Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-24T20:52:48.897Z Has data issue: false hasContentIssue false

Effect of temperature anisotropy on the dynamics of geodesic acoustic modes

Published online by Cambridge University Press:  06 March 2023

J.N. Sama*
Affiliation:
Institut Jean Lamour UMR 7198, Université de Lorraine-CNRS, Nancy 54011, France
A. Biancalani
Affiliation:
Léonard de Vinci Pôle Universitaire, Research Center, Paris La Défense 92400, France Max Planck Institute for Plasma Physics, Garching 85748, Germany
A. Bottino
Affiliation:
Max Planck Institute for Plasma Physics, Garching 85748, Germany
I. Chavdarovski
Affiliation:
Korea Institute of Fusion Energy, Daejeon 34133, South Korea
D. Del Sarto
Affiliation:
Institut Jean Lamour UMR 7198, Université de Lorraine-CNRS, Nancy 54011, France
A. Ghizzo
Affiliation:
Institut Jean Lamour UMR 7198, Université de Lorraine-CNRS, Nancy 54011, France
T. Hayward-Schneider
Affiliation:
Max Planck Institute for Plasma Physics, Garching 85748, Germany
Ph. Lauber
Affiliation:
Max Planck Institute for Plasma Physics, Garching 85748, Germany
B. Rettino
Affiliation:
Max Planck Institute for Plasma Physics, Garching 85748, Germany
F. Vannini
Affiliation:
Max Planck Institute for Plasma Physics, Garching 85748, Germany
*
Email address for correspondence: juvert-njeck.sama@univ-lorraine.fr

Abstract

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

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

REFERENCES

Biancalani, A., Bottino, A., Lauber, P. & Zarzoso, D. 2014 Numerical validation of the electromagnetic gyrokinetic code NEMORB on global axisymmetric modes. Nucl. Fusion 54, 104004.CrossRefGoogle Scholar
Cerri, S.S., Henri, P., Califano, F., Del Sarto, D., Faganello, M. & Pegoraro, F. 2013 Extended fluid models: pressure tensor effects and equilibria. Phys. Plasmas 20, 112112.CrossRefGoogle Scholar
Chakrabarti, N., Guzdar, P.N., Kleva, R.G., Singh, R., Kaw, P.K., Naulin, V. & Rasmussen, J.J. 2010 Geodesic acoustic mode in toroidal plasma. AIP Conf. Proc. 1308, 108.CrossRefGoogle Scholar
Chen, L. & Zonca, F. 2007 Nonlinear equilibria, stability and generation of zonal structures in toroidal plasmas. Nucl. Fusion 47, 886891.CrossRefGoogle Scholar
Cho, Y.W. & Hahm, T.S. 2021 Effect of temperature anisotropy on residual zonal flow level. Phys. Plasmas 28, 052303.CrossRefGoogle Scholar
Conway, G.D., Smolyakov, A.I. & Ido, T. 2022 Geodesic acoustic modes in magnetic confinement devices. Nucl. Fusion 62, 013001.CrossRefGoogle Scholar
Del Sarto, D. & Pegoraro, F. 2018 a Shear-induced pressure anisotropization and correlation with fluid vorticity in a low collisionality plasma. Mon. Not. R. Astron. Soc. 475, 181.CrossRefGoogle Scholar
Del Sarto, D. & Pegoraro, F. 2018 b Shear-induced pressure anisotropization and correlation with fluid vorticity in a low collisionality plasma. In Un Comptes-Rendus de la 21e Rencontre du Non Linéaire, Paris 2018 (ed. E. Falcon, M. Lefranc, F. Ptrluis & C.-T. Pham) vol. 21, pp. 13–18. Université Paris Diderot, Non-Linéaire Publications.Google Scholar
Del Sarto, D., Pegoraro, F. & Califano, F. 2016 Pressure anisotropy and small spatial scales induced by velocity shear. Phys. Rev. E 93, 053203.CrossRefGoogle ScholarPubMed
Fu, G.Y. 2008 Energetic-particle-induced geodesic acoustic mode. Phys. Rev. Lett. 101, 185002.CrossRefGoogle ScholarPubMed
Gao, Z. 2013 Collisional damping of the geodesic acoustic mode. Phys. Plasmas 20, 032501.CrossRefGoogle Scholar
Garbet, X., Falchetto, G., Ottaviani, M., Sabot, R., Sirinelli, A. & Smolyakov, A. 2006 Coherent modes in the acoustic frequency range in tokamaks. AIP Conf. Proc. 871, 342.CrossRefGoogle Scholar
Girardo, J., Zarzoso, D., Dumont, R., Garbet, X., Sarazin, Y. & Sharapov, S. 2014 Relation between energetic and standard geodesic acoustic modes. Phys. Plasmas 21, 092507.CrossRefGoogle Scholar
Grandgirard, V., Garbet, X., Ehrlacher, C., Biancalani, A., Bottino, A., Novikau, I., Asahi, Y., Caschera, E., Dif-Pradalier, G., Donnel, P., et al. 2019 Linear collisionless dynamics of the gam with kinetic electrons: comparison simulations/theory. Phys. Plasmas 26, 122304.CrossRefGoogle Scholar
Hasegawa, A., Maclennan, C.G. & Kodama, Y. 1979 Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. Phys. Fluids 22, 2122.CrossRefGoogle Scholar
Hassam, A.B. & Kleva, R.G. 2011 Double adiabatic theory of collisionless geodesic acoustic modes in tokamaks. arXiv:1109.0057.Google Scholar
Hole, M.J., von Nessi, G., Fitzgerald, M, McClements, K.G., Svensson, J. & the MAST team 2001 Equilibrium analysis of tokamak discharges with anisotropic pressure. Plasma Phys. Control. Fusion 43, 14411456.Google Scholar
Hole, M.J., von Nessi, G., Fitzgerald, M., McClements, K.G., Svensson, J. & the MAST team 2011 Identifying the impact of rotation, anisotropy, and energetic particle physics in tokamaks. Plasma Phys. Control. Fusion 53, 074021.CrossRefGoogle Scholar
Kaufman, A.N. 1960 Plasma viscosity in a magnetic field. Phys. Plasmas 3, 610.Google Scholar
Lu, Z.X., Wang, X., Lauber, P., Fable, E., Bottino, A., Hornsby, W., Hayward-Schneider, T., Zonca, F. & Angioni, C. 2019 Theoretical studies and simulations of mode structure symmetry breaking in tokamak plasmas in the presence of energetic particles. Plasma Phys. Control. Fusion 61, 044005.CrossRefGoogle Scholar
Macmahon, A. 1965 Finite gyro radius corrections to the hydromagnetic equations for a vlasov plasma. Phys. Plasmas 3, 610.Google Scholar
Ming, Y., Zhou, D. & Wamg, W. 2018 Geodesic acoustic modes in tokamak plasmas with anisotropic distribution and a radial equilibrium electric field. Plasma Sci. Technol. 20, 085101.CrossRefGoogle Scholar
Novikau, I., Biancalani, A., Bottino, A., Conway, G.D., Gurcan, O.D., Manz, P., Morel, P., Poli, E., Di Siena, A. & ASDEX Upgrade Team 2017 Linear gyrokinetic investigation of the geodesic acoustic modes in realistic tokamak configurations. Phys. Plasmas 24, 122117.CrossRefGoogle Scholar
Qiu, Z., Chen, L. & Zonca, F. 2009 Collisionless damping of short wavelength geodesic acoustic modes. Plasma Phys. Control. Fusion 51, 012001.CrossRefGoogle Scholar
Ren, H. 2015 Geodesic acoustic mode in anisotropic plasma with heat flux. Phys. Plasmas 22, 102505.CrossRefGoogle Scholar
Ren, H. & Cao, J. 2014 Geodesic acoustic mode in anisotropic plasmas using adiabatic model and gyro-kinetics equation. Phys. Plasmas 21, 122512.CrossRefGoogle Scholar
Rettino, B., Hayward-Schneider, T., Biancalani, A., Bottino, A., Lauber, P., Chavdarovski, I., Vannini, F. & Jenko, F. 2022 Gyrokinetic modelling of anisotropic energetic particle driven instabilities in tokamak plasmas. Nucl. Fusion 62, 076027.CrossRefGoogle Scholar
Sasaki, K., Horling, P., Fall, T., Brzozowski, J.H., Brunsell, P., Hokin, S., Tennfors, E., Sallander, J., Drake, J.R., Inoue, N., et al. 1997 Anisotropy of ion temperature in a reversed-field-pinch plasma. Plasma Phys. Control. Fusion 39, 333338.CrossRefGoogle Scholar
Smolyakov, A.I., Garbet, X., Falchetto, G. & Ottaviani, M. 2008 Multiple polarization of geodesic curvature induced modes. Phys. Lett. A 372, 67506756.CrossRefGoogle Scholar
Sugama, H. & Watanabe, T.H. 2006 Collisionless damping of geodesic acoustic modes. J. Plasma Phys. 72, 825.CrossRefGoogle Scholar
Thompson, W.B. 1961 The dynamics of high temperature plasmas. Phys. Plasmas 3, 610.Google Scholar
Vannini, F., Biancalani, A., Bottino, A., Hayward-Schneider, T., Lauber, P., Mishchenko, A., Poli, E., Vlad, G. & ASDEX Upgrade Team 2021 Gyrokinetic investigation of the nonlinear interaction of Alfvén instabilities and energetic particle-driven geodesic acoustic modes. Phys. Plasmas 28, 072504.CrossRefGoogle Scholar
Vlad, G., Wang, X., Vannini, F., Briguglio, S., Carlevaro, N., Falessi, M.V., Fogaccia, G., Fusco, V., Zonca, F., Biancalani, A., et al. 2021 A linear benchmark between HYMAGYC, MEGA and ORB5 codes using the NLED-AUG test case to study Alfvénic modes driven by energetic particles. Nucl. Fusion 61, 116026.CrossRefGoogle Scholar
Winsor, N., Johnson, J.L. & Dawson, J.M. 1968 Geodesic acoustic waves in hydromagnetic systems. Phys. Fluids 11, 2448.CrossRefGoogle Scholar
Zarzoso, D., Garbet, X., Sarazin, Y., Dumont, R. & Grandgirard, V. 2012 Fully kinetic description of the linear excitation and nonlinear saturation of fast-ion-driven geodesic acoustic mode instability. Phys. Plasmas 19, 022102.CrossRefGoogle Scholar
Zhang, M. & Zhou, D. 2010 Magnetic components of geodesic acoustic modes in plasmas with anisotropic ion distribution. Plasma Sci. Technol. 12, 610.Google Scholar
Zonca, F. & Chen, L. 2008 Radial structures and nonlinear excitation of geodesic acoustic modes. Europhys. Lett. 83, 35001.CrossRefGoogle Scholar
Zonca, F., Chen, L. & Santoro, R.A. 1996 Kinetic theory of low-frequency Alfvén modes in tokamaks. Plasma Phys. Control. Fusion 38, 2011.CrossRefGoogle Scholar