1,386 research outputs found
Impurity transport in temperature gradient driven turbulence
In the present paper the transport of impurities driven by trapped electron
(TE) mode turbulence is studied. Non-linear (NL) gyrokinetic simulations using
the code GENE are compared with results from quasilinear (QL) gyrokinetic
simulations and a computationally efficient fluid model. The main focus is on
model comparisons for electron temperature gra- dient driven turbulence
regarding the sign of the convective impurity velocity (pinch) and the impurity
density gradient R/LnZ (peaking factor) for zero impurity flux. In particular,
the scaling of the impurity peaking factors with impurity charge Z and with
driving temper- ature gradient is investigated and compared with the results
for Ion Temperature Gradient (ITG) driven turbulence. In addition, the impurity
peaking is compared to the main ion peaking obtained by a self-consistent fluid
calculation of the density gradients corresponding to zero particle fluxes.
For the scaling of the peaking factor with impurity charge Z, a weak
dependence is obtained from NL GENE and fluid simulations. The QL GENE results
show a stronger dependence for low Z impurities and overestimates the peaking
factor by up to a factor of two in this region. As in the case of ITG dominated
turbulence, the peaking factors saturate as Z increases, at a level much below
neoclassical predictions. However, the scaling with Z is weak or reversed as
compared to the ITG case.
The scaling of impurity peaking with the background temperature gradients is
found to be weak in the NL GENE and fluid simulations. The QL results are also
here found to significantly overestimate the peaking factor for low Z values.
For the parameters considered, the background density gradient for zero
particle flux is found to be slightly larger than the corresponding impurity
zero flux gradient.Comment: 23 pages, 13 figures. Submitted to AIP: Physics of Plasma
Collisionless microinstabilities in stellarators II - numerical simulations
Microinstabilities exhibit a rich variety of behavior in stellarators due to
the many degrees of freedom in the magnetic geometry. It has recently been
found that certain stellarators (quasi-isodynamic ones with maximum-
geometry) are partly resilient to trapped-particle instabilities, because
fast-bouncing particles tend to extract energy from these modes near marginal
stability. In reality, stellarators are never perfectly quasi-isodynamic, and
the question thus arises whether they still benefit from enhanced stability.
Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic
configuration, QIPC, are investigated numerically and compared with the
National Compact Stellarator Experiment (NCSX) and the DIII-D tokamak. In
gyrokinetic simulations, performed with the gyrokinetic code GENE in the
electrostatic and collisionless approximation, ion-temperature-gradient modes,
trapped-electron modes and mixed-type instabilities are studied. Wendelstein
7-X and QIPC exhibit significantly reduced growth rates for all simulations
that include kinetic electrons, and the latter are indeed found to be
stabilizing in the energy budget. These results suggest that imperfectly
optimized stellarators can retain most of the stabilizing properties predicted
for perfect maximum- configurations.Comment: 15 pages, 40 figure
Collisionless microinstabilities in stellarators I - analytical theory of trapped-particle modes
This is the first of two papers about collisionless, electrostatic
micro-instabilities in stellarators, with an emphasis on trapped-particle
modes. It is found that, in so-called maximum- configurations,
trapped-particle instabilities are absent in large regions of parameter space.
Quasi-isodynamic stellarators have this property (approximately), and the
theory predicts that trapped electrons are stabilizing to all eigenmodes with
frequencies below the electron bounce frequency. The physical reason is that
the bounce-averaged curvature is favorable for all orbits, and that trapped
electrons precess in the direction opposite to that in which drift waves
propagate, thus precluding wave-particle resonance. These considerations only
depend on the electrostatic energy balance, and are independent of all
geometric properties of the magnetic field other than the maximum-
condition. However, if the aspect ratio is large and the instability phase
velocity differs greatly from the electron and ion thermal speeds, it is
possible to derive a variational form for the frequency showing that stability
prevails in a yet larger part of parameter space than what follows from the
energy argument. Collisionless trapped-electron modes should therefore be more
stable in quasi-isodynamic stellarators than in tokamaks.Comment: 9 pages, 1 figur
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
On neoclassical impurity transport in stellarator geometry
The impurity dynamics in stellarators has become an issue of moderate concern
due to the inherent tendency of the impurities to accumulate in the core when
the neoclassical ambipolar radial electric field points radially inwards (ion
root regime). This accumulation can lead to collapse of the plasma due to
radiative losses, and thus limit high performance plasma discharges in
non-axisymmetric devices.\\ A quantitative description of the neoclassical
impurity transport is complicated by the breakdown of the assumption of small
drift and trapping due to the electrostatic
potential variation on a flux surface compared to those due to
the magnetic field gradient. The present work examines the impact of this
potential variation on neoclassical impurity transport in the Large Helical
Device (LHD) stellarator. It shows that the neoclassical impurity transport can
be strongly affected by . The central numerical tool used is the
particle in cell (PIC) Monte Carlo code EUTERPE. The
used in the calculations is provided by the neoclassical code GSRAKE. The
possibility of obtaining a more general self-consistently with
EUTERPE is also addressed and a preliminary calculation is presented.Comment: 11 pages, 15 figures, presented at Joint Varenna-Lausanne
International Workshop on Theory of Fusion Plasmas, 2012. Accepted for
publication to Plasma Phys. and Control. Fusio
Collisional transport across the magnetic field in drift-fluid models
Drift ordered fluid models are widely applied in studies of low-frequency
turbulence in the edge and scrape-off layer regions of magnetically confined
plasmas. Here, we show how collisional transport across the magnetic field is
self-consistently incorporated into drift-fluid models without altering the
drift-fluid energy integral. We demonstrate that the inclusion of collisional
transport in drift-fluid models gives rise to diffusion of particle density,
momentum and pressures in drift-fluid turbulence models and thereby obviate the
customary use of artificial diffusion in turbulence simulations. We further
derive a computationally efficient, two-dimensional model which can be time
integrated for several turbulence de-correlation times using only limited
computational resources. The model describes interchange turbulence in a
two-dimensional plane perpendicular to the magnetic field located at the
outboard midplane of a tokamak. The model domain has two regions modeling open
and closed field lines. The model employs a computational expedient model for
collisional transport. Numerical simulations show good agreement between the
full and the simplified model for collisional transport
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