Fast-ion diagnostic in fusion plasmas by velocity-space tomography

Velocity distribution functions of ions in high-performance fusion plasmas can deviate substantially from simple Maxwellian distributions. They can be strongly anisotropic or have local maxima at velocities larger than the thermal velocities. The distribution functions of the fast ions in the plasma are often the key to understanding heating, current drive, and various plasma instabilities. However, the distribution functions are unfortunately not always predictable for plasmas with instabilities. These often cause fast-ion transport that is not fully understood. The measurement of fast-ion velocity distribution functions is therefore crucial to operate high-performance plasmas for eventually harvesting energy. However, until now this measurement could not be done. The velocity-space tomography approach put forward in this thesis allows this measurement, providing a new meeting ground between theory and observation. This allows studies of the behavior of fast ions in fusion plasmas at an unprecedented level of detail.
Traditionally fast-ion measurements are presented in terms of spectra of a measured quantity that is particular to each diagnostic, e.g. the power density of radiation, photon or particle count rates, or the times-of-flight in a detector. These spectra in diagnostic measurables are then compared with synthetic spectra based on numerical simulations. The results of such comparisons are often hard to interpret since it is not immediately clear how to attribute any discrepancies between measurements and predictions to the fast-ion distributions. To exploit the rich information about fast ions contained in the spectra by traditional procedures, we need to consider hundreds of measurements, keeping in mind nuisance parameters and the complicated relationships between the measurements and velocity space. Borrowing from usual position-space tomography, velocity-space tomography provides a way to process this wealth of information at once. It provides a 2D image that is straightforward to interpret, is the best useful fit to hundreds of simultaneous measurements, combines data from different diagnostics, shows the fundamental quantity of interest rather than quantities of secondary interest, and accounts for nuisance parameters.
Until today measurements by the diagnostics fast-ion D-alpha spectroscopy, collective Thomson scattering, neutron emission spectrometry, gamma-ray spectroscopy, and fast-ion loss detectors installed at the tokamaks ASDEX Upgrade, JET, MAST, DIII-D, and EAST have been interpreted using velocity-space tomography. We have measured strongly non-Maxwellian fast-ion velocity distribution functions in plasmas heated by neutral beam injection and by electromagnetic wave heating in the ion cyclotron range of frequencies. The interaction of energetic particles with plasma instabilities has revealed strong selectivity in velocity space. This has filled gaps in our yet incomplete understanding of the physics of the redistribution of fast ions due sawteeth, neoclassical tearing modes, and Alfvén eigenmodes. Fast-ion densities have been measured for the first time, and first movies following the time evolution of the fast-ion velocity distribution function in plasmas with instabilities have been presented. Velocity-space tomography based on the foreseen set of fast-ion diagnostics at the next-step fusion device ITER has revealed that co-passing and counter-passing particles, which are two out of three major classes of particles in tokamaks, cannot be told apart. An additional detector is now proposed that would allow this distinction.
Velocity-space tomography has also revealed the density, drift velocity, and anisotropic temperatures of the thermal ions, has deblurred measurements with fast-ion loss detectors, and has provided a new approach to interpret gamma-ray measurements of runaway electrons. This thesis describes the development of velocity-space tomography and demonstrates its utility for the interpretation of fast-ion measurements.