A theory about induced electric current and heating in plasma

ABSTRACT

The traditional generalized Ohm’s law in MHD (Magnetohydrodynamics) does not explicitly present the relation of electric currents and electric fields in fully ionized plasma, and leads to some unexpected concepts, such as ``the magnetic frozen-in plasma'', magnetic reconnection etc. In the single fluid model, the action between electric current and magnetic field is not considered. In the two-fluid model, the derivation is based on the two dynamic equations of ions and electrons. The electric current in traditional generalized Ohm's law depends on the velocities of the plasma, which should be decided by the two dynamic equations. However, the plasma velocity, eventually not free, is inappropriately considered as free parameter in the traditional generalized Ohm's law. In the present paper, we solve the balance equation that can give exact solution of the velocities of electrons and ions, and then derive the electric current in fully ionized plasma. In the case ignoring boundary condition, there is no electric current in the plane perpendicular to the magnetic field when external forces are ignored. The electric field in the plane perpendicular to magnetic field do not contribute to the electric currents, so do the induced electric field from the motion of the plasma across magnetic field. The lack of induced electric current will keep magnetic field in space unaffected. The velocity of the bulk velocity of the plasma perpendicular to magnetic field is not free, it is decided by electromagnetic field and the external forces. We conclude that the bulk velocity of the fully ionized plasma is not coupled with the magnetic field. The motion of the plasma do not change the magnetic field in space, but the plasma will be confined by magnetic field. Due to the confinement of magnetic field, the plasma kinetic energy will be transformed into plasma thermal energy by the Lamor motion and collisions between the same species of particles inside plasma. Because the electric field perpendicular to magnetic field do not contribute electric current, the variation of magnetic field will transfer energy directly into the plasma thermal energy by induced electric field. The heating of plasma could be from the kinetic energy and the variation of magnetic field.

The traditional generalized Ohm’s law in MHD (Magnetohydrodynamics) does not explicitly present the relation of electric currents and electric fields in fully ionized plasma, and leads to some unexpected concepts, such as ``the magnetic frozen-in plasma'', magnetic reconnection etc. In the single fluid model, the action between electric current and magnetic field is not considered. In the two-fluid model, the derivation is based on the two dynamic equations of ions and electrons. The electric current in traditional generalized Ohm's law depends on the velocities of the plasma, which should be decided by the two dynamic equations. However, the plasma velocity, eventually not free, is inappropriately considered as free parameter in the traditional generalized Ohm's law. In the present paper, we solve the balance equation that can give exact solution of the velocities of electrons and ions, and then derive the electric current in fully ionized plasma. In the case ignoring boundary condition, there is no electric current in the plane perpendicular to the magnetic field when external forces are ignored. The electric field in the plane perpendicular to magnetic field do not contribute to the electric currents, so do the induced electric field from the motion of the plasma across magnetic field. The lack of induced electric current will keep magnetic field in space unaffected. The velocity of the bulk velocity of the plasma perpendicular to magnetic field is not free, it is decided by electromagnetic field and the external forces. We conclude that the bulk velocity of the fully ionized plasma is not coupled with the magnetic field. The motion of the plasma do not change the magnetic field in space, but the plasma will be confined by magnetic field. Due to the confinement of magnetic field, the plasma kinetic energy will be transformed into plasma thermal energy by the Lamor motion and collisions between the same species of particles inside plasma. Because the electric field perpendicular to magnetic field do not contribute electric current, the variation of magnetic field will transfer energy directly into the plasma thermal energy by induced electric field. The heating of plasma could be from the kinetic energy and the variation of magnetic field.

Cite this paper

Yang, Z. and Chen, R. (2011) A theory about induced electric current and heating in plasma.*Natural Science*, **3**, 275-284. doi: 10.4236/ns.2011.34035.

Yang, Z. and Chen, R. (2011) A theory about induced electric current and heating in plasma.

References

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[12] Paschmann G., O. sonnerup B. U., Papamastroakis, I. Sckopke, N., Haerendel G., Bame S.J., Asbridge J. R., Gosling J.T., Russell C.T., and Elphic R.C., “Plasma acceleration at the earth’s magnetopause: Evidence for reconnection,” nature Lond. 282, 1979, pp. 243-246.

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[14] Yamauchi, M. and Blomberg, L., “Problems on mappings of the convection and on the fluid concept,” Phys. Chem. Earth. 22, 1997, pp. 709-714.

[15] Parker E. N., “Cosmical magnetic fields,” Clarendon Press, Oxford, 1979, pp. 31-32.

[16] Gomobsi T. I., “Gaskinetic Theory,” Cabridge Univ., New York, 1994.

[17] Song P., Gombosi T. I. and Ridley A. J., “Three-fluid Ohm’s law,” Journal of Geophysical Research, Vol. 106, Issue A5, 2001, pp. 8149-8156.

[18] Pandey B.P. and Wardle M., “Hall magnetohydrodynamics of partially ionized plasmas,” Mon. Not. R. Astron. Soc., 385, 2008, pp. 2269-2278.

[19] Chen F.F., “Introduction to plasma physics,” Plenum Press, 1974.

[20] Zhang Y., Zhang M. and Zhang H. Q., “A statistical study on the relationship between surface field variation and CME initiation,” Advances in Space Research, Vol. 39, 2007, pp. 1762-1766.

[1] Falthamma C-G., “Comments on the motion of magnetic field lines,” Am. J. Phys. 74(5), 2006, pp. 454-455.

[2] Alfven H., “On frozen-in field lines and field-line reconnection,” J. Geophys. Res. 81, 1976, pp. 4019-4021.

[3] Alfven H., “Existence of electromagnetic-hydrodynamic waves,” Nature, Vol. 150, 1942, pp.405.

[4] Lighthill M.J., “Studies on magneto-hydrodynamic waves and other anisotropic wave motions,” Phil. Trans. Roy. Soc. London, Vol. 252A, 1960, pp.397-430.

[5] Witalis E.A., “Hall magnetohydrodynamics and its applications to laboratory and cosmic plasma, IEEE Transactions on plasma science,” Vol.PS-14, No.v 6, 1986, pp. 842-848.

[6] Spitzer L. and Jr., “Physics of fully ionized gases, second revised edition,” Dover Publications, Inc. Mineola, New York, 1962.

[7] Somov B. V., “Cosmic Plasma Physics,” Kluwer Academic Publishers, Dordrecht, 2000, pp. 181-190.

[8] Volkov TF., “Hydrodynamic description of a collisionless plasma,” In: M.A. Leontovich, Ed., Reviews of Plasma Physics, New York, Consultant Bureau, Vol. 4, 1966, pp. 1-21.

[9] Sweet P.A., “the neutral point theory of solar flares,” In: Lehnert B., Ed., Electromagnetic Phenomena in Cosmical Physics, Cambridge University Press, London, 1958.

[10] Parker E. N., “Sweet's mechanism for merging magnetic fields in conducting fluids,” J. Geophys. Res., 62, 1957, pp. 509-520.

[11] Dungey J. W., “Interplanetary fields and the auroral zone,” Phys. Rev. Lett. 6, 1961, pp. 47-48.

[12] Paschmann G., O. sonnerup B. U., Papamastroakis, I. Sckopke, N., Haerendel G., Bame S.J., Asbridge J. R., Gosling J.T., Russell C.T., and Elphic R.C., “Plasma acceleration at the earth’s magnetopause: Evidence for reconnection,” nature Lond. 282, 1979, pp. 243-246.

[13] Paschmann G. and Treumann R., “Auroral Plasma Physics,” In: Paschmann G., Haaland, S., Treumann, R., Ed., ISSI Space Science Series, Vol 15, 2003, ISBN 1-4020- 0936-1.

[14] Yamauchi, M. and Blomberg, L., “Problems on mappings of the convection and on the fluid concept,” Phys. Chem. Earth. 22, 1997, pp. 709-714.

[15] Parker E. N., “Cosmical magnetic fields,” Clarendon Press, Oxford, 1979, pp. 31-32.

[16] Gomobsi T. I., “Gaskinetic Theory,” Cabridge Univ., New York, 1994.

[17] Song P., Gombosi T. I. and Ridley A. J., “Three-fluid Ohm’s law,” Journal of Geophysical Research, Vol. 106, Issue A5, 2001, pp. 8149-8156.

[18] Pandey B.P. and Wardle M., “Hall magnetohydrodynamics of partially ionized plasmas,” Mon. Not. R. Astron. Soc., 385, 2008, pp. 2269-2278.

[19] Chen F.F., “Introduction to plasma physics,” Plenum Press, 1974.

[20] Zhang Y., Zhang M. and Zhang H. Q., “A statistical study on the relationship between surface field variation and CME initiation,” Advances in Space Research, Vol. 39, 2007, pp. 1762-1766.