The collisionless hydrodynamics: On the nonexistence of collisionless shocks

TL;DR

This paper argues that collisionless shocks may not exist as stationary solutions in plasma physics, supported by theoretical development and numerical simulations showing a continuous, non-stationary evolution of plasma states.

Contribution

The paper develops a collisionless hydrodynamics framework and demonstrates that collisionless shocks do not form as steady solutions, instead exhibiting self-similar, evolving structures.

Findings

Collisionless shocks do not exist as statistically stationary solutions.

A self-similar solution with linear growth in spatial extent is found.

Numerical simulations confirm the nonexistence of steady collisionless shocks.

Abstract

Collisionless shocks, essential for astrophysics, perhaps do not exist as statistically stationary solutions. If so, any quantitative statement about a collisionless shock should be qualified by the age of the shock. A theoretical description of the upstream of the 1+1 dimensional electrostatic collisionless shock is developed -- collisionless hydrodynamics. Peculiarities of collisionless hydrodynamics prevent a shock formation when a piston is driven into cold plasma. An exact self-similar solution is found instead; the spatial extent of the solution grows linearly in time. Direct numerical simulations of plasma kinetics in 1+1 dimensions confirm the hydrodynamic result -- a statistically steady collisionless shock doesn't exist. Instead, at each fixed time, there is a continuous succession in space of marginally stable velocity distribution functions. The spatial support of this continuous succession grows linearly in time.