A positive-definite form of bounce-averaged quasilinear velocity diffusion for the parallel inhomogeneity in a tokamak

In this paper, the analytical form of the quasilinear diffusion coefficients is modified from the Kennel-Engelmann diffusion coefficients to guarantee the positive definiteness of its bounce average in a toroidal geometry. By evaluating the parallel inhomogeneity of plasmas and magnetic fields in the trajectory integral, we can ensure the positive definiteness and help illuminate some non-resonant toroidal effects in the quasilinear diffusion. When the correlation length of the plasma-wave interaction is comparable to the magnetic field variation length, the variation becomes important and the parabolic variation at the outer-midplane, the inner-midplane, and trapping tips can be evaluated by Airy functions. The new form allows the coefficients to include both resonant and non-resonant contributions, and the correlations between the consecutive resonances and in many poloidal periods. The positive-definite form is implemented in a wave code TORIC and we present an example for ITER using this form. ar X iv :1 70 7. 08 03 0v 2 [ ph ys ic s. pl as m -p h] 1 8 D ec 2 01 7 A positive-definite form of bounce-averaged quasilinear velocity diffusion for the parallel inhomogeneity in a tokamak2