Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-06-12T08:25:45.122Z Has data issue: false hasContentIssue false

Helicon and lower hybrid current drive comparisons in tokamak geometry

Published online by Cambridge University Press:  17 July 2023

Peter J. Catto*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA
Muni Zhou
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA School of Natural Science, Institute for Advanced Study, Princeton, NJ, USA
*
Email address for correspondence: catto@psfc.mit.edu

Abstract

The parallel current driven by applied helicon waves is evaluated in tokamak geometry along with the radio frequency (rf) power absorbed by the passing electrons. The results are compared with the corresponding expressions for lower hybrid current drive. The efficiency of both current drive schemes is found to be the same for any single wave frequency, single mode number limit. The evaluation of the parallel currents is performed using an adjoint technique. Tokamak geometry is retained by using an eigenfunction expansion appropriate for a transit averaged long mean free path treatment of electrons making correlated poloidal passes through the applied rf fields.

Type
Research Article
Copyright
Copyright © The Author(s), 2023. 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

Antonsen, T.M. & Chu, M.S. 1982 Radio frequency current generation by waves in toroidal geometry. Phys. Fluids 25, 12951296.CrossRefGoogle Scholar
Bonoli, P.T. 2014 Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters. Phys. Plasmas 21, 061508.CrossRefGoogle Scholar
Catto, P.J. 2021 Lower hybrid current drive in a tokamak for correlated passes through resonance. J. Plasma Phys. 87, 905870309.CrossRefGoogle Scholar
Catto, P.J. & Tolman, E.A. 2021 a Reimagining full wave quasilinear theory in a tokamak. J. Plasma Phys. 87, 905870215.CrossRefGoogle Scholar
Catto, P.J. & Tolman, E.A. 2021 b Collisional broadening of nonlinear resonant wave-particle interactions. J. Plasma Phys. 87, 905870606.CrossRefGoogle Scholar
Chiu, S.C., Chan, V.S., Harvey, R.W. & Porkolab, M. 1989 Theory of fast wave current drive for tokamak plasmas. Nucl. Fusion 29, 21752186.CrossRefGoogle Scholar
Cohen, R.H. 1987 Effect of trapped electrons on current drive. Phys. Fluids 30, 24422449.CrossRefGoogle Scholar
Cordey, J.G. 1976 Effects of particle trapping on the slowing-down of fast ions in a toroidal plasma. Nucl. Fusion 16, 499507.CrossRefGoogle Scholar
Cordey, J.G., Edlington, T. & Start, D.F.H. 1982 A theory of currents induced by radio-frequency waves in toroidal plasmas. Plasma Phys. 24, 7389.CrossRefGoogle Scholar
de Assis, A.S. & Busnardo-Neto, J. 1988 Current drive with whistler waves. Phys. Fluids 31, 943945.CrossRefGoogle Scholar
Ehst, D.A. & Karney, C.F.F. 1991 Approximate formula for radio-frequency current drive efficiency with magnetic trapping. Nucl. Fusion 31, 19331938.CrossRefGoogle Scholar
Fisch, N.J. 1978 Confining a tokamak plasma with rf-driven currents. Phys. Rev. Lett. 41, 873876.CrossRefGoogle Scholar
Fisch, N.J. & Boozer, A.H. 1980 Creating an axisymmetric plasma resistivity with waves. Phys. Rev. Lett. 45, 720722.CrossRefGoogle Scholar
Fisch, N.J. & Karney, C.F.F. 1981 Current generation with low-frequency waves. Phys. Fluids 24, 2739.CrossRefGoogle Scholar
Giruzzi, G. 1987 Impact of electron trapping on rf current drive in tokamaks. Nucl. Fusion 27, 19341939.CrossRefGoogle Scholar
Golant, V.E. 1972 Plasma penetration near the lower hybrid frequency. Sov. Phys. – Tech. Phys. 16, 19801988.Google Scholar
Hsu, C.T., Catto, P.J. & Sigmar, D.J. 1990 Neoclassical transport of isotropic fast ions. Phys. Plasmas B 2, 280290.Google Scholar
Karney, C.F.F. & Fisch, N.J. 1979 Numerical studies of current generation by radio-frequency traveling waves. Phys. Fluids 22, 18171824.CrossRefGoogle Scholar
Karney, C.F.F. & Fisch, N.J. 1985 Efficiency of current drive by fast waves. Phys. Fluids 28, 116126.CrossRefGoogle Scholar
Lashmore-Davies, C.N., Fuchs, V. & Cairns, R.A. 1998 A full wave theory of high-harmonic fast wave absorption in high-beta plasmas. Phys. Plasmas 5, 22842290.CrossRefGoogle Scholar
Lau, C., Berry, L.A., Jaeger, E.F. & Bertelli, N. 2019 Cold plasma finite element wave model for helicon waves. Plasma Phys. Control. Fusion 61, 045008.CrossRefGoogle Scholar
Lau, C., Bookman, M., Dimits, A., Dudson, B., Martin, E., Pinsker, R.I., Thomas, M. & van Compernolle, B. 2021 Helicon full wave modeling with scrape off layer turbulence on the DIII-D tokamak. Nucl. Fusion 61, 126072.CrossRefGoogle Scholar
Lau, C., Jaeger, E.F., Bertelli, N., Berry, L.A., Green, D.L., Murakami, M., Park, J.M., Pinsker, R.I. & Prater, R. 2018 AORSA full wave calculation of helicon waves in DIII-D and ITER. Nucl. Fusion 58, 066004.CrossRefGoogle Scholar
Li, J., Ding, X.T., Dong, J.Q. & Liu, S.F. 2020 a Helicon heating and current drive in toroidal plasmas. Plasma Phys. Control. Fusion 62, 095013.CrossRefGoogle Scholar
Li, X., Li, G. & Liu, H. 2021 Optimization of helicon wave off axis current drive in CFETR tokamak. Fusion Engng Des. 172, 112897.CrossRefGoogle Scholar
Li, X., Liu, H., Xiang, N. & Li, M. 2020 b Theoretical analysis of helicon wave current drive in EAST with high ${\beta _e}$ operation. Phys. Lett. A 384, 126779.CrossRefGoogle Scholar
Ono, M. 1995 High harmonic fast waves in high beta plasmas. Phys. Plasmas 2, 40754082.CrossRefGoogle Scholar
Parker, J.B. & Catto, P.J. 2012 Variational calculation of neoclassical ion heat flux and poloidal flow in the banana regime for axisymmetric magnetic geometry. Plasma Phys. Control. Fusion 54, 085011.CrossRefGoogle Scholar
Pinsker, R.I. 2015 Whistlers, helicons, and lower hybrid waves: the physics of radio frequency wave propagation and absorption for current drive via Landau damping. Phys. Plasmas 22, 090901.CrossRefGoogle Scholar
Pinsker, R.I., Prater, R., Moeller, C.P., Degrassie, J.S., Petty, C.C., Porkolab, M., Anderson, J.P., Garofalo, A.M., Lau, C., Nagy, A., Pace, D.C., Torreblanca, H., Watkins, J.G. & Zeng, L. 2018 Experiments on helicons in DIII-D—investigation of the physics of a reactor-relevant non-inductive current drive technology. Nucl. Fusion 58, 106007.CrossRefGoogle Scholar
Prater, R., Moeller, C.P., Pinsker, R.I., Porkolab, M., Meneghini, O. & Vdovin, V.L. 2014 Application of very high harmonic fast waves for off-axis current drive in the DIII-D and FNSF-AT tokamaks. Nucl. Fusion 54, 083024.CrossRefGoogle Scholar
Preinhaelter, J. & Václavík, J. 1967 The quasilinear theory of beam instabilites of the low frequency non-electrostatic plasma waves. Plasma Phys. 9, 653664.CrossRefGoogle Scholar
Taguchi, M. 1983 The effect of trapped electron on the wave-induced current. J. Phys. Soc. Japan 52, 20352040.CrossRefGoogle Scholar
Vdovin, V.L. 2013 Current generation by helicons and lower hybrid waves in modern tokamaks and reactors ITER and DEMO. Plasma Phys. Rep. 39, 95119.CrossRefGoogle Scholar
Wang, S.J., Wi, H.H., Kim, H.J., Kim, J., Jeong, J.H. & Kwak, J.G. 2017 Helicon wave coupling in KSTAR plasmas for off axis current drive in high electron pressure plasmas. Nucl. Fusion 57, 046010.CrossRefGoogle Scholar
Xiao, Y., Catto, P.J. & Molvig, K. 2007 Collisional damping for ion temperature gradient mode driven zonal flow. Phys. Plasmas 14, 032302.CrossRefGoogle Scholar
Yin, L., Zheng, P., Gong, X., Yang, C., Yin, X., Song, C., Huang, Q., Chen, Y. & Zhong, Y. 2022 New synergy effects of the lower hybrid wave and the high harmonic fast wave current drive. Nucl. Fusion 62, 066023.CrossRefGoogle Scholar