507 research outputs found
Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas
In this work, we examine the validity of several common simplifying
assumptions used in numerical neoclassical calculations for nonaxisymmetric
plasmas, both by using a new continuum drift-kinetic code and by considering
analytic properties of the kinetic equation. First, neoclassical phenomena are
computed for the LHD and W7-X stellarators using several versions of the
drift-kinetic equation, including the commonly used incompressible-ExB-drift
approximation and two other variants, corresponding to different effective
particle trajectories. It is found that for electric fields below roughly one
third of the resonant value, the different formulations give nearly identical
results, demonstrating the incompressible ExB-drift approximation is quite
accurate in this regime. However, near the electric field resonance, the models
yield substantially different results. We also compare results for various
collision operators, including the full linearized Fokker-Planck operator. At
low collisionality, the radial transport driven by radial gradients is nearly
identical for the different operators, while in other cases it is found to be
important that collisions conserve momentum
Impurities in a non-axisymmetric plasma: transport and effect on bootstrap current
Impurities cause radiation losses and plasma dilution, and in stellarator
plasmas the neoclassical ambipolar radial electric field is often unfavorable
for avoiding strong impurity peaking. In this work we use a new continuum
drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative
Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014)
042503] which employs the full linearized Fokker-Planck-Landau operator, to
calculate neoclassical impurity transport coefficients for a Wendelstein 7-X
(W7-X) magnetic configuration. We compare SFINCS calculations with theoretical
asymptotes in the high collisionality limit. We observe and explain a
1/nu-scaling of the inter-species radial transport coefficient at low
collisionality, arising due to the field term in the inter-species collision
operator, and which is not found with simplified collision models even when
momentum correction is applied. However, this type of scaling disappears if a
radial electric field is present. We also use SFINCS to analyze how the
impurity content affects the neoclassical impurity dynamics and the bootstrap
current. We show that a change in plasma effective charge Zeff of order unity
can affect the bootstrap current enough to cause a deviation in the divertor
strike point locations.Comment: 36 pages, 13 figure
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
Local and global Fokker-Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal
In transport barriers, particularly H-mode edge pedestals, radial scale
lengths can become comparable to the ion orbit width, causing neoclassical
physics to become radially nonlocal. In this work, the resulting changes to
neoclassical flow and current are examined both analytically and numerically.
Steep density gradients are considered, with scale lengths comparable to the
poloidal ion gyroradius, together with strong radial electric fields sufficient
to electrostatically confine the ions. Attention is restricted to relatively
weak ion temperature gradients (but permitting arbitrary electron temperature
gradients), since in this limit a delta-f (small departures from a Maxwellian
distribution) rather than full-f approach is justified. This assumption is in
fact consistent with measured inter-ELM H-Mode edge pedestal density and ion
temperature profiles in many present experiments, and is expected to be
increasingly valid in future lower collisionality experiments. In the numerical
analysis, the distribution function and Rosenbluth potentials are solved for
simultaneously, allowing use of the exact field term in the linearized
Fokker-Planck collision operator. In the pedestal, the parallel and poloidal
flows are found to deviate strongly from the best available conventional
neoclassical prediction, with large poloidal variation of a different form than
in the local theory. These predicted effects may be observable experimentally.
In the local limit, the Sauter bootstrap current formulae appear accurate at
low collisionality, but they can overestimate the bootstrap current near the
plateau regime. In the pedestal ordering, ion contributions to the bootstrap
and Pfirsch-Schluter currents are also modified
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