A dynamic computational model of lower hybrid current drive in the presence of an electric field is described and some results are given. Details of geometry, plasma profiles and circuit equations are treated carefully. Two dimensional velocity space effects are approximated in a one dimensional Fokker-Planck treatment. The model is unable to approximate experimental results in some cases characterized by low density, low current, high aspect ratio and a launched spectrum at high phase velocity relative to the thermal velocity. In other cases, qualitative agreement with measurements is found. A simple formula already in the literature appears to determine whether agreement of model and experiment will be good or poor. Application to an experimental discharge in which q(0) is raised above unity shows an appropriate time-scale. Computation of a planned effort for high /3 suggests potential success.

A common simplifying assumption made in the consideration of radio-frequency heating of tokamaks near the lower hybrid frequency is that the wavelength imposed by the coupling device parallel to the magnetic field is not modified by gradients along the field. In the present calculation, the parallel wavelength is allowed to vary, and important effects are found on wave penetration and damping if the toroidal aspect ratio (Rmajor/rminor) is less than approximately five. The calculation shows that heating at the center of a small aspect ratio torus is inhibited by a decrease in k∥ if waves are launched at the outside, and that it may be possible to change the plasma current via electron Landau damping with a coupler of symmetric power spectrum by placing the coupler at the top (or bottom) of the torus.

Ray tracing simulations based on experimental PBX-M equilibria show a limited range of the parallel wavenumber (n, = R,c/w) along a ray trajectory. The range of nl accessible to the excited wave is shown to have both a lower and an upper bound. The ray's phase volume is projected into (n,, R, Z) space to define a domain of wave accessibility for each toroidal mode number excited by the launcher. A comparison of circular and bean shaped plasmas with a high aspect ratio ( A -5.5) shows that the rays fill a substantially larger portion of the accessible domain in bean shaped plasmas. Furthermore, in the bean shaped case the accessible domain tends to extend to higher n N .

One key to achieving high beta in a tokamak may be the proper control of the plasma pressure and current density profiles. In principle, if steady-state RF current drive is used, the current density may be tailored by a careful selection of the wave frequency and the power spectrum. This study uses the selfconsistent theory of RF current drive in an axisymmetric torus to compute the MHD equilibrium generated by the fast (magnetosonic) wave current driver. This is accomplished by iterations in a calculation of the MHD equilibrium for a given diamagnetism function, F(i//) = RB t , and a ray-tracing calculation which determines F(i//). The various wave and plasma characteristics which determine the equilibrium are examined, and it appears possible to create a large diversity of equilibria.

The first experiments utilizing high-power radio waves in the ion cyclotron range of frequencies to heat deuterium–tritium (D–T) plasmas have been completed on the Tokamak Fusion Test Reactor [Fusion Technol. 21, 13 (1992)]. Results from the initial series of experiments have demonstrated efficient core second harmonic tritium (2ΩT) heating in parameter regimes approaching those anticipated for the International Thermonuclear Experimental Reactor [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 13th International Conference, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239]. Observations are consistent with modeling predictions for these plasmas. Efficient electron heating via mode conversion of fast waves to ion Bernstein waves has been observed in D–T, deuterium-deuterium (D–D), and deuterium–helium-4 (D–4He) plasmas with high concentrations of minority helium-3 (3He) (n3He/ne≳10%). Mode conversion current drive in D–T plasmas was simulated with experiments conducted in D–3He–4He plasmas. Results show a directed propagation of the mode converted ion Bernstein waves, in correlation with the antenna phasing.

Application of Ion Bernstein Wave Heating (IBWH) into the Princeton Beta Experiment-Modification (PBX-M) [Phys. Fluids B 2, 1271 (1990)] tokamak stabilizes sawtooth oscillations and generates peaked density profiles. A transport barrier, spatially correlated with the IBWH power deposition profile, is observed in the core of IBWH-assisted neutral beam injection (NBI) discharges. A precursor to the fully developed barrier is seen in the soft x-ray data during edge localized mode (ELM) activity. Sustained IBWH operation is conducive to a regime where the barrier supports large ∇ne, ∇Te, ∇νφ, and ∇Ti, delimiting the confinement zone. This regime is reminiscent of the H(high) mode, but with a confinement zone moved inward. The core region has better than H-mode confinement while the peripheral region is L(low)-mode-like. The peaked profile enhances NBI core deposition and increases nuclear reactivity. An increase in central Ti results from χi reduction (compared to the H mode) and better beam penetration. Bootstrap current fractions of up to 0.32–0.35 locally and 0.28 overall were obtained when an additional NBI burst is applied to this plasma.

Lower hybrid (LH) current drive experiments on the Princeton Beta Experiment-Modified (PBX-M) [Phys. Fluids B 2, 1271 (1990)] have shown that the current profile can be changed by varying the phase velocity of the waves. The radial profile of the current carrying electrons was deduced from two-dimensional hard x-ray tomography. For a certain range of phase velocities, there is a correlation between the peak of the fast electron profile and the launched wave spectrum, despite the presence of a wide spectral gap between the phase velocity and the thermal electron energy distribution. A new model is proposed to explain how first-pass wave damping is possible in such plasmas. The rf power can form a tail of energetic electrons, and subsequently waves with moderate phase velocity can damp on them. For waves with very fast phase velocity, there must be an upshift of the n∥ spectrum for any damping to occur. These hypotheses are supported by ray tracing results which are coupled to relativistic Fokker–Planck calculations of the electron distribution function.

The Compact Ignition Tokamak (C1T) is a proposed modest-size ignition experiment designed to study the physics of aJpha-particle heating. The basic concept is to achieve ignition in a modest-size minimum cost experiment by using a high plasma density to achieve the condition of n-rg ~ 2 x 10 sec m"-5 MASTER DISTRIBUTION G? T.liS KVVW * ^'' llEtt