B.E. Chapman

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.

Overview of RFX-mod results

With the exploration of the MA plasma current regime in up to 0.5 s long discharges, RFX-mod has opened new and very promising perspectives for the reversed field pinch (RFP) magnetic configuration, and has made significant progress in understanding and improving confinement and in controlling plasma stability. A big leap with respect to previous knowledge and expectations on RFP physics and performance has been made by RFX-mod since the last 2006 IAEA Fusion Energy Conference. A new self-organized helical equilibrium has been experimentally achieved (the Single Helical Axis—SHAx—state), which is the preferred state at high current. Strong core electron transport barriers characterize this regime, with electron temperature gradients comparable to those achieved in tokamaks, and by a factor of 4 improvement in confinement time with respect to the standard RFP. RFX-mod is also providing leading edge results on real-time feedback control of MHD instabilities, of general interest for the fusion community.

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.

Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell

Growth to large amplitude of a single core-resonant tearing mode in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch is accompanied by braking and eventual cessation of mode rotation. There is also a concurrent deceleration of bulk plasma rotation. The mode deceleration is shown to be well described by a time-dependent version of a magnetohydrodynamical model [R. Fitzpatrick et al., Phys. Plasmas 6, 3878 (1999)] in which a braking torque originates from eddy currents induced by the rotating mode in the conducting shell surrounding the plasma. According to the model, the electromagnetic braking torque is localized to the plasma in the immediate vicinity of the mode’s resonant surface, but viscosity transfers the torque to the rest of the plasma. Parametrizing the plasma viscous momentum diffusivity in terms of the global momentum confinement time, the model is used to predict both the momentum confinement time and the time evolution of the decelerating ...

High-speed three-wave polarimeter-interferometer diagnostic for Madison symmetric torus

A high-speed three-wave polarimeter-interferometer diagnostic has been developed on the Madison symmetric torus reversed field pinch to provide simultaneous measurement of electron density and poloidal magnetic field profile evolution. With increased digitizer bandwidth, polarimetry noise due to aliasing and cross-talk is minimized, and time response improved. System performance is demonstrated by measurements of equilibrium profile evolution during fast events such as the sawtooth crash and pellet injection.

Tomographic imaging of resistive mode dynamics in the Madison Symmetric Torus reversed-field pinch

A detailed study of the dynamics and magnetic topological effects of resistive-tearing modes is presented for different operational regimes in the Madison Symmetric Torus reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. Soft-x-ray tomography and magnetic measurements, along with numerical reconstruction of magnetic-field lines with the ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)], have been employed. Magnetic-mode dynamics has been investigated in standard plasmas during the transition to the quasi-single helicity state, in which a single mode dominates the mode spectrum. Single helical soft-x-ray structures are studied with tomography in these cases. These structures are associated with magnetic islands, indicating that helical flux surfaces appear in the plasma. Mode dynamics has also been examined during auxiliary inductive current drive, the goal of which is to reduce the tearing-mode amplitudes. In this case the phenomenology of the soft-x-ray str...

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.

E×B flow shear and enhanced confinement in the Madison Symmetric Torus reversed-field pinch

Strong E×B flow shear occurs in the edge of three types of enhanced confinement discharge in the Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch. Measurements in standard (low confinement) discharges indicate that global magnetic fluctuations drive particle and energy transport in the plasma core, while electrostatic fluctuations drive particle transport in the plasma edge. This paper explores possible contributions of E×B flow shear to the reduction of both the magnetic and electrostatic fluctuations and, thus, the improved confinement. In one case, shear in the E×B flow occurs when the edge plasma is biased. Biased discharges exhibit changes in the edge electrostatic fluctuations and improved particle confinement. In two other cases, the flow shear emerges (1) when auxiliary current is driven in the edge and (2) spontaneously, following sawtooth crashes. Both edge electrostatic and global magnetic fluctuations are reduced in these discharges, and both particl...

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.