Peculiarities of quasi-linear dynamics of diamagnetic instability of space plasmas
Category: 14-1
UDC 550.38
O.A. Pokhotelov, O.G. Onishchenko
Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia
Abstract
A theory of the nonlinear evolution of the mirror mode near instability threshold is developed. It is found that during initial stage the major instability saturation is provided by the flattening of the ion distribution function in the resonant region. The instability relaxation is connected with rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic Bernstein, Greene and Kruskal (BGK) modes [Bernstein, Greene, Kruskal, 1959]. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by “particle-in-cell” (PIC) numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode.
Keywords: MHD waves and turbulence, magnetosheath, nonlinear phenomena.
References
Balikhin, M., Pokhotelov, O., Walker, S., Boynton, R., and Beloff, N., Mirror mode peaks: THEMIS observations versus theories, Geophys. Res. Lett., 2010, vol. 37, p.L05104, doi: 10.1029/2009GL042090.
Balikhin, M.A., Sagdeev, R.Z., Walker, S.N., Pokhotelov, O.A., Sibeck, D.G., Beloff, N., and Dudnikova, G., THEMIS Observations of Mirror Structures: Magnetic Holes and Instability Thresholds, Geophys. Res. Lett., 2009, vol. 36, p. LO3105, doi: 10.1029/2008GLO36923.
Bernstein, I.B., Greene, J.M., and Kruskal, M.D., Exact nonliner plasma oscillations, Phys. Rev., 1957, vol. 108, pp. 546–550.
Califano, F., Hellinger, P., Kuznetsov, E.A., Passot, T., Sulem, P.L., and Trávniček P.M., Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 2008, vol. 13, p. A08219, doi: 10.1029/2007JA012898.
Fried B.D., Mechanism for instability of transverse plasma waves, Phys. Fluids, 1959, vol. 2, pp. 337–337.
Hellinger, P., Kuznetsov, E.A., Passot, T., Sulem, P.L., and Trávniček P.M., Mirror instability: From quasi-linear diffusion to coherent structures, Geophys. Res. Lett., 2009, vol. 36, p. L06103. doi: 10.1029/2008GL036805.
Istomin, Y.N., Pokhotelov, O.A., and Balikhin, M.A., Mirror instability in Space plasmas: Solitons and Cnoidal Waves, Phys. Plasmas, 2009a, vol. 16, p. 062905.
Istomin, Ya.N., Pokhotelov, O.A., and Balikhin, M.A., Nonzero electron temperature effects in nonlinear mirror modes, Phys. Plasmas, 2009b, vol. 16, pp. 122901.
Jovanović, D. and Shukla, P.K., Nonlinear gyrokinetic theory for steady-state mirror mode magnetic structures, Phys. Plasmas, 2009, vol. 16, p.082901.
Kivelson, M.G. and Southwood, D.J., Mirror instability, 2, The mechanism of nonlinear saturation, J. Geophys. Res., 1996, vol. 101, pp. 17.365–17.371.
Kuznetsov, E.A., Passot T., and Sulem, P.L., Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 2007, vol. 98, p.235003.
Palodhi, L., Califano, F., and Pegoraro, F., Nonlinear kinetic development of the Weibel instability and the generation of electrostatic coherent structures, Plasma Phys. Control. Fusion, 2009, vol. 51, P.125006. doi:10.1088/0741-3335/51/12/125006.
Pantellini, F.G. E., A model of the formation of stable nonpropagating magnetic structures in the solar wind based on the nonlinear mirror instability, J. Geophys. Res., 1998, vol. 103, pp. 4789–4798.
Pokhotelov, O.A. and Amariutei, O.A., Quasi-linear dynamics of Weibel instability, Ann. Geophys., 2011, vol. 29, pp.,1997–2001.
Pokhotelov, O.A., Sagdeev, R.Z., Balikhin, M.A., Onishchenko, O.G., and Fedun, V.N., Nonlinear mirror waves in non-Maxwellian space plasmas, J. Geophys. Res., 2008, vol. 113, p. A04225, doi: 10.1029/2007JA012642.
Shapiro, V.D. and Shevchenko, V.I., Quasilinear theory of instability of a plasma with anisotropic ion velocity distribution, Sov. Phys. JETP, Eng. Trans., 1964, vol. 18, pp. 1109–1116.
Soucek, J., Lucek, E., and Dandouras, I., Properties of magnetosheath mirror modes observed by Cluster and their response to changes in plasma parameters, J. Geophys. Res., 2008, vol. 113, p.A04203, doi: 10.1029/2007JA012649.
Vedenov, A.A. and Sagdeev, R.Z., Some properties of plasma with an anisotropic ion velocity distribution in a magnetic field, Plasma Physics and Problem of Controlled Thermonuclear Reactions, 1958, vol. 3, New York: Pergamon, p. 332.
Weibel, E.S., Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution, Phys. Rev. Lett., 1959, vol. 2, pp. 83–84.