On the Validity of Quasilinear Plasma Transport Equations

Abstract Significant differences regarding their validity and applicability are found for the two variants of the quasilinear transport theory (QLT) for charged particles in partially turbulent electromagnetic fields. In homogeneous turbulence, the quasilinear theory, based on the Vlasov equation for the smoothly varying phase space density of particles (V-QLT), only holds for particle propagation times less than t − t 0 < p /∣ δ K ∣, where δ K denotes the random Lorentz force and p the particle momentum. In magnetized plasmas, this requires propagation times shorter than τ gyro /2 πq L , where τ gyroso denotes the gyroperiod, so that the condition can persist over many gyroperiods only when the relative fluctuation level q L = ∣ δ B ∣/ B 0 is small. This condition does not apply to the quasilinear theory, based on the Klimontovich equation and phase space density, which accounts for the intrinsically discrete nature of matter (K-QLT). A much weaker K-QLT validity condition ∣ δn a ∣ < n a for the density fluctuations is found. The price to pay for the less severe validity condition and the much wider applicability for all propagation times is the additional presence of the drag terms, absent in V-QLT, besides the momentum diffusion terms.