Short-Time Plasma Evolution: Flow Generation and Magnetogenesis

TL;DR

This paper presents an analytical two-fluid model for short-time plasma evolution, revealing how pressure gradients generate flow and magnetic fields simultaneously, applicable to both laboratory and astrophysical plasmas.

Contribution

It introduces a self-consistent analytical framework linking plasma flow and magnetogenesis via pressure constraints, with exact solutions under Laplace's equation.

Findings

Derived magnetic field strengths consistent with experiments and astrophysics.

Identified pressure Laplace equation as key to coupled flow and magnetic field generation.

Provided exact analytical solutions for short-time plasma evolution.

Abstract

We develop a self-consistent analytical two-fluid framework for plasma evolution in the short-time regime, elucidating the fundamental mechanism underlying the coupled generation of flow and magnetic fields. We show that consistency between ion momentum and mass conservation imposes a structural constraint on the system: the total pressure must satisfy the Laplace equation, $\nabla^2 P = 0$. This constraint enables a class of exact analytical solutions in which pressure gradients simultaneously drive plasma flow and generate magnetic fields through a Biermann-type mechanism. Using representative parameters, we obtain magnetic-field strengths and flow velocities consistent with both laser-produced plasmas and large-scale astrophysical systems. This framework provides a unified description of pressure-driven magnetogenesis and plasma flow in the short-time regime.