3,438 research outputs found
Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas
The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning)
modes in strongly nonaxisymmetric toroidal systems is difficult to analyze
numerically owing to the singular nature of ideal MHD caused by lack of an
inherent scale length. In this paper, ideal MHD is regularized by using a
-space cutoff, making the ray tracing for the WKB ballooning formalism a
chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier
spectrum needed for resolving toroidally localized ballooning modes with a
global eigenvalue code is estimated from the Weyl formula. This
phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication
in Phys. Rev. Letter
Dressed test particles, oscillation centres and pseudo-orbits
A general semi-analytical method for accurate and efficient numerical
calculation of the dielectrically screened ("dressed") potential around a
non-relativistic test particle moving in an isotropic, collisionless,
unmagnetised plasma is presented. The method requires no approximations and is
illustrated using results calculated for two cases taken from the MSc thesis of
the first author: test particles with velocities above and below the ion sound
speed in plasmas with Maxwellian ions and warm electrons. The idea that the
fluctuation spectrum of a plasma can be described as a superposition of the
fields around \emph{non-interacting} dressed test particles is an expression of
the quasiparticle concept, which has also been expressed in the development of
the oscillation-centre and pseudo-orbit formalisms.Comment: 14 pages to Plasma Physics and Controlled Fusion for publication with
a cluster of papers associated with workshop Stability and Nonlinear Dynamics
of Plasmas, October 31, 2009 Atlanta, GA on occasion of the 65th birthday of
R.L. Dewar. Version 2: Reference [27] added in Sec. 5. Version 3: Revised in
response to referee
A comparison of incompressible limits for resistive plasmas
The constraint of incompressibility is often used to simplify the
magnetohydrodynamic (MHD) description of linearized plasma dynamics because it
does not affect the ideal MHD marginal stability point. In this paper two
methods for introducing incompressibility are compared in a cylindrical plasma
model: In the first method, the limit is taken, where
is the ratio of specific heats; in the second, an anisotropic mass
tensor is used, with the component parallel to the magnetic
field taken to vanish, . Use of resistive MHD reveals
the nature of these two limits because the Alfv\'en and slow magnetosonic
continua of ideal MHD are converted to point spectra and moved into the complex
plane. Both limits profoundly change the slow-magnetosonic spectrum, but only
the second limit faithfully reproduces the resistive Alfv\'en spectrum and its
wavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the
Alfv\'en continuum in the first method, while it is moved to infinity by the
second. The degeneracy in the first is broken by finite resistivity. For
numerical and semi-analytical study of these models, we choose plasma
equilibria which cast light on puzzling aspects of results found in earlier
literature.Comment: 14 pages, 10 figure
Turbulent edge structure formation in complex configurations
Formation of nonlinear structures in drift-Alfvén turbulence is investigated in the often complex edge geometries of stellarator and tokamak configurations, by analysis of drift waveturbulence simulations using a model in which three-dimensional magnetic geometries are approximated. The structures of parallel mode extension, radially sheared zonal flows and perpendicular mode spectra are highlighted in particular for three-dimensional stellaratormagnetic fields and shaped tokamaks. Specific characteristics of advanced stellarators in comparison to (lower aspect ratio) circular tokamaks are a less pronounced ballooning structure of the modes, a strong influence of local magnetic shear on amplitude structure and average, and stronger level of zonal flows due to lower geodesic curvature.This work was partly funded by grants within the
‘‘Australian-German Joint Research Co-operation scheme’’
~PPP project no. D/0205403!
Model Data Fusion: developing Bayesian inversion to constrain equilibrium and mode structure
Recently, a new probabilistic "data fusion" framework based on Bayesian
principles has been developed on JET and W7-AS. The Bayesian analysis framework
folds in uncertainties and inter-dependencies in the diagnostic data and signal
forward-models, together with prior knowledge of the state of the plasma, to
yield predictions of internal magnetic structure. A feature of the framework,
known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion
50, 085022, 2008), is the inference of magnetic flux surfaces without the use
of a force balance model. We discuss results from a new project to develop
Bayesian inversion tools that aim to (1) distinguish between competing
equilibrium theories, which capture different physics, using the MAST spherical
tokamak; and (2) test the predictions of MHD theory, particularly mode
structure, using the H-1 Heliac.Comment: submitted to Journal of Plasma Fusion Research 10/11/200
Singularity theory study of overdetermination in models for L-H transitions
Two dynamical models that have been proposed to describe transitions between
low and high confinement states (L-H transitions) in confined plasmas are
analysed using singularity theory and stability theory. It is shown that the
stationary-state bifurcation sets have qualitative properties identical to
standard normal forms for the pitchfork and transcritical bifurcations. The
analysis yields the codimension of the highest-order singularities, from which
we find that the unperturbed systems are overdetermined bifurcation problems
and derive appropriate universal unfoldings. Questions of mutual equivalence
and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio
Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations
In modeling nonequilibrium systems one usually starts with a definition of
the microscopic dynamics, e.g., in terms of transition rates, and then derives
the resulting macroscopic behavior. We address the inverse question for a class
of steady state systems, namely complex fluids under continuous shear flow: how
does an externally imposed shear current affect the microscopic dynamics of the
fluid? The answer can be formulated in the form of invariant quantities, exact
relations for the transition rates in the nonequilibrium steady state, as
discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett.
101, 240601 (2008)]. Here, we present a more pedagogical account of the
invariant quantities and the theory underlying them, known as the
nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we
investigate the relationship between the transition rates and the shear current
in the steady state. We show that a fluctuation relation of the
Gallavotti-Cohen type holds for systems satisfying NCDB.Comment: 24 pages, 11 figure
Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators
The radially local magnetohydrodynamic(MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHDstability is analyzed through the calculation and examination of the ballooning modeeigenvalue isosurfaces in the 3-space (s,α,θk); s is the edge normalized toroidal flux, α is the field linevariable, and θk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong “quantum chaos.” The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-nMHD computations are required to predict the beta limit.Research supported by U.S. DOE Contract No. DEAC02-76CH0373.
John Canik held a U.S. DOE National
Undergraduate Fellowship at Princeton Plasma Physics
Laboratory, during the summer of 2000
Minimally Constrained Model of Self-Organized Helical States in Reversed-Field Pinches
We show that the self-organized single-helical-axis (SHAx) and double-axis (DAx) states in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters. This is a significant reduction on previous repre
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