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Semi-analytical inspection of the quasi-linear absorption of lower hybrid wave in presence of $\unicode[STIX]{x1D6FC}$-particles in tokamak reactor

Part of: Focus on Fusion PLA 17th European Fusion Theory Conference

Published online by Cambridge University Press:  08 October 2018

A. Cardinali Open the ORCID record for A. Cardinali [Opens in a new window] ,
C. Castaldo  and
R. Ricci
A. Cardinali*
Affiliation:
ENEA, Fusion and Nuclear Safety Department, C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Roma), Italy
C. Castaldo
Affiliation:
ENEA, Fusion and Nuclear Safety Department, C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Roma), Italy
R. Ricci
Affiliation:
ENEA, Fusion and Nuclear Safety Department, C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Roma), Italy
*
†Email address for correspondence: alessandro.cardinali@enea.it
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Abstract

In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Franke et al., Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinali et al., Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born $\unicode[STIX]{x1D6FC}$-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the $\unicode[STIX]{x1D6FC}$-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of $\unicode[STIX]{x1D6FC}$-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with $\unicode[STIX]{x1D6FC}$-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.

Keywords

fusion energyplasma heatingplasma physicsplasma wave physicstheory and numerical simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 5 , October 2018 , 745840502
Copyright
© Cambridge University Press 2018 

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References

Amicucci, L., Cardinali, A., Castaldo, C., Cesario, R., Galli, A., Panaccione, L., Paoletti, F., Schettini, G., Spigler, R. & Tuccillo, A. A. 2016 Current drive for stability of thermonuclear plasma reactor. Plasma Phys. Control. Fusion 58, 014042.Google Scholar
Barbato, E. & Santini, F. 1991 Quasi-linear absorption of lower hybrid waves by fusion generated alpha particles. Nucl. Fusion 31, 673.Google Scholar
Barbato, E. & Saveliev, A. 2004 Absorption of lower hybrid wave power by $\unicode[STIX]{x1D6FC}$ -particles in ITER-FEAT scenarios. Plasma Phys. Control. Fusion 46, 1283.Google Scholar
Bellan, P. & Porkolab, M. 1975 Excitation of lower-hybrid waves by a slow wave structure. Phys. Rev. Lett. 34, 124.Google Scholar
Bernstein, I. 1975 Geometric optics in space and time varying plasmas. Phys. Fluids 18, 320.Google Scholar
Bonoli, P. T. & Englade, R. C. 1986 Simulation model for lower hybrid current drive. Phys. Fluids 29, 2937.Google Scholar
Bonoli, P. T., Parker, R. R., Porkolab, M., Ramos, J. J., Wukitch, S. J., Takase, Y., Bernabei, S., Hosea, J. C., Schilling, G. & Wilson, J. R. 2000 Modeling of advanced tokamak scenarios with LHCD in Alcator C-Mod. Nucl. Fusion 40, 1251.Google Scholar
Brambilla, M. 1998 Kinetic Theory of Plasma waves. Oxford University Press.Google Scholar
Brambilla, M. & Cardinali, A. 1982 Eikonal description of H.F. waves in toroidal plasmas. Plasma Phys. Control. Nucl. Fusion 24, 1187.Google Scholar
Brambilla, M. & Chen, Y. P. 1983 Quasilinear ion heating by lower hybrid waves. Nucl. Fusion 23, 541.Google Scholar
Cardinali, A., Morini, L., Castaldo, C., Cesario, R. & Zonca, F. 2007 Analysis of the validity of the techniques in the lower hybrid wave equation solution for reactor application. Phys. Plasmas 14, 112506.Google Scholar
Cardinali, A., Cesario, R., Panaccione, L., Santini, F., Amicucci, L., Castaldo, C., Ceccuzzi, S., Mirizzi, F. & Tuccillo, A. A.2015 Quasi-linear modelling of Lower Hybrid Current Drive in ITER and DEMO, invited talk to the Twenty-first Topical Conference on Radiofrequency Power in Plasmas, Lake Arrowed, CA, USA.Google Scholar
Cardinali, A., Castaldo, C., Cesario, R., Santini, F., Amicucci, L., Ceccuzzi, S., Galli, A., Mirizzi, F., Napoli, F., Panaccione, L. et al. 2017 Role of the lower hybrid spectrum in the current drive modelling for DEMO scenarios. Plasma Phys. Control. Fusion 59, 074002.Google Scholar
Cesario, R. & Cardinali, A. 1989 Parametric instabilities excited by ion sound and ion cyclotron quasi-modes during lower hybrid heating of tokamak plasmas. Nucl. Fusion 29, 1709.Google Scholar
Fisch, N. 1978 Confining a tokamak plasma with RF-driven currents. Phys. Rev. Lett. 41, 873.Google Scholar
Fisch, N. 1979 ERRATUM: Confining a tokamak Plasma with RF-Driven Currents. Phys. Rev. Lett. 42, 410.Google Scholar
Fisch, N. & Rax, J. M. 1992 Current drive by lower hybrid waves in the presence of energetic alpha particles. Nucl. Fusion 32, 549.Google Scholar
Franke, T., Barbato, E., Bosia, G., Cardinali, A., Ceccuzzi, S., Cesario, R., Van Eester, D., Federici, G., Gantenbein, G., Heloug, W. et al. 2015 Technological and physics assessments on heating and current drive systems for DEMO. Fusion Engng Des. 96–97, 46.Google Scholar
Giruzzi, G., Artaud, J. F., Baruzzo, M., Bolzonella, T., Fable, E., Garzotti, L., Ivanova-Stanik, I., Kemp, R., King, D. B., Schneider, M. et al. 2015 Modelling of Pulsed and Steady-State DEMO scenarios. Nucl. Fusion 55, 073002.Google Scholar
Graffey, J. D. 1976 Energetic ion distribution resulting from neutral beam injection in tokamak. J. Plasma Phys. 16, 149.Google Scholar
Imbeaux, F., Peysson, Y. & Eriksson, L. G. 2003 Absorption of lower hybrid waves by alpha particles in ITER. AIP Conf. Proc. 694, 271.Google Scholar
Karney, C. F. F. 1979 Stochastic ion heating by lower hybrid wave: II. Phys. Fluids 22, 2188.Google Scholar
Peysson, Y., Decker, J. & Morini, L. 2012 A versatile ray-tracing code for studying RF wave propagation in toroidal magnetized plasmas. Plasma Phys. Control. Fusion 54, 045003.Google Scholar
Porkolab, M. 1977 Parametric instabilities due to lower-hybrid radio frequency heating of tokamak plasmas. Phys. Fluids 20, 2058.Google Scholar
Schneider, M., Eriksson, L.-G., Imbeaux, F. & Artaud, J. F. 2009 Self-consistent simulations of the interaction between fusion-born alpha particles and lower hybrid waves in ITER. Nucl. Fusion 49, 125005.Google Scholar
Swanson, D. G. 2003 Plasma Waves, 2nd edn. IOP publishing.Google Scholar
Waltz, R. E. & Bass, E. M. 2014 Prediction of the fusion alpha density profile in ITER from local marginal stability to Alfvén eigenmodes. Nucl. Fusion 54, 104006.Google Scholar
Wong, K. L. & Ono, M. 1984 Effects of ion cyclotron harmonic damping on current drive in the lower hybrid frequency range. Nucl. Fusion 24, 615.Google Scholar
Zohm, H., Angioni, C., Fable, E., Federici, G., Gantenbein, G., Hartmann, T., Lackner, K., Poli, E., Porte, L., Sauter, O. et al. 2013 On the physics guidelines for a tokamak DEMO. Nucl. Fusion 53, 073019.Google Scholar
Zweben, S. J., Furth, H. P., Mikkelsen, D. R., Redi, M. H. & Strachan, J. D. 1988 Alpha storage regime in high temperature sub-ignited D-T tokamak. Nucl. Fusion 28, 2230.Google Scholar