The evolution of cosmic-ray-mediated magnetohydrodynamic shocks: A two-fluid approach

1994 ◽  
Vol 429 ◽  
pp. 748 ◽  
Author(s):  
Byung-Il Jun ◽  
David A. Clarke ◽  
Michael L. Norman
Keyword(s):  
Cosmic Ray ◽  
Two Fluid ◽  
Magnetohydrodynamic Shocks

The time-asymptotic stability of shocks in cosmic-ray hydrodynamics

1988 ◽  
Vol 39 (3) ◽  
pp. 539-548 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Short Wavelength ◽  
Cosmic Ray ◽  
Hydrodynamical Model ◽  
Shock Formation ◽  
Nonlinear Behaviour ◽  
Two Fluid

The nonlinear behaviour of short-wavelength perturbations in the two-fluid cosmic-ray hydrodynamical model is examined. We show that such a perturbation leads to shock formation and derive the appropriate wave equation. We show that a discontinuous perturbation incident on a weak cosmic-ray shock destabilizes, in a time-asymptotic sense, the shock.

Wave–wave interactions in two-fluid cosmic-ray hydrodynamics

1997 ◽  
Vol 57 (3) ◽  
pp. 631-676 ◽  
Author(s):  
G. M. WEBB ◽  
M. BRIO ◽  
G. P. ZANK ◽  
T. STORY
Keyword(s):  
Cosmic Ray ◽  
Wave Interactions ◽  
Two Fluid

scholarly journals Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

1995 ◽  
Vol 441 ◽  
pp. 629 ◽  
Author(s):  
Adam Frank ◽  
T. W. Jones ◽  
Dongsu Ryu
Keyword(s):  
Fluid Model ◽  
Cosmic Ray ◽  
Time Dependent ◽  
Two Fluid Model ◽  
Two Fluid

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

1995 ◽  
Vol 442 ◽  
pp. 822 ◽  
Author(s):  
G. M. Webb ◽  
M. Brio ◽  
G. P. Zank ◽  
T. Story
Keyword(s):  
Cosmic Ray ◽  
Pressure Balance ◽  
Two Fluid

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.

Renormalized Two‐Fluid Hydrodynamics of Cosmic‐Ray–modified Shocks

1996 ◽  
Vol 473 (1) ◽  
pp. 347-355 ◽  
Author(s):  
M. A. Malkov ◽  
H. J. Volk
Keyword(s):  
Cosmic Ray ◽  
Fluid Hydrodynamics ◽  
Two Fluid
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