Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

Abstract

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a 'hole' and 'clump'.Here, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto microturbulence via canonical toroidal momentum scattering, affecting hole and clump formation. The profile of a single bursting event in mode amplitude is shown to be stochastic, with small changes in initial conditions affecting the lifetime of a hole and clump. As an extension to the work of Lang and Fu[1], we find that an intermediate regime exists where noise serves to decrease the effective collisionality, where microturbulence works against pitch-angle scattering.

Study of the likelihood of Alfvénic mode bifurcation in NSTX and predictions for ITER baseline scenarios

“…In addition, chirping was also observed for modes located around internal transport barriers, even in positive triangularity. From the numerical side, turbulence stochasticity has been recently included in a bump-on-tail simulation [25], which showed its effect on chirping suppression.…”

Analytical solutions for nonlinear plasma waves with time-varying complex frequency

“…Therefore, by using equations ( 9), (10) and ( 11) one finds that for a vanishing integrand under v:…”

“…Commonly in the literature, the 'modified' version of the Maxwell-Ampère law is used instead to generate the same energy balance equation as equation (10):…”

“…This can lead to destabilisation 3,4 as well as stabilisation 5,6 . These nonlinear scenarios have been partially investigated analytically, however these systems are typically examined using computational means [7][8][9][10] .…”

Island formation in collisionless kinetic plasmas with perturbed orbits

“…The evolution of waves in systems near marginal stability during near-constant wave amplitude has therefore been heavily explored, allowing for analytical theory of the temporal behaviour of marginally unstable modes after nonlinear saturation. [12][13][14][15] These systems are largely examined computationally, with work including phase-space island formation 16 , stochastic phase-space island destruction 17 , and phase-space island evolution in tokamak geometries [18][19][20] . Further theory describing the growth and decay of these structures may allow for better understanding of how to modify the lifetime of phase-space islands, as well as how to manipulate holes and clumps from an 'excitation and recombination' point of view, analogous to hole-electron pairs as widely explored in solid state physics.…”