Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-01T23:49:51.369Z Has data issue: false hasContentIssue false

Radial distribution of the plasma potential in a cylindrical plasma column with a longitudinal magnetic field

Published online by Cambridge University Press:  13 August 2021

G. Liziakin*
Affiliation:
Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS), Moscow, Russia
A. Oiler
Affiliation:
Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS), Moscow, Russia Moscow Institute of Physics and Technology (National Research University), Moscow, Russia
A. Gavrikov
Affiliation:
Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS), Moscow, Russia
N. Antonov
Affiliation:
Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS), Moscow, Russia
V. Smirnov
Affiliation:
Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS), Moscow, Russia
*
Email address for correspondence: glizyakin@gmail.com

Abstract

The possibility of controlling the electrostatic field distribution in plasma has yielded wide prospects for modern technologies. As a magnetic field primarily allows for creating electric fields in plasma, it serves as an additional obstacle for the current flow through a medium. In the present paper, an axially symmetric system is considered in which the magnetic field is directed along the axis and concentric electrodes are located at the ends. The electrodes are negatively biased. A model which solves the problem of the radial distribution of the plasma potential inside the cylindrical plasma column supported by the end electrodes is proposed. The most commonly encountered configurations of the electrical connection for the end electrodes are considered, and the particular solutions to the problem of the radial distribution are presented. The contribution of ions and electrons to the transverse conductivity is evaluated in detail. The influence of a thermionic element on the radial profile of the plasma potential is considered. To verify the proposed model, an experimental study of the reflex discharge is carried out with both cold electrodes and a thermionic element on the axis. A comparison of the computational model results with experimental data is given. The presented model makes it possible to solve the problem concerning the plasma potential distribution in the case of an arbitrary number of end electrodes, and also to take into account the inhomogeneity of the distribution of plasma density, neutral gas pressure and electron temperature along the radius.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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

Amatucci, W.E., Walker, D.N., Ganguli, G., Antoniades, J.A., Duncan, D., Bowles, J.H., Gavrishchaka, V. & Koepke, M.E. 1996 Plasma response to strongly sheared flow. Phys. Rev. Lett. 77 (10), 1978.CrossRefGoogle ScholarPubMed
Barber, P.B., Swift, D.A. & Tozer, B.A. 1972 The formation of rotating plasmas in a homopolar configuration. J. Phys. D: Appl. Phys. 5 (4), 693.CrossRefGoogle Scholar
Boeuf, J.-P. 2017 Tutorial: physics and modeling of Hall thrusters. J. Appl. Phys. 121 (1), 11101.CrossRefGoogle Scholar
Burrell, K.H. 1997 Effects of E$×$ B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices. Phys. Plasmas 4 (5), 14991518.CrossRefGoogle Scholar
Cramer, W.H. 1959 Elastic and inelastic scattering of low-velocity ions: Ne+ in A, A+ in Ne, and A+ in A. J. Chem. Phys. 30 (3), 641642.CrossRefGoogle Scholar
Dahlquist, G. & Björck, Å 2008 Numerical Methods in Scientific Computing, vol. I. SIAM.Google Scholar
Del Bosco, E., Simpson, S.W., Dallaqua, R.S. & Montes, A. 1991 Speed of rotation in a vacuum arc centrifuge. J. Phys. D: Appl. Phys. 24 (11), 2008.CrossRefGoogle Scholar
Dolgolenko, D.A. & Muromkin, Y.A. 2017 Separation of mixtures of chemical elements in plasma. Phys. Uspekhi 60 (10), 994.CrossRefGoogle Scholar
Gilmore, M., Lynn, A.G., Desjardins, T.R., Zhang, Y., Watts, C., Hsu, S.C., Betts, S., Kelly, R. & Schamiloglu, E. 2015 The HelCat basic plasma science device. J. Plasma Phys. 81 (1).CrossRefGoogle Scholar
Grossman, M.W. & Shepp, T.A. 1991 Plasma isotope separation methods. IEEE Trans. Plasma Sci. 19 (6), 11141122.CrossRefGoogle Scholar
Gueroult, R., Evans, E.S., Zweben, S.J., Fisch, N.J. & Levinton, F. 2016 Initial experimental test of a helicon plasma based mass filter. Plasma Sources Sci. Technol. 25 (3), 35024.CrossRefGoogle Scholar
Gueroult, R., Rax, J.-M. & Fisch, N.J. 2019 a A necessary condition for perpendicular electric field control in magnetized plasmas. Phys. Plasmas 26 (12), 122106.CrossRefGoogle Scholar
Gueroult, R., Zweben, S.J., Fisch, N.J. & Rax, J.-M. 2019 b ExB configurations for high-throughput plasma mass separation: an outlook on possibilities and challenges. Phys. Plasmas 26 (4), 43511.CrossRefGoogle Scholar
Hooper, E.B. Jr. 1970 A review of reflex and penning discharges. In Advances in Electronics and Electron Physics (ed. L. Marton & M. Claire), vol. 27, pp. 295–343. Academic Press.Google Scholar
Jain, K.K. 1993 Observation of improved behavior by electrode biasing of a toroidal plasma having no poloidal magnetic field. Phys. Rev. Lett. 70 (6), 806809.CrossRefGoogle ScholarPubMed
Jin, S., Poulos, M.J., Van Compernolle, B. & Morales, G.J. 2019 Plasma flows generated by an annular thermionic cathode in a large magnetized plasma. Phys. Plasmas 26 (2), 22105.CrossRefGoogle Scholar
Langmuir, I. & Compton, K.T. 1931 Electrical discharges in gases part II. Fundamental phenomena in electrical discharges. Rev. Mod. Phys. 3 (2), 191257.CrossRefGoogle Scholar
Lieberman, M.A. & Lichtenberg, A.J. 2005 Principles of Plasma Discharges and Materials Processing. John Wiley & Sons.CrossRefGoogle Scholar
Litvak, A., Agnew, S., Anderegg, F., Cluggish, B., Freeman, R., Gilleland, J., Isler, R., Lee, W., Miller, R., Ohkawa, T., Putvinski, S., Sevier, L., Umstadter, K. & Winslow, D. 2003 Archimedes plasma mass filter. In 30th EPS Conference on Controlled Fusion and Plasma Physics, St. Petersburg. 7-11 July vol. 27, O-1.6 A.Google Scholar
Liziakin, G., Antonov, N., Usmanov, R., Melnikov, A., Timirkhanov, R., Vorona, N., Smirnov, V.S., Oiler, A., Kislenko, S., Gavrikov, A. & Smirnov, V.P. 2021 Experimental demonstration of plasma mass separation in a configuration with a potential well and crossed electric and magnetic fields. Plasma Phys. Control. Fusion 63 (3), 032002.CrossRefGoogle Scholar
Liziakin, G.D., Gavrikov, A.V., Murzaev, Y.A., Usmanov, R.A. & Smirnov, V.P. 2016 Parameters influencing plasma column potential in a reflex discharge. Phys. Plasmas 23 (12), 123502.CrossRefGoogle Scholar
Liziakin, G., Gavrikov, A. & Smirnov, V. 2020 Negative electric potential in a cylindrical plasma column with magnetized electrons. Plasma Sources Sci. Technol. 29 (1), 15008.CrossRefGoogle Scholar
Liziakin, G., Gavrikov, A., Usmanov, R., Timirkhanov, R. & Smirnov, V. 2017 Electric potential profile created by end electrodes in a magnetized rf discharge plasma. AIP Adv. 7 (12).CrossRefGoogle Scholar
Maggs, J.E., Carter, T.A. & Taylor, R.J. 2007 Transition from Bohm to classical diffusion due to edge rotation of a cylindrical plasma. Phys. Plasmas 14 (5), 52507.CrossRefGoogle Scholar
Murzaev, Y., Liziakin, G., Gavrikov, A., Timirkhanov, R. & Smirnov, V. 2019 A comparison of emissive and cold floating probe techniques for electric potential measurements in rf inductive discharge. Plasma Sci. Technol. 21 (4), 45401.CrossRefGoogle Scholar
Oiler, A. & Liziakin, G. 2021 Program LaPotential. Available at: http://laplas.su/resources/.Google Scholar
Paschmann, G., Haaland, S. & Rudolf, T. 2003 Auroral Plasma Physics. Springer.CrossRefGoogle Scholar
Poulos, M.J. 2019 Model for the operation of an emissive cathode in a large magnetized-plasma. Phys. Plasmas 26 (2), 22104.CrossRefGoogle Scholar
Raizer, Y.P., Kisin, V.I. & Allen, J.E. 2011 Gas Discharge Physics. Springer. Available at: http://books.google.ru/books?id=zd-KMAEACAAJ.Google Scholar
Ramsauer, C. 1922 Über den Wirkungsquerschnitt der Gasmoleküle gegenüber langsamen Elektronen. I. Fortsetzung. Ann. Phys. 371 (24), 546558.CrossRefGoogle Scholar
Shinohara, S. & Horii, S. 2007 Initial trial of plasma mass separation by crossed electric and magnetic fields. Japan. J. Appl. Phys. 46 (7R), 4276.CrossRefGoogle Scholar
Smirnov, V.P., Gavrikov, A.V., Sidorov, V.S., Tarakanov, V.P., Timirkhanov, R.A., Kuzmichev, S.D., Usmanov, R.A. & Vorona, N.A. 2018 Investigation of the influence of injection parameters on particles motion in electric and magnetic fields for designing plasma separation technique. Plasma Phys. Rep. 44 (12), 11041113.CrossRefGoogle Scholar
Smirnov, V.S., Egorov, R.O., Kislenko, S.A., Antonov, N.N., Smirnov, V.P. & Gavrikov, A.V. 2020 Simulation of ion flux of actinides and uranium fission products in the plasma separator with a potential well. Phys. Plasmas 27 (11), 113503.CrossRefGoogle Scholar
Soldatkina, E.I., Bagryansky, P.A. & Solomakhin, A.L. 2008 Influence of the radial profile of the electric potential on the confinement of a high-$β$ two-component plasma in a gas-dynamic trap. Plasma Phys. Rep. 34 (4), 259264.CrossRefGoogle Scholar
Song, P., Gombosi, T.I. & Ridley, A.J. 2001 Three-fluid Ohm's law. J. Geophys. Res.: Space Phys. 106 (A5), 81498156.CrossRefGoogle Scholar
Vorona, N.A., Gavrikov, A.V., Kuzmichev, S.D., Liziakin, G.D., Melnikov, A.D., Murzaev, Y.A., Smirnov, V.P., Timirkhanov, R.A. & Usmanov, R.A. 2019 Large Helicon plasma source for the method of plasma separation of spent nuclear fuel and radioactive waste. IEEE Trans. Plasma Sci. 47 (2).CrossRefGoogle Scholar
Zolotukhin, D.B., Daniels, K.P., Brieda, L. & Keidar, M. 2020 Onset of the magnetized arc and its effect on the momentum of a low-power two-stage pulsed magneto-plasma-dynamic thruster. Phys. Rev. E 102 (2), 021203(R).CrossRefGoogle ScholarPubMed
Zweben, S.J., Gueroult, R. & Fisch, N.J. 2018 Plasma mass separation. Phys. Plasmas 25 (9), 90901.CrossRefGoogle Scholar