Depletion

Load a depletion chain and run one CRAM burnup step.

Depletion solves the Bateman equation for atom densities $\vec{n}(t)$:

where $A$ is the transmutation matrix built from decay, capture, and fission reaction rates. Nucleide uses the Chebyshev Rational Approximation Method (CRAM) with published 16- and 48-order coefficients.

Depletion chain

A chain XML lists nuclides, half-lives, decay branches, reaction targets, and fission yields. The demo below uses a tiny three-nuclide chain:

One-step solve

deplete(chain, n0, dt, rates, order) integrates over one time step dt. In production you would loop this call, update reaction rates from a transport solve, and accumulate burnup. The demo also offers a Burnup curve run that plots nuclide densities versus cumulative time, now backed by a single depleteSeries call with a selectable integrator. Atom counts, the time step, and the burnup step count are validated inline (finite, and positive where required) before any solve runs.

Solver method

The demo’s Solver method selector mirrors the Python method= spelling (cram48 default, cram16, bateman, bateman_hp): an explicitly non-default choice overrides the CRAM order on both the one-step deplete call and the depleteSeries burnup path. The Bateman arms evaluate the analytic closed form and fall back to CRAM-48 outside decay-only triangular topology (near-degenerate half-lives, cyclic or out-of-order chains, live reactions); long chains can still suffer float64 cancellation, so CRAM-48 stays the default. See the Run depletion tutorial for the D1–D4 fallback rule and the conditioning limits.

Multi-step series and decay heat

depleteSeries(chain, n0, dts, rates, integrator, order) threads the core integrate driver over a list of step lengths with the same rates applied to every step. The integrator selector offers predictor, cecm, and cf4; the result carries times (starting at t = 0 with the initial state as row 0) plus per-node atoms, activity (Bq), and decay_heat (W) maps. The chart plots atom counts per nuclide with a toggleable total-decay-heat trace. For the scripted equivalent see the Run depletion tutorial; for the integrator math and the decay-energy resolution see the Depletion theory.

See also

• Full-deck editing lives in the deck-editor demo.
• Tutorial: Run depletion
• Theory: Depletion
• Crate docs: crates/depletion/src/lib.rs