Transition from weak to strong energetic ion transport in burning plasmas

Abstract

The change in nonlinear energetic particle mode (EPM) dynamics that accompanies the transition from weak to strong energetic ion transport is discussed in this work. It is demonstrated that the nonlinear threshold in fast ion energy density for the onset of strong convective transport occurring in avalanches is close to the linear EPM excitation threshold. This phenomenology is strictly related to the resonant character of the modes, which tend to be radially localized where the drive is strongest. After the convective loss phase, during which nonlinear EPM mode structure is displaced outwards, fast ion transport continues owing to diffusive processes. Theoretical analyses, presented here, are the basis for consistency analyses of operation scenarios in proposed burning plasma experiments. Comparisons between theoretical predictions and both simulation and experimental results are also briefly discussed.

Nonlinear Dynamics and Complex Behaviors in Magnetized Plasmas of Fusion Interest

“…Due to the intrinsic EPM resonant character and their locahzation at the radial position where the drive is strongest [48,49,50], EPMs rapidly redistribute energetic particles. Simulation results indicate that, above the hnear stability threshold, strong EPM induced fast ion transport occurs via processes that can be identified with the convective amplification of an unstable front, which coherently propagates in the radial direction as the fast ion energy density gradient (free energy source) steepens before it eventually relaxes [51]. Such strong transport events occur on time scales of a few inverse linear growth rates (generally 100 -200 AUven times, TA = RQ/VAO, with v^o the Allven speed on the magnetic axis evaluated at BQ) and have a ballistic character [52] that basically differentiates them from the diffusive and local nature of weak transport.…”

“…These functions are often assumed to weakly depend on time as well, although this is not strictly necessary. The panels from left to right refer to three subsequent times of the 3D Hybrid MHD-Gyrokinetic simulation discussed in [51], with the nonlinear evolution of the radial envelope of a single « = 4 EPM, shown as a function of the radial variable normahzed to the plasma minor radius a on top of the nonlinear distortion of the fast ion free energy source, SUH = -{^7t/Bl)Roq^{d/dr){PH-PH,eqmi), which is identically zero during the hnear unstable phase, where profiles are those given at eqmlibrium initial conditions. Particle radial transport in this case is secular due to coherent non-linear interactions with the modes.…”

“…In addition, the radial mode structure evolves on the same time scale as fast ion transport: thus, the regime is strongly non-perturbative. Since EPM induced transport events consist of a radially propagating unstable fronts producing convective fast ion radial redistribution, it is possible to speak of a single coherent avalanche [51]. This peculiarity is due to the fact that the EPM growth rate has a strong n dependence, producing a narrow toroidal mode number unstable spectrum, in contrast to the AE case.…”

“…Here, A [5Wf+5Wk) accounts for the radial dispersiveness, which reflects both equilibrium geometry and equilibrium profile changes due to "slow" cumulative effects of nonlinear EPM dynamics, while 5Wkf^L{.r,t; \A"\^) is the nonlinear fast ion response, in which we have made the dependence on EPM intensity explicit [51]. Thus, EPM wave-packets grow most strongly when linear and nonlinear dispersions balance on the rh.s., describing the convective amplification of the unstable front accompanied by rapid frequency "tuning" to the wave-particle resonance condition and balhstic fast ion transport [51].…”

“…Thus, EPM wave-packets grow most strongly when linear and nonlinear dispersions balance on the rh.s., describing the convective amplification of the unstable front accompanied by rapid frequency "tuning" to the wave-particle resonance condition and balhstic fast ion transport [51]. The stmcture of Eq.…”