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On the polarization of shear Alfvén and acoustic continuous spectra in toroidal plasmas

Part of: Laboratory and Astrophysical Plasmas: New Perspectives Focus on Fusion

Published online by Cambridge University Press:  16 September 2020

M. V. Falessi Open the ORCID record for M. V. Falessi [Opens in a new window] ,
N. Carlevaro Open the ORCID record for N. Carlevaro [Opens in a new window] ,
V. Fusco ,
E. Giovannozzi ,
P. Lauber ,
G. Vlad  and
F. Zonca Open the ORCID record for F. Zonca [Opens in a new window]
M. V. Falessi*
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy INFN – Rome section, Piazz.le Aldo Moro 2, 00185Roma, Italy
N. Carlevaro
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy Consorzio RFX, Corso Stati Uniti 4, 35127Padova, Italy
V. Fusco
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy
E. Giovannozzi
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy
P. Lauber
Affiliation:
Max Planck Institute for Plasma Physics, 85748Garching, Germany
G. Vlad
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy
F. Zonca
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang University, Hangzhou310027, PR China
*
†Email address for correspondence: matteo.falessi@enea.it
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Abstract

In this work, the FALCON code is adopted for illustrating the features of shear Alfvén and sound continuous spectra in toroidal fusion plasmas. The FALCON codes employ the local Floquet analysis discussed in (Phys. Plasmas, vol. 26, issue 8, 2019, 082502) for computing global structures of continuous spectra in general toroidal geometry. As particular applications, reference equilibria for the divertor tokamak test and ASDEX Upgrade plasmas are considered. In particular, we illustrate the importance of mode polarization for recognizing the physical relevance of the various branches of the continuous spectra in the ideal magnetohydrodynamics limit. We also analyse the effect of plasma compression and the validity of the slow sound approximation.

Keywords

plasma wavesfusion plasmaplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 5 , October 2020 , 845860501
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Albanese, R., Calabrò, G., Mattei, M. & Villone, F. 2003 Plasma response models for current, shape and position control in JET. Fusion Engng Des. 66–68, 715–718.CrossRefGoogle Scholar
Albanese, R., Crisanti, F., Martin, P., Martone, R., Pizzuto, A. & DTT Project Proposal Contributors 2019 DTT divertor tokamak test facility. Interim Design Report [ISBN:978-88-8286-378-4].Google Scholar
Albanese, R., Pizzuto, A., WPDTT2 Team & DTT Project Proposal Contributors 2017 The DTT proposal. A tokamak facility to address exhaust challenges for DEMO: introduction and executive summary. Fusion Engng Des. 122, 274–284.CrossRefGoogle Scholar
Appert, K. 1974 Continuous spectra of a cylindrical magnetohydrodynamic equilibrium. Phys. Fluids 17 (7), 1471.CrossRefGoogle Scholar
Artaud, J. F., Imbeaux, F., Garcia, J., Giruzzi, G., Aniel, T., Basiuk, V., Bécoulet, A., Bourdelle, C., Buravand, Y., Decker, J., et al. 2018 Metis: a fast integrated tokamak modelling tool for scenario design. Nucl. Fusion 58 (10), 105001.CrossRefGoogle Scholar
Barston, E. M. 1964 Electrostatic oscillations in inhomogeneous cold plasmas. Ann. Phys. 29 (2), 282–303.CrossRefGoogle Scholar
Bierwage, A., Shinohara, K., Todo, Y., Aiba, N., Ishikawa, M., Matsunaga, G., Takechi, M. & Yagi, M. 2017 Self-consistent long-time simulation of chirping and beating energetic particle modes in JT-60U plasmas. Nucl. Fusion 57 (1), 016036.CrossRefGoogle Scholar
Bowden, G. W., Hole, M. J. & Könies, A. 2015 Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria. Phys. Plasmas 22 (9), 092114.CrossRefGoogle Scholar
Chance, M. S., Greene, J. M., Grimm, R. C. & Johnson, J. L. 1977 Study of the MHD spectrum of an elliptic plasma column. Nucl. Fusion 17 (1), 65–83.CrossRefGoogle Scholar
Chavdarovski, I. & Zonca, F. 2009 Effects of trapped particle dynamics on the structures of a low-frequency shear Alfvén continuous spectrum. Plasma Phys. Control. Fusion 51 (11), 115001.CrossRefGoogle Scholar
Chavdarovski, I. & Zonca, F. 2014 Analytic studies of dispersive properties of shear Alfvén and acoustic wave spectra in tokamaks. Phys. Plasmas 21 (5), 052506.CrossRefGoogle Scholar
Chen, L. & Hasegawa, A. 1974 A theory of long-period magnetic pulsations: 1. Steady state excitation of field line resonance. J. Geophys. Res. 79 (7), 1024–1032.CrossRefGoogle Scholar
Chen, L. & Zonca, F. 2016 Physics of Alfvén waves and energetic particles in burning plasmas. Rev. Mod. Phys. 88 (1), 015008.CrossRefGoogle Scholar
Chen, L. & Zonca, F. 2017 On energetic-particle excitations of low-frequency Alfvén eigenmodes in toroidal plasma. Phys. Plasmas 24 (7), 072511.CrossRefGoogle Scholar
Cheng, C. Z. & Chance, M. S. 1986 Low-n shear Alfvén spectra in axisymmetric toroidal plasmas. Phys. Fluids 29 (11), 3695.CrossRefGoogle Scholar
Cheng, C. Z., Chen, L. & Chance, M. S. 1985 High-n ideal and resistive shear Alfvén waves in tokamaks. Ann. Phys. 161 (1), 21–47.CrossRefGoogle Scholar
Chu, M. S., Greene, J. M., Lao, L. L., Turnbull, A. D. & Chance, M. S. 1992 A numerical study of the high-nshear Alfvén spectrum gap and the high-ngap mode. Phys. Fluids B 4 (11), 3713–3721.CrossRefGoogle Scholar
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1978 Shear, periodicity, and plasma ballooning modes. Phys. Rev. Lett. 40 (6), 396–399.CrossRefGoogle Scholar
Deng, W., Lin, Z., Holod, I., Wang, Z., Xiao, Y. & Zhang, H. 2012 Linear properties of reversed shear Alfvén eigenmodes in the DIII-D tokamak. Nucl. Fusion 52 (4), 043006.CrossRefGoogle Scholar
Denk, R. 1995 Convergence improvement for the infinite determinants of hill systems. Z. Angew. Math. Mech. 75, 463–470.CrossRefGoogle Scholar
Dewar, R. L., Grimm, R. C., Johnson, J. L., Frieman, E. A., Greene, J. M. & Rutherford, P. H. 1974 Long-wavelength kink instabilities in low-pressure, uniform axial current, cylindrical plasmas with elliptic cross sections. Phys. Fluids 17 (5), 930.CrossRefGoogle Scholar
D'Ippolito, D. A. & Goedbloed, J. P. 1980 Mode coupling in a toroidal sharp-boundary plasma. I. Weak-coupling limit. Plasma Phys. 22 (12), 1091–1107.CrossRefGoogle Scholar
Falessi, M. V., Carlevaro, N., Fusco, V., Vlad, G. & Zonca, F. 2019 Shear Alfvén and acoustic continuum in general axisymmetric toroidal geometry. Phys. Plasmas 26 (8), 082502.CrossRefGoogle Scholar
Floquet, G. 1883 Sur les équations différentielles linéaires à coefficients périodiques. In Annales scientifiques de l’École normale supérieure, vol. 12, pp. 47–88.Google Scholar
Goedbloed, J. P. 1975 Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems. Phys. Fluids 18 (10), 1258.CrossRefGoogle Scholar
Goedbloed, J. P. 1998 Once more: the continuous spectrum of ideal magnetohydrodynamics. Phys. Plasmas 5 (9), 3143–3154.CrossRefGoogle Scholar
Gorelenkov, N. N., Berk, H. L., Crocker, N. A., Fredrickson, E. D., Kaye, S., Kubota, S., Park, H., Peebles, W., Sabbagh, S. A., Sharapov, S. E., et al. 2007 a Predictions and observations of global beta-induced Alfvén–acoustic modes in JET and NSTX. Plasma Phys. Control. Fusion 49 (12B), B371–B383.CrossRefGoogle Scholar
Gorelenkov, N. N., Berk, H. L., Fredrickson, E., Sharapov, S. E. & JET EFDA Contributors 2007 b Predictions and observations of low-shear beta-induced shear Alfvén acoustic eigenmodes in toroidal plasmas. Phys. Lett. A 370, 70.CrossRefGoogle Scholar
Gorelenkov, N. N., Van Zeeland, M. A., Berk, H. L., Crocker, N. A., Darrow, D., Fredrickson, E., Fu, G. -Y., Heidbrink, W. W., Menard, J. & Nazikian, R. 2009 Beta-induced Alfvén-acoustic eigenmodes in national spherical torus experiment and DIII-D driven by beam ions. Phys. Plasmas 16 (5), 056107.CrossRefGoogle Scholar
Grad, H. 1969 Plasmas. Phys. Today 32 (12), 34.CrossRefGoogle Scholar
Hasegawa, A. & Chen, L. 1974 Plasma heating by Alfvén-wave phase mixing. Phys. Rev. Lett. 32 (9), 454–456.CrossRefGoogle Scholar
Hill, G. W. 1886 On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Math. 8 (1), 1–36.CrossRefGoogle Scholar
van der Holst, B., Beliën, A. J. C. & Goedbloed, J. P. 2000 Low frequency Alfvén waves induced by toroidal flows. Phys. Plasmas 7 (10), 4208–4222.CrossRefGoogle Scholar
Horváth, L., Papp, G., Lauber, P., Por, G., Gude, A., Igochine, V., Geiger, B., Maraschek, M., Guimarais, L., Nikolaeva, V., et al. 2016 Experimental investigation of the radial structure of energetic particle driven modes. Nucl. Fusion 56 (11), 112003.CrossRefGoogle Scholar
Huysmans, G. T. A., Goedbloed, J. P. & Kerner, W. 1991 Isoparametric bicubic hermite elements for solution of the Grad-Shafranov equation. Intl J. Mod. Phys. C 02 (01), 371–376.CrossRefGoogle Scholar
Huysmans, G. T. A., Kerner, W., Borba, D., Holties, H. A. & Goedbloed, J. P. 1995 Modeling the excitation of global Alfvén modes by an external antenna in the Joint European Torus (JET). Phys. Plasmas 2 (5), 1605–1613.CrossRefGoogle Scholar
Jolliet, S., Bottino, A., Angelino, P., Hatzky, R., Tran, T. M., Mcmillan, B. F., Sauter, O., Appert, K., Idomura, Y. & Villard, L. 2007 A global collisionless pic code in magnetic coordinates. Comput. Phys. Commun. 177 (5), 409–425.CrossRefGoogle Scholar
Kieras, C. E. & Tataronis, J. A. 1982 The shear Alfvén continuous spectrum of axisymmetric toroidal equilibria in the large aspect ratio limit. J. Plasma Phys. 28 (3), 395–414.CrossRefGoogle Scholar
Könies, A. & Eremin, D. 2010 Coupling of Alfvén and sound waves in stellarator plasmas. Phys. Plasmas 17 (1), 012107.CrossRefGoogle Scholar
Lauber, P. 2013 Super-thermal particles in hot plasmas-Kinetic models, numerical solution strategies, and comparison to tokamak experiments. Phys. Rep. 533, 33–68.CrossRefGoogle Scholar
Lauber, P., Brüdgam, M., Curran, D., Igochine, V., Sassenberg, K., Günter, S., Maraschek, M., García-Muñoz, M. & Hicks, N. 2009 Kinetic Alfvén eigenmodes at ASDEX upgrade. Plasma Phys. Control. Fusion 51 (12), 124009.CrossRefGoogle Scholar
Lauber, P., Classen, I. G. J., Curran, D., Igochine, V., Geiger, B., da ç, S., García-Muñoz, M., Maraschek, M. & McCarthy, P. 2012 Nbi-driven Alfvénic modes at ASDEX upgrade. Nucl. Fusion 52 (9), 094007.CrossRefGoogle Scholar
Lauber, P. & Günter, S. 2008 Damping and drive of low-frequency modes in tokamak plasmas. Nucl. Fusion 48 (8), 084002.CrossRefGoogle Scholar
Lauber, P., Günter, S., Könies, A. & Pinches, S. D. 2007 Ligka: a linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks. J. Comput. Phys. 226 (1), 447–465.CrossRefGoogle Scholar
Lauber, P. & Lu, Z. 2018 Analytical finite-Lamor-radius and finite-orbit-width model for the LIGKA code and its application to KGAM and shear Alfvén physics. J. Phys. Conf. Ser. 1125, 012015.CrossRefGoogle Scholar
Lu, Z. X., Zonca, F. & Cardinali, A. 2012 Theoretical and numerical studies of wave-packet propagation in tokamak plasmas. Phys. Plasmas 19 (4), 042104.CrossRefGoogle Scholar
Lütjens, H., Bondeson, A. & Sauter, O. 1996 The CHEASE code for toroidal MHD equilibria. Comput. Phys. Commun. 97, 219–260.CrossRefGoogle Scholar
Magnus, W. & Winkler, S. 2013 Hill's equation. Courier Corporation.Google Scholar
Pao, Y.-P. 1975 The continuous MHD spectrum in toroidal geometries. Nucl. Fusion 15 (4), 631–635.CrossRefGoogle Scholar
Pogutse, O. P. & Yurchenko, E. I. 1978 Energy principle and kink instability in a toroidal plasma with strong magnetic field. Nucl. Fusion 18 (12), 1629–1638.CrossRefGoogle Scholar
Salat, A. & Tataronis, J. A. 1997 The shear Alfvén continuum in an asymmetric magnetohydrodynamic equilibrium. Phys. Plasmas 4 (11), 3770–3782.CrossRefGoogle Scholar
Sedláček, Z. 1971 Electrostatic oscillations in cold inhomogeneous plasma I. Differential equation approach. J. Plasma Phys. 5 (2), 239–263.CrossRefGoogle Scholar
Tataronis, J. & Grossmann, W. 1973 Decay of mhd waves by phase mixing. Z. Phys. A Hadron. Nucl. 261 (3), 203–216.CrossRefGoogle Scholar
Uberoi, C. 1972 Alfvén waves in inhomogeneous magnetic fields. Phys. Fluids 15 (9), 1673.CrossRefGoogle Scholar
Vannini, F., Biancalani, A., Bottino, A., Hayward-Schneider, T., Lauber, P., Mishchenko, A., Novikau, I. & Poli, E. 2020 Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX upgrade. Phys. Plasmas 27 (4), 042501.CrossRefGoogle Scholar
Zhang, H. S., Liu, Y. Q., Lin, Z. & Zhang, W. L. 2016 Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode. Phys. Plasmas 23 (4), 042510.CrossRefGoogle Scholar
Zonca, F., Biancalani, A., Chavdarovski, I., Chen, L., Di Troia, C. & Wang, X. 2010 Kinetic structures of shear Alfvén and acoustic wave spectra in burning plasmas. J. Phys.: Conf. Ser. 260, 012022.Google Scholar
Zonca, F. & Chen, L. 2014 a Theory on excitations of drift Alfvén waves by energetic particles: I. Variational formulation. Phys. Plasmas 21, 072120.CrossRefGoogle Scholar
Zonca, F. & Chen, L. 2014 b Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation. Phys. Plasmas 21, 072121.CrossRefGoogle Scholar
Zonca, F., Chen, L., Dong, J. Q. & Santoro, R. A. 1999 Existence of ion temperature gradient driven shear Alfvén instabilities in tokamaks. Phys. Plasmas 6 (5), 1917–1924.CrossRefGoogle Scholar
Zonca, F., Chen, L. & Santoro, R. A. 1996 Kinetic theory of low-frequency Alfvén modes in tokamaks. Plasma Phys. Control. Fusion 38 (11), 2011.CrossRefGoogle Scholar
Zonca, F., Chen, L., Santoro, R. A. & Dong, J. Q. 1998 Existence of discrete modes in an unstable shear Alfvén continuous spectrum. Plasma Phys. Control. Fusion 40 (12), 2009–2021.CrossRefGoogle Scholar