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Slab magnetised non-relativistic low-beta electron–positron plasmas: collisionless heating, linear waves and reconnecting instabilities

  • Alessandro Zocco
Abstract

The properties of a non-relativistic magnetised low-beta electron–positron plasma in slab geometry are investigated. The two species are taken to be drift kinetic while we retain Larmor radius effects in quasi-neutrality, and inertia in Ohm’s law. A linear analysis shows that, for small magnetic perturbations, Alfvénic perturbations travel at the electron Alfvén speed, which is based on the electron mass. We discuss the role of the displacement current when Larmor-scale and Debye-scale effects are both retained. We predict the existence of a kinetic electron Alfvén wave which connects to the K-modes of Mishchenko et al. (J. Plasma Phys., 2017 (submitted)) in the electrostatic limit. It is found that linear drift waves are not supported by the system if the two species have the same temperature. Tearing modes can be driven unstable by equilibrium current density gradients. Also in this case, the characteristic time is based on the electron Alfvén speed. Nonlinear hybrid fluid-kinetic equations are also derived. It is shown that each species is described, to leading order, by the kinetic reduced electron heating model (KREHM) kinetic equation of Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309). The model is extended to retain first-order Larmor radius effects. It supports collisionless dispersive waves, which can greatly impact nonlinear magnetic reconnection. Diamagnetic effects enter the nonlinear equations via the first-order magnetic compressibility. A minimal nonlinear model for two-dimensional low-frequency isothermal pair plasmas is derived.

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      Slab magnetised non-relativistic low-beta electron–positron plasmas: collisionless heating, linear waves and reconnecting instabilities
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Corresponding author
Email address for correspondence: Alessandro.zocco@ipp.mpg.de
References
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Basu, B. & Coppi, B. 1981 Theory of modes in collisionless plasmas. Phys. Fluids 24 (3), 465471.
Bessho, N. & Bhattacharjee, A. 2005 Collisionless reconnection in an electron–positron plasma. Phys. Rev. Lett. 95 (24), 245001245004.
Braginskii, S. I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1, pp. 205311. Consultants Bureau.
Chacón, L., Simakov, A. N., Lukin, V. S. & Zocco, A. 2008 Fast reconnection in nonrelativistic 2d electron–positron plasmas. Phys. Rev. Lett. 101 (2), 025003.
Chacón, L., Simakov, A. N. & Zocco, A. 2007 Steady-state properties of driven magnetic reconnection in 2d electron mhd. Phys. Rev. Lett. 99, 235001.
Coppi, B., Galvão, R. M. O., Pellat, R., Rosenbluth, M. N. & Rutherford, P. H. 1976 Fiz. Plazmy 6, 691; Sov. J. Plasma Phys. 11, 226 (1975).
Daughton, W. & Karimabadi, H. 2007 Collisionless magnetic reconnection in large-scale electron–positron plasmas. Phys. Plasmas 14 (7), 7230372310.
Drake, J. F. & Lee, Y. C. 1977 Kinetic theory of tearing instabilities. Phys. Fluids 20 (8), 13411353.
Fried, B. D., Hendrick, C. L. & McCune, J. 1968 Two-pole approximation for the plasma dispersion function. Phys. Fluids 11, 249252.
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25 (3), 502508.
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Finite-resistivity instabilities of a sheet pinch. Phys. Fluids 6, 1169.
Guo, F., Li, H., Daughton, W., Li, X. & Liu, Y.-H. 2016 Particle acceleration during magnetic reconnection in a low-beta pair plasma. Phys. Plasmas 23 (5), 055708.
Helander, P. 2014 Microstability of magnetically confined electron–positron plasmas. Phys. Rev. Lett. 113, 135003.
Helander, P. 2017 Available energy and ground states of collisionless plasmas. J. Plasma Phys. 83 (4), 715830401.
Helander, P. & Connor, J. W. 2016 Gyrokinetic stability theory of electron–positron plasmas. J. Plasma Phys. 82 (3), 905820301.
Lenard, A. & Bernstein, I. B. 1958 Plasma oscillations with diffusion in velocity space. Phys. Rev. 112 (5), 1456.
Loureiro, N. F., Dorland, W., Fazendeiro, L., Kanekar, A., Mallet, A., Vilelas, M. S. & Zocco, A. 2016 Viriato: a Fourier–Hermite spectral code for strongly magnetized fluid kinetic plasma dynamics. Comput. Phys. Commun. 206, 4563.
Loureiro, N. F., Schekochihin, A. A. & Zocco, A. 2013 Fast collisionless reconnection and electron heating in strongly magnetized plasmas. Phys. Rev. Lett. 111, 025002.
Makwana, K. D., Zhdankin, V., Li, H., Daughton, W. & Cattaneo, F. 2015 Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence. Phys. Plasmas 22 (4), 042902.
Mishchenko, A., Zocco, A., Helander, P. & Könies, A. 2017 J. Plasma Phys. (submitted).
Ottaviani, M. & Porcelli, F. 1995 Fast nonlinear magnetic reconnection. Phys. Plasmas 2 (11), 41044117.
Pedersen, T. S., Danielson, J. R., Hugenschmidt, C., Marx, G., Sarasola, X., Schauer, F., Schweikhard, L., Surko, C. M. & Winkler, E. 2012 Plans for the creation and studies of electron–positron plasmas in a stellarator. New J. Phys. 14 (3), 035010.
Saitoh, H., Pedersen, T. S., Hergenhahn, U., Stenson, E. V., Paschkowski, N. & Hugenschmidt, C. 2014 Recent status of a positron–electron experiment (apex). J. Phys. Conf. Ser. 505 (1), 012045.
Schekochihin, A. A., Parker, J. T., Highcock, E. G., Dellar, P. J., Dorland, W. & Hammett, G. W. 2016 Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence. J. Plasma Phys. 82 (2), 905820212.
Schep, T. J., Pegoraro, F. & Kuvshinov, B. N. 1994 Generalized two-fluid theory of nonlinear magnetic structures. Phys. Plasmas 1 (9), 28432852.
Stenson, E. V., Horn-Stanja, J., Stoneking, M. R. & Pedersen, T. S. 2017 Debye length and plasma skin depth: two length scales of interest in the creation and diagnosis of laboratory pair plasmas. J. Plasma Phys. 83 (1), 595830106.
Zocco, A. 2015 Linear collisionless Landau damping in Hilbert space. J. Plasma Phys. 81 (4), 7.
Zocco, A., Chacón, L. & Simakov, A. 2008 Electron inertia effects in 2d driven reconnection in electron mhd. In Theory of Fusion Plasmas, AIP Conference Proceedings, vol. 1069, pp. 349354. AIP.
Zocco, A., Chacón, L. & Simakov, A. N. 2009 Current sheet bifurcation and collapse in electron magnetohydrodynamics. Phys. Plasmas 16 (11), 110703.
Zocco, A., Loureiro, N. F., Dickinson, D., Numata, R. & Roach, C. M. 2015 Kinetic microtearing modes and reconnecting modes in strongly magnetised slab plasmas. Plasma Phys. Control. Fusion 57 (6), 065008.
Zocco, A. & Schekochihin, A. A. 2011 Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas. Phys. Plasmas 18 (10), 102309.
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Journal of Plasma Physics
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