Modulational instability of magnetosonic waves in a spin 1/2 quantum plasma

A.P. Misra, P.K. Shukla

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

The modulational instability (MI) of magnetosonic waves (MSWs) is analyzed, by using a two-fluid quantum magnetohydrodynamic model that includes the effects of the electron-1/2 spin and the plasma resistivity. The envelope modulation is then studied by deriving the corresponding nonlinear Schrodinger equation from the governing equations. The plasma resistivity is shown to play a dissipative role for the onset of MI. In the absence of resistivity, the microscopic spin properties of electrons can also lead to MI. In such a situation, the dominant spin contribution corresponds to a dense quantum plasma with the particle number density, n(0)greater than or similar to 10(28) m(-3). Also, in such a dissipative (absorbing) medium, where the group velocity vector is usually complex for real values of the wave vector, the role of the real group velocity in the propagation of one-dimensional MSW packets in a homogeneous absorbing medium is reported. The effects of quantum spin on the stability/instability conditions of the magnetosonic envelope are obtained and examined numerically. From the nonlinear dispersion relation of the modulated wave packet it is found that the effect of the spin (plasma resistivity) is to decrease (increase) the instability growth rate provided the normalized Zeeman energy does not exceed a critical value. The theoretical results may have relevance to astrophysical (e.g., magnetars) as well as to ultracold laboratory plasmas (e.g., Rydberg plasmas).
LanguageEnglish
Pages052105
JournalPhysics of Plasmas
Volume15
Issue number5
DOIs
Publication statusPublished - May 2008

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electrical resistivity
group velocity
wave packets
envelopes
magnetars
magnetohydrodynamics
nonlinear equations
astrophysics
electrons
modulation
propagation
fluids
energy

Keywords

  • ion-acoustic-waves
  • packets
  • media
  • model
  • rays

Cite this

Misra, A.P. ; Shukla, P.K. / Modulational instability of magnetosonic waves in a spin 1/2 quantum plasma. In: Physics of Plasmas. 2008 ; Vol. 15, No. 5. pp. 052105.
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Modulational instability of magnetosonic waves in a spin 1/2 quantum plasma. / Misra, A.P.; Shukla, P.K.

In: Physics of Plasmas, Vol. 15, No. 5, 05.2008, p. 052105.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Shukla, P.K.

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N2 - The modulational instability (MI) of magnetosonic waves (MSWs) is analyzed, by using a two-fluid quantum magnetohydrodynamic model that includes the effects of the electron-1/2 spin and the plasma resistivity. The envelope modulation is then studied by deriving the corresponding nonlinear Schrodinger equation from the governing equations. The plasma resistivity is shown to play a dissipative role for the onset of MI. In the absence of resistivity, the microscopic spin properties of electrons can also lead to MI. In such a situation, the dominant spin contribution corresponds to a dense quantum plasma with the particle number density, n(0)greater than or similar to 10(28) m(-3). Also, in such a dissipative (absorbing) medium, where the group velocity vector is usually complex for real values of the wave vector, the role of the real group velocity in the propagation of one-dimensional MSW packets in a homogeneous absorbing medium is reported. The effects of quantum spin on the stability/instability conditions of the magnetosonic envelope are obtained and examined numerically. From the nonlinear dispersion relation of the modulated wave packet it is found that the effect of the spin (plasma resistivity) is to decrease (increase) the instability growth rate provided the normalized Zeeman energy does not exceed a critical value. The theoretical results may have relevance to astrophysical (e.g., magnetars) as well as to ultracold laboratory plasmas (e.g., Rydberg plasmas).

AB - The modulational instability (MI) of magnetosonic waves (MSWs) is analyzed, by using a two-fluid quantum magnetohydrodynamic model that includes the effects of the electron-1/2 spin and the plasma resistivity. The envelope modulation is then studied by deriving the corresponding nonlinear Schrodinger equation from the governing equations. The plasma resistivity is shown to play a dissipative role for the onset of MI. In the absence of resistivity, the microscopic spin properties of electrons can also lead to MI. In such a situation, the dominant spin contribution corresponds to a dense quantum plasma with the particle number density, n(0)greater than or similar to 10(28) m(-3). Also, in such a dissipative (absorbing) medium, where the group velocity vector is usually complex for real values of the wave vector, the role of the real group velocity in the propagation of one-dimensional MSW packets in a homogeneous absorbing medium is reported. The effects of quantum spin on the stability/instability conditions of the magnetosonic envelope are obtained and examined numerically. From the nonlinear dispersion relation of the modulated wave packet it is found that the effect of the spin (plasma resistivity) is to decrease (increase) the instability growth rate provided the normalized Zeeman energy does not exceed a critical value. The theoretical results may have relevance to astrophysical (e.g., magnetars) as well as to ultracold laboratory plasmas (e.g., Rydberg plasmas).

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