Effects of ion-ion collisions and inhomogeneity in two-dimensional kinetic ion simulations of stimulated Brillouin backscattering

Abstract

Langdon, and E.A. Williams, Phys. Plasmas 4, 956 (1997)] hybrid code (kinetic particle ions and Boltzmann fluid electrons) have been used to investigate the saturation of stimulated Brillouin backscatter (SBBS) instability including the effects of ion-ion collisions and inhomogeneity. Ion-ion collisions tend to increase ion-wave dissipation, which decreases the gain exponent for stimulated Brillouin backscattering; and the peak Brillouin backscatter reflectivities tend to decrease with increasing collisionality in the simulations. Two types of Langevin-operator, ion-ion collision models were implemented in the simulations. In both models used the collisions are functions of the local ion temperature and density, but the collisions have no velocity dependence in the first model. In the second model, the collisions are also functions of the energy of the ion that is being scattered so as to represent a Fokker-Planck collision operator. Collisions decorrelate the ions from the acoustic waves in SBS, which disrupts ion trapping in the acoustic wave. Nevertheless, ion trapping leading to a hot ion tail and two-dimensional physics that allows the SBS ion waves to nonlinearly scatter remain robust saturation mechanisms for SBBS in a high-gain limit over a range of ion collisionality. SBS 2 backscatter in the presence of a spatially nonuniform plasma flow is also investigated.Simulations show that depending on the sign of the spatial gradient of the flow relative to the backscatter, ion trapping effects that produce a nonlinear frequency shift can enhance (auto-resonance) or decrease (anti-auto-resonance) reflectivities in agreement with theoretical arguments. PACS: 52.38.-r 52.65.Rr 3

A grid-based binary model for coulomb collisions in plasmas

“…(However, if the Lemons, et al algorithm for electron-ion collisions is reduced to just pitch-angle collisions with the drag and diffusion of the electron speed suppressed, the studies in [11] demonstrate that time steps as big as those used with the TA algorithm can be used with similarly good accuracy obtained.) We also note that, as stated earlier, the drag-diffusion algorithms [3,4,5,6] can be vulnerable to noise-induced instability [23]; and the TA algorithm is more tolerant with respect to a rare large kick than is the Lemons et al algorithm unless some clamp or limiter on the magnitude of velocity kicks is installed in the latter.…”

“…In the Langevin equation models [3,4,5,6,7,10], Langevin equations in three velocity dimensions containing drag and diffusion terms are integrated, typically with a simple first-order, forward Euler integration [3][4][5][6][7]10,11,14]. The algorithms are based on the theory describing screened Coulomb collisions in the Fokker-Planck limit [8,9,15].…”

“…IV. The merits of the grid-based TA algorithm are as follows: the grid-based TA algorithm is slightly more accurate than the Lemons, et al algoirhm in our example simulations, allows a ~10× larger time step for accurate electron-ion collisions, and tolerates the rare large Monte Carlo kick much better than does the Lemons, et al algorithm; in situations where the particles have unequal weights so that application of the traditional TA algorithm does not conserve energy and momentum algebraically, the grid-based TA scheme is a natural alternative and energy/momentum conservation can be restored; the grid-based TA scheme, like other grid-based collision algorithms, is well suited for including Coulomb collisions in a particle-fluid hybrid plasma simulation; the grid-based TA scheme can accommodate some of the self-consistent evolution of the field-particle velocity distribution without having to solve for the Rosenbluth potentials (an elliptic equation in velocity space) to update the drag-diffusion coefficients in the Langevin equations approach of [4], [5], and [6]; the gridbased collision algorithms in [4], [5], and [6] can be subject to a noise-induced instability, while the gridbased TA scheme is not; and the grid-based TA collision algorithm can be extended straightforwardly to different collision models.…”

“…The post-collision velocities of the interacting pair conserve momentum and energy relative to the pre-collision velocities. In the second type of algorithm, the collisions are modeled by defining test and field particles; and the test-particle velocity is subject to drag and diffusion in three velocity dimensions using Langevin equations whose drag and diffusion coefficients depend jointly on the velocity of the test particle and the moments of the field-particle velocity distribution deposited on the configuration-space mesh [3,4,5,6,7]. The grid-based Langevin equations model conserves particle number trivially and conserves energy and momentum approximately in a statistical sense after averaging over many collisions and over the velocity distribution functions, although energy and momentum conservation can be repaired by scaling and shifting velocities after the Monte Carlo collisions occur on each time step [4,6].…”

Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas

“…1-3 show the results of a series of BZOHAR simulations [5] using the grid-based Langevin equations ion-ion collision operator to study the collisional relaxation of a weak ion temperature anisotropy (T y = 0.95T x , T x = T z ) in which we vary the product of the characteristic ion-ion collision frequency ν * and the time step Δt for 1 000 particles per cell and N p = 2 × 10 6 particles in one spatial dimension, where…”