On the frequency of oscillations in the pair plasma generated by a strong electric field

TL;DR

This paper investigates how the frequency of plasma oscillations in electron-positron pairs, created by vacuum polarization under strong electric fields, evolves over time and approaches the classical plasma frequency.

Contribution

It derives a second order differential equation for the velocity variable and analyzes the evolution of oscillation frequency in strong electric fields, including power spectrum and effects of degeneracy and annihilation.

Findings

Oscillation frequency approaches the plasma frequency over time.

Power spectrum's characteristic frequency depends on initial electric field.

Effects of plasma degeneracy and pair annihilation are discussed.

Abstract

We study the frequency of the plasma oscillations of electron-positron pairs created by the vacuum polarization in an uniform electric field with strength E in the range 0.2 Ec < E < 10 Ec. Following the approach adopted in [1] we work out one second order ordinary differential equation for a variable related to the velocity from which we can recover the classical plasma oscillation equation when E -> 0. Thereby, we focus our attention on its evolution in time studying how this oscillation frequency approaches the plasma frequency. The time-scale needed to approach to the plasma frequency and the power spectrum of these oscillations are computed. The characteristic frequency of the power spectrum is determined uniquely from the initial value of the electric field strength. The effects of plasma degeneracy and pair annihilation are discussed.