Electrostatic fluctuations in collisional plasmas

Relaxation of weakly collisional plasma: Continuous spectra, discrete eigenmodes, and the decay of echoes

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment. We find that the linear response is a temporal convolution of two types of contribution: a continuum that depends on the continuous velocities of particles (crucial for the plasma echo), and another, consisting of discrete modes that are coherent modes of oscillation of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping), as well as collisional dissipation. The continuum is also damped by collisions but somewhat differently than the discrete modes. Up to a collision time, which is the inverse of the collision frequency ν_{c}, the continuum decay is driven by the diffusion of particle velocities and is cubic exponential, occurring over a timescale ∼ν_{c}^{-1/3}. After a collision time, however, the continuum decay is driven by the collisional damping of particle velocities and diffusion of their positions and occurs exponentially over a timescale ∼ν_{c}. This slow exponential decay causes perturbations to damp the most on scales comparable to the mean free path but very slowly on larger scales. This establishes the local thermal equilibrium, which is the essence of the fluid limit. The long-term decay of the linear response is driven by the discrete modes on scales smaller than the mean free path but, on larger scales, is governed by a combination of the slowly decaying continuum and the least damped discrete mode. This slow exponential decay implies that the echo, which results from the interference of the continuum response to two subsequent pulses, is detectable even on scales comparable to the mean free path, as long as the second pulse is introduced within a few phase-mixing timescales after the first.

Thomson scattering from dense inhomogeneous plasmas

X-ray Thomson scattering experiments in the soft and hard x-ray regime yield information on fundamental parameters of high-density systems. Pump-probe experiments with variable time delay provide insight into the excitation and relaxation dynamics in dense plasmas. On short time scales, a local thermodynamic equilibrium description might not be sufficient. Besides nonequilibrium effects on the electron distribution function, spatial inhomogeneities influence the scattering signal. Generalizing previous approaches of Belyi [Phys. Rev. E 97, 053204 (2018)2470-004510.1103/PhysRevE.97.053204] and Kozlowski et al. [Sci. Rep. 6, 24283 (2016)2045-232210.1038/srep24283], we discuss implications for Thomson scattering spectra for inhomogeneous plasmas in the warm dense matter regime based on a gradient expansion within real-time Green's-functions theory. Especially in the collective scattering regime, Thomson scattering spectra are modifed substantially by spatial inhomogeneities. Within a first-order gradient expansion, the dispersion relation for plasmons is determined. In particular, the ratio of the heights of the plasmon peaks is changed which prevents a simple estimation of the plasma temperature from the detailed balance relation.

Picosecond Thermodynamics in Underdense Plasmas Measured with Thomson Scattering

The rapid evolutions of the electron density and temperature in a laser-produced plasma were measured using collective Thomson scattering. Unprecedented picosecond time resolution, enabled by a pulse-front-tilt compensated spectrometer, revealed a transition in the plasma-wave dynamics from an initially cold, collisional state to a quasistationary, collisionless state. The Thomson-scattering spectra were compared with theoretical calculations of the fluctuation spectrum using either a conventional Bhatnagar-Gross-Krook (BGK) collision operator or the rigorous Landau collision terms: the BGK model overestimates the electron temperature by 50% in the most-collisional conditions.

Multi-angle multi-pulse time-resolved Thomson scattering on laboratory plasma jets

A single channel sub-nanosecond time-resolved Thomson scattering system used for pulsed power-driven high energy density plasma measurements has been upgraded to give electron temperatures at two different times and from two different angles simultaneously. This system was used to study plasma jets created from a 15 μm thick radial Al foil load on a 1 MA pulsed power machine. Two laser pulses were generated by splitting the initial 2.3 ns duration, 10 J, 526.5 nm laser beam into two pulses, each with 2.5 J, and delaying one relative to the other by between 3 and 14 ns. Time resolution within each pulse was obtained using a streak camera to record the scattered spectra from the two beams from two scattering angles. Analysis of the scattering profile showed that the electron temperature of the Al jet increased from 20 eV up to as much as 45 eV within about 2 ns by inverse bremsstrahlung for both laser pulses. The Thomson scattering results from jets formed with opposite current polarities showed different laser heating of the electrons, as well as possibly different ion temperatures. The two-angle scattering determined that the electron density of the plasma jet was at least 2 × 10¹⁸ cm^-3.

Theory of Thomson scattering in inhomogeneous plasmas

A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a nonuniform plasma is derived. We show that not only the imaginary part, but also the time and space derivatives of the real part of the dielectric susceptibility determine the amplitude and the width of the Thomson scattering spectral lines. As a result of inhomogeneity, these properties become asymmetric with respect to inversion of the sign of the frequency. Our theory provides a method of a remote probing and measurement of electron density gradients in plasma; this is based on the demonstrated asymmetry of the Thomson scattering lines.