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Nernst advection and the field-generating thermal instability revisited

Published online by Cambridge University Press:  25 July 2014

J. J. Bissell
J. J. Bissell*
Affiliation:
Department of Mathematical Sciences, University of Durham, DH1 3LE, UK Blackett Laboratory, Imperial College London, SW7 2BZ, UK
*
†Email address for correspondence: john.bissell@durham.ac.uk
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Abstract

It is widely held that the Nernst effect can drive instability in un-magnetised laser-plasmas by laterally compressing seed B-fields arising from the field-generating thermal instability [Tidman & Shanny, Phys. Fluids, 12:1207 (1974)]. Indeed, for wavelike perturbations, differential compression by the Nernst mechanism is thought to be most pronounced in the limit of low wave-number k → 0, and is considered particularly important given that it can ostensibly lead to instability when the more usual field-generating mechanism is stable. However, as part of a recent article [Bissell et al., New J. Phys., 15:025017 (2013)] we noted some irregularities to the Nernst mechanism which obscure its operation. For example, by taking characteristic density and temperature length-scales ln and lT respectively, we observed that consistent analytical treatment of the instability requires kln,T ≫ 1, preventing the peak-growth limit k → 0. Furthermore, the Nernst term—which compresses magnetic field perturbations—does not couple to a corresponding term acting on thermal perturbations, and as such does not describe an unstable feedback mechanism. In this article we probe the origin of such ambiguities more formally, and in so doing argue (contrary to reports existing elsewhere in the literature) that the Nernst effect does not drive instability in un-magnetised conditions, at least not in the fashion typically cited.

Keywords

52.35.-g52.25.Fi52.25.Xz52.57.-z
Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 905810108
Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Bissell, J. J., Kingham, R. J. and Ridgers, C. P. 2012 Magnetothermal instability in laser plasmas including hydrodynamic effects. Phys. Plasmas 19 (5), 052107.Google Scholar
Bissell, J. J., Ridgers, C. P. and Kingham, R. J. 2010 Field Compressing magnetothermal instability in laser plasmas. Phys. Rev. Lett. 105 (17), 175001.CrossRefGoogle ScholarPubMed
Bissell, J. J., Ridgers, C. P. and Kingham, R. J. 2013 Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas. New J. Phys. 15, 025017.Google Scholar
Bol'shov, L. A., Dreizin, Y. A. and Dykhne, A. M. 1974 Spontaneous magnetization of electronic thermal conductivity in a laser plasma. JETP Lett. 19 (5), 168–170.Google Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. Rev. Plasma Phys. 1, 205.Google Scholar
Brownell, J. H. 1979 Magnetic field generation in plasma implosions due to nernst refrigeration. Comments on Plasma Phys. Control. Fusion. 4 (5), 131–138.Google Scholar
Chandrasekhar, S. 1961 (Dover Edition 1981) Hydrodynamic and Hydromagnetic Stability.Google Scholar
Epperlein, E. M. 1984 The accuracy of Braginskii's transport coefficients for a Lorentz plasma. J. Phys. D: App. Phys. 17 (9), 1823–1827.Google Scholar
Epperlein, E. M. and Haines, M. G. 1986 Plasma transport coefficients in a magnetic field by direct numerical simulation of the Fokker-Planck equation. Phys. Fluids 29 (4), 1029–1041.Google Scholar
Froula, D. H., Divol, L., Davis, P., Palastro, J. P., Michel, P., Leurent, V., Glenzer, S. H., Pollock, B. B. and Tynan., G. 2009 Magnetically controlled plasma waveguide for laser wakeeld acceleration. Plasma Phys. Control. Fusion 51 (2), 024009.Google Scholar
Froula, D. H., et al. 2007 Quenching of the Nonlocal Electron Heat Transport by Large External Magnetic Fields in a Laser-Produced Plasma Measured with Imaging Thomson Scattering. Phys. Rev. Lett. 98, 135001.CrossRefGoogle Scholar
Gao, L., Nilson, P. M., Igumenschev, I. V., Hu, S. X., Davies, J. R., Stoeckl, C., Haines, M. G., Froula, D. H., Betti, R. and Meyerhofer, D. D. 2012 Magnetic field generation by the Rayleigh-Taylor instability in laser-driven planar plastic targets. Phys. Rev. Lett., 109, 115001.Google Scholar
Glenzer, S. H., et al. 1999 Thomson scattering from laser plasmas. Phys. Plasmas 6 (5), 2117–2128.Google Scholar
Haines, M. G. 1981 Thermal instability and magnetic field generation by large heat flow in a plasma, especially under laser-fusion conditions. Phys. Rev. Lett. 74, 917.Google Scholar
Haines, M. G. 1986a Magnetic field generation in laser fusion and hot-electron transport. Can. J. Phys. 64, 912–918.Google Scholar
Haines, M. G. 1986b Heat flux effects in Ohms law. Plasma Phys. Control. Fusion 28 (11), 1705–1716.Google Scholar
Hirao, A. and Ogasawara, M. 1981 Magnetic field generating thermal instability including the nernst effect. J. Phys. Soc. Japan 50 (2), 668–672.Google Scholar
Li, C. K., Frenje, J. A., Petrasso, R. D. Séguin, Amendt, P. A., Landen, O. L., Town, R. P. J., Betti, R., Knauer, J. P., Meyerhofer, D. D. and Soures, J. M. 2009 Pressure-driven, resistive magnetohydrodynamic interchange instabilities in laser-produced high-energy-density plasmas. Phys. Rev. E. 80 (1), 016407.Google Scholar
Li, C. K., Séguin, F. H., Frenje, J. A., Rygg, J. R. and Petrasso, R. D. 2007a Observation of the decay dynamics and instabilities of megagauss field structures in laser-produced plasmas. Phys. Rev. Lett. 99 (1), 015001.Google Scholar
Li, C. K., Séguin, F. H., Frenje, J. A., Rygg, J. R. and Petrasso, R. D. 2007b Observation of megagauss-field topology changes due to magnetic reconnection in laser-produced plasmas Phys. Rev. Lett. 99 (5), 055001.Google Scholar
Li, C. K., et al. 2013 Observation of strong electromagnetic fields around laser-entrance holes of ignition-scale hohlraums in inertial-confinement fusion experiments at the National Ignition Facility. New J. Phys. 15, 025040.Google Scholar
Lindl, J. D., Amendt, P., Berger, R. L., Glendinning, S. G., Glenzer, S. H., Haan, S. W., Kauffman, R. L., Landen, O. L. and Suter, L. J. 2004 The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11 (2), 339–491.Google Scholar
Manuel, M. J. E., et al. 2013 Instability-driven electromagnetic fields in coronal plasmas. Phys. Plasmas 20, 056301.Google Scholar
Nilson, P. M., et al. 2006 Magnetic Reconnection and Plasma Dynamics in Two-Beam Laser-Solid Interactions Phys. Rev. Lett. 97 (25), 255001.Google Scholar
Nishiguchi, A., Yabe, T. and Haines, M. G. 1985 Nernst effect in laser-produced plasmas. Phys. Fluids 28 (12), 3683–3690.Google Scholar
Ogasawara, M., Hirao, A. and Ohkubo, H. 1980 Hydrodynamic effects on field-generating thermal instability in laser-heated plasma. J. Phys. Soc. Japan 49 (1), 322–326.Google Scholar
Pert, G. J. 1977 Self-generated magnetic fields in plasmas. J. Plasma Phys. 18, 227–241.Google Scholar
Raven, A., Willi, O. and Rumsby, P. T. 1978 Megagauss magnetic field profiles in laser-produced plasmas. Phys. Rev. Lett. 41, 554.Google Scholar
Schurtz, G., et al. 2007 Revisiting nonlocal electron-energy transport in inertial-fusion conditions. Phys. Rev. Lett. 98, 095002.CrossRefGoogle ScholarPubMed
Stamper, J. A., Papadopoulos, K., Sudan, R. N., Dean, S. O., McLean, E. A. and Dawson, J. M. 1971 Spontaneous magnetic fields in laser-produced plasmas. Phys. Rev. Lett. 26, 1012.CrossRefGoogle Scholar
Thomas, A. G. R., Kingham, R. J. and Ridgers, C. P. 2009 Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability. New J. Phys. 11, 033001.Google Scholar
Tidman, D. A. and Shanny, R. A. 1974 Field-generating thermal instability in laser-heated plasma. Phys. Fluids 17 (6), 1207–1210.Google Scholar
Weibel, E. S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 89.Google Scholar