Kinetic effects on the parametric decays of Alfvén waves in relativistic pair plasmas
V. Muñoz, T. Hada† and S. Matsukiyo†
Departamento de Física, Facultad de Ciencias, Universidad de Chile
†Department of Earth System Science and Technology, Kyushu University
Abstract. Parametric decays of a circularly polarized wave propagating along a constant magnetic field in an electronpositron
plasma are studied. Fully relativistic effects on the particle velocity in the wave field are considered, as well as
kinetic effects in the longitudinal direction, by means of a one-dimensional relativistic Vlasov equation. In this approximation,
a dispersion relation is found for the parametric decays. This dispersion relation for the parametric decays describes the
coupling between normal modes of the system, namely electromagnetic sideband modes and Langmuir waves.
Keywords: parametric decays, Alfvén waves, relativistic plasma, electron-positron plasma
PACS: 52.27.Ep, 52.27.Ny, 52.35.Mw, 95.30.Qd
Electron-positron plasmas are different from electron-ion plasmas, because in the absence of a mass difference,
there are no high or low natural frequency scales. Such plasmas are found in pulsar magnetospheres , models
of primitive Universe , active galactic nuclei jets [3, 4], and laboratory and tokamak plasmas [5, 6]. Relativistic
effects are expected to play an important role in several of these systems. Understanding interactions between waves
and relativistic electron-positron plasmas is relevant to proposed pulsar emission mechanisms [7, 8], and may give
insight into structure formation in the early Universe .
The parametric instabilities of waves in unmagnetized electron-positron plasmas have been studied based on fluid
theory [9, 10, 11, 12], and on kinetic theory . Some of these treatments include weakly relativistic effects on
the particle motion in the wave field. However, in astrophysical environments, large particle energies are likely to be
relevant. Thus, fully relativistic effects have also been introduced [14, 15, 16]. However, all these works deal with
unmagnetized plasmas, and therefore miss an important feature of space and astrophysical plasmas.
A dispersion relation for the parametric decays of electromagnetic waves in magnetized plasmas in electron-positron
plasmas have been studied with fluid theory , in the weakly relativistic limit. Later, Matsukiyo and Hada  have
improved on that result, by not assuming charge quasineutrality. They have also performed full particle electromagnetic
simulations, and have successfully compared their results with those resulting from fluid theory. However, in fluid
theory important kinetic effects such as Landau damping are not present, and therefore a kinetic theory is highly
relevant to actually understand the simulation results.
Thus, our aim in this work is to study the parametric decays of Alfvén waves in magnetized electron-positron
plasmas, based on a kinetic theory, and considering fully relativistic effects. In this paper, we calculate the dispersion
relation for relativistic Alfvén waves propagating along a constant magnetic field in a pair plasma. Detailed numerical
analysis of this dispersion relation and comparison with particle simulations will be the subject of a future paper.
In this paper, the parametric decays of a circularly polarized wave propagating along a constant magnetic field in an
electron-positron plasma have been studied studied. The treatment has been based on the relativistic Vlasov equation,
so that kinetic effects and fully relativistic effects on the particle velocity in the wave field are considered. Kinetic
effects have been considered only in the longitudinal direction. The dispersion relation for the parametric decays of the
pump wave has been found. In the absence of the pump wave the normal modes of the system are the sideband waves
and the Langmuir waves. When the pump wave is present, these modes couple, leading to the parametric instabilities
of the system [see, e.g., 18]. For an unmagnetized plasma, the result is compatible with previously published results
This dispersion relation can be solved numerically. Work is in progress to solve it for non-relativistic temperatures,
where the plasma is described by a Maxwellian distribution function, and compare the results with particle simulations.
This numerical analysis will be the subject of a future paper.
One of us (V.M.) acknowledges a Postdoctoral Fellowship granted by JSPS (Japan). This work has been partially
supported by FONDECYT Grant No. 1060830.
1. M. F. Curtis, The Theory of Neutron Stars Magnetospheres (University of Chicago Press, Chicago, 1991).
2. T. Tajima and T. Taniuti, Phys. Rev. A 42, 3587 (1990).
3. J. F. C. Wardle, D. C. Homan, R. Ojha, and D. H. Roberts, Nature 395, 457 (1998).
4. K. Hirotani, S. Iguchi, M. Kimura, and K. Wajima, Astrophys. J. 545, 100 (2000).
5. G. P. Zank and R. G. Greaves, Phys. Rev. E 51, 6079 (1995).
6. V. I. Berezhiani and S. M. Mahajan, Phys. Rev. Lett. 73, 1110 (1994).
7. Q. Luo and D. B. Melrose, Mon. Not. R. Astron. Soc. 258, 616 (1992).
8. S. M. Mahajan, Astrophys. J. Lett. 479, L129 (1997).
9. R. T. Gangadhara, V. Krishan, and P. K. Shukla, Mon. Not. R. Astron. Soc. 262, 151 (1993).
10. P. K. Shukla, N. N. Rao, M. Y. Yu, and N. L. Tsintsadze, Phys. Rep. 138, 1 (1986).
11. L. Gomberoff, V. Muñoz, and R. M. O. Galvão, Phys. Rev. E 56, 4581 (1997).
12. V. Muñoz and L. Gomberoff, Phys. Rev. E 57, 994 (1998).
13. P. K. Shukla and L. Stenflo, Phys. Plasmas 7, 2726 (2000).
14. V. Muñoz and L. Gomberoff, Phys. Plasmas 9, 2534 (2002).
15. V. Muñoz, Phys. Plasmas 11, 3497 (2004).
16. V. Muñoz, Phys. Plasmas 11, 4883 (2004).
17. V. Muñoz and L. Gomberoff, Phys. Plasmas 5, 3171 (1998).
18. S. Matsukiyo and T. Hada, Phys. Rev. E 67, 046406
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