph = openmc.data.IncidentPhoton.from_hdf5(os.path.join(root, "photon", el + ".h5")) + for E, ref in d["mu"].items(): + tot = sum(ph.reactions[mt].xs(np.array([E]))[0] for mt in (502, 504, 515, 517, 522) if mt in ph.reactions) + mu = tot * 1e-24 * NA / d["M"] + rows.append(dict(material=el, E_keV=E / 1e3, library=mu, xcom=ref, ratio=mu / ref)) + # water: 2 H + O by mass + H = openmc.data.IncidentPhoton.from_hdf5(os.path.join(root, "photon", "H.h5")) + O = openmc.data.IncidentPhoton.from_hdf5(os.path.join(root, "photon", "O.h5")) + for E, ref in WATER["mu"].items(): + def m(ph, M): + return sum(ph.reactions[mt].xs(np.array([E]))[0] for mt in (502, 504, 515, 517, 522) if mt in ph.reactions) * 1e-24 * NA / M + mu = (2 * 1.008 * m(H, 1.008) + 15.999 * m(O, 15.999)) / 18.015 + rows.append(dict(material="water", E_keV=E / 1e3, library=mu, xcom=ref, ratio=mu / ref)) + return rows + + +def slab_model(material, thickness, E): + import openmc + m = openmc.Material(name=material) + if material == "water": + add_natural(m, "H", 2, "ao"); add_natural(m, "O", 1, "ao"); m.set_density("g/cm3", 1.0) + else: + add_natural(m, material, 1, "ao"); m.set_density("g/cm3", XCOM[material]["rho"]) + x0, x1 = openmc.XPlane(x0=0.0), openmc.XPlane(x0=thickness) + box = openmc.model.RectangularParallelepiped(-1.0, thickness + 1.0, -50, 50, -50, 50, boundary_type="vacuum") + slab = +x0 & -x1 & -box + cells = [openmc.Cell(fill=m, region=slab), openmc.Cell(region=-box & ~slab)] + model = openmc.Model(geometry=openmc.Geometry(cells), materials=openmc.Materials([m])) + s = model.settings + s.run_mode = "fixed source"; s.photon_transport = True; s.electron_treatment = "ttb" + s.batches = 10; s.particles = 40000; s.output = {"summary": False, "tallies": False} + s.source = openmc.IndependentSource(particle="photon", space=openmc.stats.Point((-0.5, 0, 0)), + angle=openmc.stats.Monodirectional((1, 0, 0)), + energy=openmc.stats.Discrete([E], [1.0])) + t = openmc.Tally(name="out") + t.filters = [openmc.SurfaceFilter([x1]), openmc.CellFromFilter([cells[0]]), openmc.CellFilter([cells[1]]), + openmc.ParticleFilter(["photon"]), openmc.CollisionFilter([0]), + openmc.EnergyFilter([E * 0.999, E * 1.001])] + # both filters are needed: a coherent scatter keeps the energy but counts as + # a collision, and a secondary photon (annihilation, fluorescence, the + # bremsstrahlung of a photoelectron) has never collided but is not the beam + t.scores = ["current"] + model.tallies = openmc.Tallies([t]) + return model + + +def brems_model(material, T): + """An electron at the centre of a small sphere of the material. The thick + target treatment stops the electron where it is born whatever the + sphere's size, so a sphere a fraction of a millimetre across lets every + bremsstrahlung photon out unabsorbed: what crosses its surface is what + was radiated.""" + import openmc + m = openmc.Material(name=material) + if material == "water": + add_natural(m, "H", 2, "ao"); add_natural(m, "O", 1, "ao"); m.set_density("g/cm3", 1.0) + R = 0.02 + else: + add_natural(m, "Fe", 1, "ao"); m.set_density("g/cm3", 7.874) + R = 0.02 + sph = openmc.Sphere(r=R) + world = openmc.Sphere(r=R + 5.0, boundary_type="vacuum") + cin = openmc.Cell(fill=m, region=-sph) + cout = openmc.Cell(region=+sph & -world) + model = openmc.Model(geometry=openmc.Geometry([cin, cout]), materials=openmc.Materials([m])) + s = model.settings + s.run_mode = "fixed source"; s.photon_transport = True; s.electron_treatment = "ttb" + s.batches = 10; s.particles = 40000; s.output = {"summary": False, "tallies": False} + s.source = openmc.IndependentSource(particle="electron", space=openmc.stats.Point((0, 0, 0)), + energy=openmc.stats.Discrete([T], [1.0])) + edges = np.logspace(3, math.log10(T * 1.01), 60) + t = openmc.Tally(name="out") + t.filters = [openmc.SurfaceFilter([sph]), openmc.CellFromFilter([cin]), openmc.CellFilter([cout]), + openmc.ParticleFilter(["photon"]), openmc.EnergyFilter(edges)] + t.scores = ["current"] + model.tallies = openmc.Tallies([t]) + return model, edges + + +def main(): + import openmc + xs = ensure_data() + exe = os.environ.get("OPENMC_EXEC", "openmc") + work = os.path.join(HERE, "work", "calibration") + out = {"attenuation": attenuation(xs), "transmission": [], "bremsstrahlung": []} + for r in out["attenuation"]: + print(f" {r['material']:6s} {r['E_keV']:6.0f} keV library {r['library']:.4f} XCOM {r['xcom']:.4f} ratio {r['ratio']:.3f}") + for material, thickness, E in (("Pb", 1.0, 1e6), ("Pb", 0.5, 500e3), ("Fe", 5.0, 1e6), ("W", 0.5, 2e6), ("water", 10.0, 1e6)): + model = slab_model(material, thickness, E) + wd = os.path.join(work, f"slab_{material}_{int(E/1e3)}") + shutil.rmtree(wd, ignore_errors=True); os.makedirs(wd) + sp = model.run(cwd=wd, output=False, openmc_exec=exe) + with openmc.StatePoint(sp) as st: + t = st.get_tally(name="out"); mc, sd = float(abs(t.mean.sum())), float(np.sqrt((t.std_dev ** 2).sum())) + rho = 1.0 if material == "water" else XCOM[material]["rho"] + mu = (WATER if material == "water" else XCOM[material])["mu"][E] + exp = math.exp(-mu * rho * thickness) + out["transmission"].append(dict(material=material, thickness_cm=thickness, E_keV=E / 1e3, mc=mc, mc_std=sd, expected=exp, ratio=mc / exp)) + print(f" slab {material:6s} {thickness:4.1f} cm {E/1e3:5.0f} keV uncollided MC {mc:.4f} ± {sd:.4f} exp(-mu x) {exp:.4f} ratio {mc/exp:.3f}") + for material in ("water", "iron"): + for T in (0.5e6, 1e6, 2e6): + model, edges = brems_model(material, T) + wd = os.path.join(work, f"brems_{material}_{int(T/1e3)}") + shutil.rmtree(wd, ignore_errors=True); os.makedirs(wd) + sp = model.run(cwd=wd, output=False, openmc_exec=exe) + with openmc.StatePoint(sp) as st: + t = st.get_tally(name="out"); cur = np.abs(t.mean.ravel()) + mids = np.sqrt(edges[:-1] * edges[1:]) + radiated = float((cur * mids).sum()) + Z = Z_EFF[material] + rule = 6e-4 * Z * (T / 1e6) / (1 + 6e-4 * Z * (T / 1e6)) + out["bremsstrahlung"].append(dict(material=material, T_keV=T / 1e3, photons_per_electron=float(cur.sum()), + radiated_fraction=radiated / T, rule=rule, ratio=radiated / T / rule)) + print(f" brems {material:5s} {T/1e3:5.0f} keV radiated fraction {radiated/T:.4f} rule {rule:.4f} ratio {radiated/T/rule:.2f} photons/e {cur.sum():.3f}") + json.dump(out, open(os.path.join(HERE, "calibration.json"), "w"), indent=1) + print("wrote calibration.json") + + +if __name__ == "__main__": + main() diff --git a/ampoule/calibration.json b/ampoule/calibration.json new file mode 100644 index 0000000..afb6f48 --- /dev/null +++ b/ampoule/calibration.json @@ -0,0 +1,213 @@ +{ + "attenuation": [ + { + "material": "Pb", + "E_keV": 100.0, + "library": 5.550046019188095, + "xcom": 5.549, + "ratio": 1.0001885058908082 + }, + { + "material": "Pb", + "E_keV": 500.0, + "library": 0.16118668656611226, + "xcom": 0.1614, + "ratio": 0.9986783554282049 + }, + { + "material": "Pb", + "E_keV": 1000.0, + "library": 0.07076329664751596, + "xcom": 0.07102, + "ratio": 0.9963854779993799 + }, + { + "material": "Pb", + "E_keV": 2000.0, + "library": 0.04592032670423756, + "xcom": 0.04606, + "ratio": 0.9969675793364647 + }, + { + "material": "Fe", + "E_keV": 100.0, + "library": 0.372988108901397, + "xcom": 0.3717, + "ratio": 1.0034654530572962 + }, + { + "material": "Fe", + "E_keV": 500.0, + "library": 0.08411943830670017, + "xcom": 0.08414, + "ratio": 0.9997556252281931 + }, + { + "material": "Fe", + "E_keV": 1000.0, + "library": 0.05987043540852975, + "xcom": 0.05995, + "ratio": 0.9986728174900709 + }, + { + "material": "Fe", + "E_keV": 2000.0, + "library": 0.04257605502138349, + "xcom": 0.04265, + "ratio": 0.9982662373126258 + }, + { + "material": "W", + "E_keV": 100.0, + "library": 4.441532647524208, + "xcom": 4.438, + "ratio": 1.0007959998927913 + }, + { + "material": "W", + "E_keV": 500.0, + "library": 0.13780588710702066, + "xcom": 0.1378, + "ratio": 1.0000427221119061 + }, + { + "material": "W", + "E_keV": 1000.0, + "library": 0.06593908329389432, + "xcom": 0.06618, + "ratio": 0.9963596750361788 + }, + { + "material": "W", + "E_keV": 2000.0, + "library": 0.04421412455291745, + "xcom": 0.04433, + "ratio": 0.9973860715749481 + }, + { + "material": "water", + "E_keV": 100.0, + "library": 0.1706394536165883, + "xcom": 0.1707, + "ratio": 0.9996453053110036 + }, + { + "material": "water", + "E_keV": 500.0, + "library": 0.09681178496814695, + "xcom": 0.09687, + "ratio": 0.9993990396216265 + }, + { + "material": "water", + "E_keV": 1000.0, + "library": 0.07063771092687213, + "xcom": 0.07072, + "ratio": 0.998836410165047 + }, + { + "material": "water", + "E_keV": 2000.0, + "library": 0.04932650424318494, + "xcom": 0.04942, + "ratio": 0.9981081392793392 + } + ], + "transmission": [ + { + "material": "Pb", + "thickness_cm": 1.0, + "E_keV": 1000.0, + "mc": 0.44753750000000003, + "mc_std": 0.0010514688799750608, + "expected": 0.44660667206451593, + "ratio": 1.0020842230842213 + }, + { + "material": "Pb", + "thickness_cm": 0.5, + "E_keV": 500.0, + "mc": 0.4000025000000001, + "mc_std": 0.000911130631561904, + "expected": 0.4001383166585231, + "ratio": 0.9996605757237718 + }, + { + "material": "Fe", + "thickness_cm": 5.0, + "E_keV": 1000.0, + "mc": 0.09531999999999999, + "mc_std": 0.0006370156111817121, + "expected": 0.09439836744453324, + "ratio": 1.0097632255770554 + }, + { + "material": "W", + "thickness_cm": 0.5, + "E_keV": 2000.0, + "mc": 0.65228, + "mc_std": 0.0007862251585950772, + "expected": 0.6519518952948509, + "ratio": 1.000503265206401 + }, + { + "material": "water", + "thickness_cm": 10.0, + "E_keV": 1000.0, + "mc": 0.4929475, + "mc_std": 0.0009091697219639047, + "expected": 0.4930227302591319, + "ratio": 0.9998474101608006 + } + ], + "bremsstrahlung": [ + { + "material": "water", + "T_keV": 500.0, + "photons_per_electron": 0.02278, + "radiated_fraction": 0.0018483219319938508, + "rule": 0.0022210559295009306, + "ratio": 0.8321816247144965 + }, + { + "material": "water", + "T_keV": 1000.0, + "photons_per_electron": 0.055514999999999995, + "radiated_fraction": 0.0034585066456075627, + "rule": 0.004432267544890149, + "ratio": 0.7803018681926792 + }, + { + "material": "water", + "T_keV": 2000.0, + "photons_per_electron": 0.13694750000000003, + "radiated_fraction": 0.006936768589932135, + "rule": 0.008825418473908319, + "ratio": 0.7859988294538288 + }, + { + "material": "iron", + "T_keV": 500.0, + "photons_per_electron": 0.03617499999999999, + "radiated_fraction": 0.0070527751304611235, + "rule": 0.0077396308791426865, + "ratio": 0.9112547149331693 + }, + { + "material": "iron", + "T_keV": 1000.0, + "photons_per_electron": 0.10096250000000002, + "radiated_fraction": 0.013809082663214135, + "rule": 0.015360378101614808, + "ratio": 0.8990066892795049 + }, + { + "material": "iron", + "T_keV": 2000.0, + "photons_per_electron": 0.271465, + "radiated_fraction": 0.027778873135272813, + "rule": 0.030256012412723042, + "ratio": 0.9181273710606834 + } + ] +} \ No newline at end of file diff --git a/ampoule/model.py b/ampoule/model.py new file mode 100644 index 0000000..80a3a7d --- /dev/null +++ b/ampoule/model.py @@ -0,0 +1,609 @@ +#!/usr/bin/env python3 +# Copyright 2026 Max Freedom Pollard +# SPDX-License-Identifier: Apache-2.0 +""" +The ampoule in real photon transport: the sealed machine of +transistor/SEALED.md and transistor/EMBODIMENT.md, built in OpenMC with the +official ENDF/B-VIII.0 photoatomic library, driven by the beta spectra of +its own ⁹⁰Sr/⁹⁰Y core, and measured where the design notes assumed. + +The build note gives the machine at assembly grade; this script builds it +as a nested set of cylinders (dimensions in cm, materials by name, every +departure from the note recorded in results.md): + + core an 8 x 10 mm SrTiO₃ pellet in a 1 mm 316L capsule, on the + axis of a 30 x 40 mm krypton cell at 5 bar with 2 mm + aluminium walls: the source and the lamp + collar a 2 mm tungsten sleeve around the lamp cell with one opening + per site, the GATE terminal of every site, its angular width + the thinning aperture + compute a borosilicate shell carrying 64 sites, 2 mm plastic + shell scintillator cells (CsI in one variant run) on an 8 x 8 + lattice of azimuth and height, with an optional 1 mm lead + septum between two sectors + boundary a plastic scintillator ring and end caps (the 24 SiPM paddles), + a silicon layer behind them, and four 5 mm CZT pixels + shield PMMA, 4 mm lead, 3 mm titanium, then air to a metre + +The betas are handled by OpenMC's thick target bremsstrahlung treatment: +an electron born in the pellet deposits its energy there and emits the +bremsstrahlung a thick target of that material would, which is right for a +ceramic pellet whose radius exceeds the range of most of the spectrum and +is the approximation stated where the numbers are quoted. Because that +treatment makes the photons at the electron's birth whatever the geometry, +the source is taken in two steps: an emission stage measures the pellet +material's bremsstrahlung spectrum and yield per second from the two beta +spectra at their real activities, and every vessel stage is then driven by +photons born in the pellet with that spectrum at that rate, which is exact +within the treatment and a hundred times cheaper per photon. + +Stages (each a fixed source run; every tally with its standard deviation to +tallies.json, already per second, because the sources carry the activity +as their strength: 1 GBq of each nuclide in equilibrium): + + emission a speck of the pellet ceramic in vacuum with the two betas: + the bremsstrahlung spectrum and yield per second, and the + electron energy deposited per second + source the nominal ampoule: photons leaving the core, the field in + every site, the boundary counts and their spectra, the energy + deposited everywhere, the dose in air at contact and at one + metre, the leakage out of the shield + gate the collar opening at 0, 25, 50, 75 and 100 percent of its + nominal width: the transfer curve of the GATE terminal + septum the nominal ampoule with the lead septum in place + synapse the Green's function between sites: photons started in each + site in turn, with the spectrum the source stage found there, + tallied in every site: 64 x 64, open and with the septum + +Run `python3 model.py` (about half an hour on a laptop) or `--quick`. +""" +import argparse +import glob +import json +import math +import os +import re +import shutil +import sys +import time + +import numpy as np + +HERE = os.path.dirname(os.path.abspath(__file__)) +ROOT = os.path.dirname(HERE) +sys.path.insert(0, os.path.join(ROOT, "neutron")) +sys.path.insert(0, HERE) +from data import ensure_data # noqa: E402 +import beta # noqa: E402 + +ACTIVITY_BQ = 1.0e9 # of each of 90Sr and 90Y, in equilibrium +DECAYS_PER_S = 2.0 * ACTIVITY_BQ +EV_J = 1.602176634e-19 + +# ---- dimensions (cm), from the build note where it gives them ------------ +R_PELLET, H_PELLET = 0.4, 0.5 # radius, half height +CAPSULE = 0.1 # 316L wall +R_KR, H_KR = 1.5, 2.0 # lamp cell inner +AL_WALL = 0.2 +R_COLLAR_IN, R_COLLAR_OUT = 1.7, 1.9 # tungsten sleeve +R_SHELL_OUT, H_SHELL = 2.5, 4.0 # borosilicate compute shell +R_SITE, H_SITE, R_CELL = 2.2, 0.1, 0.113 # site lattice radius; cell half height; cell radius (2 mm cube's volume) +N_AZ, N_Z = 8, 8 # 64 sites +Z_SITES = np.linspace(-3.5, 3.5, N_Z) +TH_SITES = np.arange(N_AZ) * 2 * math.pi / N_AZ +OPEN_HALF_DEG, OPEN_HALF_Z = 10.0, 0.3 # nominal opening: +/-10 degrees, +/-3 mm +R_TRIM = 2.7 # air ring for the trim foils +R_BOUND, H_BOUND = 3.3, 5.0 # scintillator ring and caps +SI = 0.1 +R_CZT_C, A_CZT = 3.0, 0.25 # CZT pixel centre radius, half edge +PMMA, PB, TI = 0.8, 0.4, 0.3 # shield layers +SEPTUM_ANGLE_DEG, SEPTUM_T = 22.5, 0.1 # lead sheet between sectors 0 and 1 +R_WORLD = 102.0 + +R_PMMA = R_BOUND + SI + PMMA +R_PB = R_PMMA + PB +R_TI = R_PB + TI +H_PMMA = H_BOUND + SI + PMMA +H_PB = H_PMMA + PB +H_TI = H_PB + TI + +E_EDGES = np.logspace(1, math.log10(2.5e6), 51) # eV, for spectra + +BUDGET = {"full": dict(emission=4_000_000, source=10_000_000, gate=3_000_000, septum=3_000_000, synapse=1_500_000), + "quick": dict(emission=400_000, source=600_000, gate=200_000, septum=200_000, synapse=100_000)} + + +# ---------------------------------------------------------------- materials +def add_natural(m, symbol, fraction, kind): + """Add an element as its natural isotopes, using only the isotopes the + library holds and renormalising over them. Photon interactions depend + on Z alone, so leaving out a rare isotope (¹⁸O at 0.2 percent, ²H at + 0.01 percent) changes nothing but the atomic mass at the third digit; + OpenMC's own expansion refuses rather than guess, which is right for + neutrons and needless here.""" + import openmc + import openmc.data as od + lib = add_natural.lib + if lib is None: + dl = od.DataLibrary.from_xml(os.environ["OPENMC_CROSS_SECTIONS"]) + lib = set() + for entry in dl.libraries: + if entry["type"] == "neutron": + lib.update(entry["materials"]) + add_natural.lib = lib + isos = [(n, a) for n, a in od.NATURAL_ABUNDANCE.items() + if re.match(r"([A-Z][a-z]?)\d", n) and re.match(r"([A-Z][a-z]?)\d", n).group(1) == symbol and n in lib] + if not isos: + raise ValueError(f"no natural isotope of {symbol} in the library") + if kind == "ao": + tot = sum(a for _, a in isos) + for n, a in isos: + m.add_nuclide(n, fraction * a / tot, "ao") + else: + w = [(n, a * od.atomic_mass(n)) for n, a in isos] + tot = sum(x for _, x in w) + for n, x in w: + m.add_nuclide(n, fraction * x / tot, "wo") + + +add_natural.lib = None + + +def materials(): + import openmc + def mat(name, rho, comp, kind): + m = openmc.Material(name=name) + for el, frac in comp: + add_natural(m, el, frac, kind) + m.set_density("g/cm3", rho) + return m + return { + "srtio3": mat("SrTiO3", 5.11, [("Sr", 1), ("Ti", 1), ("O", 3)], "ao"), + "ss316": mat("316L", 8.0, [("Fe", 0.655), ("Cr", 0.17), ("Ni", 0.12), ("Mo", 0.025), ("Mn", 0.02), ("Si", 0.01)], "wo"), + "kr": mat("krypton 5 bar", 5 * 3.749e-3, [("Kr", 1)], "ao"), + "al": mat("aluminium", 2.70, [("Al", 1)], "ao"), + "glass": mat("borosilicate", 2.23, [("O", 0.540), ("Si", 0.377), ("B", 0.040), ("Na", 0.028), ("Al", 0.012), ("K", 0.003)], "wo"), + "pvt": mat("plastic scintillator", 1.032, [("C", 10), ("H", 11)], "ao"), + "csi": mat("CsI", 4.51, [("Cs", 1), ("I", 1)], "ao"), + "w": mat("tungsten", 19.3, [("W", 1)], "ao"), + "pb": mat("lead", 11.35, [("Pb", 1)], "ao"), + "ti": mat("titanium", 4.51, [("Ti", 1)], "ao"), + "si": mat("silicon", 2.33, [("Si", 1)], "ao"), + "pmma": mat("PMMA", 1.19, [("C", 5), ("H", 8), ("O", 2)], "ao"), + "czt": mat("CZT", 5.8, [("Cd", 0.9), ("Zn", 0.1), ("Te", 1.0)], "ao"), + "air": mat("air", 1.205e-3, [("N", 0.755), ("O", 0.245)], "wo"), + } + + +# ---------------------------------------------------------------- geometry +def azimuth_plane(angle_rad, offset=0.0): + """The plane through the z axis at that angle (offset shifts it along + its normal); its positive side is the half space of larger azimuth.""" + import openmc + return openmc.Plane(a=-math.sin(angle_rad), b=math.cos(angle_rad), c=0.0, d=offset) + + +def build(open_fraction=1.0, septum=False, site_material="pvt"): + import openmc + openmc.reset_auto_ids() + M = materials() + cells, parts = [], {"mats": M} + + def cyl(r, h): + return -openmc.ZCylinder(r=r) & +openmc.ZPlane(z0=-h) & -openmc.ZPlane(z0=h) + + pellet = cyl(R_PELLET, H_PELLET) + cap_cyl = openmc.ZCylinder(r=R_PELLET + CAPSULE) + cap_lo, cap_hi = openmc.ZPlane(z0=-(H_PELLET + CAPSULE)), openmc.ZPlane(z0=H_PELLET + CAPSULE) + capsule = -cap_cyl & +cap_lo & -cap_hi + parts["capsule_surfaces"] = [cap_cyl, cap_lo, cap_hi] + kr = cyl(R_KR, H_KR) + alcan = cyl(R_KR + AL_WALL, H_KR + AL_WALL) + collar = cyl(R_COLLAR_OUT, H_SHELL) & ~cyl(R_COLLAR_IN, H_SHELL) + shell = cyl(R_SHELL_OUT, H_SHELL) & ~cyl(R_COLLAR_OUT, H_SHELL) + inner_air = cyl(R_COLLAR_IN, H_SHELL) & ~alcan + trim = cyl(R_TRIM, H_SHELL) & ~cyl(R_SHELL_OUT, H_SHELL) + bound = cyl(R_BOUND, H_BOUND) & ~cyl(R_TRIM, H_SHELL) + si = cyl(R_BOUND + SI, H_BOUND + SI) & ~cyl(R_BOUND, H_BOUND) + pmma = cyl(R_PMMA, H_PMMA) & ~cyl(R_BOUND + SI, H_BOUND + SI) + pb = cyl(R_PB, H_PB) & ~cyl(R_PMMA, H_PMMA) + ti_cyl = openmc.ZCylinder(r=R_TI) + ti_lo, ti_hi = openmc.ZPlane(z0=-H_TI), openmc.ZPlane(z0=H_TI) + ti_outer = -ti_cyl & +ti_lo & -ti_hi + parts["ti_surfaces"] = [ti_cyl, ti_lo, ti_hi] + ti = ti_outer & ~cyl(R_PB, H_PB) + contact = cyl(R_TI + 0.2, H_TI + 0.2) & ~ti_outer + world = -openmc.Sphere(r=R_WORLD, boundary_type="vacuum") + dose10 = -openmc.Sphere(r=10.5) & +openmc.Sphere(r=9.5) + dose100 = -openmc.Sphere(r=101.0) & +openmc.Sphere(r=99.0) + + cells.append(openmc.Cell(name="pellet", fill=M["srtio3"], region=pellet)) + cells.append(openmc.Cell(name="capsule", fill=M["ss316"], region=capsule & ~pellet)) + cells.append(openmc.Cell(name="krypton", fill=M["kr"], region=kr & ~capsule)) + cells.append(openmc.Cell(name="lamp_wall", fill=M["al"], region=alcan & ~kr)) + cells.append(openmc.Cell(name="inner_air", fill=M["air"], region=inner_air)) + + # the sites, and the collar openings that face them + sites, openings = [], [] + for iz, z0 in enumerate(Z_SITES): + for ia, th in enumerate(TH_SITES): + x0, y0 = R_SITE * math.cos(th), R_SITE * math.sin(th) + reg = (-openmc.ZCylinder(x0=x0, y0=y0, r=R_CELL) + & +openmc.ZPlane(z0=z0 - H_SITE) & -openmc.ZPlane(z0=z0 + H_SITE)) + c = openmc.Cell(name=f"site_{iz}_{ia}", fill=M[site_material], region=reg) + sites.append(c) + if open_fraction > 0: + d = math.radians(OPEN_HALF_DEG * open_fraction) + zc = z0 * (0.5 * (R_COLLAR_IN + R_COLLAR_OUT)) / R_SITE # where the pellet's sight line crosses the collar + wedge = (+azimuth_plane(th - d) & -azimuth_plane(th + d) + & +openmc.ZPlane(z0=zc - OPEN_HALF_Z) & -openmc.ZPlane(z0=zc + OPEN_HALF_Z)) + openings.append(collar & wedge) + parts["sites"] = sites + cells += sites + collar_region = collar + for o in openings: + collar_region = collar_region & ~o + cells.append(openmc.Cell(name="collar", fill=M["w"], region=collar_region)) + for i, o in enumerate(openings): + cells.append(openmc.Cell(name=f"opening_{i}", fill=M["air"], region=o)) + + shell_region = shell + for c in sites: + shell_region = shell_region & ~c.region + if septum: + a = math.radians(SEPTUM_ANGLE_DEG) + sheet = (+azimuth_plane(a, -SEPTUM_T / 2) & -azimuth_plane(a, SEPTUM_T / 2) + & +openmc.Plane(a=math.cos(a), b=math.sin(a), c=0.0, d=0.0) # the correct half + & shell) + cells.append(openmc.Cell(name="septum", fill=M["pb"], region=sheet)) + shell_region = shell_region & ~sheet + parts["septum"] = True + cells.append(openmc.Cell(name="glass", fill=M["glass"], region=shell_region)) + cells.append(openmc.Cell(name="trim_air", fill=M["air"], region=trim)) + + czts = [] + for k, (cx, cy) in enumerate([(R_CZT_C, 0), (0, R_CZT_C), (-R_CZT_C, 0), (0, -R_CZT_C)]): + reg = (+openmc.XPlane(x0=cx - A_CZT) & -openmc.XPlane(x0=cx + A_CZT) + & +openmc.YPlane(y0=cy - A_CZT) & -openmc.YPlane(y0=cy + A_CZT) + & +openmc.ZPlane(z0=-A_CZT) & -openmc.ZPlane(z0=A_CZT)) + czts.append(openmc.Cell(name=f"czt_{k}", fill=M["czt"], region=reg)) + bound_region = bound + for c in czts: + bound_region = bound_region & ~c.region + paddles = openmc.Cell(name="paddles", fill=M["pvt"], region=bound_region) + cells += czts + [paddles] + parts["czt"], parts["paddles"] = czts, paddles + cells.append(openmc.Cell(name="sipm_si", fill=M["si"], region=si)) + cells.append(openmc.Cell(name="pmma", fill=M["pmma"], region=pmma)) + cells.append(openmc.Cell(name="lead", fill=M["pb"], region=pb)) + cells.append(openmc.Cell(name="titanium", fill=M["ti"], region=ti)) + contact_c = openmc.Cell(name="contact", fill=M["air"], region=contact) + d10 = openmc.Cell(name="dose10", fill=M["air"], region=dose10) + d100 = openmc.Cell(name="dose100", fill=M["air"], region=dose100) + outer = cyl(R_TI + 0.2, H_TI + 0.2) + cells += [contact_c, d10, d100, + openmc.Cell(name="air", fill=M["air"], region=world & ~outer & ~dose10 & ~dose100)] + parts.update(contact=contact_c, dose10=d10, dose100=d100) + model = openmc.Model(geometry=openmc.Geometry(cells), materials=openmc.Materials(list(M.values()))) + s = model.settings + s.run_mode = "fixed source" + s.photon_transport = True + s.electron_treatment = "ttb" + s.output = {"summary": False, "tallies": False} + s.seed = 90 + s.batches = 20 + parts["cells"] = {c.name: c for c in cells} + return model, parts + + +def beta_sources(): + """The two betas of the core, uniform in the pellet, each with its + activity as its strength, so that every tally is per second.""" + import openmc + srcs = [] + for name in ("90Sr", "90Y"): + T, Tm, N = beta.spectrum(name) + srcs.append(openmc.IndependentSource( + particle="electron", + space=openmc.stats.CylindricalIndependent( + r=openmc.stats.PowerLaw(0.0, R_PELLET, 1.0), + phi=openmc.stats.Uniform(0.0, 2 * math.pi), + z=openmc.stats.Uniform(-H_PELLET, H_PELLET)), + energy=openmc.stats.Tabular(T * 1e3, np.append(N / np.diff(T * 1e3), 0.0), interpolation="histogram"), + strength=ACTIVITY_BQ)) + return srcs + + +def emission_model(): + """A 0.2 mm speck of the pellet ceramic in vacuum, with the two betas: + the thick target treatment stops each electron where it is born, so + what crosses the speck's surface is the bremsstrahlung the pellet + material makes, per second, before any of the vessel absorbs it.""" + import openmc + openmc.reset_auto_ids() + M = materials() + sph = openmc.Sphere(r=0.02) + world = openmc.Sphere(r=2.0, boundary_type="vacuum") + cin = openmc.Cell(name="speck", fill=M["srtio3"], region=-sph) + cout = openmc.Cell(name="vacuum", region=+sph & -world) + model = openmc.Model(geometry=openmc.Geometry([cin, cout]), materials=openmc.Materials([M["srtio3"]])) + s = model.settings + s.run_mode = "fixed source"; s.photon_transport = True; s.electron_treatment = "ttb" + s.output = {"summary": False, "tallies": False}; s.seed = 90; s.batches = 20 + srcs = [] + for src in beta_sources(): + src.space = openmc.stats.Point((0.0, 0.0, 0.0)) + srcs.append(src) + s.source = srcs + t = openmc.Tally(name="emitted") + t.filters = [openmc.SurfaceFilter([sph]), openmc.CellFromFilter([cin]), openmc.CellFilter([cout]), + openmc.ParticleFilter(["photon"]), openmc.EnergyFilter(E_EDGES)] + t.scores = ["current"] + h = openmc.Tally(name="deposited"); h.filters = [openmc.CellFilter([cin])]; h.scores = ["heating"] + model.tallies = openmc.Tallies([t, h]) + return model + + +def photon_source(emission): + """Photons born uniformly in the pellet, isotropic, with the emission + stage's spectrum and its yield per second as the strength.""" + import openmc + spec = np.array(emission["spectrum_per_s"]) + total = float(spec.sum()) + dens = np.append(spec / np.diff(E_EDGES), 0.0) + return openmc.IndependentSource( + particle="photon", + space=openmc.stats.CylindricalIndependent( + r=openmc.stats.PowerLaw(0.0, R_PELLET, 1.0), + phi=openmc.stats.Uniform(0.0, 2 * math.pi), + z=openmc.stats.Uniform(-H_PELLET, H_PELLET)), + energy=openmc.stats.Tabular(E_EDGES, dens, interpolation="histogram"), + strength=total) + + +# ---------------------------------------------------------------- tallies +def add_tallies(model, parts, synapse=False): + import openmc + ph = openmc.ParticleFilter(["photon"]) + T = [] + t = openmc.Tally(name="sites"); t.filters = [openmc.CellFilter(parts["sites"]), ph] + t.scores = ["total", "heating", "flux"]; T.append(t) + if not synapse: + t = openmc.Tally(name="site_spectrum"); t.filters = [openmc.CellFilter(parts["sites"]), ph, openmc.EnergyFilter(E_EDGES)] + t.scores = ["flux"]; T.append(t) + det = [parts["paddles"]] + parts["czt"] + t = openmc.Tally(name="detectors"); t.filters = [openmc.CellFilter(det), ph] + t.scores = ["total", "heating", "flux"]; T.append(t) + t = openmc.Tally(name="detector_spectrum"); t.filters = [openmc.CellFilter(det), ph, openmc.EnergyFilter(E_EDGES)] + t.scores = ["flux"]; T.append(t) + cap = parts["cells"]["capsule"] + t = openmc.Tally(name="core_out"); t.filters = [openmc.SurfaceFilter(parts["capsule_surfaces"]), openmc.CellFromFilter([cap]), openmc.CellFilter([parts["cells"]["krypton"]]), ph, openmc.EnergyFilter(E_EDGES)] + t.scores = ["current"]; T.append(t) + for name in ("contact", "dose10", "dose100"): + t = openmc.Tally(name=name); t.filters = [openmc.CellFilter([parts[name]]), ph, openmc.EnergyFilter(E_EDGES)] + t.scores = ["flux"]; T.append(t) + t = openmc.Tally(name="leak"); t.filters = [openmc.SurfaceFilter(parts["ti_surfaces"]), openmc.CellFromFilter([parts["cells"]["titanium"]]), openmc.CellFilter([parts["contact"]]), ph, openmc.EnergyFilter(E_EDGES)] + t.scores = ["current"]; T.append(t) + allcells = [c for c in parts["cells"].values()] + t = openmc.Tally(name="heating_by_cell"); t.filters = [openmc.CellFilter(allcells)] + t.scores = ["heating"]; T.append(t) + parts["heating_cells"] = [c.name for c in allcells] + model.tallies = openmc.Tallies(T) + + +def harvest(sp_path, parts, synapse=False): + import openmc + out = {} + nE = len(E_EDGES) - 1 + with openmc.StatePoint(sp_path) as sp: + t = sp.get_tally(name="sites") + out["sites"] = {s: [t.mean[:, 0, j].tolist(), t.std_dev[:, 0, j].tolist()] for j, s in enumerate(t.scores)} + if not synapse: + t = sp.get_tally(name="site_spectrum") + out["site_spectrum"] = t.mean.reshape(len(parts["sites"]), nE).sum(axis=0).tolist() + t = sp.get_tally(name="detectors") + out["detectors"] = {"names": ["paddles"] + [f"czt_{k}" for k in range(4)], + **{s: [t.mean[:, 0, j].tolist(), t.std_dev[:, 0, j].tolist()] for j, s in enumerate(t.scores)}} + t = sp.get_tally(name="detector_spectrum") + m = t.mean.reshape(5, nE) + out["detector_spectrum"] = {"paddles": m[0].tolist(), "czt": m[1:].sum(axis=0).tolist()} + t = sp.get_tally(name="core_out") + m = np.abs(t.mean.reshape(-1, nE)).sum(axis=0); sd = np.sqrt((t.std_dev.reshape(-1, nE) ** 2).sum(axis=0)) + out["core_out"] = {"mean": m.tolist(), "std": sd.tolist()} + for name in ("contact", "dose10", "dose100"): + t = sp.get_tally(name=name) + out[name] = {"mean": t.mean.ravel().tolist(), "std": t.std_dev.ravel().tolist()} + t = sp.get_tally(name="leak") + m = np.abs(t.mean.reshape(-1, nE)).sum(axis=0); sd = np.sqrt((t.std_dev.reshape(-1, nE) ** 2).sum(axis=0)) + out["leak"] = {"mean": m.tolist(), "std": sd.tolist()} + t = sp.get_tally(name="heating_by_cell") + out["heating_by_cell"] = {n: [float(t.mean[i, 0, 0]), float(t.std_dev[i, 0, 0])] + for i, n in enumerate(parts["heating_cells"])} + return out + + +def run(model, workdir, exe): + if os.path.isdir(workdir): + shutil.rmtree(workdir) + os.makedirs(workdir) + t0 = time.time() + sp = model.run(cwd=workdir, output=False, openmc_exec=exe) + return sp, time.time() - t0 + + +def volumes(parts): + return {"site": math.pi * R_CELL ** 2 * 2 * H_SITE, + "contact": math.pi * ((R_TI + 0.2) ** 2 * (H_TI + 0.2) - R_TI ** 2 * H_TI) * 2, + "dose10": 4 / 3 * math.pi * (10.5 ** 3 - 9.5 ** 3), + "dose100": 4 / 3 * math.pi * (101.0 ** 3 - 99.0 ** 3), + "czt": (2 * A_CZT) ** 3} + + +# ---------------------------------------------------------------- protocol +def protocol(args): + import openmc + budget = BUDGET["quick" if args.quick else "full"] + exe = os.environ.get("OPENMC_EXEC", "openmc") + work = args.workdir + path = os.path.join(HERE, "tallies.json") + results = json.load(open(path)) if (os.path.exists(path) and args.only) else {"runs": {}} + runs = results["runs"] + minutes_before = results.get("provenance", {}).get("wall_clock_minutes", 0.0) # --only adds to an existing run + wanted = lambda n: (not args.only) or any(k in n for k in args.only.split(",")) + t_start = time.time() + + def record(name, model, parts, n, synapse=False, extra=None): + add_tallies(model, parts, synapse) + model.settings.particles = max(n // model.settings.batches, 100) + sp, wall = run(model, os.path.join(work, name), exe) + r = harvest(sp, parts, synapse) + r.update(particles=int(model.settings.particles * model.settings.batches), seconds=round(wall, 1)) + if extra: + r.update(extra) + runs[name] = r + print(f" {name:18s} ({wall:.0f} s)", flush=True) + json.dump(results, open(path, "w"), indent=1) + return r + + print("the ampoule in photon transport: OpenMC", openmc.__version__, "| budget", "quick" if args.quick else "full", flush=True) + + # -- emission: the pellet's bremsstrahlung, per second ---------------- + if wanted("emission"): + model = emission_model() + model.settings.particles = max(budget["emission"] // 20, 100) + sp, wall = run(model, os.path.join(work, "emission"), exe) + with openmc.StatePoint(sp) as st: + t = st.get_tally(name="emitted") + spec = np.abs(t.mean.ravel()); spec_s = t.std_dev.ravel() + h = st.get_tally(name="deposited") + runs["emission"] = {"spectrum_per_s": spec.tolist(), "std": spec_s.tolist(), + "photons_per_s": float(spec.sum()), + "electron_heating_W": float(h.mean[0, 0, 0]) * EV_J, + "particles": int(model.settings.particles * 20), "seconds": round(wall, 1)} + mids = np.sqrt(E_EDGES[:-1] * E_EDGES[1:]) + print(f" emission {spec.sum():.3e} photons/s, mean {(spec*mids).sum()/spec.sum()/1e3:.0f} keV, " + f"{runs['emission']['electron_heating_W']*1e6:.0f} µW deposited by the betas ({wall:.0f} s)", flush=True) + json.dump(results, open(path, "w"), indent=1) + emission = runs["emission"] + + # -- source ----------------------------------------------------------- + if wanted("source"): + model, parts = build() + model.settings.source = photon_source(emission) + record("source", model, parts, budget["source"]) + # the build note leaves the site material open, plastic or CsI; the + # vessel is run with plastic throughout, and once more here with CsI + # cells so that the report can say what the denser choice buys + if wanted("source_csi"): + model, parts = build(site_material="csi") + model.settings.source = photon_source(emission) + record("source_csi", model, parts, budget["source"], extra={"site_material": "CsI"}) + + # -- gate: the collar opening ---------------------------------------- + for f in (0.0, 0.25, 0.5, 0.75): + name = f"gate_{int(f*100):03d}" + if wanted(name): + model, parts = build(open_fraction=f) + model.settings.source = photon_source(emission) + record(name, model, parts, budget["gate"], extra={"open_fraction": f}) + + # the closed collar once more with CsI cells, for the CsI contrast + if wanted("gate_000_csi"): + model, parts = build(open_fraction=0.0, site_material="csi") + model.settings.source = photon_source(emission) + record("gate_000_csi", model, parts, budget["gate"], extra={"open_fraction": 0.0, "site_material": "CsI"}) + + # -- septum ------------------------------------------------------------ + if wanted("septum"): + model, parts = build(septum=True) + model.settings.source = photon_source(emission) + record("septum", model, parts, budget["septum"], extra={"septum": True}) + + # -- synapse: the Green's function between sites ---------------------- + # The lattice is symmetric under rotation by 45 degrees and under z -> -z, + # so a source at azimuth 0 and one of four heights stands for eight + # sources by rotation and two by reflection; four runs give all 64 + # columns of G in the open geometry. The septum breaks the rotation, so + # its runs are the same four sources next to it, compared column by + # column with the open case. + if any(wanted(f"synapse_{tag}") for tag in ("open", "septum")): + spec = np.array(runs["source"]["site_spectrum"]) + mids = np.sqrt(E_EDGES[:-1] * E_EDGES[1:]) + spec = spec / spec.sum() + energy = openmc.stats.Discrete(mids.tolist(), spec.tolist()) + rep = [iz * N_AZ for iz in range(N_Z // 2)] # sites 0, 8, 16, 24: azimuth 0, z = -3.5 .. -0.5 + for tag, sep in (("open", False), ("septum", True)): + if not wanted(f"synapse_{tag}"): + continue + meas, meas_s = {}, {} + for j in rep: + iz, ia = divmod(j, N_AZ) + th, z0 = TH_SITES[ia], Z_SITES[iz] + model, parts = build(septum=sep) + model.settings.source = openmc.IndependentSource( + particle="photon", + space=openmc.stats.CylindricalIndependent( + r=openmc.stats.PowerLaw(0.0, R_CELL, 1.0), phi=openmc.stats.Uniform(0, 2 * math.pi), + z=openmc.stats.Uniform(z0 - H_SITE, z0 + H_SITE), + origin=(R_SITE * math.cos(th), R_SITE * math.sin(th), 0.0)), + energy=energy) + add_tallies(model, parts, synapse=True) + model.settings.particles = max(budget["synapse"] // 20, 100) + sp, wall = run(model, os.path.join(work, f"syn_{tag}_{j}"), exe) + with openmc.StatePoint(sp) as st: + t = st.get_tally(name="sites") + meas[j] = t.mean[:, 0, 0].copy(); meas_s[j] = t.std_dev[:, 0, 0].copy() + shutil.rmtree(os.path.join(work, f"syn_{tag}_{j}"), ignore_errors=True) + print(f" synapse_{tag} site {j:2d}: self {meas[j][j]:.4f}, to all others {meas[j].sum()-meas[j][j]:.2e} ({wall:.0f} s)", flush=True) + G = np.zeros((64, 64)); S = np.zeros((64, 64)) + for j in range(64): + iz, ia = divmod(j, N_AZ) + flip = iz >= N_Z // 2 + jz = (N_Z - 1 - iz) if flip else iz + src = jz * N_AZ # the representative source + if sep and (ia != 0 or flip): + continue # only the measured columns + for k in range(64): + kz, ka = divmod(k, N_AZ) + kz_m = (N_Z - 1 - kz) if flip else kz + ka_m = (ka - ia) % N_AZ + km = kz_m * N_AZ + ka_m + G[k, j] = meas[src][km]; S[k, j] = meas_s[src][km] + runs[f"synapse_{tag}"] = {"G": G.tolist(), "std": S.tolist(), "sources": rep, + "measured_columns": ([j for j in range(64)] if not sep else rep), + "particles_per_source": int(max(budget["synapse"] // 20, 100) * 20), + "note": "columns outside measured_columns are filled by the lattice symmetry"} + json.dump(results, open(path, "w"), indent=1) + + import openmc.data + dE, dh = openmc.data.dose_coefficients("photon", geometry="AP") + results["provenance"] = { + "dose_coefficients_ICRP116_AP": {"energy_eV": np.asarray(dE).tolist(), "pSv_cm2": np.asarray(dh).tolist()}, + "openmc_version": openmc.__version__, "library": "ENDF/B-VIII.0 official OpenMC HDF5 distribution (photoatomic, EPICS2014 based)", + "electron_treatment": "thick target bremsstrahlung", "budget": "quick" if args.quick else "full", + "decays_per_s": DECAYS_PER_S, "activity_Bq_each": ACTIVITY_BQ, "tallies_are": "per second", + "energy_edges_eV": E_EDGES.tolist(), + "volumes_cm3": volumes(None), "sites": 64, "site_layout": {"radius_cm": R_SITE, "z_cm": Z_SITES.tolist(), "azimuths_rad": TH_SITES.tolist()}, + "geometry_cm": {"pellet": [R_PELLET, H_PELLET], "capsule_wall": CAPSULE, "lamp_cell": [R_KR, H_KR], "al_wall": AL_WALL, + "collar": [R_COLLAR_IN, R_COLLAR_OUT], "shell_out": R_SHELL_OUT, "shell_half_height": H_SHELL, + "opening_half_deg": OPEN_HALF_DEG, "opening_half_z": OPEN_HALF_Z, "trim_out": R_TRIM, + "boundary": [R_BOUND, H_BOUND], "si": SI, "czt_half_edge": A_CZT, "pmma": PMMA, "pb": PB, "ti": TI, + "outer_radius": R_TI, "outer_half_length": H_TI, "septum_deg": SEPTUM_ANGLE_DEG, "septum_t": SEPTUM_T}, + "wall_clock_minutes": round(minutes_before + (time.time() - t_start) / 60, 1), + } + json.dump(results, open(path, "w"), indent=1) + print(f"wrote {path} ({(time.time()-t_start)/60:.0f} min)") + + +def main(): + p = argparse.ArgumentParser(description=__doc__.split("\n")[1]) + p.add_argument("--quick", action="store_true") + p.add_argument("--only", default="") + p.add_argument("--workdir", default=os.path.join(HERE, "work")) + args = p.parse_args() + ensure_data() + protocol(args) + + +if __name__ == "__main__": + main() diff --git a/ampoule/report.py b/ampoule/report.py new file mode 100644 index 0000000..9354342 --- /dev/null +++ b/ampoule/report.py @@ -0,0 +1,466 @@ +#!/usr/bin/env python3 +# Copyright 2026 Max Freedom Pollard +# SPDX-License-Identifier: Apache-2.0 +""" +The ampoule, reported: every derived number, results.md, and figure 17, +from tallies.json and calibration.json. Needs numpy and matplotlib only. + +Derived here and nowhere else: the photon budget leaving the core and its +spectrum; the interaction rate, flux and deposited power of every site, the +pile up they imply and the proposal budget they support; the accidental and +true coincidence rates between sites; the boundary count rate and what the +precision law makes of it; the energy budget of the whole vessel; the dose +in air at contact, ten centimetres and a metre from ICRP 116 coefficients; +the transfer curve of the tungsten collar; the Green's function between +sites, its structure, and what the lead septum does to it; and the table +of every number the design notes assumed against the number computed. +""" +import json +import math +import os +import sys + +import numpy as np + +HERE = os.path.dirname(os.path.abspath(__file__)) +# an optional directory argument reads and writes there instead (a scratch run) +BASE = os.path.abspath(sys.argv[1]) if len(sys.argv) > 1 else HERE +FIGS = os.path.join(os.path.dirname(HERE), "figures") if BASE == HERE else BASE +OUT = [] +TAU_D = 100e-9 # s, resolving time of a scintillator cell (transistor note: 100 ns) +TAU_W = 100e-9 # s, coincidence window (benchtop cell) +EV = 1.602176634e-19 + + +def say(s=""): + OUT.append(s) + + +def pm(m, s, d=3): + return f"{m:.{d}g} ± {s:.{d}g}" + + +def si(x, unit="", d=3): + """A number in engineering notation with a unit; a rate below one per + second is written as a plain decimal, never with a milli prefix.""" + if x == 0: + return f"0 {unit}" + if unit.startswith("/") and abs(x) < 1: + return f"{x:.2g} {unit}" + e = int(math.floor(math.log10(abs(x)) / 3) * 3) + e = max(min(e, 12), -12) + pre = {-12: "p", -9: "n", -6: "µ", -3: "m", 0: "", 3: "k", 6: "M", 9: "G", 12: "T"}[e] + return f"{x / 10 ** e:.{d}g} {pre}{unit}" + + +def times(x): + """A ratio as a multiplier: 0.033×, 0.33×, 1.05×, 3.1×, 25×.""" + return f"{x:.2g}×" if (x < 0.1 or x >= 10) else f"{x:.2f}×" + + +SUP = str.maketrans("0123456789-", "⁰¹²³⁴⁵⁶⁷⁸⁹⁻") + + +def pow10(x): + """A number to one figure as m×10ⁿ.""" + m, e = f"{x:.0e}".split("e") + return f"{m}×10{str(int(e)).translate(SUP)}" + + +def dose_rate(spec, volume, decays, E_edges, dose_E, dose_h): + """µSv per hour from a flux spectrum tally (particle cm per second, per + bin, when decays is 1) in a cell of the given volume.""" + mids = np.sqrt(E_edges[:-1] * E_edges[1:]) + h = np.exp(np.interp(np.log(mids), np.log(dose_E), np.log(dose_h))) # pSv cm2 + flux = np.array(spec) / volume * decays # cm-2 s-1 per bin + return float((flux * h).sum() * 1e-12 * 3600 * 1e6) + + +def main(): + doc = json.load(open(os.path.join(BASE, "tallies.json"))) + runs, prov = doc["runs"], doc["provenance"] + cal = json.load(open(os.path.join(BASE, "calibration.json"))) + D = 1.0 # every tally is already per second + em = runs["emission"] + E = np.array(prov["energy_edges_eV"]); mids = np.sqrt(E[:-1] * E[1:]) + V = prov["volumes_cm3"] + src = runs["source"] + dE, dh = np.array(prov["dose_coefficients_ICRP116_AP"]["energy_eV"]), np.array(prov["dose_coefficients_ICRP116_AP"]["pSv_cm2"]) + geo = prov["geometry_cm"] + + say("# The ampoule in photon transport (regenerated by report.py from tallies.json and calibration.json)\n") + say(f"OpenMC {prov['openmc_version']}, {prov['library']}, electrons by the {prov['electron_treatment']} " + f"treatment, budget {prov['budget']} ({prov['wall_clock_minutes']} minutes of wall clock). The core is " + f"1 GBq each of ⁹⁰Sr and ⁹⁰Y in equilibrium, {prov['decays_per_s']:.0e} decays per second in all; the " + "sources carry those activities as their strength, so every rate below is a tally per second, with its " + "Monte Carlo standard deviation.\n") + + # ---- 0. calibration --------------------------------------------------- + say("## 0. Calibration: the photon instrument against references that are not OpenMC\n") + say("| material | energy (keV) | μ/ρ from the library (cm²/g) | NIST XCOM | ratio |") + say("|---|---|---|---|---|") + worst_att = 0.0 + for r in cal["attenuation"]: + worst_att = max(worst_att, abs(r["ratio"] - 1)) + say(f"| {r['material']} | {r['E_keV']:.0f} | {r['library']:.4f} | {r['xcom']:.4f} | {r['ratio']:.3f} |") + say(f"\nThe library's total attenuation agrees with XCOM to {worst_att*100:.1f} percent at worst across " + "lead, iron, tungsten and water from 100 keV to 2 MeV: the data.\n") + say("| slab | energy (keV) | uncollided fraction, Monte Carlo | exp(−μx) | ratio |") + say("|---|---|---|---|---|") + worst_tr = 0.0 + for r in cal["transmission"]: + worst_tr = max(worst_tr, abs(r["ratio"] - 1)) + say(f"| {r['thickness_cm']:g} cm {r['material']} | {r['E_keV']:.0f} | {r['mc']:.4f} ± {r['mc_std']:.4f} | {r['expected']:.4f} | {r['ratio']:.3f} |") + say(f"\nUncollided transmission through slabs of up to three mean free paths reproduces the exponential to " + f"{worst_tr*100:.1f} percent at worst: the transport.\n") + say("| target | electron energy (keV) | photons escaping per electron | energy radiated, fraction of T | thick target rule | ratio |") + say("|---|---|---|---|---|---|") + for r in cal["bremsstrahlung"]: + say(f"| {r['material']} | {r['T_keV']:.0f} | {r['photons_per_electron']:.3f} | {r['radiated_fraction']:.4f} | {r['rule']:.4f} | {r['ratio']:.2f} |") + say("\nThe energy an electron radiates as it stops, measured as what escapes a sphere thin enough to " + "absorb little of it, lands within the few tens of percent that the thick target rule " + "6×10⁻⁴ Z T is good for. OpenMC's thick target bremsstrahlung treatment was validated by its authors " + "against ESTAR and Geant4 (Lund and Romano, 2018); this only shows that the version and data in " + "hand behave as published. It is the source term of everything below, and it is the least certain " + "link in the chain: the numbers that descend from it should be read to about ten percent.\n") + + # ---- 1. the source ---------------------------------------------------- + say("## 1. The source: what the core actually emits\n") + cur = np.array(src["core_out"]["mean"]); cur_s = np.array(src["core_out"]["std"]) + n_out = cur.sum() * D + e_mean = (cur * mids).sum() / cur.sum() + f100 = cur[mids > 1e5].sum() / cur.sum(); f500 = cur[mids > 5e5].sum() / cur.sum() + heat = src["heating_by_cell"] + groups = {"core (pellet and capsule)": ["pellet", "capsule"], "lamp cell (krypton and wall)": ["krypton", "lamp_wall", "inner_air"], + "collar": ["collar"], "compute shell (glass and sites)": ["glass"] + [k for k in heat if k.startswith("site_")] + [k for k in heat if k.startswith("opening_")], + "trim ring": ["trim_air"], "boundary (paddles, CZT, silicon)": ["paddles", "sipm_si"] + [k for k in heat if k.startswith("czt_")], + "shield (PMMA, lead, titanium)": ["pmma", "lead", "titanium"], "outside": ["contact", "dose10", "dose100", "air"]} + power = {g: sum(heat[k][0] for k in ks if k in heat) * EV for g, ks in groups.items()} + power["core (pellet and capsule)"] += em["electron_heating_W"] # the betas themselves, from the emission stage + total_power = sum(power.values()) + emitted = np.array(em["spectrum_per_s"]); e_emit = (emitted * mids).sum() / emitted.sum() + say(f"- bremsstrahlung made in the pellet ceramic: {si(emitted.sum(), '/s')}, " + f"{emitted.sum()/prov['decays_per_s']:.4f} photons per decay at a mean energy of {e_emit/1e3:.0f} keV; " + f"the betas deposit {si(em['electron_heating_W'], 'W')} there") + say(f"- photons leaving the source capsule into the lamp cell: **{si(n_out, '/s')}** " + f"(± {math.sqrt((cur_s**2).sum())/cur.sum():.1%}), {n_out/emitted.sum():.0%} of those made, mean energy " + f"**{e_mean/1e3:.0f} keV**, {f100:.0%} above 100 keV and {f500:.1%} above 500 keV: the pellet and its " + "capsule absorb the soft end of their own light") + say(f"- power deposited in the whole vessel: **{si(total_power, 'W')}** against the design note's 181 µW for " + "1 GBq of ⁹⁰Sr/⁹⁰Y (SEALED.md ledger), the difference being the beta spectra used and the photons that escape") + say("") + say("| where the energy goes | power |") + say("|---|---|") + for g, p in power.items(): + say(f"| {g} | {si(p, 'W')} |") + say("") + say("Almost all of the decay energy stops in the pellet and its capsule, as the design intends: it is " + "the lamp's heat and the betavoltaic's supply. What leaves as photons is the bremsstrahlung of a " + f"thick target, {emitted.sum()*e_emit*EV/total_power:.1%} of the power, and that is the whole budget the " + "compute shell, the boundary and the shield have to work with.\n") + + # ---- 2. the compute shell -------------------------------------------- + say("## 2. The compute shell: what each site sees\n") + tot = np.array(src["sites"]["total"][0]) * D; tot_s = np.array(src["sites"]["total"][1]) * D + flux = np.array(src["sites"]["flux"][0]) / V["site"] * D + ph = np.array(src["sites"]["heating"][0]) * D * EV + r_mean, r_min, r_max = tot.mean(), tot.min(), tot.max() + pile = r_mean * TAU_D + say(f"- interaction rate per site: mean **{si(r_mean, '/s')}**, from {si(r_min, '/s')} to {si(r_max, '/s')} " + f"(the lattice is symmetric, so the spread is the height dependence and statistics); " + f"photon flux {si(flux.mean(), '/cm²/s')}; deposited {si(ph.mean(), 'W')} per site") + say(f"- all 64 sites together: **{si(tot.sum(), '/s')}** interactions, against the design note's proposal " + f"budget of 10⁶ per second (SEALED.md Section 8): the shell is fed {times(tot.sum()/1e6)} what the sampler was priced at") + say(f"- pile up: the mean site interacts {pile:.2g} times per {TAU_D*1e9:.0f} ns resolving time, so " + f"{(1-math.exp(-pile))*100:.2g} percent of its events overlap another; the theory's floor plan n ≳ λτ_d asks for " + f"{tot.sum()*TAU_D:.2g} sites at this activity, and there are 64") + acc = 2 * TAU_W * r_mean ** 2 + say(f"- accidental coincidences between two mean sites in a {TAU_W*1e9:.0f} ns window: 2τ r² = " + f"**{si(acc, '/s')}**, the raw material of the coincidence multiplier; the precision law " + f"then gives {acc/2**8:.2g} four bit readings of it per second and {acc/2**16:.2g} eight bit ones") + csi = runs.get("source_csi") + if csi: + tot_c = np.array(csi["sites"]["total"][0]) * D + pile_c = tot_c.mean() * TAU_D; acc_c = 2 * TAU_W * tot_c.mean() ** 2 + csi_ratio = tot_c.sum() / tot.sum() + say(f"- **the same shell with CsI cells**, the build note's other option: mean **{si(tot_c.mean(), '/s')}** per site, " + f"**{si(tot_c.sum(), '/s')}** over all 64, {times(csi_ratio)} the plastic figure and {times(tot_c.sum()/1e6)} the " + f"proposal budget; pile up {pile_c:.2g} per resolving time ({(1-math.exp(-pile_c))*100:.2g} percent of events overlap, " + f"{tot_c.sum()*TAU_D:.2g} sites needed); accidental coincidences between two mean sites {si(acc_c, '/s')}, " + f"{acc_c/2**8:.2g} four bit and {acc_c/2**16:.2g} eight bit readings per second") + say("") + spec = np.array(src["site_spectrum"]); spec = spec / spec.sum() + e_site = (spec * mids).sum() + say(f"The field in a site has mean energy {e_site/1e3:.0f} keV, and {spec[mids < 1e5].sum():.0%} of it is below " + "100 keV: what reaches the shell is already the soft end of the bremsstrahlung, filtered by the " + "capsule, the lamp wall and the collar. " + + (f"Which cell material the builder chooses decides whether the sampler is fed at all: 2 mm of plastic is a " + f"Compton scatterer that a {e_site/1e3:.0f} keV field crosses almost untouched, and 2 mm of CsI, with the " + f"photoelectric effect of iodine and caesium and four times the density, interacts {times(csi_ratio)} as often. " + f"The note offered either; the transport says CsI, and " + + ("that with CsI the shell meets the proposal budget" if tot_c.sum() >= 1e6 else + f"that even with CsI the shell is {times(1e6/tot_c.sum())} short of the proposal budget") + + ". The rest of this report runs the vessel with plastic cells, the conservative choice; the collar's " + "contrast is given for both, and the septum's factor, a ratio of couplings through the same lead, is " + "given for plastic." if csi else "") + "\n") + + # ---- 3. the gate -------------------------------------------------------- + say("## 3. The GATE: the tungsten collar's transfer curve\n") + say("Every site faces the lamp cell through an opening in a 2 mm tungsten sleeve; the opening's width " + "is the site's thinning aperture, the mechanical GATE terminal of the reference transistor. The " + "collar was run at five widths.\n") + say("| opening (percent of nominal) | mean site rate | relative to open |") + say("|---|---|---|") + curve = [] + for f, name in ((0.0, "gate_000"), (0.25, "gate_025"), (0.5, "gate_050"), (0.75, "gate_075"), (1.0, "source")): + r = runs[name] + m = np.array(r["sites"]["total"][0]).mean() * D + s = np.sqrt((np.array(r["sites"]["total"][1]) ** 2).sum()) / 64 * D # standard error of the mean over the 64 sites + curve.append((f, m, s)) + for f, m, s in curve: + say(f"| {f*100:.0f} | {si(m, '/s')} ± {si(s, '/s', 2)} | {m/curve[-1][1]:.3f} |") + contrast = curve[-1][1] / curve[0][1] + contrast_s = contrast * math.sqrt((curve[-1][2] / curve[-1][1]) ** 2 + (curve[0][2] / curve[0][1]) ** 2) + g0c = runs.get("gate_000_csi") + if csi and g0c: + m0c = np.array(g0c["sites"]["total"][0]).mean() * D + s0c = np.sqrt((np.array(g0c["sites"]["total"][1]) ** 2).sum()) / 64 * D + s1c = np.sqrt((np.array(csi["sites"]["total"][1]) ** 2).sum()) / 64 * D + contrast_c = tot_c.mean() / m0c + contrast_cs = contrast_c * math.sqrt((s1c / tot_c.mean()) ** 2 + (s0c / m0c) ** 2) + csi_line = (f" With CsI cells, which the soft end of the spectrum reaches and the closed collar removes, the " + f"contrast is **{contrast_c:.2f}** (± {contrast_cs:.2f}): {si(m0c, '/s')} closed against {si(tot_c.mean(), '/s')} open.") + else: + csi_line = "" + say(f"\nON/OFF contrast of the collar: **{contrast:.2f}** (± {contrast_s:.2f}) with plastic cells.{csi_line} The closed state is not dark, because 2 mm of " + "tungsten stops the soft bremsstrahlung and passes the hard tail (a 1 MeV photon has a 30 percent " + "chance of crossing it uncollided), and because photons scattered in the glass reach the sites " + "from the side. The aperture is an analog knob over a modest range, which is what the neutron " + "sector's absorber turned out to be too, and for the same reason: an absorber in a path is a " + "filter, not a barrier, unless it is thick enough to stop the whole spectrum.\n") + + # ---- 4. the synapse --------------------------------------------------- + say("## 4. The synapse: the Green's function between sites\n") + say("A photon born in site j (isotropically, with the spectrum the source stage found in the sites) " + "interacts in site k with probability G_kj. This is the weight matrix of the theory's transport " + "synapse for the real geometry, the object Open Problem 4 asked for, measured 64 × 64.\n") + G = np.array(runs["synapse_open"]["G"]); Gs = np.array(runs["synapse_open"]["std"]) + N_AZ, N_Z = 8, 8 + diag = np.mean([G[j, j] for j in range(64)]) + az_nb, z_nb, dg_nb, far = [], [], [], [] + for j in range(64): + iz, ia = divmod(j, N_AZ) + for k in range(64): + if k == j: + continue + kz, ka = divmod(k, N_AZ) + da = min(abs(ka - ia), N_AZ - abs(ka - ia)); dz = abs(kz - iz) + if da == 1 and dz == 0: + az_nb.append(G[k, j]) + elif da == 0 and dz == 1: + z_nb.append(G[k, j]) + elif da == 1 and dz == 1: + dg_nb.append(G[k, j]) + else: + far.append(G[k, j]) + fan = np.array([G[:, j].sum() - G[j, j] for j in range(64)]) + say("| coupling | mean G_kj (interactions in k per photon born in j) |") + say("|---|---|") + say(f"| a site with itself (G_jj) | {diag:.2e} |") + say(f"| nearest neighbour around the ring (Δθ = 45°) | {np.mean(az_nb):.2e} |") + say(f"| nearest neighbour along the axis (Δz = 1 cm) | {np.mean(z_nb):.2e} |") + say(f"| diagonal neighbour | {np.mean(dg_nb):.2e} |") + say(f"| everything farther | {np.mean(far):.2e} (mean), {np.max(far):.2e} (largest) |") + say(f"| all other sites together, per photon born | {fan.mean():.2e} |") + say("") + say(f"A photon born in a 2 mm site has a {diag:.1%} chance of interacting in it and a {fan.mean():.1%} chance of " + "interacting in any of the other 63; the rest is lost to the glass, the collar, the boundary and the " + "shield. That is the fan out tax of theory Section 1.3 for this geometry: the weights of the " + f"synapse are of order {pow10(np.mean(az_nb))}, and a signal handed from a site to its nearest neighbour " + f"is attenuated by {pow10(1/np.mean(az_nb))} at every hop. The compiler's toy fabric (transport/compiler_demo.py) " + f"had weights of order a tenth; the real shell is {math.log10(0.1/np.mean(az_nb)):.0f} orders down, which the sampler's rate " + "coding absorbs as budget rather than as error (theory Section 10.1), but which sets what a " + "gigabecquerel actually buys. These are plastic cells; CsI cells would raise every entry, the self " + "term and the couplings alike, by roughly the material ratio of Section 2, and the fan out fraction with them.\n") + Gsep = np.array(runs["synapse_septum"]["G"]) + srcs = runs["synapse_septum"]["sources"] + blocked, control = [], [] + for j in srcs: + iz, ia = divmod(j, N_AZ) + if ia != 0: + continue + for kz in range(N_Z): + k1 = kz * N_AZ + 1; k7 = kz * N_AZ + 7 + if G[k1, j] > 0: + blocked.append(Gsep[k1, j] / G[k1, j]) + if G[k7, j] > 0: + control.append(Gsep[k7, j] / G[k7, j]) + say(f"**The septum.** A 1 mm lead sheet between sector 0 and sector 1 leaves sector 0's coupling to sector 1 " + f"at {np.mean(blocked):.2f} of its open value and its coupling to sector 7, on the unshielded side, at " + f"{np.mean(control):.2f}: the inhibitory septum of the build note blocks the soft part of the coupling " + "and passes the hard part, a factor rather than a wall, like the collar and like the cadmium sheet of " + "the neutron gate. Fixed absorbers program weights in this machine; they do not cut wires.\n") + + # ---- 5. the boundary ----------------------------------------------------- + say("## 5. The boundary: what the mouth actually counts\n") + det = src["detectors"] + names = det["names"] + rates = np.array(det["total"][0]) * D; rs = np.array(det["total"][1]) * D + paddle, czt = rates[0], rates[1:].sum() + say("| detector | interaction rate | deposited power |") + say("|---|---|---|") + heats = np.array(det["heating"][0]) * D * EV + say(f"| scintillator paddles and caps (24 SiPM tiles) | {si(paddle, '/s')} ± {si(rs[0], '/s', 2)} | {si(heats[0], 'W')} |") + say(f"| four CZT pixels together | {si(czt, '/s')} | {si(heats[1:].sum(), 'W')} |") + say("") + total_det = paddle + czt + say(f"- detected boundary events: **{si(total_det, '/s')}**, against the design note's budget of 10⁷ per second " + f"(SEALED.md Section 7): **{times(total_det/1e7)}** the assumption; the fraction of photons leaving the core that " + f"interact in the boundary is {total_det/n_out:.0%}") + say(f"- by the precision law, that budget supports {total_det/2**16:.0f} eight bit reads per second, " + f"{total_det/2**12:.0f} at six bits and {total_det/2**8:.0f} at four; the note priced 153, 2,441 and 39,062") + ds = np.array(src["detector_spectrum"]["paddles"]); ds = ds / max(ds.sum(), 1e-30) + say(f"- the paddle spectrum has mean energy {(ds*mids).sum()/1e3:.0f} keV; a 6 mm plastic paddle is a Compton " + "scatterer, not a photopeak detector, and the CZT pixels are where the energy division channels of " + "gates/edm_channels.md would be read\n") + + # ---- 6. dose ---------------------------------------------------------------- + say("## 6. The dose outside: the health physics the build note deferred\n") + dc = dose_rate(src["contact"]["mean"], V["contact"], D, E, dE, dh) + d10 = dose_rate(src["dose10"]["mean"], V["dose10"], D, E, dE, dh) + d100 = dose_rate(src["dose100"]["mean"], V["dose100"], D, E, dE, dh) + leak = np.array(src["leak"]["mean"]); n_leak = leak.sum() * D + say("| where | ambient dose rate (ICRP 116, anterior posterior, photons) |") + say("|---|---|") + say(f"| at the titanium wall | **{dc:.3g} µSv/h** |") + say(f"| 10 cm from the centre | {d10:.3g} µSv/h |") + say(f"| 1 m from the centre | **{d100:.3g} µSv/h** |") + say("") + say(f"- photons escaping the shield: {si(n_leak, '/s')}, {n_leak/n_out:.1%} of what left the core, with mean energy " + f"{(leak*mids).sum()/max(leak.sum(),1e-30)/1e3:.0f} keV: the hard tail again") + say(f"- for scale, the public dose limit of 1 mSv per year is 0.11 µSv/h continuously; at 1 m this vessel " + f"{'stays under it' if d100 < 0.11 else f'exceeds it by {d100/0.11:.0f}×'}, and at the wall it " + f"{'is under it' if dc < 0.11 else f'is {dc/0.11:.0f}× over'}. The build note said the shield was sized " + "with margin and that the final figure was the builder's to certify; this is that figure, for the " + "photons, from the same library that licenses shielding") + say("- the bremsstrahlung of ⁹⁰Sr/⁹⁰Y is a known shielding problem precisely because it is hard: the " + "design's 4 mm of lead is a filter for it, not a wall, and a laboratory instrument at a gigabecquerel " + "would sit in a lead pot. Nothing in the computation contradicts the note's licence class, " + "institutional; it puts a number on why\n") + + # ---- 7. verdict ------------------------------------------------------------ + say("## 7. The design notes, checked\n") + say("| what the notes assumed | where | computed here |") + say("|---|---|---|") + say(f"| deposited power, 181 µW per GBq | SEALED.md ledger | {si(total_power, 'W')} for the pair |") + say(f"| boundary budget 10⁷ detected events per second | SEALED.md Section 7 | {si(total_det, '/s')} |") + say(f"| percent level boundary collection | SEALED.md Section 7 | {total_det/n_out:.0%} of core photons |") + say(f"| proposal budget 10⁶ per second across 64 sites | SEALED.md Section 8 | {si(tot.sum(), '/s')} with plastic cells" + + (f", {si(tot_c.sum(), '/s')} with CsI" if csi else "") + " |") + say(f"| cells of plastic scintillator or CsI | EMBODIMENT.md Section 1.2 | " + + (f"CsI, by {times(csi_ratio)} in rate" if csi else "plastic only was run") + " |") + say(f"| pile up ceiling, sites ≳ λ τ_d | THEORY.md Section 3.2 | {tot.sum()*TAU_D:.2g} sites needed with plastic" + + (f", {tot_c.sum()*TAU_D:.2g} with CsI" if csi else "") + ", 64 present |") + say(f"| the aperture as the GATE terminal | transistor/README.md | contrast {contrast:.2f} through 2 mm of tungsten" + + (f" with plastic cells, {contrast_c:.2f} with CsI" if csi_line else "") + " |") + say(f"| lead septa as inhibitory blocking | EMBODIMENT.md Section 1.2 | coupling reduced to {np.mean(blocked):.2f}, not cut |") + say(f"| weights written by geometry | README, the scattering gate | nearest neighbour G ≈ {pow10(np.mean(az_nb))}, fan out {fan.mean():.1%} |") + say(f"| shield sized with margin, dose to be certified | EMBODIMENT.md Section 1.5 | {dc:.3g} µSv/h at the wall, {d100:.3g} µSv/h at 1 m |") + say("") + b_ratio = total_det / 1e7 + boundary_verdict = (f"closes at the boundary with {times(b_ratio)} the assumed count" if b_ratio >= 1 else + f"falls short at the boundary by {times(1/b_ratio)}" if b_ratio >= 0.1 else + f"fails at the boundary by an order of magnitude, {times(1/b_ratio)}") + if csi: + site_verdict = (f"reaches its proposal budget in the sites only with CsI cells ({times(tot_c.sum()/1e6)} the budget, " + f"against {times(tot.sum()/1e6)} with plastic)" if tot_c.sum() >= 1e6 else + f"misses its proposal budget in the sites with either cell material ({times(tot.sum()/1e6)} with plastic, " + f"{times(tot_c.sum()/1e6)} with CsI)") + else: + site_verdict = f"is fed {times(tot.sum()/1e6)} its proposal budget in the sites" + say(f"*The ampoule's budget {boundary_verdict} and {site_verdict}; its wall is thinner than its own spectrum; " + "and its two mechanical controls, the aperture and the septum, are knobs rather than switches for the same " + "reason the neutron gate's absorber was. The machine the theory can seal today is a rate coded sampler " + "whose weights are small and whose photons are hard, and every one of those adjectives is now a number.*") + + open(os.path.join(BASE, "results.md"), "w").write("\n".join(OUT) + "\n") + print("\n".join(OUT[-6:])) + print("wrote ampoule/results.md") + figure(cur, mids, D, curve, G, Gsep, srcs, power, dc, d10, d100, ds, leak, spec, + (tot_c.mean(), np.sqrt((np.array(csi["sites"]["total"][1]) ** 2).sum()) / 64 * D) if csi else None) + + +def figure(cur, mids, D, curve, G, Gsep, srcs, power, dc, d10, d100, ds, leak, spec, csi_point=None): + import matplotlib + matplotlib.use("Agg") + import matplotlib.pyplot as plt + from matplotlib.colors import LogNorm + INK, BLUE, RED, GREEN, AMBER, PURPLE, GREY = ( + "#16213e", "#2563eb", "#dc2626", "#16a34a", "#d97706", "#7c3aed", "#94a3b8") + plt.rcParams.update({ + "figure.facecolor": "white", "axes.facecolor": "white", "savefig.facecolor": "white", + "axes.edgecolor": INK, "axes.labelcolor": INK, "text.color": INK, "xtick.color": INK, + "ytick.color": INK, "axes.titlecolor": INK, "font.size": 11, "axes.titlesize": 12, + "axes.titleweight": "bold", "axes.grid": True, "grid.color": "#e5e7eb", + "grid.linewidth": 0.8, "axes.spines.top": False, "axes.spines.right": False, + "figure.dpi": 130, "svg.hashsalt": "nuclear-computer"}) + fig, ((A, B), (C, Dax)) = plt.subplots(2, 2, figsize=(13.4, 9.6)) + + # A: spectra per second per keV + def per_keV(y): + edges = np.sqrt(mids[:-1] * mids[1:]) + w = np.diff(np.concatenate([[mids[0] ** 2 / edges[0]], edges, [mids[-1] ** 2 / edges[-1]]])) / 1e3 + return np.array(y) * D / np.maximum(w, 1e-30) + A.plot(mids / 1e3, per_keV(cur), color=BLUE, lw=2.0, label="leaving the source capsule") + A.plot(mids / 1e3, per_keV(spec * cur.sum()), color=AMBER, lw=1.6, ls="--", label="in a site (shape, scaled)") + A.plot(mids / 1e3, per_keV(leak), color=RED, lw=1.8, label="escaping the shield") + A.axvline(2280, color=GREY, ls=":", lw=1.2) + A.set_xscale("log"); A.set_yscale("log") + A.text(2150, A.get_ylim()[1] * 0.5, "⁹⁰Y endpoint", color=GREY, fontsize=8, ha="right", va="top") + A.set_xlim(10, 3000); A.set_xlabel("photon energy (keV)"); A.set_ylabel("photons per second per keV") + A.set_title("A. The bremsstrahlung of 1 GBq of ⁹⁰Sr/⁹⁰Y, and what gets out") + A.legend(frameon=False, fontsize=8.5, loc="lower left") + + # B: the collar transfer curve + x = [f * 100 for f, _, _ in curve]; y = [m for _, m, _ in curve]; e = [s for _, _, s in curve] + B.errorbar(x, y, yerr=e, fmt="-o", color=BLUE, lw=2.2, ms=6, capsize=3, label="mean site interaction rate, plastic cells") + if csi_point: + B.errorbar([100], [csi_point[0]], yerr=[csi_point[1]], fmt="D", color=AMBER, ms=7, capsize=3, label="CsI cells, collar open") + B.axhline(1 / TAU_D, color=RED, ls="--", lw=1.3); B.text(2, 1 / TAU_D * 1.15, "pile up ceiling, 1/τ_d", color=RED, fontsize=8.5) + B.axhline(1e6 / 64, color=AMBER, ls=":", lw=1.3); B.text(2, 1e6 / 64 * 1.15, "design proposal budget per site", color=AMBER, fontsize=8.5) + B.set_yscale("log"); B.set_ylim(min(y) / 3, 3e7); B.set_xlim(-5, 108) + B.set_xlabel("collar opening (percent of nominal)"); B.set_ylabel("interactions per second per site") + B.set_title("B. The GATE terminal: the tungsten collar's transfer curve") + B.legend(frameon=False, fontsize=8.5, loc="lower right") + + # C: the Green's function + Gp = np.maximum(G, 1e-6) + im = C.imshow(Gp, norm=LogNorm(vmin=1e-5, vmax=max(Gp.max(), 1e-2)), cmap="Blues", origin="lower") + for b in range(8, 64, 8): + C.axhline(b - 0.5, color=GREY, lw=0.5); C.axvline(b - 0.5, color=GREY, lw=0.5) + C.set_xlabel("photon born in site j (8 heights × 8 azimuths)"); C.set_ylabel("interacts in site k") + C.set_title("C. The synapse: G between the 64 sites") + C.grid(False) + plt.colorbar(im, ax=C, fraction=0.046, pad=0.03, label="G_kj per photon") + + # D: energy budget and dose + labels = list(power); vals = [power[k] * 1e6 for k in labels] + Dax.barh(range(len(labels)), vals, color=[GREY, AMBER, INK, BLUE, GREY, GREEN, PURPLE, RED], height=0.6) + Dax.set_yticks(range(len(labels))); Dax.set_yticklabels([l.split(" (")[0] for l in labels], fontsize=8.5) + Dax.set_xscale("log"); Dax.set_xlabel("deposited power (µW)") + Dax.set_title("D. Where the energy goes, and the dose outside") + Dax.text(0.98, 0.96, f"ambient dose rate\nat the wall: {dc:.3g} µSv/h\nat 10 cm: {d10:.3g} µSv/h\nat 1 m: {d100:.3g} µSv/h", + transform=Dax.transAxes, fontsize=9, ha="right", va="top", color=INK, + bbox=dict(boxstyle="round", fc="white", ec=GREY)) + + fig.suptitle("Figure 17. The ampoule in real photon transport", fontsize=13, fontweight="bold", y=1.0) + fig.tight_layout() + for ext in ("svg", "png"): + kw = {"metadata": {"Date": None}} if ext == "svg" else {} + fig.savefig(os.path.join(FIGS, f"fig17_ampoule.{ext}"), bbox_inches="tight", **kw) + plt.close(fig) + print("wrote fig17_ampoule") + + +if __name__ == "__main__": + main() diff --git a/ampoule/results.md b/ampoule/results.md new file mode 100644 index 0000000..21b2190 --- /dev/null +++ b/ampoule/results.md @@ -0,0 +1,147 @@ +# The ampoule in photon transport (regenerated by report.py from tallies.json and calibration.json) + +OpenMC 0.16.0, ENDF/B-VIII.0 official OpenMC HDF5 distribution (photoatomic, EPICS2014 based), electrons by the thick target bremsstrahlung treatment, budget full (7.6 minutes of wall clock). The core is 1 GBq each of ⁹⁰Sr and ⁹⁰Y in equilibrium, 2e+09 decays per second in all; the sources carry those activities as their strength, so every rate below is a tally per second, with its Monte Carlo standard deviation. + +## 0. Calibration: the photon instrument against references that are not OpenMC + +| material | energy (keV) | μ/ρ from the library (cm²/g) | NIST XCOM | ratio | +|---|---|---|---|---| +| Pb | 100 | 5.5500 | 5.5490 | 1.000 | +| Pb | 500 | 0.1612 | 0.1614 | 0.999 | +| Pb | 1000 | 0.0708 | 0.0710 | 0.996 | +| Pb | 2000 | 0.0459 | 0.0461 | 0.997 | +| Fe | 100 | 0.3730 | 0.3717 | 1.003 | +| Fe | 500 | 0.0841 | 0.0841 | 1.000 | +| Fe | 1000 | 0.0599 | 0.0600 | 0.999 | +| Fe | 2000 | 0.0426 | 0.0427 | 0.998 | +| W | 100 | 4.4415 | 4.4380 | 1.001 | +| W | 500 | 0.1378 | 0.1378 | 1.000 | +| W | 1000 | 0.0659 | 0.0662 | 0.996 | +| W | 2000 | 0.0442 | 0.0443 | 0.997 | +| water | 100 | 0.1706 | 0.1707 | 1.000 | +| water | 500 | 0.0968 | 0.0969 | 0.999 | +| water | 1000 | 0.0706 | 0.0707 | 0.999 | +| water | 2000 | 0.0493 | 0.0494 | 0.998 | + +The library's total attenuation agrees with XCOM to 0.4 percent at worst across lead, iron, tungsten and water from 100 keV to 2 MeV: the data. + +| slab | energy (keV) | uncollided fraction, Monte Carlo | exp(−μx) | ratio | +|---|---|---|---|---| +| 1 cm Pb | 1000 | 0.4475 ± 0.0011 | 0.4466 | 1.002 | +| 0.5 cm Pb | 500 | 0.4000 ± 0.0009 | 0.4001 | 1.000 | +| 5 cm Fe | 1000 | 0.0953 ± 0.0006 | 0.0944 | 1.010 | +| 0.5 cm W | 2000 | 0.6523 ± 0.0008 | 0.6520 | 1.001 | +| 10 cm water | 1000 | 0.4929 ± 0.0009 | 0.4930 | 1.000 | + +Uncollided transmission through slabs of up to three mean free paths reproduces the exponential to 1.0 percent at worst: the transport. + +| target | electron energy (keV) | photons escaping per electron | energy radiated, fraction of T | thick target rule | ratio | +|---|---|---|---|---|---| +| water | 500 | 0.023 | 0.0018 | 0.0022 | 0.83 | +| water | 1000 | 0.056 | 0.0035 | 0.0044 | 0.78 | +| water | 2000 | 0.137 | 0.0069 | 0.0088 | 0.79 | +| iron | 500 | 0.036 | 0.0071 | 0.0077 | 0.91 | +| iron | 1000 | 0.101 | 0.0138 | 0.0154 | 0.90 | +| iron | 2000 | 0.271 | 0.0278 | 0.0303 | 0.92 | + +The energy an electron radiates as it stops, measured as what escapes a sphere thin enough to absorb little of it, lands within the few tens of percent that the thick target rule 6×10⁻⁴ Z T is good for. OpenMC's thick target bremsstrahlung treatment was validated by its authors against ESTAR and Geant4 (Lund and Romano, 2018); this only shows that the version and data in hand behave as published. It is the source term of everything below, and it is the least certain link in the chain: the numbers that descend from it should be read to about ten percent. + +## 1. The source: what the core actually emits + +- bremsstrahlung made in the pellet ceramic: 114 M/s, 0.0569 photons per decay at a mean energy of 144 keV; the betas deposit 181 µW there +- photons leaving the source capsule into the lamp cell: **43.9 M/s** (± 0.1%), 39% of those made, mean energy **252 keV**, 87% above 100 keV and 7.6% above 500 keV: the pellet and its capsule absorb the soft end of their own light +- power deposited in the whole vessel: **183 µW** against the design note's 181 µW for 1 GBq of ⁹⁰Sr/⁹⁰Y (SEALED.md ledger), the difference being the beta spectra used and the photons that escape + +| where the energy goes | power | +|---|---| +| core (pellet and capsule) | 182 µW | +| lamp cell (krypton and wall) | 46.1 nW | +| collar | 760 nW | +| compute shell (glass and sites) | 43 nW | +| trim ring | 6.86 pW | +| boundary (paddles, CZT, silicon) | 38.5 nW | +| shield (PMMA, lead, titanium) | 587 nW | +| outside | 1.04 nW | + +Almost all of the decay energy stops in the pellet and its capsule, as the design intends: it is the lamp's heat and the betavoltaic's supply. What leaves as photons is the bremsstrahlung of a thick target, 1.4% of the power, and that is the whole budget the compute shell, the boundary and the shield have to work with. + +## 2. The compute shell: what each site sees + +- interaction rate per site: mean **515 /s**, from 148 /s to 1.1 k/s (the lattice is symmetric, so the spread is the height dependence and statistics); photon flux 453 k/cm²/s; deposited 4.22 pW per site +- all 64 sites together: **32.9 k/s** interactions, against the design note's proposal budget of 10⁶ per second (SEALED.md Section 8): the shell is fed 0.033× what the sampler was priced at +- pile up: the mean site interacts 5.1e-05 times per 100 ns resolving time, so 0.0051 percent of its events overlap another; the theory's floor plan n ≳ λτ_d asks for 0.0033 sites at this activity, and there are 64 +- accidental coincidences between two mean sites in a 100 ns window: 2τ r² = **0.053 /s**, the raw material of the coincidence multiplier; the precision law then gives 0.00021 four bit readings of it per second and 8.1e-07 eight bit ones +- **the same shell with CsI cells**, the build note's other option: mean **16 k/s** per site, **1.02 M/s** over all 64, 31× the plastic figure and 1.02× the proposal budget; pile up 0.0016 per resolving time (0.16 percent of events overlap, 0.1 sites needed); accidental coincidences between two mean sites 51 /s, 0.2 four bit and 0.00078 eight bit readings per second + +The field in a site has mean energy 240 keV, and 18% of it is below 100 keV: what reaches the shell is already the soft end of the bremsstrahlung, filtered by the capsule, the lamp wall and the collar. Which cell material the builder chooses decides whether the sampler is fed at all: 2 mm of plastic is a Compton scatterer that a 240 keV field crosses almost untouched, and 2 mm of CsI, with the photoelectric effect of iodine and caesium and four times the density, interacts 31× as often. The note offered either; the transport says CsI, and that with CsI the shell meets the proposal budget. The rest of this report runs the vessel with plastic cells, the conservative choice; the collar's contrast is given for both, and the septum's factor, a ratio of couplings through the same lead, is given for plastic. + +## 3. The GATE: the tungsten collar's transfer curve + +Every site faces the lamp cell through an opening in a 2 mm tungsten sleeve; the opening's width is the site's thinning aperture, the mechanical GATE terminal of the reference transistor. The collar was run at five widths. + +| opening (percent of nominal) | mean site rate | relative to open | +|---|---|---| +| 0 | 81.2 /s ± 7.3 /s | 0.158 | +| 25 | 352 /s ± 15 /s | 0.684 | +| 50 | 471 /s ± 17 /s | 0.915 | +| 75 | 495 /s ± 17 /s | 0.961 | +| 100 | 515 /s ± 10 /s | 1.000 | + +ON/OFF contrast of the collar: **6.34** (± 0.58) with plastic cells. With CsI cells, which the soft end of the spectrum reaches and the closed collar removes, the contrast is **11.94** (± 0.37): 1.34 k/s closed against 16 k/s open. The closed state is not dark, because 2 mm of tungsten stops the soft bremsstrahlung and passes the hard tail (a 1 MeV photon has a 30 percent chance of crossing it uncollided), and because photons scattered in the glass reach the sites from the side. The aperture is an analog knob over a modest range, which is what the neutron sector's absorber turned out to be too, and for the same reason: an absorber in a path is a filter, not a barrier, unless it is thick enough to stop the whole spectrum. + +## 4. The synapse: the Green's function between sites + +A photon born in site j (isotropically, with the spectrum the source stage found in the sites) interacts in site k with probability G_kj. This is the weight matrix of the theory's transport synapse for the real geometry, the object Open Problem 4 asked for, measured 64 × 64. + +| coupling | mean G_kj (interactions in k per photon born in j) | +|---|---| +| a site with itself (G_jj) | 1.31e-02 | +| nearest neighbour around the ring (Δθ = 45°) | 3.33e-05 | +| nearest neighbour along the axis (Δz = 1 cm) | 1.10e-04 | +| diagonal neighbour | 2.24e-05 | +| everything farther | 3.60e-06 (mean), 2.93e-05 (largest) | +| all other sites together, per photon born | 5.39e-04 | + +A photon born in a 2 mm site has a 1.3% chance of interacting in it and a 0.1% chance of interacting in any of the other 63; the rest is lost to the glass, the collar, the boundary and the shield. That is the fan out tax of theory Section 1.3 for this geometry: the weights of the synapse are of order 3×10⁻⁵, and a signal handed from a site to its nearest neighbour is attenuated by 3×10⁴ at every hop. The compiler's toy fabric (transport/compiler_demo.py) had weights of order a tenth; the real shell is 3 orders down, which the sampler's rate coding absorbs as budget rather than as error (theory Section 10.1), but which sets what a gigabecquerel actually buys. These are plastic cells; CsI cells would raise every entry, the self term and the couplings alike, by roughly the material ratio of Section 2, and the fan out fraction with them. + +**The septum.** A 1 mm lead sheet between sector 0 and sector 1 leaves sector 0's coupling to sector 1 at 0.49 of its open value and its coupling to sector 7, on the unshielded side, at 1.00: the inhibitory septum of the build note blocks the soft part of the coupling and passes the hard part, a factor rather than a wall, like the collar and like the cadmium sheet of the neutron gate. Fixed absorbers program weights in this machine; they do not cut wires. + +## 5. The boundary: what the mouth actually counts + +| detector | interaction rate | deposited power | +|---|---|---| +| scintillator paddles and caps (24 SiPM tiles) | 2.83 M/s ± 7.1 k/s | 25 nW | +| four CZT pixels together | 426 k/s | 3.93 nW | + +- detected boundary events: **3.25 M/s**, against the design note's budget of 10⁷ per second (SEALED.md Section 7): **0.33×** the assumption; the fraction of photons leaving the core that interact in the boundary is 7% +- by the precision law, that budget supports 50 eight bit reads per second, 794 at six bits and 12703 at four; the note priced 153, 2,441 and 39,062 +- the paddle spectrum has mean energy 254 keV; a 6 mm plastic paddle is a Compton scatterer, not a photopeak detector, and the CZT pixels are where the energy division channels of gates/edm_channels.md would be read + +## 6. The dose outside: the health physics the build note deferred + +| where | ambient dose rate (ICRP 116, anterior posterior, photons) | +|---|---| +| at the titanium wall | **67.8 µSv/h** | +| 10 cm from the centre | 26.5 µSv/h | +| 1 m from the centre | **0.261 µSv/h** | + +- photons escaping the shield: 3.4 M/s, 7.7% of what left the core, with mean energy 565 keV: the hard tail again +- for scale, the public dose limit of 1 mSv per year is 0.11 µSv/h continuously; at 1 m this vessel exceeds it by 2×, and at the wall it is 616× over. The build note said the shield was sized with margin and that the final figure was the builder's to certify; this is that figure, for the photons, from the same library that licenses shielding +- the bremsstrahlung of ⁹⁰Sr/⁹⁰Y is a known shielding problem precisely because it is hard: the design's 4 mm of lead is a filter for it, not a wall, and a laboratory instrument at a gigabecquerel would sit in a lead pot. Nothing in the computation contradicts the note's licence class, institutional; it puts a number on why + +## 7. The design notes, checked + +| what the notes assumed | where | computed here | +|---|---|---| +| deposited power, 181 µW per GBq | SEALED.md ledger | 183 µW for the pair | +| boundary budget 10⁷ detected events per second | SEALED.md Section 7 | 3.25 M/s | +| percent level boundary collection | SEALED.md Section 7 | 7% of core photons | +| proposal budget 10⁶ per second across 64 sites | SEALED.md Section 8 | 32.9 k/s with plastic cells, 1.02 M/s with CsI | +| cells of plastic scintillator or CsI | EMBODIMENT.md Section 1.2 | CsI, by 31× in rate | +| pile up ceiling, sites ≳ λ τ_d | THEORY.md Section 3.2 | 0.0033 sites needed with plastic, 0.1 with CsI, 64 present | +| the aperture as the GATE terminal | transistor/README.md | contrast 6.34 through 2 mm of tungsten with plastic cells, 11.94 with CsI | +| lead septa as inhibitory blocking | EMBODIMENT.md Section 1.2 | coupling reduced to 0.49, not cut | +| weights written by geometry | README, the scattering gate | nearest neighbour G ≈ 3×10⁻⁵, fan out 0.1% | +| shield sized with margin, dose to be certified | EMBODIMENT.md Section 1.5 | 67.8 µSv/h at the wall, 0.261 µSv/h at 1 m | + +*The ampoule's budget falls short at the boundary by 3.08× and reaches its proposal budget in the sites only with CsI cells (1.02× the budget, against 0.033× with plastic); its wall is thinner than its own spectrum; and its two mechanical controls, the aperture and the septum, are knobs rather than switches for the same reason the neutron gate's absorber was. The machine the theory can seal today is a rate coded sampler whose weights are small and whose photons are hard, and every one of those adjectives is now a number.* diff --git a/ampoule/tallies.json b/ampoule/tallies.json new file mode 100644 index 0000000..ca38d0b --- /dev/null +++ b/ampoule/tallies.json @@ -0,0 +1,30862 @@ +{ + "runs": { + "emission": { + "spectrum_per_s": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 1000.0, + 500.0, + 0.0, + 0.0, + 17500.0, + 0.0, + 500.0, + 21500.0, + 572000.0, + 7160000.0, + 587500.0, + 2842500.0, + 6757000.0, + 10001000.0, + 11850000.0, + 12268000.0, + 11696000.0, + 10693500.0, + 9385500.0, + 7768000.0, + 6526500.0, + 5093000.0, + 3871000.0, + 2870000.0, + 1932000.0, + 1147000.0, + 543500.0, + 213500.0, + 26000.0, + 0.0 + ], + "std": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 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A falsifiable roadmap (with ki the photon keystone searched for in ENSDF: every gateway of every isomer that holds a bit for a second, in observed and allowed classes, with its release cascade; every level restoring coincidence within rotor reach and the areal density wall each one meets; every isomer with a signal gateway and a veto gateway; the NEEC class ranked +ampoule/ +the sealed machine in real photon transport: the vessel of the build note in OpenMC with ENDF/B-VIII.0 photoatomic data and its own beta spectra, calibrated against XCOM and the thick target rule; the photon budget, site rates in plastic and in CsI, pile up, the collar's transfer curve, the 64 × 64 Green's function and what the septum does to it, the boundary count rate, the energy budget, and the dose outside + + transistor/ the reference transistor: one pinout at three scales, the valve, the datasheet with characteristic curves and maximum ratings; with four accompanying notes: SEALED.md (the machine), EMBODIMENT.md (the build, at assembly grade), VALVE.md (the logic), COMPONENTS.md (the full inventory of a working computer, missing pieces simulated), POWER.md (the metabolism), and SCALING.md (the trajectory) @@ -539,15 +543,26 @@

The photon keystone, searched

The photon keystone, searched

Two lines of the theory change as a result. The convertible class of Section 2 is no longer a conjecture but a table, and its entries fail Section 1.1 by orders of magnitude, so the photon sector amplifier cannot be found in the chart and must be engineered, which is what Phase B1's experiments have been for all along. And the inhibition that the neutron result added to the keystone's requirements is available in the photon sector without new physics, so it no longer belongs on the list of things the keystone must be discovered to have; it is a property of any isomer with two gateways, and the search that must still succeed is the one for gain.

+

The ampoule, transported

+

The sealed machine of the two notes above was a design at assembly grade whose every number, beyond the decay constants, was an assumption. ampoule/ builds the vessel shell by shell in OpenMC with the official ENDF/B-VIII.0 photoatomic library, drives it with the beta spectra of its own ⁹⁰Sr/⁹⁰Y core through a thick target bremsstrahlung treatment, calibrates the instrument first (attenuation to 0.4 percent of NIST XCOM, slab transmission to 1.0 percent of the exponential, thick target yields within the rule's own tolerance), and replaces the assumptions with tallies.

+
    +
  • The light is scarce and hard. A gigabecquerel of each nuclide makes 0.0569 bremsstrahlung photons per decay, and its own pellet and capsule absorb the soft majority of them: 43.9 M/s leave the core, at a mean energy of 252 keV, while the vessel deposits 183 µW against the ledger's 181 µW per GBq. Everything the compute shell, the boundary and the shield do, they do with that.
    • +
  • The budget closes only where the cells are dense. The boundary ring counts 3.25 M/s, 7% of the photons leaving the core but 0.33× the note's 10⁷ per second, so the precision law gives 50 eight bit reads per second where the note priced 153. The 64 sites, as 2 mm plastic cells, see 32.9 k/s of interactions together, 0.033× the proposal budget the sampler was priced at; the same cells in CsI, the note's other option, see 1.02 M/s, 31× more, which meets the budget. The build note is amended: the cells are CsI, and the mouth is a factor 3.0 narrower than it was priced.
    • +
  • The weights are small and the controls are knobs. The Green's function between sites, measured 64 × 64, puts a nearest neighbour coupling at 3×10⁻⁵ per photon and the whole fan out of a site to its 63 neighbours at 0.1%: the fan out tax of theory Section 1.3 for a real shell, three orders below the compiler's toy fabric, and an attenuation of 3×10⁴ per hop. The tungsten collar, the reference transistor's GATE terminal, has an ON/OFF contrast of 6.34 with plastic cells and 11.94 with CsI, and the lead septum, the build note's inhibitory blocking, leaves the coupling it sits across at 0.49 of its open value against 1.00 on the unshielded side. Both are filters for a hard spectrum, not barriers: the same finding as the cadmium sheet of the neutron gate, for the same reason.
    • +
  • The wall is thinner than the spectrum. 3.4 M/s escape the shield, 7.7% of what left the core at a mean 565 keV, and the ambient dose rate is 67.8 µSv/h at the titanium wall and 0.261 µSv/h at one metre (ICRP 116). The build note deferred this figure to the builder; it is now on the table, and it says a gigabecquerel ⁹⁰Sr ampoule behind 4 mm of lead is an instrument for a lead pot, which is the licence class the note already gave it.
    • +
+

The ampoule in photon transport

+

The machine the theory can seal today is therefore a rate coded sampler whose photons are hard, whose weights are small, whose mouth is narrower than it was priced, and whose two mechanical controls are analog. Every one of those adjectives was an adjective; each is now a number, and the notes are corrected where the numbers say so.

+

Open problems and how to contribute

  1. Keystone: propose or measure a compact state meeting the leak condition with β>1 in a level restoring or convertible class (theory, Section 2). This is problem number one. A concrete, computable subproblem: search ENSDF for heterogeneous pairs of isomers whose cascade lines and gateway lines are mutually resonant (gate A's output pumps gate B and vice versa); the search space is already tabulated in /gates. The computed neutron gate (neutron/) adds a second requirement that the photon sector had not been asked for: the state must also supply a signal controlled inhibition, because the only one the neutron sector has is heat and it is worth a fraction of the gain. A gate with gain but no inversion is a linear amplifier with a comparator bolted to its boundary, and the machine it builds is the Bernstein machine of Section 6 with better numbers, not a logic family.
  2. Tighten the throughput law for fan out reuse: when is a count "spent"?
  3. A learning rule: aperture update Δα ∝ coincidence(pre,post) is Hebbian or STDP using the same coincidence primitive as the AND gate (Appendix B.4); formalize and simulate.
    4. -
  4. Transport level 𝒢 for a real geometry that implements a target weight matrix (signed weights via complementary channels).
    5. +
  5. Transport level 𝒢 for a real geometry that implements a target weight matrix (signed weights via complementary channels). The measurement half is done: ampoule/ has the 64 × 64 Green's function of the build note's compute shell, nearest neighbour weights of 3×10⁻⁵ per photon with 0.1% total fan out; what remains is to run the compiler of theory Section 11 on that geometry rather than on the toy fabric.
  6. Tier 2: a concrete two qubit gate on nuclear spin or Mössbauer DOF with a room temperature error budget.
  7. The addressed long retention write. The broadband route to self written memory is dead by a bandwidth ratio of 10¹⁸, and the narrowline route is now open in principle (nuclear lamps, radiogenic feeding, resonance addressing: theory Section 9); what remains is a state that is simultaneously parent fed, gradient addressable, and long lived. A concrete, computable search: scan the catalog in /gates for isomers with lifetime above seconds whose feeding parents emit Mössbauer class lines, and rank by the addressing sensitivity Γ/(dE/dB).
    8. -
  8. Measure realized bits per detected quantum for a pixelated spectroscopic boundary against the log_2(N_E N_x N_τ) ceiling of the boundary theory.
    9. +
  9. Measure realized bits per detected quantum for a pixelated spectroscopic boundary against the log_2(N_E N_x N_τ) ceiling of the boundary theory. The boundary's raw budget is now computed, 3.25 M/s detected in the build note's ring, 0.33× what it was priced at (ampoule/); the ceiling is still to be measured against it.

Open an Issue stating the claim and the test; pair every Pull Request with the Issue it closes.

diff --git a/neutron/data.py b/neutron/data.py index b705bb9..8e3791d 100644 --- a/neutron/data.py +++ b/neutron/data.py @@ -8,8 +8,8 @@ The library is the one the OpenMC project distributes at openmc.org (ENDF/B-VIII.0 processed to HDF5 by NJOY, neutron data at 250 to 2500 K, thermal scattering at 284 to 800 K). The archive is 3.4 GB compressed and -13.7 GB unpacked, and this machine needs 53 files from it, so the archive -is streamed and only those members are written to disk: about 1.5 GB, +13.7 GB unpacked, and this machine needs 129 files from it, so the archive +is streamed and only those members are written to disk: about 2 GB, the two large ones being the uranium evaluations and the water thermal scattering law. Nothing is modified; the files are the library's own. @@ -40,10 +40,24 @@ "Fe58", "Ni58", "Ni60", "Ni61", "Ni62", "Ni64", "P31", # for the SHEBA-II "S32", "S33", "S34", "S36", "N15", "U236", # and STACY benchmarks "U234", "U235", "U238", # the fuel + # the ampoule's materials (/ampoule): OpenMC expands an element into its + # natural isotopes and needs their neutron files even in a photon run + "Sr84", "Sr86", "Sr87", "Sr88", "Ti46", "Ti47", "Ti48", "Ti49", "Ti50", "Y89", + "Kr78", "Kr80", "Kr82", "Kr83", "Kr84", "Kr86", + "Mo92", "Mo94", "Mo95", "Mo96", "Mo97", "Mo98", "Mo100", + "Cs133", "I127", "Te120", "Te122", "Te123", "Te124", "Te125", "Te126", "Te128", "Te130", + "W180", "W182", "W183", "W184", "W186", "Pb204", "Pb206", "Pb207", "Pb208", + "Mg24", "Mg25", "Mg26", "K39", "K40", "K41", "Na23", ] THERMAL = ["c_H_in_H2O"] +# photoatomic and electron data for the ampoule's materials (/ampoule): the +# source ceramic and capsule, krypton, the glass and scintillator of the +# compute shell, tungsten and lead, the detectors, and the shield +PHOTON = ["H", "B", "C", "N", "O", "F", "Na", "Mg", "Al", "Si", "K", "Ti", "Cr", "Mn", + "Fe", "Ni", "Mo", "Kr", "Sr", "Y", "Zn", "Cd", "Te", "Cs", "I", "W", "Pb"] MEMBERS = ([f"{LIBRARY}/neutron/{n}.h5" for n in NUCLIDES] + - [f"{LIBRARY}/thermal/{t}.h5" for t in THERMAL]) + [f"{LIBRARY}/thermal/{t}.h5" for t in THERMAL] + + [f"{LIBRARY}/photon/{e}.h5" for e in PHOTON]) def data_dir(): @@ -94,6 +108,8 @@ def write_cross_sections(root): lines.append(f' ') for t in THERMAL: lines.append(f' ') + for e in PHOTON: + lines.append(f' ') lines.append("") path = os.path.join(root, LIBRARY, "cross_sections.xml") open(path, "w").write("\n".join(lines) + "\n") @@ -124,6 +140,10 @@ def verify(log=print): for t in THERMAL: d = openmc.data.ThermalScattering.from_hdf5(os.path.join(root, LIBRARY, "thermal", t + ".h5")) log(f" {t}: {', '.join(sorted(d.temperatures, key=lambda s: float(s[:-1])))}") + for e in PHOTON: + d = openmc.data.IncidentPhoton.from_hdf5(os.path.join(root, LIBRARY, "photon", e + ".h5")) + log(f" {e:3s} photoatomic, Z = {d.atomic_number}, {len(d.reactions)} reactions, " + f"bremsstrahlung {'yes' if d.bremsstrahlung else 'no'}") if __name__ == "__main__": diff --git a/transistor/EMBODIMENT.md b/transistor/EMBODIMENT.md index 379004e..947ffe0 100644 --- a/transistor/EMBODIMENT.md +++ b/transistor/EMBODIMENT.md @@ -73,4 +73,8 @@ A sealed cylindrical vessel, outer envelope 90 mm diameter × 170 mm, about 4 kg | krypton leak into vessel | lamp dimming, pressure alarm inferred from saturable channel drift | soft threshold operating points shift | channels are re trimmed; unit derates, does not fail | | the one unfixable | source decay | throughput halves per 28.8 years | by design: correctness is invariant (theory Section 7); print the curve on the label | +## 5. What the transport calculation changed + +The vessel above has been run in OpenMC with its own beta spectra ([/ampoule](../ampoule/)); four lines of this note are corrected by it. The scintillating cells of Section 1.2 are CsI, not plastic: a 2 mm plastic cell in the 252 keV field the core delivers interacts 515 /s, and the 64 together reach 0.033× the proposal budget of SEALED.md Section 8, while CsI cells interact 31× as often, 1.02 M/s in all, which meets it. The tungsten aperture inserts of the same section are analog trims and not shutters: the collar's ON/OFF contrast is 6.34 with plastic cells and 11.94 with CsI, because 2 mm of tungsten passes the hard half of the bremsstrahlung. The lead septa are attenuators and not blocks: a 1 mm sheet leaves the coupling it sits across at 0.49 of its open value. And the health physics calculation Section 1.5 left to the builder now has a first figure: 67.8 µSv/h at the titanium wall and 0.261 µSv/h at a metre, from 3.4 M/s escaping at a mean 565 keV, which places this vessel where Section 0 already put it, in an institution with a lead pot. The counting ring of Section 1.4 sees 3.25 M/s, 0.33× the 10⁷ per second the performance line at the top of this note was priced on, so the 8 bit reads are 50 per second and not 153 until the ring collects more than its present 7% of the core's light. + *Nothing in this note is exotic to a nuclear instrumentation shop: ISO sealed sources, Mössbauer foils and drives from catalog, channel plates from any microfluidics fab, SiPMs and CZT from the PET industry. The novelty is entirely in what the assembly is for. That is the point.* diff --git a/transistor/SEALED.md b/transistor/SEALED.md index 3795198..845a7ec 100644 --- a/transistor/SEALED.md +++ b/transistor/SEALED.md @@ -80,4 +80,6 @@ A sealed cylinder, roughly a liter, one GBq of ⁹⁰Sr/⁹⁰Y at the core (181 - at year 29: exactly half of all of the above, same answers; - assembly grade specification: every shell, dimension, material, and procedure is in the [build note](EMBODIMENT.md); license class: GBq sealed sources are institutional (this is the tier between the exempt benchtop cell and the reactor gate of [the reference transistor](README.md)); the ampoule is a laboratory instrument, not a consumer object, and the document says so. +**Transported.** The vessel of this note has now been run in real photon transport ([/ampoule](../ampoule/), numbers in [`ampoule/results.md`](../ampoule/results.md)), and three of its numbers move. Its core sends 43.9 M/s of bremsstrahlung into the lamp cell at a mean energy of 252 keV, 0.0569 photons per decay, and deposits 183 µW against the ledger of Section 5, which holds. The boundary counts 3.25 M/s, 0.33× the 10⁷ per second assumed in Section 7, from 7% of those photons: the mouth is a factor 3.0 narrower than priced, and the digital port reads 50 eight bit words per second rather than 150. The proposal budget of Section 8 is reached only if the sites are CsI, at 1.02 M/s; in plastic they see 32.9 k/s, 0.033× the budget. What the transport adds that the note could not is the character of the light: it is hard, so the tungsten apertures switch with a contrast of 6.34 (11.94 with CsI cells) and the lead septa leave the coupling they block at 0.49 of its open value, and the wall passes 7.7% of it for an ambient dose of 67.8 µSv/h at contact and 0.261 µSv/h at a metre. The ampoule computes in rates as this note says; its knobs are analog, its lead is a filter, its mouth is narrower, and the build note is amended accordingly. + *The ampoule closes the loop the charter opened: a lump of structured matter, bathed in its own radiation, computing. Nothing enters but fields; nothing leaves but light; nothing inside it can be recalled, recharged, or corrected, and by the aging theorem nothing needs to be.*