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University of Wisconsin Physics Department

Research funding includes support from:

Department of Energy

National Science Foundation

Energy transport in conventional RFP plasmas has long been thought to result from parallel losses on stochastic magnetic field lines that wander from the core to the edge. The low safety factor in the RFP permits many possible resonant surfaces for resistive MHD tearing, the origin of the dominant magnetic fluctuations. In conventional RFP plasmas — i.e., those formed by steady toroidal induction — a spectrum of modes arises through linear tearing instability from current profile peaking and subsequent nonlinear mode coupling. These modes produce neighboring magnetic islands that are densely packed, filling the minor radius. Island overlap results in magnetic stochasticity that produces rapid radial transport.


The origin of this problem is tearing instability from current profile peaking, a consequence of ohmic current drive. The dominance of the poloidal magnetic field component in the RFP equilibrium means that simple toroidal induction cannot drive enough parallel current in the outer region of the plasma where the applied parallel electric field is small. The outer region is also more resistive, further exacerbating the current peaking tendency. When tearing sets in, the nonlinear interaction creates a dynamo emf which enters Ohm’s law to limit the current profile peaking. This is a strong effect, keeping the profile near to marginal stability. Somewhat remarkably, the dynamo emf also produces the required poloidal current in the outer region of the plasma that maintains a reversed toroidal magnetic field. Hence the formation and maintenance of this self-organized equilibrium is coupled to transport. If the scaling of the dynamo constituent fluctuations is naturally favorable, then as the plasma resistivity decreases, the required dynamo emf decreases and magnetic stochasticity could cease to be a problem for energy and particle transport. However, a suitably strong scaling for magnetic fluctuations has not been observed (particularly with Lundquist number).


An obvious alternative is to change the current drive scenario. In particular, an increase in parallel current drive in the outer region of the plasma is desired. Since this region is dominated by poloidal magnetic field, poloidal current drive is the essential added ingredient. Self-consistently, the added poloidal current drive will take the place of the dynamo emf to maintain directly toroidal field reversal. For pulsed operation, toroidal induction is still suitable for the core, and even much of the current toward the edge.


A ten-fold improvement in the confinement of energy and particles in MST plasmas has been demonstrated by reducing magnetic stochasticity associated with MHD tearing, the main cause of transport in conventional RFP plasmas. This improvement has occurred in steps over several years by modifying and refining the inductive electric field that drives the plasma current, a technique referred to as pulsed poloidal (or parallel) current drive (PPCD). For several reasons, the improved confinement in MST can be described as “tokamak-like” in relative comparison to tokamak and other strongly magnetized plasmas. For example, the electron temperature profile in PPCD plasmas is peaked, instead of flat as in standard RFP plasmas. Also, the electron heat diffusivity falls to ~5 m2/s, which is comparable to the transport level measured in tokamak plasmas of the same size and current. Fast electrons are confined, indicative of reduced magnetic stochasticity and restoration of at least some closed magnetic surfaces, as exist in strongly magnetized plasmas. The total beta value is increased to ~15% with Ohmic heating alone, which is as large (or larger) than the total demonstrated in advanced tokamak plasmas with powerful auxiliary heating. This collection of results alters the view that RFP plasmas are condemned to poor confinement.


We are working on several experimental techniques for current profile control in MST, building on our PPCD results. Establishing the ultimate lower bound of magnetic turbulence in the RFP is the overriding theme of this research, and finer control in targeting the current drive to a specified region of the plasma is a primary goal of the proposed work. An emerging theme is understanding the mechanism controlling the next layer of transport. For example, the diffusion of fast electrons in PPCD plasmas has a non-stochastic character, suggesting electrostatic turbulence might be more important, as observed in tokamak and stellarator plasmas.


A secondary goal of our planned experiments is to investigate energy, particle, and current density transport as magnetic fluctuations are varied controllably. Such a study will be highly valuable to fusion plasma physics in general. The proposed experiments aim to alter magnetic fluctuations by a large factor, producing a valuable test of theories that describe transport from the parallel streaming of particles in a fluctuating magnetic field. These theories apply generally to all toroidal magnetic configurations, and to some extent — given a magnetic fluctuation spectrum — the resultant transport is not dependent on the cause of the fluctuations. Thus, observation of the effects of a controlled variation of magnetic fluctuations on particle, energy, and current density transport is a basic experiment of broad application.


The optimal current profile control technique for present day RFP plasmas is expected to be rf current drive. Feasibility studies for two rf approaches are underway, one based on the (slow) lower hybrid (LH) wave and one based on the electron Bernstein wave (EBW). Ray tracing and Fokker-Planck calculations predict good absorption and directional control for both waves, as required for effective current drive. The LH and EBW approaches have complementary strengths. The physics and application of LHCD are well established in tokamak research, but innovation in antenna design is required for MST use. In contrast, the EBW approach benefits from simpler antenna requirements, but the wave physics is not yet well established for any high beta fusion plasma.


We are testing LHCD by launching the waves with a compact antenna structure mounted on the inner surface of the vacuum vessel wall. To date, antennas have been tested in MST plasmas up to a power level of 80 kW. During the next three years we plan a staged-power approach culminating in a medium power (~0.4 MW) current drive experiment. To test EBW current drive, a cold plasma electron cyclotron wave is being launched from a simple horn antenna structure, which mode-converts to the warm plasma EBW in the extreme edge and then propagates into the plasma. Spontaneous EBW emission from MST plasmas has been observed, suggesting the reciprocal process of transmitting the wave into the plasma will occur. During the next three years we plan a staged-power approach culminating in a medium power (~0.3 MW) current drive experiment. Subsequent higher power current drive experiments for tearing stabilization using LHCD or EBW at the MW level will be determined by the level of success at medium power.


Two other, more speculative current profile control tools might become available, motivated by other purposes. Oscillating field current drive (OFCD) is being tested for current sustainment, but it might also provide effective edge-localized current drive. Neutral beam injection is being installed primarily for auxiliary heating purposes, but it might also produce significant current drive in the core.


Magnetic fluctuation induced particle transport, for each species, is given by the product of the species’s current density fluctuations and magnetic fluctuations. Energy transport is the product of heat flux fluctuations and magnetic fluctuations. Despite their importance, only recently have techniques been developed to directly measure magnetic fluctuations in the hot plasma core. These measurements are at the leading edge of diagnostic innovation; MST has functioned both as a driver and a proving ground for this development.