![]() Vrain high-temperature gas-cooled reactor. Applications and comparisons to measurements are made for the small fast burst reactor CALIBAN and the Fort St. For simplified infinite-medium and one-dimensional geometries, the TRMM accurately calculates eigenvalues, eigenfunctions, and eigenfunction expansion solutions. Results from the TRMM are verified using analytic solutions, time-dependent Monte Carlo simulations, and modal expansion from diffusion theory. Interpretation of the resulting Markov process transition rate matrix as the operator in the adjoint α-eigenvalue problem provides more » an avenue for determining a large finite set of α eigenvalues and eigenfunctions of a nuclear system. To obtain the α-eigenvalue spectrum, the transition rate matrix method (TRMM) tallies transition rates describing neutron behavior in a discretized position-direction-energy phase space using Monte Carlo. Applications in which this response is of interest include pulsed-neutron experiments, accelerator-driven subcritical systems, and fast burst reactors, where a steady-state assumption used in neutron transport is invalid for characterizing the time-dependent flux. For a nuclear system in which the entire α-eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source. ![]()
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