Investigation of the scattering of electrons by ions in the plasma of inertial confinement fusion in a magnetic field

In this paper, the processes of electron-ion scattering in the plasma of inertial confinement fusion in a magnetic field were studied. The proposed model for studying the processes of scattering between charged particles is based on solving the equation of motion in a central field taking into account the external magnetic field, as well as the Coulomb logarithm, which is determined using the scattering angle in a pair collision. Collisions between an electron and an ion that interact via the Yukawa potential were investigated. Also, the Coulomb logarithm in a dense plasma in a magnetic field was calculated. The effect of taking into account the magnetic field on the scattering angles, the scattering cross-section and the Coulomb logarithm are studied. From the results obtained, it is established that taking into account the magnetic field led to a non-monotonic change in the scattering angle and a decrease in the scattering cross-section for weak particle interactions. It is also revealed that for large values of the interaction parameterβ, the magnetic field does not affect the value of the Coulomb logarithm. Thus, the obtained results allow us to study the effect of taking into account the magnetic field on the processes of electron scattering on an ion in the approximation of pair collisions in an external constant magnetic field in a dense plasma.

Orbital scattering by random interactions with extended substructures

ABSTRACT This paper presents N-body and stochastic models that describe the motion of tracer particles in a potential that contains a large population of extended substructures. Fluctuations of the gravitational field induce a random walk of orbital velocities that is fully specified by drift and diffusion coefficients. In the impulse and local approximations, the coefficients are computed analytically from the number density, mass, size, and relative velocity of substructures without arbitrary cuts in forces or impact parameters. The resulting Coulomb logarithm attains a well-defined geometrical meaning, ln (Λ) = ln (D/c), where D/c is the ratio between the average separation and the individual size of substructures. Direct-force and Monte Carlo N-body experiments show excellent agreement with the theory if substructures are sufficiently extended (c/D ≳ 10−3) and not spatially overlapping (c/D ≲ 10−1). However, close encounters with point-like objects (c/D ≪ 10−3) induce a heavy-tailed, non-Gaussian distribution of high-energy impulses that cannot be described with Brownian statistics. In the point-mass limit (c/D ≈ 0), the median Coulomb logarithm measured from N-body models deviates from the theoretical relation, converging towards a maximum value 〈ln (Λ)〉 ≈ 8.2 independently of the mass and relative velocity of nearby substructures.

An introduction to the physics of the Coulomb logarithm, with emphasis on quantum-mechanical effects

An introduction to the physical interpretation of the Coulomb logarithm is given with particular emphasis on the quantum-mechanical corrections that are required at high temperatures. Excerpts from the literature are used to emphasize the historical understanding of the topic, which emerged more than a half-century ago. Several misinterpretations are noted. Quantum-mechanical effects are related to diffraction by scales of the order of the Debye screening length; they are not due to quantum uncertainty related to the much smaller distance of closest approach.