While reconnection-driven ion heating is common in laboratory and astrophysical plasmas, the underlying mechanisms for converting magnetic to kinetic energy remain not fully understood. Reversed field pinch discharges are often characterized by rapid ion heating during impulsive reconnection, generating an ion distribution with an enhanced bulk temperature, mainly perpendicular to magnetic field. In the Madison Symmetric Torus, a subset of discharges with the strongest reconnection events develop a very anisotropic, high energy tail parallel to magnetic field in addition to bulk perpendicular heating, which produces a fusion neutron flux orders of magnitude higher than that expected from a Maxwellian distribution. Here, we demonstrate that two factors in addition to a perpendicular bulk heating mechanism must be considered to explain this distribution. First, ion runaway can occur in the strong parallel-to-B electric field induced by a rapid equilibrium change triggered by reconnection-based relaxation; this effect is particularly strong on perpendicularly heated ions which experience a reduced frictional drag relative to bulk ions. Second, the confinement of ions varies dramatically as a function of velocity. Whereas thermal ions are governed by stochastic diffusion along tearing-altered field lines (and radial diffusion increases with parallel speed), sufficiently energetic ions are well confined, only weakly affected by a stochastic magnetic field. High energy ions traveling mainly in the direction of toroidal plasma current are nearly classically confined, while counter-propagating ions experience an intermediate confinement, greater than that of thermal ions but significantly less than classical expectations. The details of ion confinement tend to reinforce the asymmetric drive of the parallel electric field, resulting in a very asymmetric, anisotropic distribution.

Ion runaway in the presence of a large-scale, reconnection-driven electric field has been conclusively measured in the Madison Symmetric Torus reversed-field pinch (RFP). Measurements of the acceleration of a beam of fast ions agree well with test particle and Fokker-Planck modeling of the runaway process. However, the runaway mechanism does not explain all measured ion heating in the RFP, particularly previous measurements of strong perpendicular heating. It is likely that multiple energization mechanisms occur simultaneously and with differing significance for magnetically coupled thermal ions and magnetically decoupled tail and beam ions.

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.

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. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4798397]

An overview of recent results from the MST programme on physics important for the advancement of the reversed field pinch (RFP) as well as for improved understanding of toroidal magnetic confinement more generally is reported. Evidence for the classical confinement of ions in the RFP is provided by analysis of impurity ions and energetic ions created by 1 MW neutral beam injection (NBI). The first appearance of energetic-particle-driven modes by NBI in a RFP plasma is described. MST plasmas robustly access the quasi-single-helicity state that has commonalities to the stellarator and 'snake' formation in tokamaks. In MST the dominant mode grows to 8% of the axisymmetric field strength, while the remaining modes are reduced. Predictive capability for tearing mode behaviour has been improved through nonlinear, 3D, resistive magnetohydrodynamic computation using the measured resistivity profile and Lundquist number, which reproduces the sawtooth cycle dynamics. Experimental evidence and computational analysis indicates two-fluid effects, e.g., Hall physics and gyro-viscosity, are needed to understand the coupling of parallel momentum transport and current profile relaxation. Large Reynolds and Maxwell stresses, plus separately measured kinetic stress, indicate an intricate momentum balance and a possible origin for MST's intrinsic plasma rotation. Gyrokinetic analysis indicates that micro-tearing modes can be unstable at high beta, with a critical gradient for the electron temperature that is larger than for tokamak plasmas by roughly the aspect ratio.

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.

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-Alfvénic ion density of up to 25% of the electron density with both a significant velocity space gradient and a sharp radial density gradient. There are several effects on the background plasma including enhanced toroidal rotation, electron heating, and an altered current density profile. The abundant fast particles affect the plasma stability. Fast ions at the island of the core-most resonant tearing mode have a stabilizing effect, and up to 60% reduction in the magnetic fluctuation amplitude is observed during NBI. The sharp reduction in amplitude, however, has little effect on the underlying magnetic island structure. Simultaneously, beam driven instabilities are observed as repetitive ∼50 μs bursts which coincide with fast particle redistribution; data indicate a saturated core fast ion density well below purely classical predictions.

A new E∥B neutral particle analyzer, which has recently been installed on Madison Symmetric Torus (MST) reversed-field pinch (RFP), has now been calibrated, allowing the measurement of the fast ion density and energy distribution. This diagnostic, dubbed the advanced neutral particle analyzer (ANPA), can simultaneously produce time resolved measurements of the efflux of both hydrogen and deuterium ions from the plasma over a 35 keV energy range with an energy resolution of 2-4 keV and a time resolution of 10 μs. These capabilities are needed to measure both majority ion heating that occurs during magnetic reconnection events in MST and the behavior of the fast ions from the 1 MW hydrogen neutral beam injector on MST. Calibration of the ANPA was performed using a custom ion source that resides in the flight tube between the MST and the ANPA. In this work, the ANPA will be described, the calibration procedure and results will be discussed, and initial measurements of the time evolution of 25 keV neutral beam injection-born fast ions will be presented.