Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-20T07:37:29.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical treatment of particle motion in circularly polarized slab-mode wave fields

Published online by Cambridge University Press:  30 January 2018

Cedric Schreiner Open the ORCID record for Cedric Schreiner [Opens in a new window] ,
Rami Vainio  and
Felix Spanier
Cedric Schreiner*
Affiliation:
Max-Planck-Institute for Solar System Research, Justus-von-Liebig-Weg 3, DE-37077 Göttingen, Germany
Rami Vainio
Affiliation:
Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
Felix Spanier
Affiliation:
Centre for Space Research, North-West University, 2520 Potchefstroom, South Africa
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Wave–particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and chaotic particle trajectories become possible. We demonstrate this effect by considering a linearly polarized, monochromatic wave, which can be seen as the superposition of two circularly polarized waves. Test particle simulations are provided to illustrate and expand our analytical considerations.

Keywords

plasma simulationplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 1 , February 2018 , 905840104
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arnold, V. I. 1978 Mathematical Methods of Classical Mechanics. Springer.Google Scholar
Balakirev, V. A., Buts, V. A., Tolstoluzhkii, A. P. & Turkin, Yu. A. 1989 Charged particle dynamics in the field of two electromagnetic waves. Zh. Eksp. Teor. Fiz. 95, 1231–1245.Google Scholar
Bell, A. R. 1978 The acceleration of cosmic rays in shock fronts. I. Mon. Not. R. Astron. Soc. 182, 147–156.Google Scholar
Bouquet, S. & Bourdier, A. 1998 Notion of integrability for time-dependent hamiltonian systems: illustrations from the relativistic motion of a charged particle. Phys. Rev. E 57 (2), 1273–1283.Google Scholar
Bourdier, A. & Drouin, M. 2009 Dynamics of a charged particle in progressive plane waves propagating in vacuum or plasma: stochastic acceleration. Laser Part. Beams 27, 545.Google Scholar
Bourdier, A. & Gond, S. 2001 Dynamics of a charged particle in a linearly polarized traveling electromagnetic wave. Phys. Rev. E 63 (3), 036609.Google Scholar
Bourdier, A. & Patin, D. 2005 Dynamics of a charged particle in a linearly polarized traveling wave. Eur. Phys. J. D 32, 361–376.Google Scholar
Dalena, S., Chuychai, P., Mace, R. L., Greco, A., Qin, G. & Matthaeus, W. H. 2012 Streamline generation code for particle dynamics description in numerical models of turbulence. Comput. Phys. Commun. 183 (9), 1974–1985.Google Scholar
Essén, H. & Stén, J. C.-E. 2015 A new look at the pushing force of an electromagnetic wave on a classical charged particle. Eur. J. Phys. 36, 055029.Google Scholar
Kilian, P., Burkart, T. & Spanier, F. 2012 The influence of the mass ratio on particle acceleration by the filamentation instability. In High Performance Computing in Science and Engineering ’11 (ed. Nagel, Wolfgang E., Krner, Dietmar B. & Resch, Michael M.), pp. 5–13. Springer.Google Scholar
Kilian, P., Muñoz, P., Schreiner, C. & Spanier, F. 2017 Plasma waves as a benchmark problem. J. Plasma Phys. 83, 707830101.Google Scholar
Kong, L.-B. & Liu, P.-K. 2007 Analytical solution for relativistic charged particle motion in a circularly polarized electromagnetic wave. Phys. Plasmas 14 (6), 063101.Google Scholar
Lange, S., Spanier, F., Battarbee, M., Vainio, R. & Laitinen, T. 2013 Particle scattering in turbulent plasmas with amplified wave modes. Astron. Astrophys. 553, A129.Google Scholar
Lehmann, G. & Spatschek, K. H. 2010 Classification and stability of plasma motion in periodic linearly polarized relativistic waves. Phys. Plasmas 17 (7), 072102.Google Scholar
Melzani, M., Winisdoerffer, C., Walder, R., Folini, D., Favre, J. M., Krastanov, S. & Messmer, P. 2013 Apar-T: Code, validation, and physical interpretation of particle-in-cell results. Astron. Astrophys. 558, A133.Google Scholar
Murakami, A., Nomura, Y. & Momota, H. 1982 Stochasticity of phase trajectory of a charged particle in a plasma wave. J. Phys. Soc. Japan 51, 4053.CrossRefGoogle Scholar
Palmadesso, P. J. 1972 Resonance, particle trapping, and landau damping in finite amplitude obliquely propagating waves. Phys. Fluids 15, 2006–2013.Google Scholar
Prelle, M. J. & Singer, M. F. 1983 Elementary first integrals of differential equations. Trans. Am. Math. Soc. 279 (1), 215–229.Google Scholar
Qian, B.-L. 2000 Relativistic motion of a charged particle in a superposition of circularly polarized plane electromagnetic waves and a uniform magnetic field. Phys. Plasmas 7, 537–543.Google Scholar
Roberts, C. S. & Buchsbaum, S. J. 1964 Motion of a charged particle in a constant magnetic field and a transverse electromagnetic wave propagating along the field. Phys. Rev. 135 (2), A381.CrossRefGoogle Scholar
Sakai, J. & Kamimura, T. 1972 De-trapping of trapped particles by a second wave. Phys. Lett. A 41, 75–76.Google Scholar
Schlickeiser, R. 1989 Cosmic-ray transport and acceleration. I – Derivation of the kinetic equation and application to cosmic rays in static cold media. II – Cosmic rays in moving cold media with application to diffusive shock wave acceleration. Astrophys. J. 336, 243–293.Google Scholar
Schreiner, C., Kilian, P. & Spanier, F. 2017a Particle scattering off of right-handed dispersive waves. Astrophys. J. 834, 161.Google Scholar
Schreiner, C., Kilian, P. & Spanier, F. 2017b Recovering the damping rates of cyclotron damped plasma waves from simulation data. Commun. Comput. Phys. 21 (4), 947–980.Google Scholar
Shklyar, D. R. & Zimbardo, G. 2014 Particle dynamics in the field of two waves in a magnetoplasma. Plasma Phys. Control. Fusion 56 (9), 095002.Google Scholar
Smith, G. R. & Kaufman, A. N. 1978 Stochastic acceleration by an obliquely propagating wave - An example of overlapping resonances. Phys. Fluids 21, 2230–2241.Google Scholar
Sudan, R. N. & Ott, E. 1971 Theory of triggered VLF emissions. J. Geophys. Res. 76, 4463–4476.CrossRefGoogle Scholar
Teschl, G. 2012 Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics, vol. 140. American Mathematical Society.Google Scholar
Tran, M. Q. 1982 Stochastic behavior of particles in a circularly polarized standing wave. IEEE Trans. Plasma Sci. 10, 16–18.Google Scholar
Varvoglis, H. 1984 Chaotic ion motion in magnetosonic plasma waves. Astron. Astrophys. 132, 321–325.Google Scholar