Abstract
With allowance for the centrifugal and gradient drifts of ions, a new approximate dispersion equation is obtained for the ion Bernstein (IB) wave propagating strictly transverse to the external inhomogeneous magnetic field. Using this equation, it is shown that if, in the high-temperature plasma, the drift of ions is taken into account, the resonance frequency ranges in the vicinities of the ion cyclotron frequency harmonics can strongly overlap. In this case, the ion Bernstein waves turn out to be strongly damped, despite the absence of the longitudinal component of the wave vector.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
I. B. Bernstein, Phys. Rev. 109, 10 (1958).
K. N. Stepanov, Sov. Phys. JETP 8, 808 (1959).
E. Gusakov and A. Popov, Europhys. Lett. 99, 15001 (2012).
E. Z. Gusakov and A. Yu. Popov, Phys. Plasmas 23, 082503 (2016).
E. Z. Gusakov and A. Yu. Popov, Nucl. Fusion 59, 104003 (2019).
E. Westerhof, S. K. Nielsen, J. W. Oosterbeek, M. Salewski, M. R. de Baar, W. A. Bongers, A. Bürger, B. A. Hennen, S. B. Korsholm, F. Leipold, D. Moseev, M. Stejner, and D. J. Thoen, Phys. Rev. Lett. 103, 125001 (2009).
S. K. Nielsen, M. Salewski, E. Westerhof, W. Bongers, S. B. Korsholm, F. Leipold, J. W. Oosterbeek, D. Moseev, and M. Stejner, Plasma Phys. Control. Fusion 55, 115003 (2013).
S. Kubo, M. Nishiura, K. Tanaka, T. Shimozuma, Y. Yoshimura, H. Igami, H. Takahash, T. Mutoh, N. Tamura, Y. Tatematsu, T. Saito, T. Notake, S. B. Korsholm, F. Meo, S. K. Nielsen, et al., Rev. Sci. Instrum. 81, D535 (2010).
A. Bruschi, E. Alessi, W. Bin, O. D’Arcangelo, B. Baiocchi, F. Belli, G. Calabrò, I. Casiraghi, V. Cocilovo, L. Figini, C. Galperti, S. Garavaglia, G. Granucci, G. Grosso, S. B. Korsholm, et al., Nucl. Fusion 57, 076004 (2017).
W. Bin, A. Bruschi, O. D’Arcangelo, G. Grosso, L. Lubiako, E. Alessi, C. Castaldo, C. Centioli, M. De. Angeli, L. Figini, C. Galperti, S. Garavaglia, G. Granucci, M. Lontano, S. Magagnino, et al., Rev. Sci. Instrum. 87, 11E507 (2016).
G. M. Batanov, V. D. Borzosekov, L. M. Kovrizhnykh, L. V. Kolik, E. M. Konchekov, D. V. Malakhov, A. E. Petrov, K. A. Sarksyan, N. N. Skvortsova, V. D. Stepakhin, and N. K. Kharchev, Plasma Phys. Rep. 39, 444 (2013).
B. Zurro, A. Baciero, V. Tribaldos, M. Liniers, Á. Cappa, A. Lopez-Fraguas, D. Jiménez-Rey, J. M. Fontdecaba, and O. Nekhaieva, Nucl. Fusion 53, 083017 (2016).
M. Martínez, B. Zurro, A. Baciero, D. Jiménez-Rey, and V. Tribaldos, Plasma Phys. Control. Fusion 60, 025024 (2018).
D. G. Vasilkov, G. M. Batanov, M. S. Berezhetskii, V. D. Borzosekov, S. E. Grebenshchikov, N. K. Kharchev, Yu. V. Khol’nov, L. V. Kolik, E. M. Konchekov, A. A. Letunov, V. P. Logvinenko, D. V. Malakhov, A. I. Meshcheryakov, A. E. Petrov, K. A. Sarksyan, et al., in Proceedings of the 41st EPS Conference on Plasma Physics, Berlin, 2014, ECA 38F, P4.053 (2014).
S. Kubo, H. Takahash, T. Shimozuma, Y. Yoshimura, M. Nishiura, H. Igami, S. Ogasawara, and R. Makino, EPJ Web Conf. 32, 02007 (2012).
S. Eguilior, F. Castejґon, E. de la Luna, Á. Cappa, K. Likin, A. Fernández, and TJ-II Team, Plasma Phys. Control. Fusion 45, 105 (2003).
F. Castejon, L. Barrera, Á. Cappa, S. Eguilior, J. Herranz, D. López-Bruna, E. de la Luna, F. Medina, M. A. Ochando, L. Eliseev, A. Melnikov, O. Chmyga, L. G. Eliseev, L. Krupnik, and O. Zhezhera, in Proceedings of the 36th EPS Conference on Plasma Physics, Sofia, 2009, ECA 33E, P4.178 (2009).
B. Ph. van Milligen, B. A. Carreras, C. Hidalgo, A. Cappa, and TJ-II Team, Phys. Plasmas 25, 062503 (2018).
S. K. Hansen, S. K. Nielsen, J. Stober, J. Rasmussen, M. Salewski, M. Stejner, M. Hoelzl, and the ASDEX Upgrade Team, in Proceedings of the 46th EPS Conference on Plasma Physics, Milan, 2019, ECA 43C, P1.1075 (2019). http://ocs.ciemat.es/EPS2019PAP/pdf/P1.1075.pdf.
T. H. Stix, Waves in Plasmas (AIP, New York, 1992).
D. G. Swanson, Plasma Waves (IOP, Bristol, 2003).
M. Brambilla, Plasma Phys. 18, 669 (1976).
S. Cho and D. G. Swanson, Phys. Fluids 31, 1123 (1988).
A. Cardinali and F. Romanelli, Phys. Fluids B 41, 504 (1988).
C. N. Lashmore-Davies and R. O. Dendy, Phys. Rev. Lett. 62, 1982 (1989).
A. D. Piliya and A. N. Saveliev, Plasma Phys. Control. Fusion 36, 2059 (1994).
A. D. Piliya, A. Yu. Popov, and E. N. Tregubova, Plasma Phys. Control. Fusion 45, 1309 (2003).
F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, 2nd ed. (Plenum, New York and London, 1984).
C. F. F. Karney and A. Bers, Phys. Rev. Lett. 39, 550 (1977).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, 2nd. ed. (Fizmatlit, Moscow, 2009; Academic, New York, 1980).
N. N. Lebedev, Special Functions and Their Applications, 2nd ed. (Fizmatlit, Moscow, 1963; Prentice-Hall, Englewood Cliffs, NJ, 1965).
A. V. Timofeev, Resonance Phenomena in Plasma Oscillations, 2nd ed. (Fizmatlit, Moscow, 2009) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by I. Grishina
Rights and permissions
About this article
Cite this article
Popov, A.Y. On the Issue of Damping of a Transverse Ion Bernstein Wave in an Inhomogeneous Magnetic Field. Plasma Phys. Rep. 46, 636–640 (2020). https://doi.org/10.1134/S1063780X20060069
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063780X20060069