Vi. Erofeev, DERIVATION OF AN EQUATION FOR 3-WAVE INTERACTIONS BASED ON THE KLIMONTOVICH-DUPREE EQUATION, Journal of Plasma Physics, 57, 1997, pp. 273-298
A collision integral for three-wave interactions in a collisionless pl
asma is derived from the full plasma description by means of the Klimo
ntovich-Dupree and Maxwell equations. This collision integral differs
from its traditional counterpart (calculated within the framework of V
lasov theory) by an additional functional factor. This means that the
changes in the wave spectral density, which are induced by three-wave
interactions, occur with a rate other than that calculated in Vlasov t
heory.