Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-23T07:44:18.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Orbits of magnetized charged particles in parabolic and inverse electrostatic potentials

Part of: Diagnostics of Dust in Plasmas

Published online by Cambridge University Press:  28 January 2016

P. M. Bellan
P. M. Bellan*
Affiliation:
Applied Physics and Materials Science Department, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Analytic solutions are presented for the orbit of a charged particle in the combination of a uniform axial magnetic field and parabolic electrostatic potential. These trajectories are shown to correspond to the sum of two individually rotating vectors with one vector rotating at a constant fast frequency and the other rotating in the same sense but with a constant slow frequency. These solutions are related to Penning trap orbits and to stochastic orbits. If the lengths of the two rotating vectors are identical, the particle has zero canonical angular momentum in which case the particle orbit will traverse the origin. If the potential has an inverse dependence on distance from the source of the potential, the particle can impact the source. Axis-encircling orbits are where the length of the vector associated with the fast frequency is longer than the vector associated with the slow frequency. Non-axis-encircling orbits are the other way around.

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 1 , February 2016 , 615820101
Copyright
© Cambridge University Press 2016 

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

Allen, J. E., Boyd, R. L. F. & Reynolds, P. 1957 The collection of positive ions by a probe immersed in a plasma. Proc. Phys. Soc. Lond. B 70, 297–304.CrossRefGoogle Scholar
Bellan, P. M. 1993 Transport inferred from consideration of particle orbits in drift turbulence. Plasma Phys. Control. Fusion 35 (2), 169–178.Google Scholar
Bellan, P. M. 2006 Fundamentals of Plasma Physics. Cambridge University Press.CrossRefGoogle Scholar
Bellan, P. M. 2007 Consideration of the relationship between Kepler and cyclotron dynamics leading to prediction of a nonmagnetohydrodynamic gravity-driven Hamiltonian dynamo. Phys. Plasmas 14 (12), 122901.Google Scholar
Bellan, P. M. 2008 Dust-driven dynamos in accretion disks. Astrophys. J. 687 (1), 311–339.Google Scholar
Bender, B. & Thomas, E.2015 Trajectory frequency analysis of a simulated, magnetized dusty plasma in a radially increasing electric field. Abstract 51, 14th Workshop on the Physics of Dusty Plasma, May 26–29, 2015 Auburn AL.Google Scholar
Brown, L. S. & Gabrielse, G. 1986 Geonium theory – physics of a single electron or ion in a Penning trap. Rev. Mod. Phys. 58 (1), 233–311.Google Scholar
Chandran, B. D. G., Verscharen, D., Quataert, E., Kasper, J. C., Isenberg, P. A. & Bourouaine, S. 2013 Stochastic heating, differential flow, and the alpha-to-proton temperature ratio in the solar wind. Astrophys. J. 776 (1), 45.Google Scholar
Davidson, R. C. 1974 Theory of Nonneutral Plasmas. pp. 7,8. W. A. Benjamin.Google Scholar
Davidson, R. C. & Krall, N. A. 1970 Vlasov equilibria and stability of an electron gas. Phys. Fluids 13 (6), 1543–1555.Google Scholar
Dubin, D. H. E. & O’Neil, T. M. 1999 Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states). Rev. Mod. Phys. 71 (1), 87–172.CrossRefGoogle Scholar
Elmore, W. C., Tuck, J. L. & Watson, K. M. 1959 On the inertial-electrostatic confinement of a plasma. Phys. Fluids 2 (3), 239–246.Google Scholar
Hirsch, R. L. 1967 Inertial-electrostatic confinement of ionized fusion gases. J. Appl. Phys. 38 (11), 4522–4534.Google Scholar
Kuzmin, S. G. & O’Neil, T. M. 2005 Motion of guiding center drift atoms in the electric and magnetic field of a Penning trap. Phys. Plasmas 12 (1), 012101.Google Scholar
McChesney, J. M., Stern, R. A. & Bellan, P. M. 1987 Observations of fast stochastic ion heating by drift waves. Phys. Rev Lett. 59, 1436–1439.Google Scholar
Perkins, R. J. & Bellan, P. M. 2010 Wheels within wheels: Hamiltonian dynamics as a hierarchy of action variables. Phys. Rev. Lett. 105 (12), 124301.Google Scholar
Perkins, R. J. & Bellan, P. M. 2015 Orbit-averaged quantities, the classical Hellmann–Feynman theorem, and the magnetic flux enclosed by gyro-motion. Phys. Plasmas 22 (2), 022108.CrossRefGoogle Scholar
Schmidt, G. 1979 Physics of High Temperature Plasmas. Academic.Google Scholar
Shukla, P. K. & Mamun, A. A. 2002 Introduction to Dusty Plasma Physics. Institute of Physics Publishing.CrossRefGoogle Scholar
Stasiewicz, K., Lundin, R. & Marklund, G. 2000 Stochastic ion heating by orbit chaotization on electrostatic waves and nonlinear structures. Phys. Scr. T 84, 60–63.CrossRefGoogle Scholar
Stasiewicz, K., Markidis, S., Eliasson, B., Strumik, M. & Yamauchi, M. 2013 Acceleration of solar wind ions to 1 MeV by electromagnetic structures upstream of the earth’s bow shock. Europhys. Lett. 102 (4), 49001.CrossRefGoogle Scholar
Thomas, E., Merlino, R. L. & Rosenberg, M. 2012 Magnetized dusty plasmas: the next frontier for complex plasma research. Plasma Phys. Control. Fusion 54 (12), 124034.Google Scholar
Thomas, E., Merlino, R. L. & Rosenberg, M. 2013 Design criteria for the magnetized dusty plasma experiment. IEEE Trans. Plasma Sci. 41 (4), 811–815.Google Scholar
Vranjes, J. & Poedts, S. 2010 Drift waves in the corona: heating and acceleration of ions at frequencies far below the gyrofrequency. Mon. Not. R. Astron. Soc. 408 (3), 1835–1839.Google Scholar
Vrinceanu, D., Granger, B. E., Parrott, R., Sadeghpour, H. R., Cederbaum, L. S., Mody, A., Tan, J. & Gabrielse, G. 2004 Strongly magnetized antihydrogen and its field ionization. Phys. Rev. Lett. 92 (13), 133402.Google Scholar