George Vahala

EBW power deposition and current drive in WEGA?comparison of simulation with experiment

Detailed computational studies of electrostatic electron Bernstein waves (EBWs) propagation in the WEGA stellarator are performed and compared with experimental results. Using the WEGA antenna, the two O-/X-mode radiation lobes are modelled by sets of rays whose intensities are proportional to the measured radiation pattern. After projecting these rays onto the plasma periphery, the O–X-EBW mode conversion efficiency around the upper hybrid resonance is determined from a full wave adaptive mesh solver of the cold plasma equations. From the roots of the electrostatic EBW dispersion relation, ray tracing is performed to determine the power absorption on the first or second cyclotron harmonic as well as current drive assuming the Fisch–Boozer mechanism. Good agreement is achieved between our EBW simulations on specific WEGA equilibria and the experimental results from the antenna launch of 2.45 GHz waves. The experimentally observed off-axis power deposition and the outward shift dependence of the absorption maxima on increasing magnetic field can only be explained by the existence of a hot electron component in the WEGA plasma. It is this hot electron component that permits wave absorption at the second harmonic near the plasma boundary. Moreover, the simulations not only reproduce the current density reversal at the plasma centre for low magnetic fields but also the destruction of this current density reversal for larger magnetic fields.

Spectra and growth rates of a generalized screw pinch

The theory of Weitzner for the bumpy θ pinch is extended to the case of a generalized screw pinch in which the equilibrium magnetic field is B = (eBr, eBθ, Bz). e represents the slow periodic z variation of the axisymmetric equilibrium and the stability relative to their r variation. Perturbation expansions in e and in the bumpiness of the flux surfaces are performed on the linearized equations of ideal magnetohydrodynamics. From the theory of Grad there should be four stable continua, two of which are found for modes with ω2 = O (e2), while for the transverse modes a generalized Suydam criterion for local instability is derived. The (global) growth rates of the most unstable transverse modes are computed numerically for various Bθ and the results are compared to those of the bumpy θ pinch (where Bθ ≡ 0)) as well as to the ordinary screw pinch (where Br ≡ 0).

Spectral properties of the kinetic Alfvén wave in cylindrical tokamak geometry

It is shown, for a tokamak‐like cylindrical plasma and small poloidal and toroidal mode numbers, that the full gyrokinetic shear Alfven spectrum is discrete when k∥≠0. Calculations of the global eigenmodes of the magnetohydrodynamic (MHD) limit, and their first‐order finite Larmor radius (FLR) corrections, are presented. First‐order FLR theory is found to be a good approximation to full FLR theory, even for modes with high radial node number. In the presence of a positive density gradient, such as that which may occur with pellet fueling of the plasma, the existence of global MHD eigenmodes above the Alfven continuum is confirmed.

Analytic, high β, flux conserving equilibria for cylindrical tokamaks

Using Grad’s theory of generalized differential equations, the temporal evolution from low to high β due to ’’adiabatic’’ and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed.

Turbulence theory for the dissipative trapped electron instability

Drift orbit diffusion induced by turbulence acting on trapped electrons is shown to reduce and broaden the magnetic drift resonance and produce the dominant nonlinear saturation mechanism for the dissipative trapped electron instability. The fluctuation level obtained from such a theory is found to be consistent with present experimental observations.

Stability of large aspect ratio diffuse profile tokamaks with circular flux surfaces

It is shown that the stability of axisymmetric diffuse profile tokamaks is always governed by that of the straight cylindrical screw pinch if one assumes small deviations from circular flux surfaces and small inverse aspect ratio e, regardless of the ordering of β in e. Unstable modes with very small growth rates or those which are very highly localized are excluded from this treatment. Suydam‐type modes are included. The sharp boundary and diffuse profile results are compared and commented on.

Simulation of EBW Heating in WEGA

Discharges in the WEGA stellarator are sustained exclusively by 2.45 GHz RF heating. Plasma density is typically above the critical density so only electron Bernstein waves (EBW) can propagate inside the plasma. Experiments show a dependence on the magnitude of the magnetic field that points to resonant wave damping at 2.45GHz. EBW propagation has been simulated with O‐X‐EBW conversion efficiency and ray‐tracing calculations, showing possible mechanisms for the experimental results. Growth of the parallel wave number up to ∼30, along with the characteristic admixture of energetic electrons produced by the RF heating, allows for strong resonant absorption at the Doppler shift electron cyclotron (EC) resonance. Thus, the deposition region shifts with changes in the magnitude of the magnetic field. Our modeling also predicts that the experimentally designed antenna should drive a substantial current.

Guiding center helically symmetric plasmas

The stability analysis of nearly cylindrical magnetically confined plasma is generalized to include the effects of pressure anisotropy. Specifically, the equilibrium and normal mode equations for helically symmetric plasmas are derived and it is shown that these equations reduced to all previous diffuse profile bumpy theta pinch and helical calculations. The equations presented are valid for arbitrary helical wavenumber k, arbitrary degree of helicity L, and O (δ0) pressure anisotropy, where δ measures the percent deviation of the plasma surface from that of a cylinder. Numerical calculations of the effect of pressure anisotropy on locally unstable modes are presented.

Stable equilibrium statistical states for spheromaks

Incompressible nondissipative magnetohydrodynamic turbulence is treated for spherical systems. From the absolute equilibrium expectation values of the fields one can investigate those initially quiescent states for which no large mean square velocity will develop. This stable state is force‐free and gives rise to the Hill vortex structure for the magnetic flux surfaces.

EBW H&CD Potential for Spherical Tokamaks

Spherical tokamaks (STs), which feature relatively high neutron flux and good economy, operate generally in high‐s regimes, in which the usual EC O‐ and X‐ modes are cut‐off. In this case, electron Bernstein waves (EBWs) seem to be the only option that can provide features similar to the EC waves—controllable localized heating and current drive (H&) that can be utilized for core plasma heating as well as for accurate plasma stabilization. We first derive an analytical expression for Gaussian beam OXB conversion efficiency. Then, an extensive numerical study of EBW H&CD performance in four typical ST plasmas (NSTX L‐ and H‐mode, MAST Upgrade, NHTX) is performed. Coupled ray‐tracing (AMR) and Fokker‐Planck (LUKE) codes are employed to simulate EBWs of varying frequencies and launch conditions. Our results indicate that an efficient and universal EBW H&CD system is indeed viable. In particular, power can be deposited and current reasonably efficiently driven across the whole plasma radius. Such a system coul...