The stability of cosmic-ray-dominated shocks - A secondary instability

1993 ◽  
Vol 405 ◽  
pp. 199 ◽  
Author(s):  
Dongsu Ryu ◽  
Hyesung Kang ◽  
T. W. Jones
Keyword(s):  
Cosmic Ray ◽  
Secondary Instability ◽  
The Stability

scholarly journals Cosmic ray tracking to monitor the stability of historical buildings: a feasibility study

2019 ◽  
Vol 30 (4) ◽  
pp. 045901 ◽  
Author(s):  
G Bonomi ◽  
M Caccia ◽  
A Donzella ◽  
D Pagano ◽  
V Villa ◽  
...  
Keyword(s):  
Feasibility Study ◽  
Cosmic Ray ◽  
Historical Buildings ◽  
The Stability

A cosmic-ray-driven plasma instability

1989 ◽  
Vol 41 (1) ◽  
pp. 89-95 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Thermal Plasma ◽  
Cosmic Ray ◽  
Mhd Equations ◽  
Mutual Interaction ◽  
Shock Acceleration ◽  
Wave Effects ◽  
The Stability

The stability of the MHD equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves used in cosmic-ray-shock acceleration theory (e.g. McKenzie & Völk 1982) is analysed for linear compressive instabilities. It is found that the inclusion of wave effects implies that the forward propagating sub-Alfvénic mode is unstable on wavelength scales greater than 1 parsec. The role of the instability in astrophysical models is considered.

The interaction of long-wavelength compressive waves with a cosmic ray shock

1987 ◽  
Vol 37 (3) ◽  
pp. 363-372 ◽  
Author(s):  
G. P. Zank ◽  
J. F. Mckenzie
Keyword(s):  
Dispersion Equation ◽  
Transmission Coefficient ◽  
Cosmic Ray ◽  
Long Wavelength ◽  
The Stability ◽  
Two Fluid

This paper investigates the stability of a cosmic ray shock to long-wavelength perturbations. The problem is formulated in terms of finding the transmission coefficient for compressive waves across a cosmic ray shock by solving the generalized, two-fluid Rankine-Hugoniot relations. For strong shocks, the transmission coefficient confirms that compressive waves can undergo considerable amplification on passage through such shocks. The resonances of the transmission coefficient provides us with the dispersion equation governing the stability of the shock to long-wavelength ripple-like distortions. By using the principle of the argument method, it is established that cosmic ray shocks are stable.

Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation

2007 ◽  
Vol 583 ◽  
pp. 229-272 ◽  
Author(s):  
GIUSEPPE BONFIGLI ◽  
MARKUS KLOKER
Keyword(s):  
Stability Theory ◽  
Three Dimensional ◽  
Amplitude Distribution ◽  
Detailed Comparison ◽  
Secondary Instability ◽  
Linear Stability Theory ◽  
Local Maxima ◽  
Instability Modes ◽  
The Stability ◽  
Secondary Instabilities

Detailed comparison of spatial direct numerical simulations (DNS) and secondary linear stability theory (SLST) is provided for the three-dimensional crossflow-dominated boundary layer also considered at the DLR-Göttingen for experiments and theory. Secondary instabilities of large-amplitude steady and unsteady crossflow vortices arising from one single primary mode have been analysed. SLST results have been found to be reliable with respect to the dispersion relation and the amplitude distribution of the modal eigenfunction in the crosscut plane. However, significant deviations have been found in the amplification rates, the SLST results being strongly dependent on the necessarily simplified representation of the primary state. The secondary instability mechanisms are shown to be local, i.e. robust with respect to violations of the periodicity assumption made in the SLST for the wall-parallel directions. Perturbations associated with different local maxima of the spanwise periodic eigenfunctions develop independently from each other interacting only with the primary vortices next to them. Characteristic structures induced by different secondary instability modes have been analysed and an analogy with the Kelvin–Helmholtz instability mechanism has been highlighted.

Short-wavelength compressive instabilities in cosmic ray shocks and heat conduction flows

1987 ◽  
Vol 37 (3) ◽  
pp. 347-361 ◽  
Author(s):  
G. P. Zank ◽  
J. F. Mckenzie
Keyword(s):  
Solar Wind ◽  
Heat Conduction ◽  
Cosmic Ray ◽  
Theoretical Models ◽  
Dissipative Heating ◽  
Wave Action ◽  
Background Flow ◽  
Wave Amplification ◽  
Shock Transition ◽  
The Stability

In this paper we discuss the stability of three genetically similar non-uniform flows to compressive disturbances whose wavelengths are much shorter than the length scales characterizing the background flow. The results are relevant to theoretical models of cosmic ray shocks and solar wind type flows involving heat conduction. A JWKB expansion solution yields an equation which determines how the amplitudes of the perturbations may grow (or decay) as they propagate within such structures. It is shown that, in all three of the models considered, the perturbations exhibit spatial growth if the background flow is sufficiently supersonic and decelerating. The associated equations describing the evolution of the wave action are also studied with a view to deciding whether or not the behaviour of this attractive variable can provide an unambiguous answer to the question of stability. In the case of a shock transition dominated by heat conduction, it is shown that the effects of dissipative heating within the transition more than offset those of wave growth, with the result that wave amplification is accompanied by wave action decay. Therefore in general it would appear that the wave action equation alone cannot unambiguously settle stability questions.

On the stability of cosmic ray dominated shocks

1992 ◽  
Author(s):  
Hyesung Kang ◽  
Dongsu Ryu ◽  
T. W. Jones
Keyword(s):  
Cosmic Ray ◽  
The Stability

Three-dimensionalization of barotropic vortices on the f-plane

1994 ◽  
Vol 265 ◽  
pp. 25-64 ◽  
Author(s):  
W. D. Smyth ◽  
W. R. Peltier
Keyword(s):  
Time Dependence ◽  
Shear Layer ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Small Scale ◽  
Two Dimensional ◽  
Longitudinal Modes ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
The Stability

We examine the stability characteristics of a two-dimensional flow which consists initially of an inflexionally unstable shear layer on an f-plane. Under the action of the primary instability, the vorticity in the shear-layer initially coalesces into two Kelvin–Helmholtz vortices which subsequently merge to form a single coherent vortex. At a sequence of times during this process, we test the stability of the two-dimensional flow to fully three-dimensional perturbations. A somewhat novel approach is developed which removes inconsistencies in the secondary stability analyses which might otherwise arise owing to the time-dependence of the two-dimensional flow.In the non-rotating case, and before the onset of pairing, we obtain a spectrum of unstable longitudinal modes which is similar to that obtained previously by Pierrehumbert & Widnall (1982) for the Stuart vortex, and by Klaassen & Peltier (1985, 1989, 1991) for more realistic flows. In addition, we demonstrate the existence of a new sequence of three-dimensional subharmonic (and therefore ‘helical’) instabilities. After pairing is complete, the secondary instability spectrum is essentially unaltered except for a doubling of length- and timescales that is consistent with the notion of spatial and temporal self-similarity. Once pairing begins, the spectrum quickly becomes dominated by the unstable modes of the emerging subharmonic Kelvin–Helmholtz vortex, and is therefore similar to that which is characteristic of the post-pairing regime. Also in the context of non-rotating flow, we demonstrate that the direct transfer of energy into the dissipative subrange via secondary instability is possible only if the background flow is stationary, since even slow time-dependence acts to decorrelate small-scale modes and thereby to impose a short-wave cutoff on the spectrum.The stability of the merged vortex state is assessed for various values of the planetary vorticity f. Slow rotation may either stabilize or destabilize the columnar vortices, depending upon the sign of f, while fast rotation of either sign tends to be stabilizing. When f has opposite sign to the relative vorticity of the two-dimensional basic state, the flow becomes unstable to new mode of instability that has not been previously identified. Modes whose energy is concentrated in the vortex cores are shown to be associated, even at non-zero f, with Pierrehumbert's (1986) elliptical instability. Through detailed consideration of the vortex interaction mechanisms which drive instability, we are able to provide physical explanations for many aspects of the three-dimensionalization process.

scholarly journals Stochastic electron motion driven by space plasma waves

2014 ◽  
Vol 21 (1) ◽  
pp. 61-85 ◽  
Author(s):  
G. V. Khazanov ◽  
A. A. Tel’nikhin ◽  
T. K. Kronberg
Keyword(s):  
Langmuir Wave ◽  
Nonlinear Resonance ◽  
Cosmic Ray ◽  
Space Plasma ◽  
Plasma Waves ◽  
Relativistic Electrons ◽  
Stochastic Motion ◽  
Hamiltonian Chaos ◽  
Radiation Belt Electrons ◽  
The Stability

Abstract. Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is responsible for the dynamical balance between the accelerating process and relativistic electron precipitation events. We have also considered the efficiency of the mechanism of stochastic surfing acceleration of cosmic electrons at the supernova remnant shock front, and the accelerating process driven by a Langmuir wave packet in producing cosmic ray electrons. The dynamics of cosmic electrons is formulated in terms of a dissipative map involving the effect of synchrotron emission. We present analytical and numerical methods for studying Hamiltonian chaos and dissipative strange attractors, and for determining the heating extent and energy spectra.

Sign in / Sign up

Export Citation Format

Share Document