Theory of trapped-ion-temperature-gradient-driven turbulence and transport in low-collisionality plasmas

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Abstract
A novel theory for the nonlinear evolution of the trapped‐ion‐temperature‐gradient‐driven mode, based on the turbulent trapping of resonant ions in the electrostatic potential of the waves, is proposed. A statistical description is adopted whereby the self‐consistent evolution of the two‐point correlation function of the trapped‐particle distribution function is followed in phase space. Threshold‐dependent, non‐steady‐state turbulence (nonlinear instability) is shown to develop when the decay of the correlation function is overcome by a source term that derives its free energy from the relaxation of the average distribution function. This nonlinear instability leads to anomalous thermal and particle transport that in turn reconfigure the equilibrium temperature and density profiles in such a way as to return the system toward its marginal point. Expressions for the nonlinear dispersion relation and threshold, as well as estimates of the thermal and particle transport level, are derived. The estimated flux levels are sufficiently high as to make any significant departure away from marginality unlikely. The scenario outlined serves to underscore the desirability for pellet injection in experimental devices such as the Compact Ignition Tokamak [Bull. Am. Phys. Soc. 3 2, 1921 (1987)] that operate in the very low ion collisionality regime where this mode would be expected to become relevant. As with a number of recent theories, the present work further reinforces the notion that unfavorably drifting trapped particles pose a serious menace to confinement and suggests inboard, off‐axis radio‐frequency heating as one means of reducing the size of this population, at least for the case of those energetic trapped particles created during auxiliary heating.