General formulation of interactions and energy loss of particles in plasmas: Quantum-wave-packet model versus a semiclassical approach

Abstract

In this work we present a general quantum-mechanical and statistical formulation of the process of interactions of external test particles with plasmas, considering the calculation of the energy-loss coefficients, including energy losses, mean-free paths, and straggling, and describing in detail the differences between protons, positrons, and electrons. Two relevant aspects contained in this formulation are studied: the competing action of loss and gain processes in the interaction with the plasma, and the role of thermal fluctuations in those interactions. We propose two different approaches to evaluate processes of electronic interactions in plasmas. To formulate the first approach we introduce modifications to the quantum-wave-packet dielectric method, which provides a reliable description over wide ranges of plasma densities and temperatures as compared with full quantum-mechanical dielectric theory. The second approach is a semiclassical dielectric method. It consists of including statistical quantum distributions and restrictions in the energy-loss expression, combined with the classical dielectric function for hot plasmas obtained from the linearized Vlasov-Poisson equation. We compare the results from both methods on an extensive range of parameters that include low, intermediate, and high energies, with densities and temperatures going from normal laboratory conditions to very high values, such as those of interest for studies on inertial fusion, Tokamak plasmas, and astrophysical media. We give also special consideration to the case of electrons, where the restrictions imposed by the identity with plasma electrons produce important effects.