Measurement of a 2D fast-ion velocity distribution function by tomographic inversion of fast-ion D-alpha spectra

We present the first measurement of a local fast-ion 2D velocity distribution function f(v||, v⊥). To this end, we heated a plasma in ASDEX Upgrade by neutral beam injection and measured spectra of fast-ion Dα (FIDA) light from the plasma centre in three views simultaneously. The measured spectra agree very well with synthetic spectra calculated from a TRANSP/NUBEAM simulation. Based on the measured FIDA spectra alone, we infer f(v||, v⊥) by tomographic inversion. Salient features of our measurement of f(v||, v⊥) agree reasonably well with the simulation: the measured as well as the simulated f(v||, v⊥) are lopsided towards negative velocities parallel to the magnetic field, and they have similar shapes. Further, the peaks in the simulation of f(v||, v⊥) at full and half injection energies of the neutral beam also appear in the measurement at similar velocity-space locations. We expect that we can measure spectra in up to seven views simultaneously in the next ASDEX Upgrade campaign which would further improve measurements of f(v||, v⊥) by tomographic inversion

Strong Scattering of High Power Millimeter Waves in Tokamak Plasmas with Tearing Modes

In tokamak plasmas with a tearing mode, strong scattering of high power millimeter waves, as used for heating and noninductive current drive, is shown to occur. This new wave scattering phenomenon is shown to be related to the passage of the O point of a magnetic island through the high power heating beam. The density determines the detailed phasing of the scattered radiation relative to the O-point passage. The scattering power depends strongly nonlinearly on the heating beam power

High-definition velocity-space tomography of fast-ion dynamics

Velocity-space tomography of the fast-ion distribution function in a fusion plasma is usually a photon-starved tomography method due to limited optical access and signal-to-noise ratio of fast-ion Dα (FIDA) spectroscopy as well as the strive for high-resolution images. In high-definition tomography, prior information makes up for this lack of data. We restrict the target velocity space through the measured absence of FIDA light, impose phase-space densities to be non-negative, and encode the known geometry of neutral beam injection (NBI) sources. We further use a numerical simulation as prior information to reconstruct where in velocity space the measurements and the simulation disagree. This alternative approach is demonstrated for four-view as well as for two-view FIDA measurements. The high-definition tomography tools allow us to study fast ions in sawtoothing plasmas and the formation of NBI peaks at full, half and one-third energy by time-resolved tomographic movies

Deuterium temperature, drift velocity, and density measurements in non-Maxwellian plasmas at ASDEX Upgrade

We measure the deuterium density, the parallel drift velocity, and parallel and perpendicular temperatures (T∥, T⊥) in non-Maxwellian plasmas at ASDEX Upgrade. This is done by taking moments of the ion velocity distribution function measured by tomographic inversion of five simultaneously acquired spectra of Dα-light. Alternatively, we fit the spectra using a bi-Maxwellian distribution function. The measured kinetic temperatures (T∥ = 9 keV, T⊥ = 11 keV) reveal the anisotropy of the plasma and are substantially higher than the measured boron temperature (7 keV). The Maxwellian deuterium temperature computed with TRANSP (6 keV) is not uniquely measurable due to the fast ions. Nevertheless, simulated kinetic temperatures accounting for fast ions based on TRANSP (T∥= 8.3 keV, T⊥ = 10.4 keV) are in excellent agreement with the measurements. Similarly, the Maxwellian deuterium drift velocity computed with TRANSP (300 km s-1) is not uniquely measurable, but the simulated kinetic drift velocity accounting for fast ions agrees with the measurements (400 km s-1) and is substantially larger than the measured boron drift velocity (270 km s-1). We further find that ion cyclotron resonance heating elevates T∥ and T⊥ each by 2 keV without evidence for preferential heating in the Dα spectra. Lastly, we derive an expression for the 1D projection of an arbitrarily drifting bi-Maxwellian onto a diagnostic line-of-sight

Tomography of fast-ion velocity-space distributions from synthetic CTS and FIDA measurements

We compute tomographies of 2D fast-ion velocity distribution functions from synthetic collective Thomson scattering (CTS) and fast-ion D-alpha (FIDA) 1D measurements using a new reconstruction prescription. Contradicting conventional wisdom we demonstrate that one single 1D CTS or FIDA view suffices to compute accurate tomographies of arbitrary 2D functions under idealized conditions. Under simulated experimental conditions, single-view tomographies do not resemble the original fast-ion velocity distribution functions but nevertheless show their coarsest features. For CTS or FIDA systems with many simultaneous views on the same measurement volume, the resemblance improves with the number of available views, even if the resolution in each view is varied inversely proportional to the number of views, so that the total number of measurements in all views is the same. With a realistic four-view system, tomographies of a beam ion velocity distribution function at ASDEX Upgrade reproduce the general shape of the function and the location of the maxima at full and half injection energy of the beam ions. By applying our method to real many-view CTS or FIDA measurements, one could determine tomographies of 2D fast-ion velocity distribution functions experimentally

Combination of fast-ion diagnostics in velocity-space tomographies:Paper

Fast-ion Dα (FIDA) and collective Thomson scattering (CTS) diagnostics provide indirect measurements of fastion velocity distribution functions in magnetically confined plasmas. Here we present the first prescription for velocity-space tomographic inversion of CTS and FIDA measurements that can use CTS and FIDA measurements together and that takes uncertainties in such measurements into account. Our prescription is general and could be applied to other diagnostics. We demonstrate tomographic reconstructions of an ASDEX Upgrade beam ion velocity distribution function. First, we compute synthetic measurements from two CTS views and two FIDA views using a TRANSP/NUBEAM simulation, and then we compute joint tomographic inversions in velocity-space from these. The overall shape of the 2D velocity distribution function and the location of the maxima at full and half beam injection energy are well reproduced in velocity-space tomographic inversions, if the noise level in the measurements is below 10%. Our results suggest that 2D fast-ion velocity distribution functions can be directly inferred from fast-ion measurements and their uncertainties, even if the measurements are taken with different diagnostic methods