286 research outputs found
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Plasma fluctuations as Markovian noise
Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.Physic
Thirty Years of Turnstiles and Transport
To characterize transport in a deterministic dynamical system is to compute
exit time distributions from regions or transition time distributions between
regions in phase space. This paper surveys the considerable progress on this
problem over the past thirty years. Primary measures of transport for
volume-preserving maps include the exiting and incoming fluxes to a region. For
area-preserving maps, transport is impeded by curves formed from invariant
manifolds that form partial barriers, e.g., stable and unstable manifolds
bounding a resonance zone or cantori, the remnants of destroyed invariant tori.
When the map is exact volume preserving, a Lagrangian differential form can be
used to reduce the computation of fluxes to finding a difference between the
action of certain key orbits, such as homoclinic orbits to a saddle or to a
cantorus. Given a partition of phase space into regions bounded by partial
barriers, a Markov tree model of transport explains key observations, such as
the algebraic decay of exit and recurrence distributions.Comment: Updated and corrected versio
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Two-fluid temperature-dependent relativistic waves in magnetized streaming pair plasmas
A relativistic two-fluid temperature-dependent approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. In the model the generalized vorticity rather than the magnetic field is frozen into the fluid. For parallel propagation four transverse modes are found. Two are electromagnetic plasma modes which at high temperature become light waves. The remaining two are Alfveacutenic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and is always subluminous. We find that the instability cannot be suppressed by temperature effects in the limit of large (finite) magnetic field. The fast Alfveacuten mode can be superluminous only at large wavelengths, however it is always subluminous at high temperatures. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is studied for finite and large strong magnetic fields and the results are qualitatively described.Institute for Fusion Studie
Generalized poisson brackets and nonlinear Liapunov stability application to reduces mhd
A method is presented for obtaining Liapunov
functionals (LF) and proving nonlinear stability. The method
uses the generalized Poisson bracket (GPB) formulation of
Hamiltonian dynamics. As an illustration, certain stationary
solutions of ideal reduced MHD (RMHD) are shown to be nonlinearly
stable. This includes Grad-Shafranov and Alfven
solutions
Two-fluid magnetic island dynamics in slab geometry: I - Isolated islands
A set of reduced, 2-D, two-fluid, drift-MHD equations is derived. Using these
equations, a complete and fully self-consistent solution is obtained for an
isolated magnetic island propagating through a slab plasma with uniform but
different ion and electron fluid velocities. The ion and electron fluid flow
profiles around the island are uniquely determined, and are everywhere
continuous. Moreover, the island phase-velocity is uniquely specified by the
condition that there be zero net electromagnetic force acting on the island.
Finally, the ion polarization current correction to the Rutherford island width
evolution equation is evaluated, and found to be stabilizing provided that the
anomalous perpendicular ion viscosity significantly exceeds the anomalous
perpendicular electron viscosity
Elastic Radiation in a HalfâSpace
A Green's function for the elastic wave equation, which satisfies certain boundary conditions on the surface of a homogeneous halfâspace, is derived by means of the Fourier transformation. This halfâspace Green's function is then applied to the computation of radiative effects due to the earth's surface when a radiating source is located on or within that surface. The results obtained are to be taken as an extension of a previous and similar formulation for the infinite medium due to Case and Colwell.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70190/2/JMAPAQ-11-8-2546-1.pd
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Bootstrap current close to magnetic axis in tokamaks
It is shown that the bootstrap current density close to the magnetic axis in tokamaks does not vanish in simple electron-ion plasmas because the fraction of the trapped particles is finite. The magnitude of the current density could be comparable to that in the outer core region. This may reduce or even eliminate the need of the seed current
An extended hybrid magnetohydrodynamics gyrokinetic model for numerical simulation of shear Alfv\'en waves in burning plasmas
Adopting the theoretical framework for the generalized fishbonelike
dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic
simulation model has been derived analytically by taking into account both
thermal ion compressibility and diamagnetic effects in addition to energetic
particle kinetic behaviors. The extended model has been used for implementing
an eXtended version of Hybrid Magnetohydrodynamics Gyrokinetic Code (XHMGC) to
study thermal ion kinetic effects on Alfv\'enic modes driven by energetic
particles, such as kinetic beta induced Alfv\'en eigenmodes in tokamak fusion
plasmas
Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems
Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most
fundamental concepts in plasma physics. While the former describes the
surprising damping of linear plasma waves in a collisionless plasma, the latter
describes exact undamped nonlinear solutions of the Vlasov equation. There does
exist a relationship between the two: Landau damping can be described as the
phase-mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which
can be viewed as BGK modes in the linear limit. While these concepts have been
around for a long time, unexpected new results are still being discovered. For
Landau damping, we show that the textbook picture of phase-mixing is altered
profoundly in the presence of collision. In particular, the continuous spectrum
of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum,
even in the limit of zero collision. Furthermore, we show that these discrete
eigenmodes form a complete set of solutions. Landau-damped solutions are then
recovered as true eigenmodes (which they are not in the collisionless theory).
For BGK modes, our interest is motivated by recent discoveries of electrostatic
solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is
quite mature, there appear to be no exact three-dimensional solutions in the
literature (except for the limiting case when the magnetic field is
sufficiently strong so that one can apply the guiding-center approximation). We
show, in fact, that two- and three-dimensional solutions that depend only on
energy do not exist. However, if solutions depend on both energy and angular
momentum, we can construct exact three-dimensional solutions for the
unmagnetized case, and two-dimensional solutions for the case with a finite
magnetic field. The latter are shown to be exact, fully electromagnetic
solutions of the steady-state Vlasov-Poisson-Amp\`ere system
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