Locked ͑i.e., nonrotating͒ dynamo modes give rise to a serious edge loading problem during the operation of high current reversed field pinches. Rotating dynamo modes generally have a far more benign effect. A simple analytic model is developed in order to investigate the slowing down effect of electromagnetic torques due to eddy currents excited in the vacuum vessel on the rotation of dynamo modes in both the Madison Symmetric Torus ͑MST͒ ͓Fusion Technol. 19, 131 ͑1991͔͒ and the Reversed Field Experiment ͑RFX͒ ͓Fusion Eng. Des. 25, 335 ͑1995͔͒. This model strongly suggests that vacuum vessel eddy currents are the primary cause of the observed lack of mode rotation in RFX. The eddy currents in MST are found to be too weak to cause a similar problem. The crucial difference between RFX and MST is the presence of a thin, highly resistive vacuum vessel in the former device. The MST vacuum vessel is thick and highly conducting. Various locked mode alleviation methods are discussed.

Reduction of core-resonant mϭ1 magnetic fluctuations and improved confinement in the Madison Symmetric Torus ͓Dexter et al., Fusion Technol. 19, 131 ͑1991͔͒ reversed-field pinch have been routinely achieved through control of the surface poloidal electric field, but it is now known that the achieved confinement has been limited in part by edge-resonant mϭ0 magnetic fluctuations. Now, through refined poloidal electric field control, plus control of the toroidal electric field, it is possible to reduce simultaneously the mϭ0 and mϭ1 fluctuations. This has allowed confinement of high-energy runaway electrons, possibly indicative of flux-surface restoration in the usually stochastic plasma core. The electron temperature profile steepens in the outer region of the plasma, and the central electron temperature increases substantially, reaching nearly 1.3 keV at high toroidal plasma current ͑500 kA͒. At low current ͑200 kA͒, the total beta reaches 15% with an estimated energy confinement time of 10 ms, a tenfold increase over the standard value which for the first time substantially exceeds the constant-beta confinement scaling that has characterized most reversed-field-pinch plasmas.

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.

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Electrostatic fluctuations have been measured in a large reversed-field pinch, and are large ihe/n ~20%-40%, 7'^/r~10%-25%). Frequency and wave-number spectra are broad (AA2~70-150, Am-3-6), and differ from measured magnetic fluctuation spectra. The transport inferred from correlation measurements indicates that electrostatic fluctuations can account for significant particle losses, but contribute < 15% to energy loss.PACS numbers: 52.55.-s In toroidal magnetic confinement devices, cross-field transport exceeds diffusion predicted by collisional processes. Some theoretical models invoke electrostatic turbulence to explain this anomalous transport. Charge separation results in a fluctuating electric field, E = -VO; the ExB drift then drives transport. Electrostatic fluctuations may be responsible for particle transport in tokamak [1-4] and stellarator [5] edge plasmas, and perhaps also energy transport. Early measurements on ZETA [6] indicated that the role of electrostatic losses could be significant. More recent investigations have begun in several reversed-field-pinch (RFP) experiments [7][8][9]. The RFP and tokamak have similar edge plasma equilibrium density and temperature. However, the RFP contains greater magnetic shear, unfavorable magnetic curvature, and fewer magnetically trapped particles.In this Letter, we report measurements of edge electrostatic fluctuations (in density, potential, and electron temperature) in the MST RFP. We find that the amplitudes are large and the frequency and wave-number spectra are broad, similar to fluctuations in tokamaks. The deduced fluctuation-induced particle transport is comparable to the total particle losses. However, the fluctuation-induced energy transport is relatively small. MST [10,11] is a large RFP (^=0.52 m, 7^ = 1.5 m), with typical plasma parameters /^ < 600 kA, AZ^=(0.5-2.0) X 10'^ cm~^ r^o<500 eV, and pulse length < 80 msec. The present studies were conducted in low-current plasmas [/,, < 250 kA, /z,-=(0.6-0.8) x 10^^ cm~\ T^o < 180 eV], shown in Fig. 1. For these conditions, a single-turn loop voltage K/ = 15.5 V, pinch parameter O = Bp(a)/{Bt) = \.S5 (where (Bf) is the volume-averaged toroidal field), and reversal parameter F=Bt(a)/{Bt} = -0.15 were obtained.Probe measurements were made at r/a>:0.92 (where r/a = l at the wall), 40° above the outer midplane. Graphite toroidal rail limiters extend 1 cm from the wall at the inner and outer midplane. Triple probes were constructed using 0.5-mm-diam tungsten tips, spaced 1.6 mm apart. Two triple clusters, separated by 11.4 mm, were fixed on a single probe support. Measurements were made using a triple probe technique [12]. Ion saturation current Js was collected by a floating double probe biased to -300 V [> (5-10)A:rJ. The floating potential V/ was measured across a 100 kn impedance to the ground. The local plasma density rie, electron temperature Te, and (1) plasma potential Opi were then inferred bywhere ks is Boltzmann's constant, V^ is the potential of the positive-biased tip, and a, p, and f are consta...

Theoretical studies have predicted that the Z-pinch can be stabilized with a sufficiently sheared axial flow [U. Shumlak and C. W. Hartman, Phys. Rev. Lett. 75, 3285 (1995)]. A Z-pinch experiment is designed to generate a plasma which contains a large axial flow. Magnetic fluctuations and velocity profiles in the plasma pinch are measured. Experimental results show a stable period which is over 700 times the expected instability growth time in a static Z-pinch. The experimentally measured axial velocity shear is greater than the theoretical threshold during the stable period and approximately zero afterwards when the magnetic mode fluctuations are high.

Ion temperatures have been measured in the Madison Symmetric Torus (MST) [Dexter et aL, Fusion Technol. 19, 131 ( 199 1 j] reversed-field pinch (RFP) with a five channel charge exchange analyzer. The characteristic anomalously high ion temperature of RFP discharges has been observed in the MST. The ion heating expected from ion-electron collisions is calculated and shown to be too small to explain the measured ion temperatures. The charge exchange determined ion temperature is also compared to measurements of the thermally broadened CV 227.1 nm line. The ion temperature, Ti~250 eV for 1=360 kA, increases by more than 100% during discrete dynamo bursts in MST discharges. Magnetic field fluctuations in the range OS-5 MHz were also measurd during the dynamo bursts. Structure in the fluctuation frequency spectrum at the ion cyclotron frequency suggests that the mechanism of ion heating involves the dissipation of dynamo fluctuations at ion cyclotron frequencies.

Fast ions are observed to be very well confined in the Madison Symmetric Torus reversed field pinch despite the presence of stochastic magnetic field. The fast-ion energy loss is consistent with the classical slowing down rate, and their confinement time is longer than expected by stochastic estimates. Fast-ion confinement is measured from the decay of d-d neutrons following a short pulse of a 20 keV atomic deuterium beam. Ion confinement agrees with computation of particle trajectories in the stochastic magnetic field, and is understood through consideration of ion guiding center islands.