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  • 1
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    Time dependent simulation of cosmic-ray shocks including Alfven transport (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Time evolution of plane, cosmic-ray modified shocks was simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven wave energy transport equations. Nonlinear feedback from the cosmic-rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the time scale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic-rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.
    Keywords: SPACE RADIATION
    Type: NASA-CR-192931 , NAS 1.26:192931
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  • 2
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    Oblique MHD cosmic-ray modified shocks: Two-fluid numerical simulations (1991)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: We present the first results of time dependent, two-fluid, cosmic-ray (CR) modified, MHD shock simulations. The calculations were carried out with a new numerical code for 1-D ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time-dependent evolution of MHD shocks including the acceleration of the CR and their feedback on the shock structures. We report tests of the combined numerical method including comparisons with analytical steady state results published earlier by Webb, as well as internal consistency checks for more general MHD CR shock structures after they appear to have converged to dynamical steady states. We also present results from an initial time dependent simulation which extend the parameter space domain of previous analytical models. These new results support Webb's suggestion that equilibrium oblique shocks are less effective than parallel shocks in the acceleration of CR. However, for realistic models of anisotropic CR diffusion, oblique shocks may achieve dynamical equilibrium on shorter timescale than parallel shocks.
    Keywords: SPACE RADIATION
    Type: NASA-CR-192930 , NAS 1.26:192930
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  • 3
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    Alfven wave transport effects in the time evolution of parallel cosmic-ray modified shocks (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Some of the issues associated with a more complete treatment of Alfven transport in cosmic ray shocks are explored qualitatively. The treatment is simplified in some important respects, but some new issues are examined and for the first time a nonlinear, time dependent study of plane cosmic ray mediated shocks with both the entropy producing effects of wave dissipation and effects due to the Alfven wave advection of the cosmic ray relative to the gas is included. Examination of the direct consequences of including the pressure and energy of the Alfven waves in the formalism began.
    Keywords: SPACE RADIATION
    Type: NASA-CR-192932 , NAS 1.26:192932
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  • 4
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    Numerical simulations of time-dependent cosmic ray mediated shocks (1992)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: Recent research in unsteady shocks that are influenced by nonlinear aspects of diffusive particle acceleration and that involve multidimensional flows is outlined, and some of the difficulties in making further progress are discussed. It is suggested that in many situations it is probably not appropriate to assume steady states for astrophysical CR shocks. This results both from the need to be concerned about the finite rate at which CR pressure builds and modifies a shock and from the existence of instabilities. Even so, it seems likely that CR-modified shocks can develop to a state with substantial CR pressure. The overall acceleration efficiency and the CR particle momentum distribution produced in time-dependent flows typically depend on several details such as the ratio of various time scales and the initial proportion of relativistic to nonrelativistic particles in the CR populations.
    Keywords: SPACE RADIATION
    Type: In: Particle acceleration in cosmic plasmas; Proceedings of the Workshop, Bartol Research Inst., Newark, DE, Dec. 4-6, 1991 (A93-39976 16-93); p. 148-157.
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  • 5
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    The stability of cosmic-ray-dominated shocks - A secondary instability (1993)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: Previous studies in one spatial dimension showed that the precursors of cosmic-ray-dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray-dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent.
    Keywords: SPACE RADIATION
    Type: Astrophysical Journal, Part 1 (ISSN 0004-637X); 405; 1; p. 199-206.
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  • 6
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    Cosmic-ray acceleration during the impact of shocks on dense clouds (1993)
    In:  Other Sources
    Details
    Publication Date: 2019-08-28
    Description: In order to elucidate the properties of diffusive shock acceleration in nonuniform environments, an extensive set of simulations of the dynamical interactions between plane nonradiative shocks and dense gas clouds was carried out initially in static equilibrium with their environments. These time-dependent calculations are based on the two-fluid model for diffusive cosmic ray transport, and include the dynamically active energetic proton component of the cosmic rays as well as passive electron and magnetic field components. Except when the incident shock is itself already dominated by cosmic ray pressure, it is found that the presence of the cloud adds little to the net acceleration efficiency of the original shock and can, in fact, reduce slightly the net amount of energy transferred to cosmic rays after a given time. It is found that, in 2D cloud simulations, the always-weak bow shock and the shock inside the cloud are less important to acceleration during the interaction than the tail shock.
    Keywords: SPACE RADIATION
    Type: Astrophysical Journal, Part 1 (ISSN 0004-637X); 402; 2; p. 560-573.
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