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.
Energy confinement comparable with tokamak quality is achieved in the Madison Symmetric Torus (MST) reversed field pinch (RFP) at a high beta and low toroidal magnetic field. Magnetic fluctuations normally present in the RFP are reduced via parallel current drive in the outer region of the plasma. In response, the electron temperature nearly triples and beta doubles. The confinement time increases tenfold (to ∼10 ms), which is comparable with Land H-mode scaling values for a tokamak with the same plasma current, density, heating power, size and shape. Runaway electron confinement is evidenced by a 100-fold increase in hard x-ray bremsstrahlung. Fokker-Planck modelling of the x-ray energy spectrum reveals that the high energy electron diffusion is independent of the parallel velocity, uncharacteristic of magnetic transport and more like that for electrostatic turbulence. The high core electron temperature correlates strongly with a broadband reduction of resonant modes at mid-radius where the stochasticity is normally most intense. To extend profile control and add auxiliary heating, rf current drive and neutral beam heating are in development. Low power lower-hybrid and electron Bernstein wave injection experiments are underway. Dc current sustainment via ac helicity injection (sinusoidal inductive loop voltages) is also being tested. Low power neutral beam injection shows that fast ions are well-confined, even in the presence of relatively large magnetic fluctuations.
The ability to obtain high plasma densities with high fractional ionization using readily available, low-cost components makes the helicon a candidate plasma source for many applications, including plasma rocket propulsion, fusion component testing, and materials processing. However, operation of a helicon can be a sensitive function of the magnetic field strength and geometry as well as the driving frequency, especially when using light feedstock gases such as hydrogen or helium. In this paper, results from a coupled rf and transport model are compared with experiments in the axially inhomogeneous Mini-Radio Frequency Test Facility ͓Goulding et al., , p. 107͔ ͑Mini-RFTF͒. Experimental observations of the radial shape of the density profile can be quantitatively reproduced by iteratively converging a high-resolution rf calculation including the rf parallel electric field with a transport model using reasonable choices for the transport parameters. The experimentally observed transition into the high density helicon mode is observed in the model, appearing as a nonlinear synergism between radial diffusion, the rf coupling to parallel electric fields that damp near the plasma edge, and propagation of helicon waves that collisionally damp near the axis of the device. Power deposition from various electric field components indicates that inductive coupling and absorption in the edge region can reduce the efficiency for high-density operation. The effects of absorption near the lower hybrid resonance in the near-field region of the antenna are discussed. Ponderomotive effects are also examined and found to be significant only in very low density and edge regions of the Mini-RFTF discharge.
The National Spherical Torus Experiment (NSTX) has made considerable progress in advancing the scientific understanding of high performance long-pulse plasmas needed for future spherical torus (ST) devices and ITER. Plasma durations up to 1.6 s (five current redistribution times) have been achieved at plasma currents of 0.7 MA with non-inductive current fractions above 65% while simultaneously achieving β T and β N values of 17% and 5.7 (%m T MA −1 ), respectively. A newly available motional Stark effect diagnostic has enabled validation of currentdrive sources and improved the understanding of NSTX 'hybrid'-like scenarios. In MHD research, ex-vessel radial field coils have been utilized to infer and correct intrinsic EFs, provide rotation control and actively stabilize the n = 1 resistive wall mode at ITER-relevant low plasma rotation values. In transport and turbulence research, the low aspect ratio and a wide range of achievable β in the NSTX provide unique data for confinement scaling studies, and a new microwave scattering diagnostic is being used to investigate turbulent density fluctuations with wavenumbers extending from ion to electron gyro-scales. In energetic particle research, cyclic neutron rate drops have been associated with the destabilization of multiple large toroidal Alfven eigenmodes (TAEs) analogous to the 'sea-of-TAE' modes predicted for ITER, and three-wave coupling processes have been observed for the first time. In boundary physics research, advanced shape control has enabled studies of the role of magnetic balance in H-mode access and edge localized mode stability. Peak divertor heat flux has been reduced by a factor of 5 using an H-mode-compatible radiative divertor, and lithium conditioning has demonstrated particle pumping and results in improved thermal confinement. Finally, non-solenoidal plasma start-up experiments have achieved plasma currents of 160 kA on closed magnetic flux surfaces utilizing coaxial helicity injection.
Abstract. The well developed linear theory of ICRF (including FW, HHFW and IBW) interactions with plasma has enjoyed considerable success in describing antenna coupling and wave propagation, and provides a well-known framework for calculating power absorption, current drive, etc. In some situations, less well studied nonlinear effects are of interest, such as flow drive, ponderomotive forces, rf sheaths, parametric decay and related interactions with the edge plasma. Standard ICRF codes have begun to integrate this physics to achieve improved modeling capabilities. This paper concentrates on basic rf-plasma-interaction physics with illustrative applications to tokamaks. For FW antennas, the parallel electric field near launching structures is known to drive rf-sheaths which can give rise to convective cells, interaction with plasma "blobs", impurity production, and edge power dissipation. In addition to sheaths, IBW waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized, and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. It is argued that there are significant opportunities now for new predictive capabilities by advances in integrated simulation.
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