Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo

The α eigenvalue has implications for time-dependent problems where the system is sub- or supercritical. We present methods and results from calculating the α-eigenvalue spectrum for a continuous-energy infinite medium with a simplified Monte Carlo transport code. We formulate the α-eigenvalue problem, detail the Monte Carlo code physics, and provide verification and results. We have a method for calculating the α-eigenvalue spectrum in a continuous-energy infinite-medium. The continuous-time Markov process described by the transition rate matrix provides a way of obtaining the α-eigenvalue spectrum and kinetic modes. These are useful for the approximation of the time dependence of the system.