Mode conversion from the fast magnetosonic wave to a slow wave near the two-ion hybrid resonance is shown to explain recent experimental fast-wave damping results. A model for tunneling and mode conversion of the fast wave in the two-ion resonance zone incorporating k^ and plasma-density and magnetic-field profiles is used to explain the observations. The strong dependence of the absorption on & n and the species concentration which is obtained has important consequences for major plasma-heating programs which are planned for tokamaks.Recent experiments on the TFR, 1 ' 2 ATC, 3 TMOl, 4 and T-4 5 tokamaks have measured the damping of the fast wave as the resonance layer for the second ion-cyclotron harmonic ((o = 2co cd ) is scanned across the plasma cross section. When the second-harmonic resonance for deuterium is in the central plasma region, a strong absorption of the wave is noted. Wave absorption rapidly decreases outside two locations for the cyclotron harmonic resonance zone which are not symmetric with respect to the magnetic axis. A preliminary analysis 2 of the TFR experiment showed that the asymmetry could be explained by the presence of a two-ion hybrid resonance within the plasma due to a hydrogen-impurity component in the deuterium plasma. The experiments on the TMOl 4 and T-4 5 tokamaks found that the presence of even a small amount of hydrogen impurity can greatly increase the wave-absorption process and lower the eigenmode Q. We establish here that the damping rate of the fast wave can be attributed to a mode-conversion process in the two-ion hybridresonance layer which is very sensitive to the k u value of the eigenmode. The result of a detailed analysis of the mode-conversion problem is in semiquantitative agreement with the observations.Local dispersion relation, mode conversion, and its associated damping decrement.-We start with the wave equationwhere K is the hot-plasma dielectric tensor 6 derived from the coupled kinetic Vlasov-Maxwell equations. We further note that for the fast magnetosonic wave the wavelength transverse to the magnetic field is much larger than the ion gyroradius so that A / =fe JL 2 p i 2 /2«l. We then expand the Bessel functions which occur in each element of the 3x3 dielectric tensor to second order in their argument Xj. The resulting tensor is incor-porated in the dispersion relation obtained from the wave equation. The resulting matrix is expanded and terms are collected to second order in \j. We find from numerical computations that, at spatial locations outside the ion-cyclotron-harmonic resonances (lci>-tt ci 2 )-* + (co 2 -4a> ci 2 )-*].S, R, and L are defined as in StiLx, 6 ti\\ is the parallel index of refraction and Z f is the derivative of the plasma dispersion function. We assume the \/R variation in toroidal field and a p...

Sheet electron beams focused by periodically cusped magnetic (PCM) fields are stable against low-frequency velocity-shear instabilities (such as diocotron mode). This is in contrast to more familiar unstable behavior in uniform solenoidal magnetic fields. Two rectangular-cross-section magnetic configurations capable of focusing in both transverse dimensions are investigated: (i) a closed-side two-plane PCM configuration that is topologically equivalent to conventional round-cross-section PPM focusing; and (ii) an open-side configuration that uses ponderomotive PCM focusing in the vertical plane and simple vzBu Lorentz force focusing in the horizontal plane. Both configurations are capable of stable sheet beam confinement. The open-side configuration appears more practical both for focusing and for realizing matched (cold) beam conditions in which the beam envelope is free from oscillations. For realistic beams with finite emittance, the existence of a matched cold beam solution implies less emittance growth at beam injection.

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A tandem-mirror plasma has been sustained and heated by rf alone without the need for neutral beams. End plug density and energy are maintained by ion cyclotron-resonance heating which traps and heats a fraction of the central-cell loss stream. The central-cell plasma is maintained by gas fueling and rf heating. Magnetohydrodynamic stability limits the ratio of the central-cell to plug plasma pressure, and the central-cell electron temperature must be kept high enough for ionization. A quasi steady state is achieved that lasts much longer than the decay times of the plugs and central cell.PACS numbers: 52.55. Mg, 52.50.Gj, 52.55.Ke The tandem-mirror approach to the development of a fusion reactor promises to have many advantages over simple mirrors as well as other magnetic confinement devices. 1 In a tandem mirror, a central-cell plasma in a solenoid is bounded by "plug" plasmas in mirror cells. The TMX experiment 2 demonstrated that electrostatic confinement of central-cell ions by the plug plasmas significantly reduced end losses. Calculations indicate that the overall Q (power gain) of a tandem-mirror fusion reactor can be quite high (~5-10) if the volume of the central cell greatly exceeds that of the plugs. 3 In previous experiments, plug plasmas were fueled and heated by energetic neutral beams. However, technological constraints on neutral-beam heating when scaled to a reactor could be eased or eliminated by supplementing or replacing neutral-beam power with rf power. We show in the Phaedrus experiment that a tandem-mirror plasma can be sustained by rf alone, without the application of neutral beams.The operation of a tandem mirror can be thought of as taking place in two stages, a transient stage followed by a quasi-state stage. In the transient stage, plasma is injected into the machine by stream guns. In fact, earlier experiments with Phaedrus 4 and Gamma 6 5 were restricted to the transient stage. Such plasmas side-stepped many of the issues of tandem-mirror physics because plasma characteristics were dominated by the external plasma between the plugs and the stream guns. The high-density external plasma line-tied the plasma to the stream guns, significantly reducing both magnetohydrodynamic (MHD) instabilities and microinstabilities and fixing the electron temperature. When the stream guns were turned off in Phaedrus, the plasma decayed away in approximately 150 jus in the plugs and 400 JUS in the central cell. Quasi-steady-state operation after stream guns are turned off requires sources of particles and energy for both the plug and central-cell plasmas and also adds constraints that must be satisfied in order to maintain microstability and MHD stability. In TMX, fueling and heating were provided by neutral beams in the plugs and gas puffing in the central cell. In the Phaedrus experiment, fueling is provided only by gas puffing in the central cell while rf provides heating. In both experiments, stability was provided by high plug energy density and the presence of the central-cell loss flow.The ...

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