Collisionless plasma shocks in striated electron temperatures

The existence of low frequency waveguide modes of ion acoustic waves is demonstrated in magnetized plasmas for electron temperature striated along the magnetic field lines. At higher frequencies, in a band between the ion cyclotron and the ion plasma frequency, radiative modes develop and propagate obliquely to the field away from the striation. Arguments for the subsequent formation and propagation of electrostatic shock are presented and demonstrated numerically. For such plasma conditions, the dissipation mechanism is the “leakage” of the harmonics generated by the wave steepening.

💡 Research Summary

The paper investigates the propagation of ion‑acoustic waves (IAWs) in a magnetized plasma where the electron temperature varies along the magnetic‑field direction, forming a “striated” temperature profile. The authors first show that at low frequencies (well below the ion cyclotron frequency Ω_i) the temperature gradient creates a waveguide: the IAW is confined to the region of higher electron temperature and behaves like a guided mode. In this regime the dispersion relation is modified by the anisotropic electron pressure tensor, and the phase speed depends on the local electron temperature while the wave amplitude decays sharply outside the striation.

When the wave frequency lies between Ω_i and the ion plasma frequency ω_pi, the guiding effect breaks down. The wave couples to radiative modes that propagate obliquely to the magnetic field and leak energy away from the striation. The authors derive the conditions for this mode conversion, showing that the critical angle and the leakage rate are controlled by the steepness of the temperature gradient, the magnetic‑field strength, and the wavevector orientation.

A central focus of the work is the nonlinear steepening of the guided wave. As the IAW amplitude grows, harmonic generation occurs. In a collisionless plasma the harmonics cannot be dissipated by binary collisions; instead they are radiated out of the striation via the radiative modes. This “leakage” of higher‑frequency components provides an effective, non‑collisional dissipation mechanism. The loss of harmonic energy steepens the wave front while maintaining an electrostatic shock structure that propagates at a nearly constant speed. The authors argue that this leakage‑driven dissipation replaces the usual viscous or thermal conductivity terms that are required for shock formation in collisional plasmas.

To substantiate the theory, the authors perform two‑dimensional particle‑in‑cell (PIC) simulations. The simulated plasma has a magnetic field B‖z and an electron‑temperature profile T_e(z)=T_0