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Updated: May 27, 2026

Building Langmuir Probes and Emissive Probes for Plasma Potential Measurements in Low Pressure, Low Temperature Plasmas

Building Langmuir Probes and Emissive Probes for Plasma Potential Measurements in Low Pressure, Low Temperature Plasmas

Published on: May 25, 2021

Rarefaction shock in plasma with a bi-Maxwellian electron distribution function.

A Diaw¹, P Mora

¹Centre de Physique Théorique, École Polytechnique, CNRS, FR-91128 Palaiseau, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 9, 2011

Summary

A rarefaction shock forms in plasma expansion when hot and cold electron temperatures differ significantly. This shock influences ion acceleration, with theoretical models showing excellent agreement with numerical simulations.

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Published on: August 1, 2017

Area of Science:

Plasma Physics
Astrophysics
Computational Physics

Background:

Collisionless plasma expansion into a vacuum is fundamental to space and laboratory plasmas.
Bi-Maxwellian electron distributions can lead to complex plasma behaviors, including shock formation.
Previous studies identified conditions for shock waves but lacked a complete theoretical description of rarefaction shocks and their impact on ion acceleration.

Purpose of the Study:

To theoretically and numerically investigate the one-dimensional collisionless expansion of plasma with bi-Maxwellian electrons into a vacuum.
To develop a comprehensive model for rarefaction shocks and their effect on ion acceleration.
To validate the theoretical model against numerical simulations.

Main Methods:

Theoretical modeling of plasma expansion with a bi-Maxwellian electron distribution.
Derivation of analytical expressions for rarefaction shock characteristics.
Numerical simulations using a hybrid code to model plasma expansion.

Main Results:

A shock wave is predicted when the hot to cold electron temperature ratio exceeds 5+√24.
The theoretical model provides a complete description of the rarefaction shock and its influence on ion acceleration.
Excellent agreement was found between analytical predictions and hybrid code simulation results.

Conclusions:

The study successfully models rarefaction shocks in bi-Maxwellian plasmas.
The findings clarify the role of electron temperature anisotropy in plasma expansion dynamics.
The validated theoretical framework can be applied to understand ion acceleration in similar plasma environments.