Multigroup neutron diffusion with k-effective, checked against the closed-form analytic eigenvalue.
See it run - a worked example, 100% in this browser tab
The problem
Reactor-physics k-effective estimates are easy to get subtly wrong, and many calculators assert a number without checking it against the analytic eigenvalue.
The local-first solution
This plugin discretizes the 1-2 group neutron diffusion equation with second-order central finite differences in the browser, finds k-effective by power iteration, and checks the bare-slab result against the closed-form analytic eigenvalue.
What it does
1D one or two energy group diffusion with second-order central finite differences
k-effective eigenvalue via power (fission-source) iteration
Vacuum (extrapolated) and reflective boundary conditions
Bare-slab check against the closed-form k = nu Sigma_f / (Sigma_a + D B^2)
Converged group flux profiles and k-convergence history charts
Honest scope
Every figure is exact arithmetic over the discretized operator with no engine call, network, or AI, and accuracy is verified against the analytic eigenvalue rather than asserted. Cross sections are dated material inputs you confirm, and the output always surfaces the set it used plus the analytic relative error. This is not nuclear-safety or licensing advice.
Authorities cited
Duderstadt, J. J. & Hamilton, L. J. (1976). Nuclear Reactor Analysis. Wiley. Ch. 5 (one-speed diffusion theory, the slab eigenvalue and geometric buckling) and Ch. 7 (multigroup diffusion).
Lamarsh, J. R. & Baratta, A. J. (2001). Introduction to Nuclear Engineering, 3rd ed. Prentice Hall. Ch. 5-6 (bare-reactor critical equation k = nu Sigma_f / (Sigma_a + D B^2), extrapolation distance, and two-group treatment).
Stacey, W. M. (2007). Nuclear Reactor Physics, 2nd ed. Wiley-VCH. Ch. 3-5 (finite-difference diffusion discretization and power iteration for the k-eigenvalue).
Bell, G. I. & Glasstone, S. (1970). Nuclear Reactor Theory. Van Nostrand Reinhold. (Diffusion approximation, extrapolation length d = 2 D, the Milne-problem 0.7104/Sigma_tr transport value.)
Geometric buckling of a slab: B = pi / (L + 2d), fundamental cosine mode; the bare-slab criticality condition is the smallest-buckling (largest-k) eigenmode.
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems, 2nd ed. SIAM. (Power iteration converges to the dominant eigenpair; Gauss-Seidel for the M-matrix inner solve.)
Solve for k-effective
Run the solver in the browser and save the verified result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing leaves your machine to anyone's cloud.