Theory and Simulation of Turbulent Heating by the Modified Two-Stream Instability

TLDR

The modified two‑stream instability has a characteristic frequency and growth rate comparable to the lower‑hybrid frequency. The study explores applications of the instability to experimental scenarios. The authors analyze the instability both linearly—electrostatic and electromagnetic dispersion relations and numerical root dependence on plasma parameters—and nonlinearly, addressing quasilinear effects, trapping‑induced stabilization, a mass‑ratio scaling law, and turbulence‑driven cross‑field vortex motion. Simulations confirm the theory, showing the instability as a potent turbulent heating mechanism that heats ions perpendicular to B0 and electrons parallel to B0 to comparable temperatures, with the final state satisfying (Ti⊥/mi)¹/² ≈ (Te‖/mi)¹/² ∼ 12U, where U is the initial relative drift speed.

Abstract

Results of an analytical and numerical study of the nonresonant, modified plasma two-stream instability, which is driven by relative streaming of electrons and ions across a magnetic field B0 are presented. The instability has characteristic frequency and growth rate comparable to the lower-hybrid frequency. The linear theory is discussed both in the electrostatic and fully electromagnetic cases, and a detailed numerical study of the dependence of the unstable roots of the dispersion relation for a wide range of plasma parameters is presented. The nonlinear theory includes discussions of (1) quasilinear theory, (2) trapping, which is responsible for nonlinear stabilization, (3) a derivation of a fully nonlinear scaling law which shows how results scale with electron-ion mass ratio, and (4) the effect of cross-field vortex-like motion caused by turbulence induced E × B drifts. One-and two-dimensional computer simulations with dense k-space spectra are presented in support of this theory. The simulations show that the instability can be a very important turbulent heating mechanism that heats the ions (perpendicular to B0) and the electrons (parallel to B0) comparably. The final state has (Ti⊥/mi)1/2 ≈ (Te‖/mi)1/2∼12U, where U is the initial relative drift speed. Applications to experimental situations are discussed.