Applicability of semi-classical theories in the strong field plasma regime

TL;DR

This paper investigates the limits of classical plasma models in strong electromagnetic fields, identifying conditions where quantum effects like pair creation become significant and when classical theories remain valid.

Contribution

It provides a detailed analysis of plasma oscillations to delineate classical and quantum regimes, highlighting the suppression of certain quantum mechanisms and the relevance of pair creation at modest field strengths.

Findings

Classical models are effective below the Compton frequency.

Electron spin effects are negligible at low frequencies.

Schwinger pair creation can occur at fields around 10% of the critical field.

Abstract

For many purposes, classical plasma dynamics models can work surprisingly well even for strong electromagnetic fields, approaching the Schwinger critical fields, and high frequencies, approaching the Compton frequency. However, the applicability of classical models tends to depend rather sensitively on the details of the problem. In the present paper, we study the specific case of plasma oscillations to draw a line between the classical and quantum relativistic regimes. Due to the field geometry of study, mechanisms like radiation reaction and Breit-Wheeler pair production, which tend to be important for electromagnetic fields, are rather effectively suppressed. Moreover, we find that the polarization current due to the electron spin is generally negligible for frequencies below the Compton frequency, compared to the free current, whose magnitude is well-approximated by the classical Vlasov theory. However, we show that pair creation due to the Schwinger mechanism can sometimes be important for surprisingly modest field strengths, of the order of 10 % of the critical field or even smaller. A rough guideline for when the classical Vlasov theory can be applied is given