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 (I p ∼ 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, inboardoutboard asymmetric spatial structure that peaks in the core where fast ions reside. The measured mode frequencies are close to the computed shear Alfv en 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 fast ions compared to single frequency for hydrogen fast ions. Furthermore, as the safety factor (q) decreases, the toroidal mode number of the dominant EP mode transits from n ¼ 5 to n ¼ 6 while retaining the same poloidal mode number m ¼ 1. The transition occurs when the m ¼ 1, n ¼ 5 wave-particle resonance condition cannot be satisfied as the fast-ion safety factor (q fi ) decreases. The fast-ion temporal dynamics, measured by a neutral particle analyzer, resemble a classical predator-prey relaxation oscillation. It contains a slow-growth phase arising from the beam fueling followed by a rapid drop when the EP modes peak, indicating that the fluctuation-induced transport maintains a stiff fast-ion density profile. The inferred transport rate is strongly enhanced with the onset of multiple EP modes. V C 2014 AIP Publishing LLC. [http://dx.
In planar metamaterial lenses, the focal point moves with the frequency. Here it is shown numerically that this movement can be controlled by properly engineering the dimensions of the metamaterial-based phase shifters that constitute the lens. In particular, such lenses can be designed to exhibit unusual chromatic aberration with the focal length increasing, rather than decreasing, with the frequency. It is proposed that such an artificial "reverse" chromatic aberration may optimize the transverse resolution of millimeter wave diagnostics of plasmas and be useful in compensating for the natural "ordinary" chromatic aberration of other components in an optical system. More generally, optimized chromatic aberration will allow for simultaneous focusing of several objects located at different distances and emitting or reflecting at different frequencies.
Energetic ions are well confined in the core of the reversed field pinch and a substantial population develops rapidly during tangential neutral beam injection. A saturated fast ion density is observed within several milliseconds and coincides with the onset of energetic particle mode activity. First measurements of the fusion product profile determine the fast ion density and pressure profiles, the latter of which when combined with neutral particle analysis of the energy distribution. These are key measurements in explaining the limiting behavior of the fast ion profile in response to a combination of effects. Tearing mode activity affects the fast ion profile, and the fast ions noticeably influence the core-most tearing mode. The nonlinear situation settles into a marginally stable state where the EPM transports fast ions down a steep gradient to a region where their confinement is limited by stochastic orbit and charge exchange losses. In the state at marginal stability (achieved in one set of experimental conditions with full 1 MW neutral beam power), a critical fast ion beta gradient is measured that limits the core , or nearly four times the core thermal , but less than a strictly classical calculation predicts.
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