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Anisotropic model for resonant heating of ions by Alfvén waves

Published online by Cambridge University Press:  09 August 2013

T. X. ZHANG
T. X. ZHANG*
Affiliation:
National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China (tianxi.zhang@aamu.edu) Department of Physics, Alabama A & M University, Huntsville, AL 35762, USA
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Abstract

Anisotropic heating of ions by Alfvén waves with frequency in the ion–cyclotron frequency range and propagation parallel to the magnetic field lines is investigated. First, particle–Alfvén wave interactions are quasilinearly examined from the kinetic theory in a hot multi-ion-magnetized plasma. As a result, the parallel and perpendicular heating rates of ions are derived analytically. Then, in terms of this anisotropic heating model and the dispersion relation of magnetic field-aligned left-hand polarized electromagnetic ion–cyclotron–Alfvén (EMICA) waves, the resonant heating of H, 2H, 3H, 3He, and 4He ions in a typical preheated laboratory plasma is numerically studied. It is shown that the EMICA waves can efficiently heat ions through cyclotron resonances primarily in the perpendicular direction. The perpendicular temperatures of H, 2H, 3H, 3He, and 4He increase much faster than the parallel ones. In comparison with the result from the previously developed isotropic heating model, the parallel heating by the EMICA waves is about much weaker, while the perpendicular heating is more efficient. Parameters such as density, temperature, magnetic field, wave-energy density, and ion species can affect the efficiency of the Alfvén wave heating in a similar way as shown in the isotropic heating model. The anisotropic model can be applied to explain the measurements of why O+5 and Mg+9 are heated extreme perpendicularly in solar coronal holes.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Issue 5 , October 2013 , pp. 963 - 971
Copyright
Copyright © Cambridge University Press 2013 

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References

Alfvén, H., 1942 Existence of electromagnetic-hydrodynamic waves. Nature 150, 405–406.CrossRefGoogle Scholar
Andre, M., 1985 Dispersion surfaces. J. Plasma Phys. 33, 1–19.CrossRefGoogle Scholar
Belcher, J. W. and Burchsted, R., 1974 Energy densities of Alfvén waves between 0.7 and 1.6 AU. J. Geophys. Res. 79, 4765–4768.CrossRefGoogle Scholar
Bernstein, I. B., 1958 Waves in a plasma in a magnetic field. Phys. Rev. 109, 10–21.CrossRefGoogle Scholar
Bernstein, I. B. and Engelmann, F. 1966 Quasilinear theory of plasma waves. Phys. Fluids 9 937–952.CrossRefGoogle Scholar
Chaston, C. C., Hu, Y. D. and Fraser, B. J., 2000 Quasilinear ion-cyclotron heating in the near-Earth magnetotail. J. Geophys. Res. 105, 5507–5516.CrossRefGoogle Scholar
Chen, L. and Hasegawa, A., 1974 Plasma heating by spatial resonance of Alfvén waves. Phys. Fluids 17, 1399–1403.CrossRefGoogle Scholar
Cramer, N. F. and Yung, C. M., 1986 Surface waves in a two-ion-species magnetized plasma. Plasma Phys. Contr. Fusion 28, 1043–1054.CrossRefGoogle Scholar
Davila, J. M., 1987 Heating of the solar corona by the resonant absorption of Alfvén waves. Astrophys. J. 317, 514–521.CrossRefGoogle Scholar
de Pontieu, B., 1999 Numerical simulations of spicules driven by weakly damped Alfvén waves. I. WKB approach. Astron. Astrophys. 347, 696–710.Google Scholar
de Pontieu, B., Martens, P. C. and Hudson, H. S., 2001 Chromospheric damping of Alfvén waves. Astrophys. J. 558, 859–871.CrossRefGoogle Scholar
Drummond, W. E. and Rosenbluth, M. N., 1962 Anomalous diffusion arising from micro-instabilities in a plasma. Phys. Fluids 5, 1507–1513.CrossRefGoogle Scholar
Elfimov, A. G. 2001 Alfvén wave heating and current drive. Phys. Fluids 8, 2050–2056.Google Scholar
Elfimov, A. G., Tataronis, J. A. and Hershkowitz, N., 1994 The influence of multiple ion species on Alfvén wave dispersion and Alfvén wave plasma heating. Phys. Plasmas 1, 2637–2644.CrossRefGoogle Scholar
Geary, J. L., Leboeuf, J. N. and Tajima, T., 1990 Computer simulation of Alfvén wave heating. Phys. Fluids B 2, 773–786.CrossRefGoogle Scholar
Gekelman, W., Vinvena, S., Leneman, D. and Maggs, J., 1997 Laboratory experiments on shear Alfvn waves and their relationship to space plasmas. J. Geophys. Res. 102, 7225–7236.CrossRefGoogle Scholar
Golovato, S. N., Shohet, J. L. and Tataronis, J. A., 1976 Alfvén-wave heating in the Proto-Cleo Stellarator. Phys. Rev. Lett. 37, 1272–1274.CrossRefGoogle Scholar
Gomberoff, L., Muñoz, V. and Valdivia, J. A., 2004 Ion cyclotron instability triggered by drifting minor ion species: cascade effect and exact results. Planet. Space Sci. 52, 679–684.CrossRefGoogle Scholar
Gomberoff, L. and Valdivia, J. A. 2002 Proton-cyclotron instability induced by the thermal anisotropy of minor ions. J. Geophys. Res. 107, CiteID 1494, doi:10.1029/2002JA009357.CrossRefGoogle Scholar
Gomberoff, L. and Valdivia, J. A. 2003 Ion cyclotron instability due to the thermal anisotropy of drifting ion species. J. Geophys. Res. 108, CiteID 1050, doi:10.1029/2002JA009576.CrossRefGoogle Scholar
Grossmann, W. and Smith, R. A., 1988 Heating of solar coronal loops by resonant absorption of Alfvn waves. Astrophys. J. 332, 476–498.CrossRefGoogle Scholar
Hasegawa, A. and Chen, L., 1975 Kinetic process of plasma heating due to Alfvén waves excitation. Phys. Rev. Lett. 35, L370–L373.CrossRefGoogle Scholar
Hu, Y. Q., Esser, R. and Habbal, S. R., 2000 A four-fluid turbulence-driven solar wind model for preferential acceleration and heating of heavy ions. J. Geophys. Res. 105, 5093–5112.CrossRefGoogle Scholar
Intrator, T.et al. 1995 Alfvén wave current drive in the Phaedrus-T tokamak. Phys. Plasmas 2, 2263–2271.CrossRefGoogle Scholar
Ionson, J. A., 1978 Resonant absorption of Alfvénic surface waves and the heating of solar coronal loops. Astrophys. J. 226, 650–673.CrossRefGoogle Scholar
Isenberg, P. A., Lee, M. A. and Hollweg, J. V., 2001 The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 1. Outward propagating waves. J. Geophys. Res. 106, 5649–5660.CrossRefGoogle Scholar
Kennel, C. F. and Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377–2388.CrossRefGoogle Scholar
Krall, N. A. and Trivepiece, A. W. 1973 Principles of Plasma Physics. New York: McGraw Hill.CrossRefGoogle Scholar
Lysak, R. L. and Song, Y. 2003 Nonlocal kinetic theory of Alfvn waves on dipolar field lines. J. Geophys. Res. 108, CiteID 1327, doi:10.1029/2003JA009859.CrossRefGoogle Scholar
Machida, S., Spangler, S. R. and Goertz, C. K., 1987 Simulation of amplitude-modulated circularly polarized Alfvén waves for beta less than one. J. Geophys. Res. 92, 7413–7422.CrossRefGoogle Scholar
Markovskii, S. A., 2001 Generation of ion cyclotron waves in coronal holes by a global resonant magnetohydrodynamic mode. Astrophys. J. 557, 337–342.CrossRefGoogle Scholar
McClements, K. G., Harrison, R. A. and Alexander, D. 1991 The detection of wave activity in the solar corona using UV line spectra. Sol. Phys. 131, 41–48.Google Scholar
Moya, P. S., Muñoz, V., Rogan, J. and Valdivia, J. A., 2011 Study of the cascading effect during the acceleration and heating of ions in the solar wind. J. Atmos. Solar-Terr. Phys. 73, 1390–1397.CrossRefGoogle Scholar
Moya, , Vinãs, A. F., Muñoz, V. and Valdivia, J. A. 2012 Ann. Geophys. 30, 1361–1369.CrossRefGoogle Scholar
Obiki, T.et al. 1977 Alfvén-wave heating experiment in the Heliotron-D. Phys. Rev. Lett. 39, L812–L815.CrossRefGoogle Scholar
Ofman, L., Davila, J. M. and Steinolfson, R. S., 1994 Coronal heating by the resonant absorption of Alfvén waves: the effect of viscous stress tensor. Astrophys. J. 421, 360–371.CrossRefGoogle Scholar
Poedts, S., Goossens, M. and Kerner, W., 1989 Numerical simulation of coronal heating by resonant absorption of Alfvn waves. Sol. Phys. 123, 83–115.CrossRefGoogle Scholar
Rosenbluth, M. N. and Rutherford, P. H., 1975 Excitation of Alfvén waves by high-energy ions in a Tokamak. Phys. Rev. Lett. 34, L1428–L1431.CrossRefGoogle Scholar
Ross D. W., Chen, G. L. and Mahajan, S. M., 1982 Kinetic description of Alfvén wave heating. Phys. Fluids 25, 652–667.Google Scholar
Sakurai, T., Ichimoto, K., Raju, K. P. and Singh, J., 2002 Spectroscopic observation of coronal waves. Sol. Phys. 209, 265–286.CrossRefGoogle Scholar
Seough, J. and Yoon, P. H., 2012 Quasilinear theory of anisotropy-beta relations for proton cyclotron and parallel firehose instabilities. J. Geophys. Res. 117, A08101.CrossRefGoogle Scholar
Seough, J., Yoon, P. H., Kim, K. H. and Lee, D. H. 2013 Solar-wind proton anisotropy and beta relation. Phys. Rev. Lett. 110, 071103.Google Scholar
Sharapov, S. E.et al. 2002 Alfvén wave cascades in a tokamak. Phys. Plasmas 9, 2027–2036.CrossRefGoogle Scholar
Stix, T. H., 1975 Fast-wave heating of a two-component plasma. Nucl. Fusion 15, 737–754.CrossRefGoogle Scholar
Stix, T. X. 1992 Waves in Plasmas. New York: AIP.Google Scholar
Tanaka, M., Sato, T. and Hasegawa, A., 1989 Excitation of kinetic Alfvén waves by resonant mode conversion and longitudinal heating of magnetized plasmas. Phys. Fluids B 1, 325–332.CrossRefGoogle Scholar
Tsushima, A., Amagishi, Y. and Inutake, M., 1982 Observations of spatial Alfvén resonance. Phys. Lett. 88A, 457–460.CrossRefGoogle Scholar
Weisen, H.et al. 1989 Mode conversion to the kinetic Alfvén wave in low-frequency heating experiments in the TCA tokamak. Phys. Rev. Lett. 63, L2476–L2479.Google Scholar
White, R. B., Yoshikawa, S. and Oberman, C., 1982 Alfvén wave cyclotron resonance heating. Phys. Fluids 25, 384–388.CrossRefGoogle Scholar
Witherspoon, F. D., Prager, S. C. and Sprott, J. C., 1984 Experimental observation of the shear Alfvn resonance in a Tokamak. Phys. Rev. Lett. 53, L1559–L1562.CrossRefGoogle Scholar
Wygant, J. R.et al. 2002 Evidence for kinetic Alfvén waves and parallel electron energization at 4-6 RE altitudes in the plasma sheet boundary layer. J. Geophys. Res. 107, CiteID 1201, doi:10.1029/2001JA900113.CrossRefGoogle Scholar
Yoon, P. H., 1992 Quasilinear evolution of Alfén-ion-cyclotron and mirror instabilities driven by ion temperature anisotropy. Phys. Fluids B 4, 3627–3637.CrossRefGoogle Scholar
Zhang, T. X. 1995 Solar 3He-rich events and ion acceleration in two stages. Astrophys. J. 449, 916–929.CrossRefGoogle Scholar
Zhang, T. X. 1999 Solar 3He-rich events and electron acceleration in two stages. Astrophys. J. 518, 954–964.CrossRefGoogle Scholar
Zhang, T. X., 2003 Preferential heating of particles by H-cyclotron waves generated by a global magnetohydrodynamic mode in solar coronal holes. Astrophys. J. Lett. 597, L69–L72.CrossRefGoogle Scholar
Zhang, T. X. 2004 An explanation for huge enhancements of ultra-heavy ions in solar 3He-rich events. Astrophys. J. Lett. 617, L77–L80.Google Scholar
Zhang, T. X. and Li, B., 2004 A kinetic model for resonant heating of ions by Alfvén waves in laboratory plasmas. Phys. Plasmas 11, 2172–2177.CrossRefGoogle Scholar
Zhang, T. X., Wang, J. X. and Xiao, C. J., 2005 Resonant heating of ions by parallel propagating Alfvén waves in solar coronal holes. Chin. J. Astron. Astrophys. 5, 285–294.CrossRefGoogle Scholar