S. Assadi

Global confinement and discrete dynamo activity in the MST reversed field pinch

Results obtained on the Madison Symmetric Torus (MST) reversed‐field pinch [Fusion Technol. 19, 131 (1991)] after installation of the design poloidal field winding are presented. Values of βθe0≡2μ0ne0Te0/B2θ(a)∼12% are achieved in low‐current (I=220 kA) operation; here, ne0 and Te0 are central electron density and temperature, and Bθ(a) is the poloidal magnetic field at the plasma edge. An observed decrease in βθe0 with increasing plasma current may be due to inadequate fueling, enhanced wall interaction, and the growth of a radial field error at the vertical cut in the shell at high current. Energy confinement time varies little with plasma current, lying in the range of 0.5–1.0 msec. Strong discrete dynamo activity is present, characterized by the coupling of m=1, n=5–7 modes leading to an m=0, n=0 crash (m and n are poloidal and toroidal mode numbers). The m=0 crash generates toroidal flux and produces a small (2.5%) increase in plasma current.

Locked modes and magnetic field errors in the Madison Symmetric Torus

In the Madison Symmetric Torus (MST) reversed‐field pinch [Fusion Technol. 19, 131 (1991)] magnetic oscillations become stationary (locked) in the lab frame as a result of a process involving interactions between the modes, sawteeth, and field errors. Several helical modes become phase locked to each other to form a rotating localized disturbance, the disturbance locks to an impulsive field error generated at a sawtooth crash, the error fields grow monotonically after locking (perhaps due to an unstable interaction between the modes and field error), and over tens of milliseconds of growth confinement degrades and the discharge eventually terminates. Field error control has been partially successful in eliminating locking.

Turbulent transport in the Madison Symmetric Torus reversed-field pinch

Measurements of edge turbulence and the associated transport are ongoing in the Madison Symmetric Torus (MST) reversed‐field pinch [Fusion Technol. 19, 131 (1991)] using magnetic and electrostatic probes. Magnetic fluctuations are dominated by m=1 and n ∼2R/a, tearing modes. Particle losses induced by magnetic field fluctuations have been found to be ambipolar (〈J∥ Br〉/B0=0). Electrostatic fluctuations are broadband and turbulent, with mode widths Δm∼3–7 and Δn∼70–150. Particle, parallel current, and energy transport arising from coherent motion with the fluctuating Ẽ×B drift have been measured. Particle transport via this channel is comparable to the total particle loss from MST. Energy transport (from 〈PEφ 〉/B0) due to electrostatic fluctuations is relatively small, and parallel current transport (from 〈J∥ Eφ〉/B0) may be small as well.

First results from the Madison Symmetric Torus reversed field pinch

The first period of physics operation of the Madison Symmetric Torus (MST) reversed field pinch [Plasma Physics and Controlled Nuclear Fusion Research 1988 (IAEA, Vienna, 1989), Vol 2, p. 757] has produced information on sawtooth oscillations, edge magnetic and electrostatic fluctuations, and equilibrium parameters at large plasma size. Sawtooth oscillations are prevalent at all values of pinch parameter and might constitute discrete dynamo events. Both electrostatic and magnetic fluctuations are of sufficient magnitude to be relevant to transport in the reversed field pinch. In the plasmas studied to date (up to a plasma current of 0.5 MA) the poloidal beta value is about 10% or greater.

Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

Three‐wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed‐field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in ‘‘k‐space.’’ The strength of nonlinear three‐wave interactions satisfying the sum rules m1+m2=m3 and n1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the ‘‘crash’’ phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.

STUDIES OF A REVERSED FIELD PINCH IN A POLOIDAL DIVERTOR CONFIGURATION

An attempt has been made to form a reversed field pinch (RFP) in a poloidal divertor configuration which positions the plasma far from a conducting wall. In this configuration, the plasma is localized within a magnetic separatrix formed by a combination of toroidal currents in the plasma and four internal aluminium rings. Plasmas were formed with a plasma current of ~ 135 kA, toroidal field reversal lasting ~1 ms, line averaged density of ~(1-2) × 1013 cm−3 and central electron temperature of ~50 eV, but a large asymmetry in the magnetic field (δB/B ~ 40%) set in at about the time when the toroidal field reversed at the wall. This behaviour might be expected on the basis of MHD stability analysis of a cylindrical plasma bounded by a large vacuum region and a distant conducting wall. The symmetric equilibrium before the asymmetry develops and the asymmetry itself are described.

Studies of large, non-circular, reversed field pinch discharges

Reversed field pinch (RFP) discharges have been produced in a large (1.39 metre major radius, 0.56 metre average minor radius), thick walled (5 cm), aluminium vacuum vessel with indented sides. The discharges are self-reversed and ramped up to a current of 300 kA over a time of 10 ms. Reversal is sustained for 10 resistive diffusion times, despite the presence of large magnetic fluctuations. The influence of the bad poloidal magnetic curvature on RFP stability is examined by measurement of magnetic fluctuations near the plasma edge in the separate bad and good curvature regions of the non-circular plasma for RFP and non-reversed discharges with an edge safety factor, qa, of 0.4 and 1.4. For qa ~ 1.4 discharges, the poloidal field curvature is small. The large device size permits RFP startup at a low toroidal loop voltage (200 V), which is applied to a gap exposed to plasma, but successfully protected against arcing (up to 300 V). RFP plasmas have also been obtained with a toroidal limiter.

Locked modes and magnetic field errors in MST

In the MST reversed field pinch magnetic oscillations become stationary (locked) in the lab frame as a result of a process involving interactions between the modes, sawteeth, and field errors. Several helical modes become phase locked to each other to form a rotating localized disturbance, the disturbance locks to an impulsive field error generated at a sawtooth crash, the error fields grow monotonically after locking (perhaps due to an unstable interaction between the modes and field error), and over the tens of milliseconds of growth confinement degrades and the discharge eventually terminates. Field error control has been partially successful in eliminating locking.

Results from the MST reversed field pinch with the design poloidal field windings

Summary form only given. The focus of experimental investigations in the MST reversed field pinch (RFP) is fluctuations, transport, and confinement in a large RFP (R=1.5 m). Initial operation of MST, using the core bias windings as the ohmic heating windings as well, provided observations of magnetic and electrostatic fluctuations in the plasma edge, as well as sawteeth phenomena in the magnetic field and plasma energy. The observed magnetic and electrostatic fluctuation levels warrant further investigation into their relationship to transport. The more distinct sawteeth activity, which could be interpreted as dynamo activity, occurs at all values of the pinch parameter, somewhat in contrast to other RFPs. The temporary poloidal field winding configuration also generated relatively large radial magnetic fields at the poloidal gap