Radiation Debris

Radiation and Debris Environment Assessment (space-systems/mission-design/radiation-debris)

Use when the task is a space environment assessment for mission design: estimating the trapped radiation belt dose the spacecraft accumulates, adding the solar particle event contribution, checking the single-event upset rate for sensitive electronics, sizing shielding against total ionizing dose, and estimating the orbital debris collision probability over the mission life.

Units convention (stated once): altitude in km, inclination in degrees, dose rate in rad(Si) per day, mission life in years, shielding in mm of aluminum, device cross-section in cm^2, spacecraft debris cross-section in m^2, LET in MeV cm^2/mg, fluence in protons/cm^2, flux in particles/m^2/year for debris and particles/cm^2/day for the LET spectrum.

The models are simplified engineering proxies with the shape of the AE-8/AP-8 trapped belt, JPL-style solar particle, and ORDEM/MASTER debris environment families. They are trend tools for mission design, not flight qualification data; a real program uses the actual environment models with the actual component test data.

Domain quick reference

• Trapped belt dose rate: two Gaussian flux bands, a proton belt peaking near 3500 km and an electron belt peaking near 20000 km, scaled by an inclination factor from 0.3 (equatorial) to 1.0 (polar). At the proton belt peak in a polar orbit the unshielded rate is about 60.8 rad/day; at 600 km in a sun-synchronous-like orbit it is about 0.26 rad/day.
• Inclination factor: 1 - 0.7 * cos^2(inclination), symmetric about 90 degrees, so an 80 degree and a 100 degree orbit see the same belt fraction. Equatorial orbits skim the belt edges; polar orbits cross the full belt structure every orbit.
• Solar particle event fluence: integral fluence above energy E is a power law, Phi = 1e8 * (E / 10 MeV)^(-3) * mission_years protons/cm^2, the order of a 1-in-5-year worst-week event above 10 MeV. Over 5 years at 10 MeV that is 5e8 protons/cm^2; at 100 MeV the fluence drops by a factor of 1000.
• Single-event upset rate (RPP model): the Weibull cross-section sigma = sigma_sat * (1 - exp(-((LET - L0) / W)^S)) above the LET threshold, summed over the LET spectrum. The rate scales linearly with the saturation cross-section: doubling sigma_sat doubles the rate. A spectrum entirely below the threshold gives zero upsets.
• Total ionizing dose versus shielding: two-component exponential attenuation. The electron component (default 70 percent of the unshielded dose) is absorbed with a 3 mm aluminum 1/e length; the proton component (30 percent) penetrates with a 60 mm 1/e length. The shielded dose always sits below the unshielded dose and falls monotonically with thickness.
• Shielding sizing: shielding_for_dose_limit returns the minimum aluminum thickness meeting a dose limit, or None when even the maximum thickness cannot (the proton component floor sits above the limit). At the proton belt peak (60.8 rad/day, 1 year) a 10 krad limit needs about 4.5 mm of aluminum.
• Debris flux: a Gaussian density band peaking near 850 km where the catalogued debris population is densest, scaled by a size power law (s / 1 cm)^(-2.6). At the peak the flux of particles above 1 cm is 5e-5 per m^2 per year; at 550 km it drops by about 63 percent.
• Collision probability: Poisson statistics, P = 1 - exp(-flux * area
  • mission_years). For small expected collisions the probability is approximately the product; it grows with mission life and cross-section, and is exactly 0 for zero area or zero flux.
• Verdicts: dose_verdict is ADEQUATE (at least 20 percent margin to the limit), MARGINAL (below the limit with less margin), or EXCEEDED (at or above the limit). debris_verdict is LOW below 1 percent, MODERATE to 10 percent, HIGH above.
• ECSS-E-ST-10C (systems engineering general requirements) frames the space environment assessment within the ECSS lifecycle; ECSS standards are free to download from https://ecss.nl/standards/ (name + paraphrase + link only).

Workflow

1. Define the orbit and mission: altitude in km, inclination in degrees, and mission life in years.
2. Get the unshielded trapped belt dose rate with trapped_belt_dose_rate, and the solar particle event fluence with spe_fluence at the energies of interest (10 and 100 MeV are the usual reference points).
3. Build the LET spectrum with power_law_let_spectrum (or supply a measured spectrum as (LET, differential flux) pairs), then compute the single-event upset rate with seu_rate from the device saturation cross-section, LET threshold, Weibull width and shape.
4. Compute the total ionizing dose behind the chosen shielding with tid_after_shielding, or invert it with shielding_for_dose_limit to size the shielding against the component dose limit; check the dose margin with dose_verdict.
5. Get the debris flux with debris_flux_per_m2_yr at the mission altitude, then the collision probability with collision_probability from the spacecraft cross-section and mission life; grade it with debris_verdict.
6. Build the RadiationDebrisAssessment with all the mission parameters and use report for a single dict summary of dose, SEU rate, and debris risk with the verdicts.
7. Sanity-check the result: a low earth orbit sun-synchronous mission at 600 km with a few mm of aluminum accumulates a fraction of a krad over 5 years with a collision probability below 1 percent; an orbit through the proton belt peak without shielding accumulates tens of krad per year.

Worked example

A 600 km sun-synchronous-like orbit (98 degrees inclination), 5-year mission, 3 mm aluminum shielding, a 10 m^2 debris cross-section, and a sensitive part with sigma_sat 1e-6 cm^2, LET threshold 10 MeV cm^2/mg, Weibull width 15 and shape 1 against a power law LET spectrum (k = 1e5, exponent 2.5, 0.1 to 100 MeV cm^2/mg):

• trapped_belt_dose_rate(600, 98) = 0.263 rad/day.
• spe_fluence(10, 5) = 5e8 protons/cm^2 above 10 MeV.
• tid_after_shielding(0.263, 5, 3) = 0.261 krad, verdict ADEQUATE against a 50 krad limit (unshielded it would be 0.481 krad, and behind 10 mm it drops to 0.134 krad).
• seu_rate = 4.8e-4 upsets per device per day, about 0.18 per device per year.
• debris_flux_per_m2_yr(600) = 2.50e-5 per m^2 per year; collision_probability(2.50e-5, 10, 5) = 1.25e-3, verdict LOW.

The design conclusion: the orbit is benign for dose at this shielding, the part is borderline for single-event effects (one upset every several years per device, so the system needs error correction or a harder part), and the debris risk is low.

Pitfalls

• Treating the proxies as qualification data: the simplified models reproduce environment shapes, not the AE-8/AP-8 or ORDEM/MASTER detail. A real program must run the actual environment models and the actual component test data before committing to a design.
• Forgetting the solar particle event contribution: a long mission or an event-rich period adds a proton fluence spike that dominates the dose behind thin shielding; the belt dose alone understates the requirement.
• Sizing shielding with a single attenuation length: the electron component stops in a few mm of aluminum while the proton component penetrates far deeper; a single exponential predicts a dose of zero behind modest shielding and misses the proton floor.
• Ignoring the LET threshold in SEU analysis: a device with a high threshold sees almost no upsets in a soft spectrum; folding the threshold into the Weibull fit is the difference between zero and a real rate.
• Using the debris flux at the wrong altitude: the flux at 550 km is about a third of the flux at 850 km; evaluating the collision probability at the wrong altitude misrates the risk by a factor of several.
• Adding collision probabilities instead of compounding: P = 1 - exp(-lambda) from the mission-life lambda; summing yearly probabilities is only valid while every yearly probability is tiny.
• Neglecting the cross-section of the deployed configuration: solar arrays and antennas multiply the debris cross-section; sizing the risk on the bus cross-section alone understates the probability.

Behavior contract (gate 3)

The trapped belt dose, solar particle fluence, RPP single-event rate, shielding attenuation, and debris collision math is exercised by the gate 3 contract test: scripts/test_radiation_debris.py against scripts/radiation_debris_logic.py (stdlib unittest, offline). Run from the repo root: python3 skills/space-systems/mission-design/radiation-debris/scripts/test_radiation_debris.py

Compliance

• Standards referenced, not reproduced: ECSS-E-ST-10C (systems engineering general requirements) frames the space environment assessment within the ECSS lifecycle, and the environment models above are common space engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.