971 research outputs found
Magnetic moment non-conservation in magnetohydrodynamic turbulence models
The fundamental assumptions of the adiabatic theory do not apply in presence
of sharp field gradients as well as in presence of well developed
magnetohydrodynamic turbulence. For this reason in such conditions the magnetic
moment is no longer expected to be constant. This can influence particle
acceleration and have considerable implications in many astrophysical problems.
Starting with the resonant interaction between ions and a single parallel
propagating electromagnetic wave, we derive expressions for the magnetic moment
trapping width (defined as the half peak-to-peak difference in the
particle magnetic moment) and the bounce frequency . We perform
test-particle simulations to investigate magnetic moment behavior when
resonances overlapping occurs and during the interaction of a ring-beam
particle distribution with a broad-band slab spectrum.
We find that magnetic moment dynamics is strictly related to pitch angle
for a low level of magnetic fluctuation, , where is the constant and uniform background magnetic field.
Stochasticity arises for intermediate fluctuation values and its effect on
pitch angle is the isotropization of the distribution function .
This is a transient regime during which magnetic moment distribution
exhibits a characteristic one-sided long tail and starts to be influenced by
the onset of spatial parallel diffusion, i.e., the variance
grows linearly in time as in normal diffusion. With strong fluctuations
isotropizes completely, spatial diffusion sets in and
behavior is closely related to the sampling of the varying magnetic field
associated with that spatial diffusion.Comment: 13 pages, 10 figures, submitted to PR
Perpendicular momentum injection by lower hybrid wave in a tokamak
The injection of lower hybrid waves for current drive into a tokamak affects
the profile of intrinsic rotation. In this article, the momentum deposition by
the lower hybrid wave on the electrons is studied. Due to the increase in the
poloidal momentum of the wave as it propagates into the tokamak, the parallel
momentum of the wave increases considerably. The change of the perpendicular
momentum of the wave is such that the toroidal angular momentum of the wave is
conserved. If the perpendicular momentum transfer via electron Landau damping
is ignored, the transfer of the toroidal angular momentum to the plasma will be
larger than the injected toroidal angular momentum. A proper quasilinear
treatment proves that both perpendicular and parallel momentum are transferred
to the electrons. The toroidal angular momentum of the electrons is then
transferred to the ions via different mechanisms for the parallel and
perpendicular momentum. The perpendicular momentum is transferred to ions
through an outward radial electron pinch, while the parallel momentum is
transferred through collisions.Comment: 22 pages, 4 figure
The p-Laplace equation in domains with multiple crack section via pencil operators
The p-Laplace equation
\n \cdot (|\n u|^n \n u)=0 \whereA n>0, in a bounded domain \O \subset
\re^2, with inhomogeneous Dirichlet conditions on the smooth boundary \p \O
is considered. In addition, there is a finite collection of curves
\Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assume
homogeneous Dirichlet boundary conditions} \quad u=0, modeling a multiple
crack formation, focusing at the origin 0 \in \O. This makes the above
quasilinear elliptic problem overdetermined. Possible types of the behaviour of
solution at the tip 0 of such admissible multiple cracks, being a
"singularity" point, are described, on the basis of blow-up scaling techniques
and a "nonlinear eigenvalue problem". Typical types of admissible cracks are
shown to be governed by nodal sets of a countable family of nonlinear
eigenfunctions, which are obtained via branching from harmonic polynomials that
occur for . Using a combination of analytic and numerical methods,
saddle-node bifurcations in are shown to occur for those nonlinear
eigenvalues/eigenfunctions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.065
The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions
Fundamental global similarity solutions of the standard form
u_\g(x,t)=t^{-\a_\g} f_\g(y), with the rescaled variable y= x/{t^{\b_\g}},
\b_\g= \frac {1-n \a_\g}{10}, where \a_\g>0 are real nonlinear eigenvalues (\g
is a multiindex in R^N) of the tenth-order thin film equation (TFE-10) u_{t} =
\nabla \cdot(|u|^{n} \n \D^4 u) in R^N \times R_+, n>0, are studied. The
present paper continues the study began by the authors in the previous paper
P. Alvarez-Caudevilla, J.D.Evans, and V.A. Galaktionov, The Cauchy problem
for a tenth-order thin film equation I. Bifurcation of self-similar oscillatory
fundamental solutions, Mediterranean Journal of Mathematics, No. 4, Vol. 10
(2013), 1759-1790.
Thus, the following questions are also under scrutiny:
(I) Further study of the limit n \to 0, where the behaviour of finite
interfaces and solutions as y \to infinity are described. In particular, for
N=1, the interfaces are shown to diverge as follows: |x_0(t)| \sim 10 \left(
\frac{1}{n}\sec\left( \frac{4\pi}{9} \right) \right)^{\frac 9{10}} t^{\frac
1{10}} \to \infty as n \to 0^+.
(II) For a fixed n \in (0, \frac 98), oscillatory structures of solutions
near interfaces.
(III) Again, for a fixed n \in (0, \frac 98), global structures of some
nonlinear eigenfunctions \{f_\g\}_{|\g| \ge 0} by a combination of numerical
and analytical methods
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