A maximum likelihood method for linking particle-in-cell and Monte-Carlo transport simulations

Abstract

The expectation-maximization (E-M) algorithm [Dempster et al., J. R. Stat. Soc. B 39 (1977) 1–38] is a maximum likelihood technique to estimate the probability density function (PDF) of a set of measurements. A high performance implementation of the E-M algorithm to characterize multidimensional data sets using a PDF parameterized as a Gaussian mixture was developed. The resulting PDFs compare favorably to histogram based techniques—no binning artifacts and less noisy (especially in the tails). The motivation, the mathematical properties and the implementation details will be discussed. The PDF estimator is used extensively in the radiographic chain model [Kwan et al., Comput. Phys. Comm. 142 (2001) 263–269] in simulations which quantify bremsstrahlung X-ray emission from rod-pinch diodes and other devices. In these devices, electrons hit an anode and produce X-ray photons. The PIC code MERLIN [Kwan and Snell, in: Lecture Notes in Physics, Springer, 1985] is used to model the dynamics of a low-energy (up to ∼2.25 MeV) radiographic electron source. The photon production is modeled with the Monte-Carlo transport code MCNP [Briesmeister, ed., MCNP—A General Monte Carlo N-Particle Transport Code, 2000]. The estimator is used to upsample and uniformly weight the PIC electrons to provide a suitable population for the Monte-Carlo calculation that would be computationally prohibitive to generate directly.