A. F. Almagri

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.

High confinement plasmas in the Madison Symmetric Torus reversed-field pinch

Reduction of core-resonant m=1 magnetic fluctuations and improved confinement in the Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] 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 m=0 magnetic fluctuations. Now, through refined poloidal electric field control, plus control of the toroidal electric field, it is possible to reduce simultaneously the m=0 and m=1 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 kA). At low current (200 kA), the total beta reaches 15% with an estimated energy confinement time of 10 ms, a tenfold ...

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.

High current plasma electron emitter

A high current plasma electron emitter based on a miniature plasma source has been developed. The emitting plasma is created by a pulsed high current gas discharge. The electron emission current is 1 kA at 300 V with a pulse duration of 10 ms. The prototype injector described in this paper will be used for a 20 kA electrostatic current injection experiment in the Madison symmetric torus reversed-field pinch. The source will be replicated in order to attain this total current requirement. The source has a simple design and has proven to be very reliable in operation. A high emission current, small size (3.7 cm in diameter) and low impurity generation make the source suitable for a variety of fusion and technological applications.

Tokamak-like confinement at a high beta and low toroidal field in the MST reversed field pinch

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 ten-fold (to ~10 ms), which is comparable with L- and 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.

Fast flow phenomena in a toroidal plasma

The bulk fluid velocity is measured spectroscopically with 10 μs time resolution in the Madison Symmetric Torus (MST) reversed‐field pinch (RFP) [Fusion Technol. 19, 131 (1991)], a diagnostic capability used to study the fast flow dynamics associated with locked modes and the RFP dynamo. The phase velocity of the tearing modes and the fluid velocity accelerate between sawtooth events, reaching a maximum speed of about 20 km/s in a few ms. Both slow down at the sawtooth crash in ≊100 μs. This deceleration time scale is as calculated for the tearing modes from the action of electromagnetic torque on the magnetic islands, but is much faster than expected from the viscous torque on the bulk fluid. In the RFP, correlated fluctuations in the tearing modes and fluid velocity probably also generate current via the ‘‘RFP dynamo,’’ 〈ũ×B〉, where u is the bulk fluid velocity. Initial data indicate a possible increase in 〈uφBr〉 during sawtooth events, coincident with toroidal flux generation.

Measurement of the dynamo effect in a plasma

A series of the detailed experiments has been conducted in three laboratory plasma devices to measure the dynamo electric field along the equilibrium field line (the {alpha} effect) arising from the correlation between the fluctuating flow velocity and magnetic field. The fluctuating flow velocity is obtained from probe measurement of the fluctuating E x B drift and electron diamagnetic drift. The three major findings are (1) the {alpha} effect accounts for the dynamo current generation, even in the time dependence through a ``sawtooth`` cycle; (2) at low collisionality the dynamo is explained primarily by the widely studied pressureless Magnetohydrodynamic (MHD) model, i.e., the fluctuating velocity is dominated by the E x B drift; (3) at high collisionality, a new ``electron diamagnetic dynamo`` is observed, in which the fluctuating velocity is dominated by the diamagnetic drift. In addition, direct measurements of the helicity flux indicate that the dynamo activity transports magnetic helicity from one part of the plasma to another, but the total helicity is roughly conserved, verifying J.B. Taylor`s conjecture.

Experimental determination of the magnetic field spectrum in the Helically Symmetric Experiment using passing particle orbits

The leading terms of the magnetic field spectrum for the Helically Symmetric Experiment [Fusion Technol. 27, 273 (1995)] at low magnetic field are determined by analyzing the orbits of passing particles. The images produced by the intersection of electron orbits with a fluorescent mesh are recorded with a charge coupled device and transformed into magnetic coordinates using a neural network. To obtain the spectral components, the transformed orbits are then fit to an analytic expression that models the drift orbits of the electrons. The results confirm for the first time that quasihelical stellarators have a large effective transform that results in small excursions of particles from a magnetic surface. The drift orbits are also consistent with a very small toroidal curvature component in the spectrum. An external magnetic perturbation, nearly resonant with the transform, is shown to induce a large excursion of the particle orbit off a flux surface.

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.