The work described in “Gyrokinetic Simulations with External Resonant Magnetic Perturbations: Island Torque and Nonambipolar Transport with Rotation” by R.E. Waltz and F.L. Waelbroeck (Physics of Plasmas 2012) (see also Weekly Highlight from March 2 2012) has been extended to apply the generalized Rutherford island width formula to the screening of external resonant magnetic field perturbation (RMP) fields. RMP screening and mode locking in relation to toroidal rotation is an important but complex and poorly understood problem. The novel feature in this approach is the relation to high-n turbulence, with Δ, the “internal island delta prime” associated with the induced screening current internal to the island, simulated with the GYRO gyrokinetic turbulence code. It is found that the locking angle α scales like Im(Δ) which is proportional to the island torque (Maxwell stress), and which scales like β (wvac) (I1/2) Er, where I is the intensity of the turbulence, Er is the radial electric field associated with the toroidal rotation, β is the plasma beta, and w_vac is the vacuum island width. Re(Δ) which determines the screening has a similar scaling with β, wvac, and I but scales with an off-set in Er like (Er – Er0)2. The minimum screening at Er = Er0 corresponds to a toroidal rotation with the electrons at rest, as found in other studies. Nevertheless, the parameterization with (w/ wvac) is not very clear and a more practical approach to RMP screening and magnetic breaking torque follows from the resistive MHD and two fluid linear response codes. From the result that turbulent island torque scales as I1/2, it is conjectured that the resonant RMP torque scales as the square root of the input turbulent viscosity.

Global, linear eigenvalue simulations of benchmark DIII-D discharge 142111 using GYRO have reproduced the experimental reverse shear Alfvén eigenmode (RSAE) frequency sweep within 20% error or less. Both the first and second harmonic RSAE are faithfully recreated. The only significant variation from experiment occurs near low frequencies, where an unstable beta-induced Alfvén eigenmode (BAE) in the simulation but absent in experiment keeps the RSAE sweep 20% above the experimental value. The disagreement in the RSAE frequency and the unstable BAE are eliminated by reducing the driving energetic particle density down to the marginal level, bringing the whole spectrogram into line with experiment. The dependence of the limiting BAE frequency on the energetic particle density offers the possibility of a sensitive experimental probe of the density of beam ions near the reversed shear surface.

A software library has been developed that allows M3D-C1 output to be read easily by a variety of codes. The library provides interfaces for c, Fortran, and Python and is now in use by several codes, including TRIP3D, ORBIT-RF, and OMFIT. The immediate interest is to enable transport calculations using the 3D fields calculated with M3D-C1. The capability of TRIP3D to read M3D-C1 data can now be used to quantify the effects of plasma response on edge stochasticity. It was found that the effect of the plasma response is to significantly reduce the stochasticity of the edge relative to the level predicted by vacuum modeling, even in the case of incomplete screening, due to the highly nonlinear dependence of magnetic diffusivity on island size. Additionally, the ability of the particle orbit tracing code ORBIT-RF to read M3D-C1 fields will allow the study of fast-ion loss due to non-axisymmetric fields in the presence of plasma response. Finally, OMFIT modules that are currently in development allow M3D-C1 data to be easily read, visualized, and analyzed within the OMFIT framework.

NIMROD simulations of the EXTRAPT2R RFP device have been carried out to compare with experiments investigating the plasma response to n=12 RMP fields. Two simulations are initiated with a higher and lower toroidal rotation; in the experiment, rotation is controlled with non-resonant fields. Once the boundary RMP fields reach full amplitude, the lower rotation simulation immediately enters the reconnected state with a large n=12 island, and the toroidal rotation drops. In the higher rotation simulation, the plasma remains in the unreconnected state briefly as the rotation gradually slows, until the island finally appears. Both simulations maintain a new quasi-steady state at lower rotation, and with amplitude oscillations in the n=12 fields for a short time, until the mode eventually locks to the boundary fields and the rotation drops to zero. The experiments do see the slowing and the n=12 amplitude oscillations, but not the eventual locking. Further simulations will scan certain physical parameters, such as viscosity, which have considerable experimental uncertainty. These results were presented at the EPS conference in Stockholm, Sweden.