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Run Kinetics

Nucleide point kinetics solves prescribed-reactivity transients with the nucleide-kinetics crate. This tutorial covers the Python API; the implementation lives in crates/kinetics. For the physics and math, see the Point kinetics theory page.

Solve a step transient

from nucleide.kinetics import solve

betas = [0.00021, 0.00141, 0.00127, 0.00255, 0.00074, 0.00032]
lambdas = [0.01, 0.03, 0.1, 0.3, 1.0, 3.0]
out = solve(
    betas,
    lambdas,
    Lambda=1e-5,
    rho={"kind": "step", "t_step": 1.0, "rho_init": 0.0, "rho_final": 0.002},
    t=[0.5, 1.0, 1.05, 2.0, 10.0],
    n0=1.0,
)
print(out["n"])  # neutron level at each output time
print(out["C"][0])  # precursor groups at the first output time

Reactivities are in Δk and times in seconds. Precursor initials default to equilibrium; pass C0=[...] to override. method selects "trapezoidal" (default, second order) or "backward_euler" (extra damping); rtol / atol control the adaptive stepper.

Reactivity schedules

rho is a spec dict with kind selecting the schedule:

step = {"kind": "step", "t_step": 1.0, "rho_init": 0.0, "rho_final": 0.002}
ramp = {
    "kind": "ramp",
    "t_start": 1.0,
    "t_end": 3.0,
    "rho_init": 0.0,
    "rho_rise": 0.002,
    "rho_final": 0.002,
}
pulse = {"kind": "impulse", "t_start": 1.0, "t_end": 2.0, "rho_init": 0.0, "rho_max": 0.002}
table = {"kind": "polyline", "times": [0.0, 1.0, 3.0], "values": [0.0, 0.0, 0.002]}
flat = {"kind": "constant", "rho": 0.0}

Steps are right-continuous (t >= t_step reads the post-step level) and the solver lands exactly on every schedule knot.

Inhour and prompt-jump helpers

from nucleide.kinetics import equilibrium, inhour_rho, initial_rate, prompt_jump, stable_period

c0 = equilibrium(betas, lambdas, 1e-5, n0=1.0)
print(initial_rate(betas, lambdas, 1e-5, step, n0=1.0))  # == n0 * rho(0) / Lambda
print(stable_period(betas, lambdas, 1e-5, rho=0.002))  # asymptotic period in seconds
print(inhour_rho(betas, lambdas, 1e-5, omega=0.056))  # reactivity for a growth rate
print(prompt_jump(1.0, rho_before=0.0, rho_after=0.002, beta_total=sum(betas)))

prompt_jump needs rho_after < beta_total (no finite prompt equilibrium past prompt critical); stable_period needs 0 < rho < beta_total.

OpenMC IFP data note

OpenMC’s iterated-fission-probability estimator reports effective delayed fractions and the generation time but no precursor decay constants: pass its betas/Lambda through unchanged and supply lambdas from the same delayed-neutron library the IFP run used (the from_ifp provenance note in crates/kinetics/src/params.rs).

See also

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