First-order thermal correction to the quadratic response tensor and rate for second harmonic plasma emission

TL;DR

This paper derives the first-order thermal correction to the quadratic response tensor for three-wave interactions in warm plasmas, showing it significantly affects second harmonic plasma emission rates in certain conditions.

Contribution

It introduces the first-order thermal correction to the cold-plasma quadratic response tensor for unmagnetized plasmas with arbitrary isotropic distributions, and assesses its impact on emission rates.

Findings

FOTC depends on the second moment of the distribution function.

FOTC increases the emission rate when Langmuir phase speed is less than about three times the electron thermal speed.

The correction is significant in physical situations with warm plasma conditions.

Abstract

Three-wave interactions in plasmas are described, in the framework of kinetic theory, by the quadratic response tensor (QRT). The cold-plasma QRT is a common approximation for interactions between three fast waves. Here, the first-order thermal correction (FOTC) to the cold-plasma QRT is derived for interactions between three fast waves in a warm unmagnetized collisionless plasma, whose particles have an arbitrary isotropic distribution function. The FOTC to the cold-plasma QRT is shown to depend on the second moment of the distribution function, the phase speeds of the waves, and the interaction geometry. Previous calculations of the rate for second harmonic plasma emission (via Langmuir-wave coalescence) assume the cold-plasma QRT. The FOTC to the cold-plasma QRT is used here to calculate the FOTC to the second harmonic emission rate, and its importance is assessed in various physical situations. The FOTC significantly increases the rate when the ratio of the Langmuir phase speed to the electron thermal speed is less than about 3.