7,411 research outputs found
Covariant Phase Space Formulations of Superparticles and Supersymmetric WZW Models
We present new covariant phase space formulations of superparticles moving on
a group manifold, deriving the fundamental Poisson brackets and current
algebras. We show how these formulations naturally generalise to the
supersymmetric Wess-Zumino-Witten models.Comment: 15pp., LaTe
Contributions of the low-latitude boundary layer to the finite width magnetotail convection model
Convection of plasma within the terrestrial nightside plasma sheet contributes to the structure and, possibly, the dynamical evolution of the magnetotail. In order to characterize the steady state convection process, we have extended the finite tail width model of magnetotail plasma sheet convection. The model assumes uniform plasma sources and accounts for both the duskward gradient/curvature drift and the earthward E × B drift of ions in a two-dimensional magnetic geometry. During periods of slow convection (i.e., when the cross-tail electric potential energy is small relative to the source plasma\u27s thermal energy), there is a significant net duskward displacement of the pressure-bearing ions. The electrons are assumed to be cold, and we argue that this assumption is appropriate for plasma sheet parameters. We generalize solutions previously obtained along the midnight meridian to describe the variation of the plasma pressure and number density across the width of the tail. For a uniform deep-tail source of particles, the plasma pressure and number density are unrealistically low along the near-tail dawn flank. We therefore add a secondary source of plasma originating from the dawnside low-latitude boundary layer (LLBL). The dual plasma sources contribute to the plasma pressure and number density throughout the magnetic equatorial plane. Model results indicate that the LLBL may be a significant source of near-tail central plasma sheet plasma during periods of weak convection. The model predicts a cross-tail pressure gradient from dawn to dusk in the near magnetotail. We suggest that the plasma pressure gradient is balanced in part by an oppositely directed magnetic pressure gradient for which there is observational evidence. Finally, the pressure to number density ratio is used to define the plasma “temperature.” We stress that such quantities as temperature and polytropic index must be interpreted with care as they lose their nominal physical significance in regions where the two-source plasmas intermix appreciably and the distributions become non-Maxwellian
On the possibility of quasi-static convection in the quiet magnetotail
Abstract
The magnetotail is known to serve as a reservoir of energy transferred into the terrestrial magnetosphere from the solar wind. In principle, the stored energy can be dissipated impulsively, as in a substorm, or steadily through the process of steady adiabatic plasma convection. However, some theoretical arguments have suggested that quasi-static adiabatic convection cannot occur throughout the magnetotail because of the structure of the magnetic field. Here we reexamine the question. We show that in a magnetotail of finite width, downtail pressure gradients depend strongly on the ratio of the potential across half the tail to the ion temperature in the far tail (60 RE). For pertinent quiet time ratios (∼3), a Tsyganenko quiet-time magnetic field model is consistent with steady convection
Domain Decomposition preconditioning for high-frequency Helmholtz problems with absorption
In this paper we give new results on domain decomposition preconditioners for
GMRES when computing piecewise-linear finite-element approximations of the
Helmholtz equation , with
absorption parameter . Multigrid approximations of
this equation with are commonly used as preconditioners
for the pure Helmholtz case (). However a rigorous theory for
such (so-called "shifted Laplace") preconditioners, either for the pure
Helmholtz equation, or even the absorptive equation (), is
still missing. We present a new theory for the absorptive equation that
provides rates of convergence for (left- or right-) preconditioned GMRES, via
estimates of the norm and field of values of the preconditioned matrix. This
theory uses a - and -explicit coercivity result for the
underlying sesquilinear form and shows, for example, that if , then classical overlapping additive Schwarz will perform optimally for
the absorptive problem, provided the subdomain and coarse mesh diameters are
carefully chosen. Extensive numerical experiments are given that support the
theoretical results. The theory for the absorptive case gives insight into how
its domain decomposition approximations perform as preconditioners for the pure
Helmholtz case . At the end of the paper we propose a
(scalable) multilevel preconditioner for the pure Helmholtz problem that has an
empirical computation time complexity of about for
solving finite element systems of size , where we have
chosen the mesh diameter to avoid the pollution effect.
Experiments on problems with , i.e. a fixed number of grid points
per wavelength, are also given
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