3,292 research outputs found
The Screened Field of a Test Particle
The screened field (forward field and wake) of a test particle moving at
constant velocity through an unmagnetized collisionless plasma is calculated
analytically and numerically. This paper is based on unpublished material from
my MSc thesis, supervised by the late Dr K. C. Hines.Comment: 27 pp, 14 fig Publ "In Celeb Of KC Hines,"
www.worldscibooks.com/physics/7604.html. Based on Chs 2 & 3 of
"Particle-field interactions in a plasma," RL Dewar, MSc Thesis, U Melbourne
'67. v2: and interchanged after Eq. (4.1); v3: typos
corrected pp 3, 4, 5, 19, in partic. repl. by & putting
hat on k in arg. of \Phi in Eq.(2.5). See also arXiv 1107.520
Zonal flow generation by modulational instability
This paper gives a pedagogic review of the envelope formalism for excitation
of zonal flows by nonlinear interactions of plasma drift waves or Rossby waves,
described equivalently by the Hasegawa-Mima (HM) equation or the
quasigeostrophic barotropic potential vorticity equation, respectively. In the
plasma case a modified form of the HM equation, which takes into account
suppression of the magnetic-surface-averaged electron density response by a
small amount of rotational transform, is also analyzed. Excitation of zonal
mean flow by a modulated wave train is particularly strong in the modified HM
case. A local dispersion relation for a coherent wave train is calculated by
linearizing about a background mean flow and used to find the nonlinear
frequency shift by inserting the nonlinearly excited mean flow. Using the
generic nonlinear Schroedinger equation about a uniform carrier wave, the
criterion for instability of small modulations of the wave train is found, as
is the maximum growth rate and phase velocity of the modulations and zonal
flows, in both the modified and unmodified cases.Comment: Accepted for publication in the Proceedings of the CSIRO/COSNet
Workshop on Turbulence and Coherent Structures, Canberra, Australia, 10-13
January 2006 (World Scientific, in preparation, eds. J.P. Denier and J.S.
Frederiksen): 15 pages, 2 figures (3 figure files) - resubmitted to correct
one-line overflow onto page 1
Nonlinear Simulation of Drift Wave Turbulence
In a two-dimensional version of the modified Hasegawa-Wakatani (HW) model,
which describes electrostatic resistive drift wave turbulence, the resistive
coupling between vorticity and density does not act on the zonal components
(). It is therefore necessary to modify the HW model to treat the
zonal components properly. The modified equations are solved numerically, and
visualization and analysis of the solutions show generation of stable zonal
flows, through conversion of turbulent kinetic energy, and the consequent
turbulence and transport suppression. It is demonstrated by comparison that the
modification is essential for generation of zonal flows.Comment: Accepted for publication in the Proceedings of the CSIRO/COSNet
Workshop on Turbulence and Coherent Structures, Canberra, Australia, 10-13
January 2006 (World Scientific, in press, eds. J.P. Denier and J.S.
Frederiksen): 12 pages, 6 figure
MHD Memes
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect
on a career that has stimulated the mutual exchange of ideas (or memes in the
terminology of Richard Dawkins) between many researchers. This paper will
revisit a meme Allan encountered in his early career in magnetohydrodynamics,
the continuation of a magnetohydrodynamic mode through a singularity, and will
also mention other problems where Allan's work has had a powerful
cross-fertilizing effect in plasma physics and other areas of physics and
mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference
Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear
Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of
California, Berkeley, US
Generalised action-angle coordinates defined on island chains
Straight-field-line coordinates are very useful for representing magnetic
fields in toroidally confined plasmas, but fundamental problems arise regarding
their definition in 3-D geometries because of the formation of islands and
chaotic field regions, ie non-integrability. In Hamiltonian dynamical systems
terms these coordinates are a form of action-angle variables, which are
normally defined only for integrable systems. In order to describe 3-D magnetic
field systems, a generalisation of this concept was proposed recently by the
present authors that unified the concepts of ghost surfaces and
quadratic-flux-minimising (QFMin) surfaces. This was based on a simple
canonical transformation generated by a change of variable , where and are poloidal and toroidal
angles, respectively, with a new poloidal angle chosen to give
pseudo-orbits that are a) straight when plotted in the plane and
b) QFMin pseudo-orbits in the transformed coordinate. These two requirements
ensure that the pseudo-orbits are also c) ghost pseudo-orbits. In the present
paper, it is demonstrated that these requirements do not \emph{uniquely}
specify the transformation owing to a relabelling symmetry. A variational
method of solution that removes this lack of uniqueness is proposed.Comment: 10 pages. Accepted by Plasma Physics and Controlled Fusion as part of
a cluster of refereed papers in a special issue containing papers arising
from the Joint International Stellarator & Heliotron Workshop and
Asia-Pacific Plasma Theory Conference, held in Canberra and Murramarang
Resort, Australia, 30 January - 3 February, 201
Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
We describe a magnetohydrodynamic (MHD) constrained energy functional for
equilibrium calculations that combines the topological constraints of ideal MHD
with elements of Taylor relaxation.
Extremizing states allow for partially chaotic magnetic fields and
non-trivial pressure profiles supported by a discrete set of ideal interfaces
with irrational rotational transforms.
Numerical solutions are computed using the Stepped Pressure Equilibrium Code,
SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted 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 65th
birthday of R.L. Dewar. V2 is revised for referee
Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity
The vanishing of the divergence of the total stress tensor (magnetic plus
kinetic) in a neighborhood of an equilibrium plasma containing a toroidal
surface of discontinuity gives boundary and jump conditions that strongly
constrain allowable continuations of the magnetic field across the surface. The
boundary conditions allow the magnetic fields on either side of the
discontinuity surface to be described by surface magnetic potentials, reducing
the continuation problem to that of solving a Hamilton--Jacobi equation. The
characteristics of this equation obey Hamiltonian equations of motion, and a
necessary condition for the existence of a continued field across a general
toroidal surface is that there exist invariant tori in the phase space of this
Hamiltonian system. It is argued from the Birkhoff theorem that existence of
such an invariant torus is also, in general, sufficient for continuation to be
possible. An important corollary is that the rotational transform of the
continued field on a surface of discontinuity must, generically, be irrational.Comment: Prepared for submission to Phys. Letts.
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