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Linear collisionless Landau damping in Hilbert space

Published online by Cambridge University Press:  01 April 2015

Alessandro Zocco
Alessandro Zocco*
Affiliation:
Max-Planck-Institut für Plasmaphysik, Wendelsteinstrasse, D-17489, Greifswald, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The equivalence between the Laplace transform (Landau, J. Phys. USSR10 (1946), 25) and Hermite transform (Zocco and Schekochihin, Phys. Plasmas18, 102309 (2011)) solutions of the linear collisionless Landau damping problem is proven.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 4 , August 2015 , 905810402
Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Abramowitz, M. and Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover Publications.Google Scholar
Antonsen, T. M. and Coppi, B. 1981 Phys. Lett. A 81 (6), 335–338.Google Scholar
Connor, J. W., Hastie, R. J. and Zocco, A. 2012 Plasma Phys. Control. Fusion 54 (3), 035003.Google Scholar
Coppi, B., Mark, J. W. K., Sugiyama, L. and Bertin, G. 1979 Phys. Rev. Lett. 42 (16), 1058–1061.Google Scholar
Crew, G. B., Antonsen, T. M. Jr. and Coppi, B. 1982 Nuclear Fusion 22 (1), 41.Google Scholar
Fried, B. D., Hendrick, C. L. and McCune, J. 1968 Phys. Fluids 11 (249).Google Scholar
Frieman, E. A. and Chen, L. 1982 Phys. Fluids 25 (3), 502–508.Google Scholar
Hammett, G. W., Beer, M. A., Dorland, W., Cowley, S. C. and Smith, S. A. 1993 Plasma Phys. Control. Fusion 35 (8), 973.Google Scholar
Hasegawa, A. and Chen, L. 1975 Phys. Rev. Lett. 35, 370–373.Google Scholar
Hatch, D., Jenko, F., Bañón, Navarro, A. and Bratanov, V. 2013 Phys. Rev. Lett. 111, 175001.Google Scholar
Landau, L. 1946 J. Phys. USSR 10, 25.Google Scholar
Louarn, B., Wahlund, J. E., Chust, T., de Feraudy, H., Roux, A., Holback, B., Dovner, P. O., Eriksson, A. I. and Holmgren, G. 1994 Geophys. Res. Lett. 21 (17), 1847.Google Scholar
Loureiro, N. F., Schekochihin, A. A. and Zocco, A. 2013 Phys. Rev. Lett. 111, 025002.Google Scholar
McCabe, J. H. 1984 J. Plasma Phys. 32, 479.Google Scholar
Parker, J. T. and Dellar, P. J. 2014 Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit. ArXiv e-prints.Google Scholar
Pegoraro, F., Porcelli, F. and Schep, T. J. 1989 Phys. Fluids B 1 (2), 364–374.Google Scholar
Porcelli, F. 1991 Phys. Rev. Lett. 66 (4), 425–428.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. and Tatsuno, T. 2009 Astrophys. J. Suppl. 182 (1), 310–377.Google Scholar
Smith, S. A. 1997 Moments, fluid moments, and subgrid scales in plasma turbulence. PhD thesis, Princeton University, p. 27.Google Scholar
Sugama, H., Watanabe, T.-H. and Horton, W. 2001 Phys. Plasmas 8 (6), 2617–2628.Google Scholar
Yamada, M., Kulsrud, R. and Ji, H. 2010 Rev. Mod. Phys. 82, 603.Google Scholar
Zocco, A., Loureiro, N., Dickinson, D., Numata, R. and Roach, C. 2014 Kinetic microtearing modes and reconnecting modes in strongly magnetised slab plasmas. ArXiv e-prints.Google Scholar
Zocco, A. and Schekochihin, A. A. 2011 Phys. Plasmas 18 (10), 102309.Google Scholar