Point kinetics

Solve a step-reactivity point-kinetics transient and read the prompt-jump estimate.

Prescribed-reactivity point kinetics tracks the neutron population $n(t)$ and $G$ delayed-neutron precursor groups $C_i(t)$ under a caller-supplied reactivity schedule $\rho(t)$ in Δk (E1):

\frac{dn}{dt} = \frac{\rho - \beta}{\Lambda}\,n + \sum_i \lambda_i C_i, \qquad \frac{dC_i}{dt} = \frac{\beta_i}{\Lambda}\,n - \lambda_i C_i. \tag{E1}

Precursors start at the equilibrium ratio (E2):

C_i(0) = \frac{\beta_i}{\lambda_i \Lambda}\,n_0, \tag{E2}

and a step $\rho^- \to \rho^+$ carries the prompt-jump estimate (E4):

n^+ = n^-\,\frac{\beta - \rho^-}{\beta - \rho^+}, \qquad \rho^+ < \beta. \tag{E4}

Step transient

The demo below solves one step-reactivity transient with the crate’s stiff-aware implicit integrator and reports the (E4) jump next to the $n(t)$ curve. Delayed data are caller-supplied: the One-group preset replays fixtures/kinetics/step_oracle.json ( $\beta = 0.0065$ , $\lambda = 0.08\ \mathrm{s}^{-1}$ , $\Lambda = 10^{-4}\ \mathrm{s}$ , step $0 \to 0.002\ \Delta k$ at $t = 1\ \mathrm{s}$ ), and the Six-group preset uses the hand-picked synthetic set from fixtures/kinetics/inhour_check.json. All inputs are validated inline (finite, with $0 \le t_{\mathrm{step}} \lt t_{\mathrm{end}}$ and $n_0 \ge 0$ ) before any solve runs. When $\rho^+ \ge \beta$ the (E4) formula has no solution and the readout says so while the solver still runs.

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Inhour and prompt-jump scalars

The Inhour analysis button below the transient runs the E3–E4 leftovers over the current delayed data: inhourRho at ω = 0.05 1/s, stablePeriod at ρ = 0.002 Δk, and the standalone promptJump factor.

Point kinetics

Step transient

Inhour and prompt-jump scalars

See also