Paul Nonn

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.

The Phaedrus-T antenna system

Abstract A two strap fast wave antenna has been developed which is capable of operating at arbitrary phasing for any level of plasma loading resistance. Recent advances in the understanding of the rf-edge plasma interaction have been incorporated in the design as well. The result is an antenna which operates without Faraday shielding while greatly reducing rf-induced scrape-off layer perturbations and impurity influx.

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.

Alfvén wave experiments in the Phaedrus‐T tokamak*

Heating in the Alfven resonant regime has been demonstrated in the Phaedrus‐T tokamak [Fusion Technol. 19, 1327 (1991)]. Electron heating during injection of radio‐frequency (rf) power is indicated by a 30%–40% drop in loop voltage and modifications in sawtooth activity. Heating was observed at a frequency ωrf≊0.7Ωi on axis, using a two‐strap fast wave antenna operated at 7 and 9.2 MHz with 180° phasing (N∥∼100). Numerical modeling with the fast wave code fastwa [Plasma Phys. Controlled Fusion 33, 417 (1991)] indicates that for Phaedrus‐T parameters the kinetic Alfven wave is excited via mode conversion from a surface fast wave at the Alfven resonance and is subsequently damped on electrons.

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.

Alfvén wave current drive in the Phaedrus‐T tokamak

The first experimental evidence of Alfven Wave Current Drive (AWCD) in a tokamak is shown. In a low‐density experiment, an estimated 20–35 kA out of 65 kA total current, or 30%–55% of the total current has been driven. The estimated efficiency for current driven per unit RF input power is approximately ICD/PRF≊0.2 A/W, which is near the predicted efficiency, and corresponds to the commonly used figure of merit, neR0ICD/PRF≊0.4×1018 A m−2 W−1, where ne is plasma density and R0 is the major radius. The significant 30%–40% drop in loop voltage observed cannot be explained by any plausible increase in electron temperature Te, or decrease in inductive plasma energy, or changes in plasma resistivity. Independently measured loop voltage, Te, effective ionic charge Zeff, and plasma inductance and resistance are all consistent with this conclusion.

An improved capacitive divider probe for plasma potential measurements in the phaedrus tokamak

High bandwidth capacitive probes are useful tools for potentials measurements in the tokamak scrape off layer. An improved capacitive divider probe design with very high frequency bandwidth is shown. The gain of this system is between 0 and −8 dB for frequencies from 0.1 Hz to more than 100 MHz, with the −3 dB point at approximately 40 MHz. The probe structure, circuits, performance, and experimental results from the Phaedrus‐T tokamak are given.

Recent improvements in confinement and beta in the MST reversed-field pinch

In the general area of confinement improvement and concept advancement, recent results in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) include good confinement of both thermal and large-orbit ions and near doubling of total beta to 26% with deuterium pellet injection. Current profile control enables MST to reduce stochastic transport and achieve tokamak-like confinement. In standard RFP operation, substantial MHD tearing mode activity results in stochastic transport and an energy confinement time of about 1 ms in MST. Application of inductive current profile control reduces MHD activity and accompanying stochasticity, improving confinement by about a factor of ten. Previous work concentrated on electron confinement in improved-confinement RFP operation. Recent work confirms that ions are also well confined, and that high beta and improved confinement can be achieved simultaneously. PACS numbers: 52.55.Hc, 52.55.Dy (Some figures in this article are in colour only in the electronic version)

Alfvén ion–ion hybrid wave heating in the Phaedrus‐T tokamak

In the Phaedrus‐T tokamak [R. A. Breun et al., Fusion Technol. 19, 1327 (1991)], Alfven waves are indirectly driven by a fast wave antenna array. Small fractions of minority ions are shown to have a large effect on the Alfven spectrum, as measured at the edge. An ion–ion hybrid Alfven mode has been identified by measuring dispersion properties. Landau damping is predicted to be large and spatially localized. These Alfvenic waves are experimentally shown to generate correlated electron heating and changes in density near the core of the tokamak plasma. Fast wave antenna fields can mode convert at a hybrid Alfven resonance and provide a promising route to spatially localized tokamak heating and current drive, even for low effective ionic charge Zeff≊1.3–2.