Resonance broadening theory of plasma turbulence

Motion of charged particles in random electric fields is studied analytically. It is shown that the velocity increments of particles are described as a nonstationary stochastic process that results in the time dependency of the Fokker–Planck diffusion coefficient. The diffusion rate of particles in velocity space is analyzed by different methods. Direct calculation of the Fokker–Planck diffusion coefficient based on particle trajectories reveals that the turbulent collisions broaden the resonance region in velocity space and that the turbulent collision frequency is proportional to the square root of velocity variance. Calculation of a transition probability by quantum mechanical approach supports the above conclusion in which fluctuations in the coordinate due to random fields are considered in the Hamiltonian. The Vlasov approach clarifies the subtle point of erroneous assumption made earlier to derive conventional (Dupree–Weinstock) resonance broadening theory. The diffusion rate in strong turbulence is found to be much lower than both the quasilinear and the conventional resonance broadening predictions and scales as D∼E4/3.