Nonlinear Saturation of the Weibel Instability in a Dense Fermi Plasma

TL;DR

This paper investigates the nonlinear saturation of the Weibel instability in dense Fermi plasmas, revealing how magnetic field amplitudes relate to growth rates through kinetic simulations, relevant for high-intensity laser experiments.

Contribution

It introduces a new linear dispersion relation for transverse waves in dense quantum plasmas and analyzes the nonlinear saturation of magnetic fields.

Findings

Magnetic field amplitudes are proportional to the linear growth rate.

Growth rate depends on Fermi energy and temperature anisotropy.

Results are relevant for intense laser-solid density plasma experiments.

Abstract

We present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi-Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner-Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields are proportional to the linear growth rate of the instability. The present results are important for understanding the origin of intense magnetic fields in dense Fermionic plasmas, such as those in the next generation intense laser-solid density plasma experiments.