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 tenfold (to ∼10 ms), which is comparable with Land 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.

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The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.

The National Spherical Torus Experiment (NSTX) has undergone a major upgrade, and the NSTX Upgrade (NSTX-U) Project was completed in the summer of 2015. NSTX-U first plasma was subsequently achieved, diagnostic and control systems have been commissioned, the H-mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During ten run weeks of operation, NSTX-U surpassed NSTX record pulse-durations and toroidal fields (TF), and high-performance ~1 MA H-mode plasmas comparable to the best of NSTX have been sustained near and slightly above the n  =  1 no-wall stability limit and with H-mode confinement multiplier H98y,2 above 1. Transport and turbulence studies in L-mode plasmas have identified the coexistence of at least two ion-gyro-scale turbulent micro-instabilities near the same radial location but propagating in opposite (i.e. ion and electron diamagnetic) directions. These modes have the characteristics of ion-temperature gradient and micro-tearing modes, respectively, and the role of these modes in contributing to thermal transport is under active investigation. The new second more tangential neutral beam injection was observed to significantly modify the stability of two types of Alfven eigenmodes. Improvements in offline disruption forecasting were made in the areas of identification of rotating MHD modes and other macroscopic instabilities using the disruption event characterization and forecasting code. Lastly, the materials analysis and particle probe was utilized on NSTX-U for the first time and enabled assessments of the correlation between boronized wall conditions and plasma performance. These and other highlights from the first run campaign of NSTX-U are described.

The saturation mechanism of Magneto-Rotational Instability (MRI) is examined through analytical quasilinear theory and through nonlinear computation of a single mode in a rotating disk. We find that large-scale magnetic field is generated through the alpha effect (the correlated product of velocity and magnetic field fluctuations) and causes the MRI mode to saturate. If the large-scale plasma flow is allowed to evolve, the mode can also saturate through its flow relaxation. In astrophysical plasmas, for which the flow cannot relax because of gravitational constraints, the mode saturates through field generation only.available in accretion disks and other astrophysical settings because of strong gravitational constraints that maintain a Keplerian profile (V φ ∝ r −1/2 ). Instead, the MRI may saturate (cease linear growth) if the non-linear evolution of the instability generates a mean component of the magnetic field that is sufficient to stabilize the mode.We remark that for most plasma instabilities, if the energy source is fixed and unvarying (and nonlinear coupling to other modes is ignored), the mode will grow without bound, until limited by dissipation or some physical dimension of the system. In this sense, the MRI might be atypical.In this paper we investigate the linear growth and non-linear saturation mechanism and amplitude of a single MRI mode in thick-disk geometry, i.e., L r ∼ 1. Our primary tool is linear and non-linear MHD computation in cylindrical (r, φ, z) geometry which is periodic in the azimuthal (φ) and axial (z) directiona. We solve a model initial value problem in which the inner and outer radial boundaries are impermeable, perfectly conducting, concentric cylinders that can rotate independently at specified rates. They are coupled to the internal flow by hydrodynamic viscosity. The initial mean (azimuthally and axially averaged) profile V φ (r) is Keplerian, and in most cases is assumed to be maintained for all times by external forces. Perturbations to the equilibrium that depend on (r, φ, z) are then introduced, and evolve dynamically according to the single fluid MHD equations. Linear growth rates and eigenfunctions are found by integrating the linearized, single fluid, visco-resistive MHD equations forward in time until an exponentially growing solution is obtained. The saturation mechanism and amplitude of the mode are determined by solving the non-linear MHD equations for a single mode, with azimuthal mode number m and axial mode number k, beginning from a small initial perturbation. At finite amplitude, the mode will interact with itself to modify the mean background state, which in turn alters both its temporal evolution and its radial dependence. In this sense it differs from a quasi-linear calculation,