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Plasmas in the MST reversed field pinch bifurcate to a helical equilibrium, forming a Single Helical Axis (SHAx) at high plasma current (Ip?500 kA) and low density (ne?0.5 x 1019 m-3). Modeling of these plasmas requires an equilibrium solver that does not assume axisymmetry. The V3FIT 3D equilibrium reconstruction code is applied to helical equilibria with diagnostic measurements as constraints. The 11-chord interferometer-polarimeter, 22-point Thomson scattering system, and 4-camera soft X-ray probes have been included in addition to external magnetics. Inputs have been adapted for MST's close-fitting conducting shell. Investigations into the role of shell eddy currents have been made, including comparison to eigenfunctions generated from the Newcomb equation. At the plasma boundary, ?60{\%} of the static n=5 toroidal field BT seen by magnetic probes is generated by currents in the shell. The generated VMEC equilibrium serves as the input for applications relevant to the 1 MW, 25 keV neutral beam injector. During beam injection, fast ion confinement is reduced in periods with a SHAx compared to axisymmetric plasmas. A single particle orbit code has been applied to calculate particle trajectories in the 3D case, confirming a strong influence of SHAx equilibria on fast ion orbits. EPM magnetic bursts terminate at the transition to SHAx. Alfv\'{e}n continua have been generated to study this phenomenon with the reduced-MHD code STELLGAP. Work Supported by USDoE and NSF.

The modification of the shear Alfven spectrum due to a core resonant magnetic island is used to explain the Alfvenic activity observed on the Madison symmetric torus (MST) reversed-field pinch during neutral beam injection. Theoretical studies show that the Alfven continua in the core of the island provide a gap in which the observed Alfvenic bursts reside. Numerical simulations using a new code called SIESTAlfven have identified the bursts as the first observation of an island-induced Alfven eigenmode (IAE) in an RFP. The IAE arises from a helical coupling of harmonics due to the magnetic island.

In order to characterize the Madison Symmetric Torus (MST) reversed-field pinch (RFP) plasmas that bifurcate to a helical equilibrium, the V3FIT equilibrium reconstruction code was modified to include a conducting boundary. RFP plasmas become helical at a high plasma current, which induces large eddy currents in MST's thick aluminum shell. The V3FIT conducting boundary accounts for the contribution from these eddy currents to external magnetic diagnostic coil signals. This implementation of V3FIT was benchmarked against MSTFit, a 2D Grad-Shafranov solver, for axisymmetric plasmas. The two codes both fit Bθ measurement loops around the plasma minor diameter with qualitative agreement between each other and the measured field. Fits in the 3D case converge well, with q-profile and plasma shape agreement between two distinct toroidal locking phases. Greater than 60% of the measured n = 5 component of Bθ at r = a is due to eddy currents in the shell, as calculated by the conducting boundary model.

Alfvenic modes are observed due to neutral beam injection for the first time in a reversed field pinch plasma. Modeling of the beam deposition and slowing down shows that the velocity and radial localization are high. This allows instability drive from inverse Landau damping of a bump-on-tail in the parallel distribution function or from free energy in the fast ion density gradient. Mode switching from a lower frequency toroidal mode number n = 5 mode that scales with beam injection velocity to a higher frequency n = 4 mode with Alfvenic scaling is observed.

Fast ions are well confined in the stochastic magnetic field of the multiple-helicity (MH) reversed-field pinch (RFP), with fast ion confinement times routinely a factor of 5 to 10 higher than thermal confinement time. Recent experiments have examined the behavior and confinement of beam-born fast ions in the three-dimensional (3D) helical RFP state. In lower current discharges, where the onset of the helical state is uncertain, high power neutral beam injection (NBI) tends to suppress the transition to the single helicity mode. In high current discharges (Ip ~ 0.5 MA), where the onset of n = 5 single helicity is quite robust, a short blip of NBI is used to probe the confinement of fast ions with minimal perturbation to the 3D equilibrium. The fast ion confinement time is measured to be substantially lower than fast ions in comparable MH RFP states, and there is a strong dependence on the strength of the helical perturbation. The established helical equilibrium is stationary in the laboratory frame but the locking occurs over the entire range of possible phase with respect to the Madison Symmetric Torus vessel. This effectively scans both the location of the NBI with respect to the helical structure and the pitch of the NBI-born fast ions. Fast ion confinement is observed to be insensitive to this angle, and in fact counter-NB injection into quasi-single helicity discharges shows fast ion confinement times similar to co-injection cases, in contrast to the MH RFP, where counter-injected fast ion confinement time is substantially lower.

Multiple bursty energetic-particle (EP) driven modes with fishbone-like structure are observed during 1 MW tangential neutral-beam injection in a reversed field pinch (RFP) device. The distinguishing features of the RFP, including large magnetic shear (tending to add stability) and weak toroidal magnetic field (leading to stronger drive), provide a complementary environment to tokamak and stellarator configurations for exploring basic understanding of EP instabilities. Detailed measurements of the EP mode characteristics and temporal-spatial dynamics reveal their influence on fast ion transport. Density fluctuations exhibit a dynamically evolving, inboard-outboard asymmetric spatial structure that peaks in the core where fast ions reside. The measured mode frequencies are close to the computed shear Alfven frequency, a feature consistent with continuum modes destabilized by strong drive. The frequency pattern of the dominant mode depends on the fast-ion species. Multiple frequencies occur with deuterium f...

The behavior of energetic ions is fundamentally important in the study of fusion plasmas. While well-studied in tokamak, spherical torus, and stellarator plasmas, relatively little is known in reversed field pinch plasmas about the dynamics of fast ions and the effects they cause as a large population. These studies are now underway in the Madison Symmetric Torus with an intense 25 keV, 1 MW hydrogen neutral beam injector (NBI). Measurements of the time-resolved fast ion distribution via a high energy neutral particle analyzer, as well as beam-target neutron flux (when NBI fuel is doped with 3–5% D2) both demonstrate that at low concentration the fast ion population is consistent with classical slowing of the fast ions, negligible cross-field transport, and charge exchange as the dominant ion loss mechanism. A significant population of fast ions develops; simulations predict a super-Alfvenic ion density of up to 25% of the electron density with both a significant velocity space gradient and a sharp radial...

Internal fluctuations arising from energetic-particle-driven instabilities, including both density and radial magnetic field, are measured in a reversed-field-pinch plasma. The fluctuations peak near the core where fast ions reside and shift outward along the major radius as the instability transits from the n = 5 to n = 4 mode. During this transition, strong nonlinear three-wave interaction among multiple modes accompanied by enhanced fast-ion transport is observed.