Self-consistent full-wave and Fokker-Planck calculations for ion cyclotron heating in non-Maxwellian plasmas

Abstract

Magnetically confined plasmas can contain significant concentrations of nonthermal plasma particles arising from fusion reactions, neutral beam injection, and wave-driven diffusion in velocity space. Initial studies in one-dimensional and experimental results show that nonthermal energetic ions can significantly affect wave propagation and heating in the ion cyclotron range of frequencies. In addition, these ions can absorb power at high harmonics of the cyclotron frequency where conventional two-dimensional global-wave models are not valid. In this work, the all-orders global-wave solver AORSA [E. F. Jaeger et al., Phys. Rev. Lett. 90, 195001 (2003)] is generalized to treat non-Maxwellian velocity distributions. Quasilinear diffusion coefficients are derived directly from the wave fields and used to calculate energetic ion velocity distributions with the CQL3D Fokker-Planck code [R. W. Harvey and M. G. McCoy, Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear Plasmas, Montreal, Canada, 1992 (USDOC NTIS Document No. DE93002962)]. For comparison, the quasilinear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker-Planck solutions.

Sawtooth control in ITER using ion cyclotron resonance heating

“…A similar iterative coupling between the AORSA wave field code [31] and the Fokker-Planck CQL3D code [32] (which neglects orbit widths) has been developed. AORSA is used to solve the RF wave electric fields assuming a Maxwellian electron distribution and a combination of thermal and energetic ion species.…”

“…ASCOT has been used to model the alpha particle population whilst SELFO [28], SCENIC [29,30] and a coupling of AORSA [31] with CQL3D [32] have been used to simulate the ICRH distribution. Finally, the HAGIS drift kinetic code [33] has been employed to study the effect of the various fast ion populations on internal kink stability.…”

Advances in numerical simulations of ion cyclotron heating of non-Maxwellian plasmas

“…Dumont et al [11] have explored the consequences of suprathermal populations on wave propagation and absorption in a slab model of toroidal plasmas. The most advanced self-consistent simulations in toroidal geometry have been recently made by combining the full-wave toroidal code AORSA with the quasilinear-Fokker-Planck code CQL3D [12,13]. It is also worth mentioning that the importance of high energy ions in fusion plasmas [14,15] has stimulated a considerable effort to determine the evolution of the most energetic populations created by IC resonant interactions.…”

Kinetic theory of plasma waves

“…The action-angle formalism is discussed in [33][34][35][36][37]. Comments on how to solve the relevant set of equations -with a focus on accounting for the realistic geometry -are given in [38][39][40][41][42][43][44][45][46][47][48][49][50][51] while the role of decorrelation is the key subject in [52][53][54][55].…”

“…SOME ASPECTS OF NONUNIFORM PLASMA MODELING III.A. Mode Coupling [38][39][40][41][42][43][44][45][46][47][48][49][50][51] Before commenting on the particular issues brought about by the impact of the plasma inhomogeneities on the orbits of the particles and the challenges this leads to when trying to write down a rigorous expression for the dielectric response, a simplified problem is looked at first, namely that of the wave propagation in a tokamak in absence of a poloidal field i.e. where the guiding center orbits are assumed to simply being given by ϕ(t) = ϕ(t o ) + v // (t − t o ).…”