Mathias Hoppe

SOFT: A synthetic synchrotron diagnostic for runaway electrons

Improved understanding of the dynamics of runaway electrons can be obtained by measurement and interpretation of their synchrotron radiation emission. Models for synchrotron radiation emitted by relativistic electrons are well established, but the question of how various geometric effects -- such as magnetic field inhomogeneity and camera placement -- influence the synchrotron measurements and their interpretation remains open. In this paper we address this issue by simulating synchrotron images and spectra using the new synthetic synchrotron diagnostic tool SOFT (Synchrotron-detecting Orbit Following Toolkit). We identify the key parameters influencing the synchrotron radiation spot and present scans in those parameters. Using a runaway electron distribution function obtained by Fokker-Planck simulations for parameters from an Alcator C-Mod discharge, we demonstrate that the corresponding synchrotron image is well-reproduced by SOFT simulations, and we explain how it can be understood in terms of the parameter scans. Geometric effects are shown to significantly influence the synchrotron spectrum, and we show that inherent inconsistencies in a simple emission model (i.e. not modeling detection) can lead to incorrect interpretation of the images.

Interpretation of runaway electron synchrotron and bremsstrahlung images

The crescent spot shape observed in DIII-D runaway electron synchrotron radiation images is shown to result from the high degree of anisotropy in the emitted radiation, the finite spectral range of the camera and the distribution of runaways. The finite spectral camera range is found to be particularly important, as the radiation from the high-field side can be stronger by a factor 106than the radiation from the low-field side in DIII-D. By combining a kinetic model of the runaway dynamics with a synthetic synchrotron diagnostic we see that physical processes not described by the kinetic model (such as radial transport) are likely to be limiting the energy of the runaways. We show that a population of runaways with lower dominant energies and larger pitch-angles than those predicted by the kinetic model provide a better match to the synchrotron measurements. Using a new synthetic bremsstrahlung diagnostic we also simulate the view of the gamma ray imager diagnostic used at DIII-D to resolve the spatial distribution of runaway-generated bremsstrahlung.

Spatiotemporal evolution of runaway electrons from synchrotron images in Alcator C-Mod

In the Alcator C-Mod tokamak, relativistic runaway electron (RE) generation can occur during the flattop current phase of low density, diverted plasma discharges. Due to the high toroidal magnetic field (B = 5.4 T), RE synchrotron radiation is measured by a wide-view camera in the visible wavelength range (~400-900 nm). In this paper, a statistical analysis of over one thousand camera images is performed to investigate the plasma conditions under which synchrotron emission is observed in C-Mod. In addition, the spatiotemporal evolution of REs during one particular discharge is explored in detail via a thorough analysis of the distortion-corrected synchrotron images. To accurately predict RE energies, the kinetic solver CODE [Landreman et al 2014 Comput. Phys. Commun. 185 847-855] is used to evolve the electron momentum-space distribution at six locations throughout the plasma: the magnetic axis and flux surfaces q = 1, 4/3, 3/2, 2, and 3. These results, along with the experimentally-measured magnetic topology and camera geometry, are input into the synthetic diagnostic SOFT [Hoppe et al 2018 Nucl. Fusion 58 026032] to simulate synchrotron emission and detection. Interesting spatial structure near the surface q = 2 is found to coincide with the onset of a locked mode and increased MHD activity. Furthermore, the RE density profile evolution is fit by comparing experimental to synthetic images, providing important insight into RE spatiotemporal dynamics.

Measurements of runaway electron synchrotron spectra at high magnetic fields in Alcator C-Mod

In the Alcator C-Mod tokamak, runaway electron (RE) experiments have been performed during low density, flattop plasma discharges at three magnetic fields: 2.7, 5.4, and 7.8 T, the last being the highest field to-date at which REs have been generated and measured in a tokamak. Time-evolving synchrotron radiation spectra were measured in the visible wavelength range (~300-1000 nm) by two absolutely-calibrated spectrometers viewing co- and counter-plasma current directions. In this paper, a test particle model is implemented to predict momentum-space and density evolutions of REs on the magnetic axis and q = 1, 3/2, and 2 surfaces. Drift orbits and subsequent loss of confinement are also incorporated into the evolution. These spatiotemporal results are input into the new synthetic diagnostic SOFT [M. Hoppe, et al., Nucl. Fusion 58(2), 026032 (2018)] which reproduces experimentally-measured spectra. For these discharges, it is inferred that synchrotron radiation dominates collisional friction as a power loss mechanism and that RE energies decrease as magnetic field is increased. Additionally, the threshold electric field for RE generation, as determined by hard X-ray and photo-neutron measurements, is compared to current theoretical predictions.