Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

Abstract

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does not contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects. [http://dx.

Plasma-Resistivity-Induced Strong Damping of the Kinetic Resistive Wall Mode

“…The most severe one is probably the inconsistency of the evaluation of the perturbed drift kinetic energy perturbation from the trapped fast ions, with the assumption of the cylindrical geometry. Nevertheless, we believe that this does not affect the qualitative physics of the drift kinetic damping, as confirmed by full toroidal computations [7,14,15]. Moreover, the resistive layer contribution, as we shall show, is rigorously evaluated in our example.…”

Three-Dimensional Drift Kinetic Response of High-βPlasmas in the DIII-D Tokamak

“…On the other hand, with an assumption that all the equilibrium pressure comes from TPs (termed "full therm al" case), the kinetic response shows behavior similar to that of the thermal case. N ear the no-wall limit, the response am plitude in the full thermal case is slightly larger than that o f the other two cases, due to the lack of one extra adiabatic term arising from the boundary integration in the particle phase space for the slowing down EPs with finite birth energy [28]. This extra term eventually plays a dam ping role.…”

“…In experiments, cotangential NBI was em ployed, with two injection tangency radii o f 76 and 115 cm, producing EPs with anisotropic distributions in the particle pitch angle space. This motivates us to test the sensitivity o f kinetic response against the EP models, m a r s -k implements an anisotropic NBI model that is suitable for ITER [28]. We choose an averaged injection tangency radii o f 95.5 cm and an ITER-like beam width param eter (<5f = 0.123).…”

“…Two versions o f the mars code are em ployed in this work. The mars-k code solves the linearized ideal single-fluid M HD equations with drift kinetic effects in the so-called nonperturbative approach [26,28], where the vacuum, the external coils, and the m odeled resistive wall (vacuum vessel) as shown in Fig. 1 are included into the com putations [2], mars-k is capable o f m odeling the plasm a response experim ent by com puting the response with self-consistent inclusion o f the kinetic effects, yielding the so-called kinetic plasm a response.…”

Excitation of Flow-Stabilized Resistive Wall Mode by Coupling with Stable Eigenmodes in Tokamaks

“…[11,12], In order to check whether the RWM excitation mecha nism described above plays a role in experiments, it is necessary to take into account other damping mechanisms, which are not included in our model. For instance, it has been reported that resonant interactions with energetic particles can stabilize RWMs [9,28], and the effect of such interactions on the excitation mechanism described in this Letter should be clarified. As discussed in [9], the resonant interaction of RWMs with energetic particles depends on the relationship between the rotation frequency and the characteristic frequencies of energetic particles, and this interaction becomes ineffective in some cases.…”