943 research outputs found
Numerical calculation of the runaway electron distribution function and associated synchrotron emission
Synchrotron emission from runaway electrons may be used to diagnose plasma
conditions during a tokamak disruption, but solving this inverse problem
requires rapid simulation of the electron distribution function and associated
synchrotron emission as a function of plasma parameters. Here we detail a
framework for this forward calculation, beginning with an efficient numerical
method for solving the Fokker-Planck equation in the presence of an electric
field of arbitrary strength. The approach is continuum (Eulerian), and we
employ a relativistic collision operator, valid for arbitrary energies. Both
primary and secondary runaway electron generation are included. For cases in
which primary generation dominates, a time-independent formulation of the
problem is described, requiring only the solution of a single sparse linear
system. In the limit of dominant secondary generation, we present the first
numerical verification of an analytic model for the distribution function. The
numerical electron distribution function in the presence of both primary and
secondary generation is then used for calculating the synchrotron emission
spectrum of the runaways. It is found that the average synchrotron spectra
emitted from realistic distribution functions are not well approximated by the
emission of a single electron at the maximum energy
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
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 than 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
(GRI) diagnostic used at DIII-D to resolve the spatial distribution of
runaway-generated bremsstrahlung.Comment: 21 pages, 11 figure
Dynamics of positrons during relativistic electron runaway
Sufficiently strong electric fields in plasmas can accelerate charged
particles to relativistic energies. In this paper we describe the dynamics of
positrons accelerated in such electric fields, and calculate the fraction of
created positrons that become runaway accelerated, along with the amount of
radiation that they emit. We derive an analytical formula that shows the
relative importance of the different positron production processes, and show
that above a certain threshold electric field the pair production by photons is
lower than that by collisions. We furthermore present analytical and numerical
solutions to the positron kinetic equation; these are applied to calculate the
fraction of positrons that become accelerated or thermalized, which enters into
rate equations that describe the evolution of the density of the slow and fast
positron populations. Finally, to indicate operational parameters required for
positron detection during runaway in tokamak discharges, we give expressions
for the parameter dependencies of detected annihilation radiation compared to
bremsstrahlung detected at an angle perpendicular to the direction of runaway
acceleration. Using the full leading order pair production cross section, we
demonstrate that previous related work has overestimated the collisional pair
production by at least a factor of four
Spatiotemporal analysis of the runaway distribution function from synchrotron images in an ASDEX Upgrade disruption
Synchrotron radiation images from runaway electrons (REs) in an ASDEX Upgrade discharge disrupted by argon injection are analysed using the synchrotron diagnostic tool Soft and coupled fluid-kinetic simulations. We show that the evolution of the runaway distribution is well described by an initial hot-tail seed population, which is accelerated to energies between 25-50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. We find that, although the avalanche component carries the vast majority of the current, it is the high-energy seed remnant that dominates synchrotron emission. With insights from the fluid-kinetic simulations, an analytic model for the evolution of the runaway seed component is developed and used to reconstruct the radial density profile of the RE beam. The analysis shows that the observed change of the synchrotron pattern from circular to crescent shape is caused by a rapid redistribution of the radial profile of the runaway density
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