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Volumn 58, Issue 4, 1998, Pages 4911-4928

Ion leakage from quasiparallel collisionless shocks: Implications for injection and shock dissipation

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; COMPOSITION; COMPUTER SIMULATION; MAGNETOHYDRODYNAMICS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PLASMA CONFINEMENT; PLASMA SHOCK WAVES; PLASMA TURBULENCE; SPECTRUM ANALYSIS; TRANSPORT PROPERTIES;

EID: 0032185280     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.4911     Document Type: Article
Times cited : (102)

References (57)
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    • (unpublished)
    • M. A. Malkov (unpublished).
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    • It should be noted that the magnetosonic (MS) component is also observed and may even prevail in 1D and 2D simulations 24. The latter, however, are computationally very expensive and therefore rather incomplete. We have chosen an Alfvén [formula presented] type of polarization for a number of reasons. First, in a real 3D situation the MS waves experience a strong Cherenkov damping for even slightly oblique propagation, and thus they should occupy a significantly smaller volume in [formula presented] space than that of the Alfvén waves for similar generation and spectral transformation processes. Second, the criterion of modulational stability is satisfied for [formula presented] waves in the case [formula presented] unlike for MS waves [formula presented] see e.g., We will concentrate exclusively on the case [formula presented] i.e., the plasma downstream is a high β plasma [formula presented] and the magnetosonic wave must be modulationally unstable. However, the above arguments and stability criteria may be applied to the complicated strongly turbulent shock environment only with care, since they have been obtained for homogeneous plasma and in the framework of an essentially perturbative approach. However, the main and in fact very simple reason for choosing the [formula presented]-type polarization is that the calculation of the distribution of leaking particles is practically very similar for [formula presented] and MS waves. Moreover, the [formula presented] wave allows some additional group of particles to leak upstream (see Sec. V), and in this sense the MS case is a subset of the [formula presented] case. We used this in Sec. IX while comparing our results with hybrid simulations. JGREA2
    • It should be noted that the magnetosonic (MS) component is also observed and may even prevail in 1D and 2D simulations 24. The latter, however, are computationally very expensive and therefore rather incomplete. We have chosen an Alfvén (A) type of polarization for a number of reasons. First, in a real 3D situation the MS waves experience a strong Cherenkov damping for even slightly oblique propagation, and thus they should occupy a significantly smaller volume in k space than that of the Alfvén waves for similar generation and spectral transformation processes. Second, the criterion of modulational stability is satisfied for A waves in the case CACS); see e.g., M. Longtin and B. U. Ö Sonnerup, J. Geophys. Res. 91, 6816 (1986). We will concentrate exclusively on the case MA≫1, i.e., the plasma downstream is a high β plasma (CA≪CS), and the magnetosonic wave must be modulationally unstable. However, the above arguments and stability criteria may be applied to the complicated strongly turbulent shock environment only with care, since they have been obtained for homogeneous plasma and in the framework of an essentially perturbative approach. However, the main and in fact very simple reason for choosing the A-type polarization is that the calculation of the distribution of leaking particles is practically very similar for A and MS waves. Moreover, the A wave allows some additional group of particles to leak upstream (see Sec. V), and in this sense the MS case is a subset of the A case. We used this in Sec. IX while comparing our results with hybrid simulations.JGREA2
    • (1986) J. Geophys. Res. , vol.91 , pp. 6816
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    • A reflected component of the wave field that is also known to appear upon the shock crossing has a substantially lower amplitude than that of the transmitted wave; see , PLSSAE
    • A reflected component of the wave field that is also known to appear upon the shock crossing has a substantially lower amplitude than that of the transmitted wave; see J. F. McKenzie and K. O. Westphal, Planet. Space Sci. 17, 1029 (1969)
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    • We do not take it into account in our analysis of the regular particle motion, but instead attribute it to the background turbulence. MNRAA4
    • A. Achterberg and R. D. Blandford, Mon. Not. R. Astron. Soc. 218, 551 (1986). We do not take it into account in our analysis of the regular particle motion, but instead attribute it to the background turbulence.MNRAA4
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    • Achterberg, A.1    Blandford, R.D.2
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    • This is, in fact, the density of particles that cross the shock from the downstream side for the first time, the “first generation” of injected particles 13. Subsequently, they become subject to first-order Fermi acceleration to form a population with a higher density. This process results, generally speaking, in a further transformation of abundances at higher energies. We also note that an injection rate that can be attributed to the beam density [Eq. (68)] is not to be confused with the injection rate that is normally used in studies of the diffusion-convection equation, where only the particles with momentum [formula presented] are regarded as “injected.” Here [formula presented] is an injection momentum, a somewhat artificial boundary between the thermal and nonthermal plasma, and only the latter is assumed to obey the diffusion-convection equation (see Refs. 13 46 for relevant discussions). There are also certain peculiarities in numerical schemes of injection; see, e.g.,, ASJOAB
    • This is, in fact, the density of particles that cross the shock from the downstream side for the first time, the “first generation” of injected particles 13. Subsequently, they become subject to first-order Fermi acceleration to form a population with a higher density. This process results, generally speaking, in a further transformation of abundances at higher energies. We also note that an injection rate that can be attributed to the beam density [Eq. (68)] is not to be confused with the injection rate that is normally used in studies of the diffusion-convection equation, where only the particles with momentum p>pinj≫mα(u1-u2) are regarded as “injected.” Here pinj≫mα(u1-u2) is an injection momentum, a somewhat artificial boundary between the thermal and nonthermal plasma, and only the latter is assumed to obey the diffusion-convection equation (see Refs. 1346 for relevant discussions). There are also certain peculiarities in numerical schemes of injection; see, e.g., H. Kang and T. W. Jones, Astrophys. J. 447, 944 (1995).ASJOAB
    • (1995) Astrophys. J. , vol.447 , pp. 944
    • Kang, H.1    Jones, T.W.2
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    • this case the injection rate is so high that the actual downstream temperature becomes substantially larger than it was assumed to be in the source term [formula presented] in Eqs. (81) and (A1), and the whole solution contradicts the RH conditions. To avoid this inconsistency the temperature in the source term [formula presented] was parametrized (lowered) in Ref. 13
    • In this case the injection rate is so high that the actual downstream temperature becomes substantially larger than it was assumed to be in the source term fM in Eqs. (81) and (A1), and the whole solution contradicts the RH conditions. To avoid this inconsistency the temperature in the source term fM was parametrized (lowered) in Ref. 13.
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    • H. J. Völk, in Towards a Major Atmospheric Cerenkov Detector—V, edited by O. C. de Jager, Proceedings of the Kruger National Park Workshop on TeV Gamma Ray Astrophysics, Kruger National Park, August 1997 (Potchefstroom University for CHE, 1997), p. 87.


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