Bridging the gap between collisional and collisionless shock waves

• Published in: Journal of plasma physics 2021-04, Vol.87 (2), Article 905870204
• Main Authors: Bret, Antoine, Pe'er, Asaf
• Format: Article
• Language: English
• Subjects: Mach number; Mean free path; Plasma; Plasma physics; Plasmas (physics); Shock waves; Upstream
• ISSN: 0022-3778; 1469-7807
• DOI: 10.1017/S002237782100012X

While the front of a fluid shock is a few mean-free-paths thick, the front of a collisionless shock can be orders of magnitude thinner. By bridging between a collisional and a collisionless formalism, we assess the transition between these two regimes. We consider non-relativistic, non-magnetized, planar shocks in electron–ion plasmas. In addition, our treatment of the collisionless regime is restricted to high-Mach-number electrostatic shocks. We find that the transition can be parameterized by the upstream plasma parameter $\varLambda$ which measures the coupling of the upstream medium. For $\varLambda \lesssim 1.12$, the upstream is collisional, i.e. strongly coupled, and the strong shock front is about $\mathcal {M}_1 \lambda _{\mathrm {mfp},1}$ thick, where $\lambda _{\mathrm {mfp},1}$ and $\mathcal {M}_1$ are the upstream mean free path and Mach number, respectively. A transition occurs for $\varLambda \sim 1.12$ beyond which the front is $\sim \mathcal {M}_1\lambda _{\mathrm {mfp},1}\ln \varLambda /\varLambda$ thick for $\varLambda \gtrsim 1.12$. Considering that $\varLambda$ can reach billions in astrophysical settings, this allows an understanding of how the front of a collisionless shock can be orders of magnitude smaller than the mean free path, and how physics transitions continuously between these two extremes.