Modified Kadomtsev spectrum from renormalized plasma turbulence theory

From the collisionless Vlasov-Poisson equations the renormalization of plasma turbulence is derived by a selective summing of secular terms to all orders in perturbation theory. The resulting renormalized theory agrees with earlier renormalizations of quasilinear theory and the mode coupling equation exhibits the same symmetries known in weak turbulence theory. The present formulation differs from that of Rudakov and Tsytovich by containing a separation of the turbulent k scales and by the associated feature of retaining the form of induced wave scattering in the nonresonant mode coupling terms. The theory is applied to the problem of finding the stationary spectrum for current driven ion-acoustic turbulence. Balancing the induced wave scattering off screened ions with a quasilinear growth rate, a modified Kadomtsev spectrum having a low kλD cut off is obtained self-consistently within the collisionless theory. The turbulent energy density and effective collision frequency are computed from the new spectrum.