F. Ebrahimi

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.

Improved-confinement plasmas at high temperature and high beta in the MST RFP

We have increased substantially the electron and ion temperatures, the electron density, and the total beta in plasmas with improved energy confinement in the Madison Symmetric Torus (MST). The improved confinement is achieved with a well-established current profile control technique for reduction of magnetic tearing and reconnection. A sustained ion temperature >1?keV is achieved with intensified reconnection-based ion heating followed immediately by current profile control. In the same plasmas, the electron temperature reaches 2?keV, and the electron thermal diffusivity drops to about 2?m2?s?1. The global energy confinement time is 12?ms. This and the reported temperatures are the largest values yet achieved in the reversed-field pinch (RFP). These results were attained at a density ~1019?m?3. By combining pellet injection with current profile control, the density has been quadrupled, and total beta has nearly doubled to a record value of about 26%. The Mercier criterion is exceeded in the plasma core, and both pressure-driven interchange and pressure-driven tearing modes are calculated to be linearly unstable, yet energy confinement is still improved. Transient momentum injection with biased probes reveals that global momentum transport is reduced with current profile control. Magnetic reconnection events drive rapid momentum transport related to large Maxwell and Reynolds stresses. Ion heating during reconnection events occurs globally, locally, or not at all, depending on which tearing modes are involved in the reconnection. To potentially augment inductive current profile control, we are conducting initial tests of current drive with lower-hybrid and electron-Bernstein waves.

Dynamo-free plasma in the reversed-field pinch : Advances in understanding the reversed-field pinch improved confinement mode

Generation and sustainment of the reversed field pinch (RFP) magnetic configuration normally relies on dynamo activity. The externally applied electric field tends to drive the equilibrium away from the relaxed, minimum energy state which is roughly described by a flat normalized parallel current density profile and is at marginal stability to tearing modes. Correlated fluctuations of magnetic field and velocity create a dynamo electric field which broadens the parallel current density profile, supplying the necessary edge current drive. These pervasive magnetic fluctuations are also responsible for destruction of flux surfaces, relegating the standard RFP to a stochastic-magnetic transport-limited device. Application of a tailored electric field profile (which matches the relaxed current density profile) allows sustainment of the RFP configuration without dynamo-driven edge current. The method used to ascertain that a dynamo-free RFP plasma has been created is reported here in detail. Several confinement...

Overview of results in the MST reversed field pinch experiment

Confinement in the reversed field pinch (RFP) has been shown to increase strongly with current profile control. The MST RFP can operate in two regimes: the standard regime with a naturally occurring current density profile, robust reconnection and dynamo activity; and the improved confinement regime with strong reduction in reconnection, dynamo and transport. New results in standard plasmas include the observation of a strong two-fluid Hall effect in reconnection and dynamo, the determination that the m = 0 edge resonant mode is nonlinearly driven, and the determination that tearing modes can lock to the wall via eddy currents in the shell. New results in improved confinement plasmas include observations that such plasmas are essentially dynamo-free, contain several isolated magnetic islands (as opposed to a stochastic field) and contain reduced high frequency turbulence. Auxiliary current drive and heating is now critical to RFP research. In MST, a programme to apply auxiliary systems to the RFP is underway and progress has accrued in several techniques, including lower hybrid and electron Bernstein wave injection, ac helicity injection current drive, pellet injection and neutral beam injection.

Plasma behaviour at high β and high density in the Madison Symmetric Torus RFP

Pellet fuelling of improved confinement Madison Symmetric Torus (MST) plasmas has resulted in high density and high plasma beta. The density in improved confinement discharges has been increased fourfold, and a record plasma beta (βtot = 26%) for the improved confinement reversed-field pinch (RFP) has been achieved. At higher β, a new regime for instabilities is accessed in which local interchange and global tearing instabilities are calculated to be linearly unstable, but experimentally, no severe effect, e.g., a disruption, is observed. The tearing instability, normally driven by the current gradient, is driven by the pressure gradient in this case, and there are indications of increased energy transport (as compared with low-density improved confinement). Pellet fuelling is also compared with enhanced edge fuelling of standard confinement RFP discharges for the purpose of searching for a density limit in MST. In standard-confinement discharges, pellet fuelling peaks the density profile where edge fuelling cannot, but transport appears unchanged. For a limited range of plasma current, MST discharges with edge fuelling are constrained to a maximum density corresponding to the Greenwald limit. This limit is surpassed in pellet-fuelled improved confinement discharges.

High-β, improved confinement reversed-field pinch plasmas at high density

In Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] discharges where improved confinement is brought about by modification of the current profile, pellet injection has quadrupled the density, reaching ne=4×1019m−3. Without pellet injection, the achievable density in improved confinement discharges had been limited by edge-resonant tearing instability. With pellet injection, the total beta has been increased to 26%, and the energy confinement time is comparable to that at low density. Pressure-driven local interchange and global tearing are predicted to be linearly unstable. Interchange has not yet been observed experimentally, but there is possible evidence of pressure-driven tearing, an instability usually driven by the current gradient in the reversed-field pinch.

Momentum transport from tearing modes with shear flow

A theoretical and computational study of momentum transport from reconnection from tearing modes in the presence of sheared flow in a reversed field pinch has been performed. Momentum transport from single tearing modes in the linear and nonlinear regimes and transport from multiple tearing modes is studied. It is found that, whereas a single mode produces transport, a strong enhancement in transport arises from the nonlinear coupling of multiple modes. A single tearing mode, in the presence of equilibrium flow, produces momentum transport in the vicinity of the reconnection layer. This is demonstrated from quasilinear calculation of Maxwell and Reynolds stresses. However, nonlinear, resistive magnetohydrodynamics computation of the full, multimode nonlinear dynamics reveals an additional effect. In the presence of multiple tearing modes, nonlinear coupling strongly enhances the torques and broadens their radial width. The resulting transport from current-driven instability is much more rapid than classical viscous forces.

The three-dimensional magnetohydrodynamics of ac helicity injection in the reversed field pinch

ac magnetic helicity injection (also known as oscillating field current drive, OFCD) has been proposed as a technique to sustain the plasma current in a reversed field pinch. The three-dimensional, resistive magnetohydrodynamics computation is employed to examine the full nonlinear dynamics of OFCD, including the behavior of plasma fluctuations and instabilities. The three-dimensional results are also compared with one-dimensional classical and relaxed-state modeling. In OFCD, helicity is injected by oscillating the toroidal and poloidal surface loop voltages. This technique is able to sustain the plasma current, with the edge current mainly driven directly by the OFCD-generated fields, and the core current driven by plasma fluctuations. Fluctuations increase with OFCD, although the increase is concentrated mainly in one global, nearly ideal, mode.

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics

Relaxed states of a plasma column are found analytically in single-fluid and Hall magnetohydrodynamics (MHD). We perform complete minimization of the energy with constraints imposed by invariants inherent in the corresponding models. It is shown that the relaxed state in Hall MHD is a force-free magnetic field with uniform axial flow and/or rigid azimuthal rotation. In contrast, the relaxed states in single-fluid MHD are more complex due to the coupling between velocity and magnetic field. Cylindrically and helically symmetric relaxed states are considered for both models. Helical states may be time dependent and analogous to helical waves, propagating on a cylindrically symmetric background. Application of our results to reversed-field pinches (RFP) is discussed. The radial profile of the parallel momentum predicted by the single-fluid MHD relaxation theory is shown to be in reasonable agreement with experimental observation from the Madison symmetric torus RFP experiment.

Local measurements of tearing mode flows and the magnetohydrodynamic dynamo in the Madison Symmetric Torus reversed-field pinch

The first localized measurements of tearing mode flows in the core of a hot plasma are presented using nonperturbing measurements of the impurity ion flow. Emission from charge exchange recombination is collected by a novel high optical throughput duo spectrometer providing localized (±1 cm) measurements of C+6 impurity ion velocities resolved to <500 m/s with high bandwidth (100 kHz). Poloidal tearing mode flows in the Madison Symmetric Torus reversed-field pinch are observed to be localized to the mode resonant surface with a radial extent much broader than predicted by linear magnetohydrodynamic (MHD) theory but comparable to the magnetic island width. The relative poloidal flow amplitudes among the dominant core modes do not reflect the proportions of the magnetic amplitudes. The largest correlated flows are associated with modes having smaller magnetic amplitudes resonant near the midradius. The MHD dynamo due to these flows on the magnetic axis is measured to be adequate to balance the mean Ohm’s la...