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

摘要

Three-wave interactions in plasmas are described, in the framework of kinetictheory, by the quadratic response tensor (QRT). The cold-plasma QRT is a commonapproximation for interactions between three fast waves. Here, the first-orderthermal correction (FOTC) to the cold-plasma QRT is derived for interactionsbetween three fast waves in a warm unmagnetized collisionless plasma, whoseparticles have an arbitrary isotropic distribution function. The FOTC to thecold-plasma QRT is shown to depend on the second moment of the distributionfunction, the phase speeds of the waves, and the interaction geometry. Previouscalculations of the rate for second harmonic plasma emission (via Langmuir-wavecoalescence) assume the cold-plasma QRT. The FOTC to the cold-plasma QRT isused here to calculate the FOTC to the second harmonic emission rate, and itsimportance is assessed in various physical situations. The FOTC significantlyincreases the rate when the ratio of the Langmuir phase speed to the electronthermal speed is less than about 3.