J.S. Sarff

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.

Equilibrium reconstruction in the Madison Symmetric Torus reversed field pinch

A non-linear Grad–Shafranov toroidal equilibrium reconstruction code (MSTFit) has been developed for the Madison Symmetric Torus. This is the first such code applied to the unique magnetohydrodynamic (MHD) equilibrium of the reversed field pinch. A new set of toroidal Greens tables have been computed to impose the boundary condition of the close-fitting conducting shell. The non-linear fitting routine is sufficiently versatile for incorporating data from a variety of internal and external diagnostics, including a novel constraint based on orbits from a heavy ion beam probe diagnostic. Utilizing the full complement of internal and external magnetic and pressure diagnostics, MSTFit resolves accurately subtle changes in internal magnetic structure with implications on MHD stability. We show example equilibria that confirm conservation of magnetic helicity during relaxation and two-dimensional equilibrium effects.

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.

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.

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.

Quasi-single helicity spectra in the Madison Symmetric Torus

Evidence of a self-organized collapse towards a narrow spectrum of magnetic instabilities in the Madison Symmetric Torus [R. N. Dexter, D. W. Kerst, T. W. Lovell, S. C. Prager, and J. C. Sprott, Fusion Technol. 19, 131 (1991)] reversed field pinch device is presented. In this collapsed state, dubbed quasi-single helicity (QSH), the spectrum of magnetic modes condenses spontaneously to one dominant mode more completely than ever before observed. The amplitudes of all but the largest of the m=1 modes decrease in QSH states. New results about thermal features of QSH spectra and the identification of global control parameters for their onset are also discussed.