Self-interaction of Alfvén waves in a cylindrical waveguide filled with an ideally conducting compressible plasma

1991 ◽  
Vol 45 (1) ◽  
pp. 89-101
Author(s):  
Nagendra Kumar ◽  
Krishna M. Srivastava
Keyword(s):  
Compressible Fluid ◽  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Alfven Waves ◽  
Cylindrical Waveguide ◽  
Radial Mode ◽  
Alfvén Waves ◽  
Nonlinear Behaviour ◽  
Compressible Plasma ◽  
Dependent Frequency

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α2 = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.

Self-interaction of compressional hydromagnetic waves in a cylindrical plasma-filled waveguide

1986 ◽  
Vol 36 (1) ◽  
pp. 135-141 ◽  
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Schrodinger Equation ◽  
Numerical Evaluation ◽  
Nonlinear Evolution ◽  
Nonlinear Schrodinger Equation ◽  
Magnetized Plasma ◽  
Radial Mode ◽  
Nonlinear Behaviour ◽  
Cylindrical Plasma ◽  
Dependent Frequency ◽  
Hydromagnetic Waves

Nonlinear behaviour of azimuthally symmetric compressional hydromagnetic waves propagating along a cylindrical cold magnetized plasma-filled waveguide is investigated. A nonlinear Schrödinger equation describing the nonlinear evolution of such waves is derived. Numerical evaluation of the dispersive and nonlinear terms reveals that such waves are modulationally stable in the fundamental radial mode of propagation. Calculations are presented for the amplitude dependent frequency and wavenumber shifts.

scholarly journals Kinetic modulational instability of broadband dispersive Alfvén waves in plasmas

2007 ◽  
Vol 73 (2) ◽  
pp. 153-157 ◽  
Author(s):  
P.K. SHUKLA ◽  
NITIN SHUKLA ◽  
L. STENFLO
Keyword(s):  
Modulational Instability ◽  
Random Phase ◽  
Alfven Waves ◽  
Nonlinear Propagation ◽  
Alfvén Waves ◽  
Nonlinear Dispersion Relation ◽  
Laboratory Plasmas ◽  
Interstellar Media ◽  
Bow Shocks ◽  
Instability Growth

Abstract.We consider a kinetic modulational instability of broadband (random phase) magnetic-field-aligned circularly polarized dispersive Alfvén waves in plasmas. By treating random phase Alfvén waves as quasi-particles, we consider their nonlinear interactions with ion quasi-modes within the framework of the wave-kinetic and Vlasov descriptions. A nonlinear dispersion relation governing such interactions is derived and analyzed. An explicit expression for the kinetic modulational instability growth rate is presented. Our results can be of relevance to the nonlinear propagation of incoherent Alfvén waves, which have been frequently observed in interstellar media, in the solar corona and in the solar wind, as well as in the foreshock regions of planetary bow-shocks and laboratory plasmas.

A note on the modulational instability of long Alfvén waves parallel to the magnetic field

1978 ◽  
Vol 19 (3) ◽  
pp. 437-447 ◽  
Author(s):  
Einar Mjølhus
Keyword(s):  
Magnetic Field ◽  
Inverse Scattering ◽  
Modulational Instability ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Stable Case ◽  
Unstable Case ◽  
Modulational Stability ◽  
Limiting Case ◽  
The Magnetic Field

An amplitude dependent criterion for modulational stability of long Alfvén waves parallel to the magnetic field is interpreted in terms of a recently obtained inverse scattering solution to the modified nonlinear Schrödinger equation. It is found that the solitons formed are of two types. In the strongly unstable case, normal solitons are formed. In the transition region of weakly unstable and stable cases, the anomalous type, which in a limiting case becomes the algebraic soliton, dominates. In the strongly stable case, no solitons are formed.

Nonlinear evolution of dispersive Alfvén waves and the effect of magnetic islands in the solar wind plasmas

2020 ◽  
Vol 27 (7) ◽  
pp. 072903
Author(s):  
Swati Sharma ◽  
R. P. Sharma ◽  
M. K. Mishra ◽  
R. Uma
Keyword(s):  
Solar Wind ◽  
Nonlinear Evolution ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Magnetic Islands
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