Two-dimensional numerical simulation of trapped ion mode turbulence in a tokamak

A two-dimensional k-space simulation of long-wavelength trapped ion mode turbulence is used to investigate Bohm (macroscopic) versus gyro-Bohm (microscopic) scaling behavior in tokamaks. A nonlinear two-field model of dissipative trapped ion turbulence evolving trapped ion and trapped electron density fluctuations shows gyro-Bohm-like scaling in contrast to earlier simulation work by Saison et al. [Plasma Phys. 20, 1 (1978)]. In fact, nearly all features of trapped ion mode turbulence and transport originally posited by Kadomtsev and Pogutse [Reviews of Plasma Physics (Consultants Bureau, New York, 1970), Vol. 5, p. 379] are recovered. However, the widely used Kadomtsev--Pogutse one-field approximation to the two-field dissipative trapped ion model is unexpectedly found to be unrepresentative with much different fluctuation levels and diffusion. Transformation to a new field basis diagonalizing the linear part of the two-field equations clarifies the importance of the damped branch not contained in the one-field equation. The two-field collisionless trapped ion mode equations are transformed into a parameterless single equation for a complex field providing a perfect scaling relation for the dependence on the driving curvature drifts