Stewart C. Prager

The Madison Symmetric Torus

AbstractThe Madison Symmetric Torus (MST) is the newest and largest reversed-field pinch (RFP) currently in operation. It incorporates a number of design features that set it apart from other pinches, including the use of the conducting shell as both a vacuum vessel and single-turn toroidal field coil. Specially insulated voltage gaps are exposed to the plasma. Magnetic field errors at these gaps as well as at the various diagnostic and pumping ports are minimized through a variety of techniques. The physics goals of MST include study of the effect of large plasma size on confinement and the detailed investigation of RFP turbulence, dynamo, and transport. Details of the design and initial operation of the device are presented.

Laser polarimetric measurement of equilibrium and fluctuating magnetic fields in a reversed field pinch (invited)

New developments in Faraday rotation polarimetry have provided the first measurements of current density profile and core magnetic fluctuations in the core of a high-temperature reversed field pinch. This has been achieved by a fast-polarimeter system with time response up to 1 μs and phase resolution <1 mrad. Recent experiments on Madison Symmetric Torus have directly measured radial magnetic field fluctuations in the plasma interior with amplitude 33 G, ∼1%. A broad spectrum of magnetic fluctuations is observed up to 100 kHz. Relaxation of the current density profile at the sawtooth crash occurs on the timescale of 100 μs. Reversed-field pinch behavior is determined in large part by magnetic fluctuations driven by the radial gradient in the parallel current density. Hence, measurement of magnetic fluctuations and the current density profile is essential to understand the link between the current density profile, fluctuations, and transport.

Overview of quasi-single helicity experiments in reversed field pinches

We report the results of an experimental and theoretical international project dedicated to the study of quasi-single helicity (QSH) reversed field pinch (RFP) plasmas. The project has involved several RFP devices and numerical codes. It appears that QSH spectra are a robust feature common to all the experiments. Our results expand and reinforce the evidence that the formation of self-organized states with one dominant helical mode (Ohmic SH state) is an approach complementary to that of active control of magnetic turbulence to improve confinement in a steady state RFP.

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.

Two-fluid tearing instability in force-free magnetic configuration

In general, the linear two-fluid tearing instabilities are driven by shear Alfven (SA), compressional Alfven (CA), and slow magnetoacoustic (MA) modes modified on short scales by two-fluid effects. Previous two-fluid theories were devoted to either the hot plasma case where coupling of the SA and the MA waves dominates, or to the cold plasma limit, β=0, where the instability is driven by the SA and the CA waves. Taking into account plasma compressibility and the Hall term, we derive general tearing equations that cover the two limiting cases and the transition between them. In particular, in the hot plasma case, equations are derived that depend on the factor β/(1+β) and span the validity of resistive to electron MHD. The important effect of resistive diffusion of the “out-of-plane” component of the magnetic field perturbation B∥(1) is also included. Two new solutions where this effect dominates are obtained within the scope of the hot plasma model. Whistler scaling γ∝Δ′2 is found for the collisionless te...

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.

Enhanced confinement in tokamaks

The physics of enhanced confinement regimes in tokamaks is reviewed and some directions for further enhancements are assessed. The H‐mode confinement regime is examined. A number of other observations of enhanced confinement, having in common peaked density profiles, are compared to the theory of ion temperature gradient modes. Two schemes of promise in enhancing confinement, second stability and control of electric fields, are discussed. The contributions of alternate concepts to understanding tokamak transport are described.

Measurement of core velocity fluctuations and the dynamo in a reversed-field pinch

Plasma flow velocity fluctuations have been directly measured in the high temperature magnetically confined plasma in the Madison Symmetric Torus (MST) Reversed-Field Pinch (RFP). These measurements show that the flow velocity fluctuations are correlated with magnetic field fluctuations. This initial measurement is subject to limitations of spatial localization and other uncertainties, but is evidence for sustainment of the RFP magnetic field configuration by the magnetohydrodynamic (MHD) dynamo. Both the flow velocity and magnetic field fluctuations are the result of global resistive MHD modes of helicity m = 1, n = 5--10 in the core of MST. Chord-averaged flow velocity fluctuations are measured in the core of MST by recording the Doppler shift of impurity line emission with a specialized high resolution and throughput grating spectrometer. Magnetic field fluctuations are recorded with a large array of small edge pickup coils, which allows spectral decomposition into discrete modes and subsequent correlation with the velocity fluctuation data.