Ion-acoustic Shocks with Self-Regulated Ion Reflection and Acceleration

Abstract

An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple "box" distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M=1.6 (no ion reflection) to M=1.8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M=3.1 to M=4.5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is also described analytically.

arXiv comment22 pages, 5 figures, submitted to PoP

References in corpus (13)

• Ion acceleration by superintense laser-plasma interaction
• PAMELA Measurements of Cosmic-ray Proton and Helium Spectra
• Monoenergetic proton beams accelerated by a radiation pressure driven shock
• Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
• Ion leakage from quasiparallel collisionless shocks: implications for injection and shock dissipation
• Ion acceleration from laser-driven electrostatic shocks
• Origin of Cosmic Rays
• Proton-Helium Spectral Anomaly as a Signature of Cosmic Ray Accelerator
• Particle acceleration by shocks in supernova remnants
• Cosmic Ray Origins: An Introduction
• The Acceleration of Thermal Protons at Parallel Collisionless Shocks: Three-dimensional Hybrid Simulations
• Advanced strategies for ion acceleration using high power lasers
• Ion-acoustic shocks with reflected ions: modeling and PIC simulations

Cited by in corpus (7)

• Acceleration of Cosmic Rays in Supernova Shocks: elemental selectivity of the injection mechanism
• Structure of a collisionless pair jet in a magnetized electron-proton plasma: flow-aligned magnetic field
• High-yield and high-angular-flux neutron generation from deuterons accelerated by laser-driven collisionless shock
• Low Mach-number collisionless electrostatic shocks and associated ion acceleration
• Electron Weibel instability and~quasi-magnetostatic structures in~an~expanding collisionless plasma
• Lower-Hybrid Drift Instability and Macroscopic Flow of Colliding Magnetized Plasmas
• Conditions of structural transition for collisionless electrostatic shock