216 research outputs found
Numerical simulation of the effect of pellet injection on ELMs
We report on numerical simulation studies of the dynamical behavior of edge
localized modes (ELMs) under the influence of repetitive injection of pellets.
In our nonlinear 2-fluid model the ELMs are excited by introducing a particle
source in the confinement region and a particle sink in the edge region. The
injection of pellets is simulated by periodically raising the edge density in a
pulsed manner. We find that when the edge density is raised to twice the normal
edge density with a duty cycle (on time:off time) of 1:2, the ELMs are
generated on an average at a faster rate and with reduced amplitudes. These
changes lead to significant improvements in the plasma beta indicative of an
improvement in the energy confinement due to pellet injection. Concurrently,
the plasma density and temperature profiles also get significantly modified. A
comparative study is made of the nature of ELM dynamics for different
magnitudes of edge density enhancements. We also discuss the relative impact on
ELMs from resonant magnetic perturbations (RMPs) compared to pellet injection
in terms of changes in the plasma temperature, density, location of the ELMs
and the nonlinear spectral transfer of energies
Azimuthally symmetric MHD and two-fluid equilibria with arbitrary flows
Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with
azimuthal symmetry, gravity and arbitrary ratios of (nonrelativistic) flow
speed to acoustic and Alfven speeds are investigated. In the two-fluid case,
the mass ratio of the two species is arbitrary, and the analysis is therefore
applicable to electron-positron plasmas. The methods of derivation can be
extended in an obvious manner to several charged species. Generalized
Grad-Shafranov equations, describing the equilibrium magnetic field, are
derived. Flux function equations and Bernoulli relations for each species,
together with Poisson's equation for the gravitational potential, complete the
set of equations required to determine the equilibrium. These are
straightforward to solve numerically. The two-fluid system, unlike the MHD
system, is shown to be free of singularities. It is demonstrated analytically
that there exists a class of incompressible MHD equilibria with magnetic
field-aligned flow. A special sub--class first identified by S. Chandrasekhar,
in which the flow speed is everywhere equal to the local Alfven speed, is
compatible with virtually any azimuthally symmetric magnetic configuration.
Potential applications of this analysis include extragalactic and stellar jets,
and accretion disks.Comment: 18 pages, 0 figure
Electron Inertial Effects on Rapid Energy Redistribution at Magnetic X-points
The evolution of non-potential perturbations to a current-free magnetic
X-point configuration is studied, taking into account electron inertial effects
as well as resistivity. Electron inertia is shown to have a negligible effect
on the evolution of the system whenever the collisionless skin depth is less
than the resistive scale length. Non-potential magnetic field energy in this
resistive MHD limit initially reaches equipartition with flow energy, in
accordance with ideal MHD, and is then dissipated extremely rapidly, on an
Alfvenic timescale that is essentially independent of Lundquist number. In
agreement with resistive MHD results obtained by previous authors, the magnetic
field energy and kinetic energy are then observed to decay on a longer
timescale and exhibit oscillatory behavior, reflecting the existence of
discrete normal modes with finite real frequency. When the collisionless skin
depth exceeds the resistive scale length, the system again evolves initially
according to ideal MHD. At the end of this ideal phase, the field energy decays
typically on an Alfvenic timescale, while the kinetic energy (which is equally
partitioned between ions and electrons in this case) is dissipated on the
electron collision timescale. The oscillatory decay in the energy observed in
the resistive case is absent, but short wavelength structures appear in the
field and velocity profiles, suggesting the possibility of particle
acceleration in oppositely-directed current channels. The model provides a
possible framework for interpreting observations of energy release and particle
acceleration on timescales down to less than a second in the impulsive phase of
solar flares.Comment: 30 pages, 8 figure
Field-guided proton acceleration at reconnecting X-points in flares
An explicitly energy-conserving full orbit code CUEBIT, developed originally
to describe energetic particle effects in laboratory fusion experiments, has
been applied to the problem of proton acceleration in solar flares. The model
fields are obtained from solutions of the linearised MHD equations for
reconnecting modes at an X-type neutral point, with the additional ingredient
of a longitudinal magnetic field component. To accelerate protons to the
highest observed energies on flare timescales, it is necessary to invoke
anomalous resistivity in the MHD solution. It is shown that the addition of a
longitudinal field component greatly increases the efficiency of ion
acceleration, essentially because it greatly reduces the magnitude of drift
motions away from the vicinity of the X-point, where the accelerating component
of the electric field is largest. Using plasma parameters consistent with flare
observations, we obtain proton distributions extending up to gamma-ray-emitting
energies (>1MeV). In some cases the energy distributions exhibit a bump-on-tail
in the MeV range. In general, the shape of the distribution is sensitive to the
model parameters.Comment: 14 pages, 4 figures, accepted for publication in Solar Physic
CENTORI: a global toroidal electromagnetic two-fluid plasma turbulence code
A new global two-fluid electromagnetic turbulence code, CENTORI, has been
developed for the purpose of studying magnetically-confined fusion plasmas on
energy confinement timescales. This code is used to evolve the combined system
of electron and ion fluid equations and Maxwell equations in toroidal
configurations with axisymmetric equilibria. Uniquely, the equilibrium is
co-evolved with the turbulence, and is thus modified by it. CENTORI is
applicable to tokamaks of arbitrary aspect ratio and high plasma beta. A
predictor-corrector, semi-implicit finite difference scheme is used to compute
the time evolution of fluid quantities and fields. Vector operations and the
evaluation of flux surface averages are speeded up by choosing the Jacobian of
the transformation from laboratory to plasma coordinates to be a function of
the equilibrium poloidal magnetic flux. A subroutine, GRASS, is used to
co-evolve the plasma equilibrium by computing the steady-state solutions of a
diffusion equation with a pseudo-time derivative. The code is written in
Fortran 95 and is efficiently parallelized using Message Passing Interface
(MPI). Illustrative examples of output from simulations of a tearing mode in a
large aspect ratio tokamak plasma and of turbulence in an elongated
conventional aspect ratio tokamak plasma are provided.Comment: 9 figure
Modified Zakharov equations for plasmas with a quantum correction
Quantum Zakharov equations are obtained to describe the nonlinear interaction
between quantum Langmuir waves and quantum ion-acoustic waves. These quantum
Zakharov equations are applied to two model cases, namely the four-wave
interaction and the decay instability. In the case of the four-wave
instability, sufficiently large quantum effects tend to suppress the
instability. For the decay instability, the quantum Zakharov equations lead to
results similar to those of the classical decay instability except for quantum
correction terms in the dispersion relations. Some considerations regarding the
nonlinear aspects of the quantum Zakharov equations are also offered.Comment: 4 figures. Accepted for publication in Physics of Plasmas (2004
Nonlinear dispersive regularization of inviscid gas dynamics
Ideal gas dynamics can develop shock-like singularities with discontinuous
density. Viscosity typically regularizes such singularities and leads to a
shock structure. On the other hand, in 1d, singularities in the Hopf equation
can be non-dissipatively smoothed via KdV dispersion. Here, we develop a
minimal conservative regularization of 3d ideal adiabatic flow of a gas with
polytropic exponent . It is achieved by augmenting the Hamiltonian by a
capillarity energy . The simplest capillarity
coefficient leading to local conservation laws for mass, momentum, energy and
entropy using the standard Poisson brackets is for
constant . This leads to a Korteweg-like stress and nonlinear terms in
the momentum equation with third derivatives of , which are related to
the Bohm potential and Gross quantum pressure. Just like KdV, our equations
admit sound waves with a leading cubic dispersion relation, solitary and
periodic traveling waves. As with KdV, there are no steady continuous
shock-like solutions satisfying the Rankine-Hugoniot conditions. Nevertheless,
in 1d, for , numerical solutions show that the gradient catastrophe
is averted through the formation of pairs of solitary waves which can display
approximate phase-shift scattering. Numerics also indicate recurrent behavior
in periodic domains. These observations are related to an equivalence between
our regularized equations (in the special case of constant specific entropy
potential flow in any dimension) and the defocussing nonlinear Schrodinger
equation (cubically nonlinear for ), with playing the
role of . Thus, our regularization of gas dynamics may be viewed as a
generalization of both the single field KdV & NLS equations to include the
adiabatic dynamics of density, velocity, pressure & entropy in any dimension.Comment: 19 pages, 20 figure file
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Existence and consequences of Coulomb pairing of electrons in a solid
It is shown from first principles that, in the periodic potential of a crystalline solid, short-range (i.e., screened) binary Coulomb interactions can lead to a two-electron bound state. It is further suggested that these composite bosonic states (charge -2e, and typically spin zero) could mediate an effectively attractive interaction between pairs of conduction electrons close to the Fermi level. This necessarily short range attractive interaction, which is crucially dependent on the band structure of the solid, and is complementary to the phonon-mediated one, may provide a source for the existence and properties of short correlation-length electron pairs (analogous to but distinct from Cooper pairs) needed to understand high temperature superconductivity. Several distinctive and observable characteristics of the proposed pairing scheme are discussed
Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation
In this work we analyze the interaction of isolated solitary structures and
ion-acoustic radiation. If the radiation amplitude is small solitary structures
persists, but when the amplitude grows energy transfer towards small spatial
scales occurs. We show that transfer is particularly fast when a fixed point of
a low dimensional model is destroyed.Comment: LaTex + 4 eps file
The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin
In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are
simulated numerically for fully nonlinear "one-dimensional" potential water
waves in a finite-depth flume between two vertical walls. In such systems, the
FPU recurrence is closely related to the dynamics of coherent structures
approximately corresponding to solitons of the integrable Boussinesq system. A
simplest periodic solution of the Boussinesq model, describing a single soliton
between the walls, is presented in an analytical form in terms of the elliptic
Jacobi functions. In the numerical experiments, it is observed that depending
on a number of solitons in the flume and their parameters, the FPU recurrence
can occur in a simple or complicated manner, or be practically absent. For
comparison, the nonlinear dynamics of potential water waves over nonuniform
beds is simulated, with initial states taken in the form of several pairs of
colliding solitons. With a mild-slope bed profile, a typical phenomenon in the
course of evolution is appearance of relatively high (rogue) waves, while for
random, relatively short-correlated bed profiles it is either appearance of
tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure
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