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Nonlinear saturation of the Weibel instability in a dense Fermi plasma

Published online by Cambridge University Press:  01 April 2009

F. HAAS ,
P. K. SHUKLA  and
B. ELIASSON
F. HAAS
Affiliation:
Institut für Theoretische Physik IV, Ruhr–Universität Bochum, D-44780 Bochum, Germany ([email protected]) Universidade do Vale do Rio dos Sinos - UNISINOS, Av. Unisinos 950, 93022–000, São Leopoldo, RS, Brazil
P. K. SHUKLA
Affiliation:
Institut für Theoretische Physik IV, Ruhr–Universität Bochum, D-44780 Bochum, Germany ([email protected])
B. ELIASSON
Affiliation:
Institut für Theoretische Physik IV, Ruhr–Universität Bochum, D-44780 Bochum, Germany ([email protected]) Department of Physics, Umeå University, SE-901 87 Umeå, Sweden
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Abstract

We present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi–Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner–Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields are proportional to the linear growth rate of the instability. The present results are important for understanding the origin of intense magnetic fields in dense Fermionic plasmas, such as those in the next-generation intense laser–solid density plasma experiments.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 2 , April 2009 , pp. 251 - 258
Copyright
Copyright © Cambridge University Press 2008

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References

[1]Wildrow, L. W. 2002 Rev. Mod. Phys. 74, 775.CrossRefGoogle Scholar
Kronberg, P. P. 2002 Phys. Today 55, 40.CrossRefGoogle Scholar
[2]Tatarakis, M. et al. 2002 Nature (London) 415, 280.Google Scholar
Wagner, U. et al. 2004 Phys. Rev. E 70, 026401.CrossRefGoogle Scholar
[3]Itoh, N., Mutoh, H., Hikita, A. and Kohyama, Y. 1992 Astrophys. J. 395, 622.CrossRefGoogle Scholar
Romatschke, P. and Venugopalan, R. 2006 Phys. Rev. Lett. 96, 062302.Google Scholar
[4]Biermann, P. 1950 Z. Naturforsch. A 5, 65.Google Scholar
[5]Estabrook, K. 1978 Phys. Rev. Lett. 41, 1808.CrossRefGoogle Scholar
[6]Wei, M. S. et al. Phys. Rev. E 70, 056412.Google Scholar
[7]Weibel, E. S. 1949 Phys. Rev. Lett. 2, 83.CrossRefGoogle Scholar
[8]Tzoufras, M., Ren, C., Tsung, F. S., Tonge, J. W., Mori, W. B., Fiore, M., Fonseca, R. A. and Silva, L. O. 2006 Phys. Rev. Lett. 96, 105002.CrossRefGoogle Scholar
[9]Malkin, V. M., Fisch, N. J. and Wurtele, J. S. 2007 Phys. Rev. E 75, 026404.Google Scholar
[10]Manfredi, G. 2005 Fields Inst. Commun. 46, 263.Google Scholar
[11]Gardner, C. L. and Ringhofer, C. 1996 Phys. Rev. E 53, 157.Google Scholar
[12]Ang, L. K. and Zhang, P. K. 2007 Phys. Rev. Lett. 98, 164802.Google Scholar
[13]Brodin, G. and Marklund, M. 2007 New J. Phys. 9, 277.CrossRefGoogle Scholar
[14]Marklund, M., Eliasson, B. and Shukla, P. K. 2007 Phys. Rev. E 76, 067401.Google Scholar
[15]Brodin, G. and Marklund, M. 2006 Phys. Rev. E 76, 055403.Google Scholar
[16]Marklund, M. and Brodin, G. 2007 Phys. Rev. Lett. 96, 025001.CrossRefGoogle Scholar
[17]Shukla, P. K. and Eliasson, B. 2006 Phys. Rev. Lett. 96, 245001.CrossRefGoogle Scholar
[18]Shaikh, D. and Shukla, P. K. 2007 Phys. Rev. Lett. 99, 125002.Google Scholar
[19]Jovanovic, D. and Fedele, R. 2007 Phys. Lett. A 364, 304.Google Scholar
[20]Bret, A. 2007 Phys. Plasmas 14, 084503.Google Scholar
[21]Haas, F. 2008 Phys. Plasmas 15, 022104.Google Scholar
[22]Haas, F. 2005 Phys. Plasmas 12, 062117.Google Scholar
[23]Califano, F., Pegoraro, F., Bulanov, S. V. and Mangeney, A. 1998 Phys. Rev. E 57, 7048.Google Scholar
[24]Pines, D. and Nozières, P.The Theory of Quantum Liquids. New York: W. A. Benjamin, 1966.Google Scholar
[25]Lindhard, J. and Dan, K. 1954 Vidensk. Selsk. Mat. Fys. Medd. 28, 1.Google Scholar
[26]Cockayne, E. and Levine, Z. H. 2006 Phys. Rev. B 74, 235107.Google Scholar
[27]Klimontovich, Yu. L. and Silin, V. P. 1961 Plasma Physics (ed. Drummond, J.). New York: McGraw-Hill, and many references therein for the Wigner–Maxwell method for quantum plasmas.Google Scholar
[28]Wigner, E. 1932 Phys. Rev. 40, 749.Google Scholar
[29]Klimontovich, Yu. L. and Silin, V. P. 1952 Zh. Eksp. Teor. Fiz. 23, 151.Google Scholar
[30]Abramowitz, M. and Stegun, I. A. (eds) 1972 Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York: Dover.Google Scholar
[31]Lewin, L. 1981 Polylogarithms and Associated Functions New York: North-Holland.Google Scholar
[32]Ross, O. 1960 Phys. Rev. 119, 1174.CrossRefGoogle Scholar
[33]Arista, N. R. and Brandt, W. 1984 Phys. Rev. A 29, 1471.CrossRefGoogle Scholar
[34]Leemans, W. P., Clayton, C. E., Mori, W. B., Marsh, K. A., Kaw, P. K., Dyson, A., Joshi, C. and Wallace, J. M. 1992 Phys. Rev. A 46, 1091.Google Scholar
[35]Fried, B. D. and Conte, S. D. 1961 The Plasma Dispersion Function. London: Academic Press.Google Scholar
[36]Brandsen, B. H. and Jochain, C. J. 1989 Introduction to Quantum Mechanics. New York: John Wiley.Google Scholar
[37]Krall, N. A. and Trivelpiece, A. W. 1973 Principles of Plasma Physics. New York: McGraw-Hill.CrossRefGoogle Scholar
[38]Davidson, R. C., Hammer, D. A., Haber, I. and Wagner, C. E. 1972 Phys. Fluids 15, 317.Google Scholar
[39]Eliasson, B. 2007 J. Comput. Phys. 225, 1508.CrossRefGoogle Scholar