Compact optimized stellarators offer novel solutions for confining high-β plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide driftorbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high β limit, and good confinement of advanced tokamaks. Quasiaxisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation ∼1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassicaltearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.

Spectral calculations of radio-frequency (rf) heating in tokamak plasmas are extended to two dimensions (2-D) by taking advantage of new computational tools for distributed memory, parallel computers. The integral form of the wave equation is solved in 2-D without any assumption regarding the smallness of the ion Larmor radius (ρ) relative to the perpendicular wavelength (λ⊥). Results are therefore applicable to all orders in k⊥ρ, where k⊥=2π/λ⊥. Previous calculations of rf wave propagation and heating in 2-D magnetized plasmas have relied on finite Larmor radius expansions (k⊥ρ≪1) and are thus limited to relatively long wavelengths. In this paper, no such assumption is made, and we consider short wavelength processes such as the excitation and absorption of ion Bernstein waves in 2-D with k⊥ρ>1. Results show that this phenomenon is far more complex than simple one-dimensional plasma models would suggest. Other applications include fully self-consistent 2-D solutions for high-harmonic fast-wave heating in spherical tokamaks. These calculations require the storage and inversion of a very large, dense matrix, but numerical convergence can be improved by writing the plasma current in the laboratory frame of reference. To accurately represent the wave spectrum in this frame, the local plasma conductivity is corrected to first order in ρ/L, where L is the equilibrium scale length. This correction is necessary to ensure accuracy in calculating the wave spectrum and hence the fraction of power absorbed by ions and electrons.

Full wave simulations of fusion plasmas show a direct correlation between the location of the fast-wave cut-off, radiofrequency (RF) field amplitude in the scrape-off layer (SOL) and the RF power losses in the SOL observed in the National Spherical Torus eXperiment (NSTX). In particular, the RF power losses in the SOL increase significantly when the launched waves transition from evanescent to propagating in that region. Subsequently, a large amplitude electric field occurs in the SOL, driving RF power losses when a proxy collisional loss term is added. A 3D reconstruction of absorbed power in the SOL is presented showing agreement with the RF experiments in NSTX. Loss predictions for the future experiment NSTX-Upgrade (NSTX-U) are also obtained and discussed.

Physics issues are discussed for compact stellarator configurations which achieve good confinement by the fact that the magnetic field modulus |B| in magnetic co-ordinates is dominated by poloidally symmetric components. Two distinct configuration types are considered: (1) those which achieve their drift optimization and rotational transform at low β and low bootstrap current by appropriate plasma shaping; and (2) those which have a greater reliance on plasma β and bootstrap currents for supplying the transform and obtaining quasi-poloidal symmetry. Stability analysis of the latter group of devices against ballooning, kink and vertical displacement modes has indicated that stable β values on the order of 15% are possible. The first class of devices is being considered for a low β near term experiment that could explore some of the confinement features of the high β configurations.

Fast Wave (FW) studies of mode conversion (MC) processes at the ion-ion hybrid layer in toroidal plasmas must capture the disparate scales of the FW and mode converted ion Bernstein (IBW) and ion cyclotron waves (ICW). Correct modeling of the MC layer requires resolving wavelengths on the order of k ⊥ ρi ∼ 1 which leads to a scaling of the maximum poloidal mode number, Mmax, proportional to 1/ρ * (ρ * ≡ ρi/L). The computational resources needed a scale with the number of radial (Nr), poloidal (N θ ), and toroidal (N φ ) elements as Nr * N φ * N

A two-dimensional integral full-wave model is used to calculate poloidal forces driven by mode conversion in tokamak plasmas. In the presence of a poloidal magnetic field, mode conversion near the ion-ion hybrid resonance is dominated by a transition from the fast magnetosonic wave to the slow ion cyclotron wave. The poloidal field generates strong variations in the parallel wave spectrum that cause wave damping in a narrow layer near the mode conversion surface. The resulting poloidal forces in this layer drive sheared poloidal flows comparable to those in direct launch ion Bernstein wave experiments.

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