scholarly journals Dynamical Implications of Diffusive and Convective Cosmic ray Propagation in Galactic Halos

1991 ◽  
Vol 144 ◽  
pp. 373-376
Author(s):  
D. Breitschwerdt ◽  
J.F. Mckenzie ◽  
H.J. Völk
Keyword(s):  
Wave Field ◽  
Strong Coupling ◽  
Thermal Plasma ◽  
Cosmic Ray ◽  
Analytic Solutions ◽  
Present Knowledge ◽  
Numerical Results ◽  
Alfvén Waves ◽  
Galactic Halos ◽  
Galactic Wind

On the basis of our present knowledge about Cosmic Ray (CR) propagation, it is argued that galactic halos should mainly consist of two parts, namely a lower region, extending from the disk-halo interface to a few kpc, in which CR diffusion prevails and an upper region, where convection dominates. The upper part is the possible site of galactic wind formation due to the strong coupling of the CRs to the thermal plasma via (mainly outwards propagating) Alfvén waves as a mediator. In the lower halo and also in the disk, the gas will be effectively static, the wave field will be almost random in its direction (due to stochastic gas motions), and the CRs must diffuse through the gas to escape. We present a model that describes both the upper and the lower halo and briefly discuss simple analytic solutions for the diffusion and numerical results for the convection region.

Magnetohydrodynamic plasma instability driven by Alfvén waves excited by cosmic rays

1984 ◽  
Vol 31 (2) ◽  
pp. 275-299 ◽  
Author(s):  
J. F. McKenzie ◽  
G. M. Webb
Keyword(s):  
Cosmic Rays ◽  
Thermal Plasma ◽  
Cosmic Ray ◽  
Nonlinear Damping ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Shock Acceleration ◽  
Alfvén Waves ◽  
Wave Growth ◽  
Streaming Instability

Hydrodynamical equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves scattering the cosmic rays used in cosmic ray shock acceleration theory (e.g. McKenzie & Völk 1982; Drury 1983; Webb 1983) are analysed for long-wavelength linear compressive instabilities. The Alfvén wave field may contain a pre-existing component as well as a component excited by the cosmic ray streaming instability. In the case of no Alfvén wave damping, adiabatic wave growth and Alfvén wave generation by the cosmic ray streaming instability, it is found that the backward propagating slow magneto-acoustic mode is driven convectively unstable by the pressure of the self-excited Alfvén waves, provided the thermal plasmaβis sufficiently large. The equations are also analysed for the case where the Alfvén wave growth is balanced by some nonlinear damping mechanisms. In the latter case both the forward and backward propagating slow magneto-acoustic modes may be driven unstable if the plasmaβis sufficiently small. The conditions under which the instabilities occur are delineated, and sample calculations of growth rates given. Possible applications of the instabilities to astrophysical situations are briefly discussed.

scholarly journals Electromagnetic Topology Analysis to Coupling Wires Enclosed in Cavities with Apertures

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Ying Li ◽  
Jianshu Luo ◽  
Guyan Ni ◽  
Jiyuan Shi
Keyword(s):  
Analytic Solutions ◽  
Numerical Results ◽  
Coupling Theory ◽  
Cavity Model ◽  
Frequency Range ◽  
Topology Analysis ◽  
Resonant Frequencies ◽  
Load Response ◽  
Aperture Coupling ◽  
Coupling Current

We use both electromagnetic topology (EMT) and the Baum-Liu-Tesche (BLT) equation to analyze a cavity model with an aperture. More precisely, we combine the aperture coupling theory and EMT to study the issues of the electromagnetic field penetration through apertures into a cavity and the coupling to a two-wire transmission line in it. We employ the equivalence principle to establish the equivalent source on the aperture. Then, we obtain the semi analytic solutions of the load response of the two-wire line in the cavity based on the Baum-Liu-Tesche (BLT) equation. In addition, based on the Agrawal model, we give the coupling current distribution at two loads for a two-wire line in the cavity. Finally, we present some numerical results to demonstrate the semi-analytic approach of this paper. In fact, these numerical results on the electric field shielding (EFS) of a rectangular cavity with an aperture agree well with the experimental results in the literature. Furthermore, for a two-wire line in the cavity with an aperture the induced current peaks at loads are observed in the frequency range, some of which are associated with the resonance of the aperture, and others correspond to the resonant frequencies of the cavity.

scholarly journals A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3195
Author(s):  
Nan-Jing Wu ◽  
Yin-Ming Su ◽  
Shih-Chun Hsiao ◽  
Shin-Jye Liang ◽  
Tai-Wen Hsu
Keyword(s):  
Least Squares ◽  
Shallow Water ◽  
Water Waves ◽  
Dynamic Pressure ◽  
Weighted Least Squares ◽  
Shallow Water Equation ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Time Marching

In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results.

scholarly journals Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

2020 ◽  
Vol 493 (4) ◽  
pp. 5323-5335 ◽  
Author(s):  
Philipp Kempski ◽  
Eliot Quataert ◽  
Jonathan Squire
Keyword(s):  
Cosmic Rays ◽  
Thermal Plasma ◽  
Acoustic Waves ◽  
Cosmic Ray ◽  
High Energy ◽  
Density Fluctuations ◽  
Sound Waves ◽  
X Ray ◽  
Acoustic Instability ◽  
Anisotropic Viscosity

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

scholarly journals Regular and Stochastic Dynamics of Relativistic Particles in Alfvén Waves

1990 ◽  
Vol 140 ◽  
pp. 155-156
Author(s):  
S. M. Carioli ◽  
V. N. Fedorenko
Keyword(s):  
Stochastic Dynamics ◽  
Interplanetary Medium ◽  
Cosmic Ray ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
One Dimensional ◽  
Test Particles ◽  
Particle Propagation ◽  
Space Dynamics ◽  
Relativistic Particles

We study the exact phase space dynamics of relativistic test particles propagating in static one-dimensional Alfvén waves, modelling cosmic ray propagation in the interplanetary medium and in the interstellar medium. The result shows that the conventional approach should not be considered adequate to explain important features of particle propagation in Alfvén waves.

Cosmic ray age, soft X-rays and the galactic wind

Nature ◽  
1977 ◽  
Vol 268 (5619) ◽  
pp. 401-402 ◽  
Author(s):  
J. J. Quenby
Keyword(s):  
Cosmic Ray ◽  
X Rays ◽  
Galactic Wind

Constant Temperature at the Surface of an Initially Uniform Temperature, Variable Conductivity Half Space

1971 ◽  
Vol 93 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Leonard Y. Cooper
Keyword(s):  
Temperature Distribution ◽  
Half Space ◽  
Constant Temperature ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Transient Temperature ◽  
Uniform Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Variable ◽  
Variable Conductivity

The transient temperature distribution resulting from a constant and uniform temperature being imposed on the surface of an initially uniform temperature, variable conductivity half space is studied. Various solution expansion ideas are discussed. These are utilized in the solution of an example problem, and the resulting approximate analytic solutions representations are compared to exact numerical results. One of these approximations is found to be superior to the others, and, in fact, it is shown to yield useful results over a range of variables where the nonlinearities of the problem are significant.

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