Transition from collisionless to collisional MRI

Recent calculations by Quataert et al. (2002) found that the growth rates of the magnetorotational instability (MRI) in a collisionless plasma can differ significantly from those calculated using MHD. This can be important in hot accretion flows around compact objects. In this paper we study the transition from the collisionless kinetic regime to the collisional MHD regime, mapping out the dependence of the MRI growth rate on collisionality. A kinetic closure scheme for a magnetized plasma is used that includes the effect of collisions via a BGK operator. The transition to MHD occurs as the mean free path becomes short compared to the parallel wavelength 2\pi/k_{\Par}. In the weak magnetic field regime where the Alfv\'en and MRI frequencies $\omega$ are small compared to the sound wave frequency k_{\Par} c_0, the dynamics are still effectively collisionless even if $\omega \ll \nu$, so long as the collision frequency \nu \ll k_{\Par} c_{0}; for an accretion flow this requires \nu \lsim \Omega \sqrt{\beta}. The low collisionality regime not only modifies the MRI growth rate, but also introduces collisionless Landau or Barnes damping of long wavelength modes, which may be important for the nonlinear saturation of the MRI.Comment: 20 pages, 4 figures, submitted to ApJ with a clearer derivation of anisotropic pressure closure from drift kinetic equatio

New Plane Wave Representation Of Point Sources

A new method to decompose the spherical wave of a 3D point source into plane waves is discussed. Using Cauchy\u27s theorem, it represents spherical waves as the summation of surface-direction-wave integrals. Results show that only 6 directions waves needed storage. Thus, the method provides a good cost reduction for plane-wave related algorithms

Dissipation in intercluster plasma

We discuss dissipative processes in strongly gyrotropic, nearly collisionless plasma in clusters of galaxies (ICM). First, we point out that Braginsky theory, which assumes that collisions are more frequent that the system's dynamical time scale, is inapplicable to fast, sub-viscous ICM motion. Most importantly, the electron contribution to collisional magneto-viscosity dominates over that of ions for short-scale Alfvenic motions. Thus, if a turbulent cascade develops in the ICM and propagates down to scales $\leq 1$ kpc, it is damped collisionally not on ions, but on electrons. Second, in high beta plasma of ICM, small variations of the magnetic field strength, of relative value $\sim 1/\beta$, lead to development of anisotropic pressure instabilities (firehose, mirror and cyclotron). Unstable wave modes may provide additional resonant scattering of particles, effectively keeping the plasma in a state of marginal stability. We show that in this case the dissipation rate of a laminar, subsonic, incompressible flows scales as inverse of plasma beta parameter. We discuss application to the problem of ICM heating.Comment: 4 pages, accepted by ApJ Let

Exterior optical cloaking and illusions by using active sources: a boundary element perspective

Recently, it was demonstrated that active sources can be used to cloak any objects that lie outside the cloaking devices [Phys. Rev. Lett. \textbf{103}, 073901 (2009)]. Here, we propose that active sources can create illusion effects, so that an object outside the cloaking device can be made to look like another object. invisibility is a special case in which the concealed object is transformed to a volume of air. From a boundary element perspective, we show that active sources can create a nearly "silent" domain which can conceal any objects inside and at the same time make the whole system look like an illusion of our choice outside a virtual boundary. The boundary element method gives the fields and field gradients (which can be related to monopoles and dipoles) on continuous curves which define the boundary of the active devices. Both the cloaking and illusion effects are confirmed by numerical simulations

Trapping cold atoms near carbon nanotubes: thermal spin flips and Casimir-Polder potential

We investigate the possibility to trap ultracold atoms near the outside of a metallic carbon nanotube (CN) which we imagine to use as a miniaturized current-carrying wire. We calculate atomic spin flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism and we compute the minimum distance to the carbon nanotube at which an atom can be trapped.Comment: 8 pages, 3 figure

Rigorous formulation of oblique incidence scattering from dispersive media

We formulate a finite-difference time-domain (FDTD) approach to simulate electromagnetic wave scattering from scatterers embedded in layered dielectric or dispersive media. At the heart of our approach is a derivation of an equivalent one-dimensional wave propagation equation for dispersive media characterized by a linear sum of Debye-, Drude- and Lorentz-type poles. The derivation is followed by a detailed discussion of the simulation setup and numerical issues. The developed methodology is tested by comparison with analytical reflection and transmission coefficients for scattering from a slab, illustrating good convergence behavior. The case of scattering from a sub-wavelength slit in a dispersive thin film is explored to demonstrate the applicability of our formulation to time- and incident angle-dependent analysis of surface waves generated by an obliquely incident plane wave.Comment: 35 pages, 8 figures, 4 table

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Computation and visualization of Casimir forces in arbitrary geometries: non-monotonic lateral forces and failure of proximity-force approximations

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a piston-like problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate non-additive and non-monotonic changes in the force due to these lateral walls.Comment: Accepted for publication in Physical Review Letters. (Expected publication: Vol. 99 (8) 2007