665 research outputs found
Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device
The properties of linear instabilities in the Large Plasma Device [W.
Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through
analytic calculations and solving numerically a system of linearized
collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et
al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully
modified to treat cylindrical geometry. Instability drive from plasma pressure
gradients and flows is considered, focusing on resistive drift waves, the
Kelvin-Helmholtz and rotational interchange instabilities. A general linear
dispersion relation for partially ionized collisional plasmas including these
modes is derived and analyzed. For LAPD relevant profiles including strongly
driven flows it is found that all three modes can have comparable growth rates
and frequencies. Detailed comparison with solutions of the analytic dispersion
relation demonstrates that BOUT accurately reproduces all characteristics of
linear modes in this system.Comment: Published in Physics of Plasmas, 17, 102107 (2010
Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions?
Solutions to a model 2D eigenmode equation describing micro-instabilities in
tokamak plasmas are presented that demonstrate a sensitivity of the mode
structure and stability to plasma profiles. In narrow regions of parameter
space, with special plasma profiles, a maximally unstable mode is found that
balloons on the outboard side of the tokamak. This corresponds to the
conventional picture of a ballooning mode. However, for most profiles this mode
cannot exist and instead a more stable mode is found that balloons closer to
the top or bottom of the plasma. Good quantitative agreement with a 1D
ballooning analysis is found provided the constraints associated with higher
order profile effects, often neglected, are taken into account. A sudden
transition from this general mode to the more unstable ballooning mode can
occur for a critical flow shear, providing a candidate model for why some
experiments observe small plasma eruptions (Edge Localised Modes, or ELMs) in
place of large Type I ELMs.Comment: 11 pages, 3 figure
High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry
We present a high-order spatial discretization of a continuum gyrokinetic
Vlasov model in axisymmetric tokamak edge plasma geometries. Such models
describe the phase space advection of plasma species distribution functions in
the absence of collisions. The gyrokinetic model is posed in a four-dimensional
phase space, upon which a grid is imposed when discretized. To mitigate the
computational cost associated with high-dimensional grids, we employ a
high-order discretization to reduce the grid size needed to achieve a given
level of accuracy relative to lower-order methods. Strong anisotropy induced by
the magnetic field motivates the use of mapped coordinate grids aligned with
magnetic flux surfaces. The natural partitioning of the edge geometry by the
separatrix between the closed and open field line regions leads to the
consideration of multiple mapped blocks, in what is known as a mapped
multiblock (MMB) approach. We describe the specialization of a more general
formalism that we have developed for the construction of high-order,
finite-volume discretizations on MMB grids, yielding the accurate evaluation of
the gyrokinetic Vlasov operator, the metric factors resulting from the MMB
coordinate mappings, and the interaction of blocks at adjacent boundaries. Our
conservative formulation of the gyrokinetic Vlasov model incorporates the fact
that the phase space velocity has zero divergence, which must be preserved
discretely to avoid truncation error accumulation. We describe an approach for
the discrete evaluation of the gyrokinetic phase space velocity that preserves
the divergence-free property to machine precision
Towards optimal explicit time-stepping schemes for the gyrokinetic equations
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory
and astrophysical plasmas. To solve these equations, massively parallel codes
have been developed and run on present-day supercomputers. This paper describes
measures to improve the efficiency of such computations, thereby making them
more realistic. Explicit Runge-Kutta schemes are considered to be well suited
for time-stepping. Although the numerical algorithms are often highly
optimized, performance can still be improved by a suitable choice of the
time-stepping scheme, based on spectral analysis of the underlying operator.
Here, an operator splitting technique is introduced to combine first-order
Runge-Kutta-Chebychev schemes for the collision term with fourth-order schemes
for the remaining terms. In the nonlinear regime, based on the observation of
eigenvalue shifts due to the (generalized) advection term, an
accurate and robust estimate for the nonlinear timestep is developed. The
presented techniques can reduce simulation times by factors of up to three in
realistic cases. This substantial speedup encourages the use of similar
timestep optimized explicit schemes not only for the gyrokinetic equation, but
also for other applications with comparable properties.Comment: 11 pages, 5 figures, accepted for publication in Computer Physics
Communication
Beyond Axisymmetry in Tokamak Plasmas
H-mode tokamak plasmas are characterised by quasi-periodic instabilities, called edge localised modes (ELMs), driven by unstable peeling-ballooning modes inside the pedestal region. For large scale tokamaks, like ITER, the resulting particle and heat fluxes are predicted to be unacceptable and ELM control methods are required. One promising method relies on the application of 3D resonant magnetic perturbations (MPs), and ELM mitigation or even complete suppression is observed. A computational framework is presented that aims to understand the effect of MPs on both plasma equilibria and stability. The ELITE stability code is used to find the linearised plasma response, i.e. the 3D part of the equilibrium, and compute the axisymmetric peeling-ballooning eigenmodes. This information is used to calculate the 3D stability under a perturbative and a variational formulation of the MHD energy principle. In practice, the axisymmetric peeling-ballooning modes are used as trial functions for the minimisation of the 3D energy functional. The symmetry breaking of the toroidal geometry leads to the coupling of toroidal modes which has a direct impact on the linear growth rates of unstable peeling-ballooning modes. This mechanism results in the modification of the plasma stability above a critical value of the applied MP field and field-line localisation of the peeling-ballooning eigenmode. It is observed that intermediate to high n ballooning modes are in general destabilised by the applied MP field, while external peeling-ballooning modes reorganise to an internal ballooning structure. In addition, extrema in the growth rate spectrum, due to low n kink modes, are observed to be strongly destabilised as predicted by perturbation theory. This work provides proof of principle examination of the 3D peeling-ballooning instability as well as a framework for the optimisation of MP coil configuration
Validation of gyrokinetic modelling of light impurity transport including rotation in ASDEX Upgrade
Upgraded spectroscopic hardware and an improved impurity concentration
calculation allow accurate determination of boron density in the ASDEX Upgrade
tokamak. A database of boron measurements is compared to quasilinear and
nonlinear gyrokinetic simulations including Coriolis and centrifugal rotational
effects over a range of H-mode plasma regimes. The peaking of the measured
boron profiles shows a strong anti-correlation with the plasma rotation
gradient, via a relationship explained and reproduced by the theory. It is
demonstrated that the rotodiffusive impurity flux driven by the rotation
gradient is required for the modelling to reproduce the hollow boron profiles
at higher rotation gradients. The nonlinear simulations validate the
quasilinear approach, and, with the addition of perpendicular flow shear,
demonstrate that each symmetry breaking mechanism that causes momentum
transport also couples to rotodiffusion. At lower rotation gradients, the
parallel compressive convection is required to match the most peaked boron
profiles. The sensitivities of both datasets to possible errors is
investigated, and quantitative agreement is found within the estimated
uncertainties. The approach used can be considered a template for mitigating
uncertainty in quantitative comparisons between simulation and experiment.Comment: 19 pages, 11 figures, accepted in Nuclear Fusio
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