Korteweg-de Vries Burgers equation for magnetosonic wave in plasma

Korteweg-de Vries Burgers (KdVB) equation for magnetosonic wave propagating in the perpendicular direction of the magnetic field is derived for homogeneous electron-ion magneto-plasmas. The dissipation in the system is taken into account through the kinematic viscosity of the ions. The effects of kinematic viscosity of ions, plasma density, and magnetic field strength on the formation of magnetosonic shocks are investigated. It is found that the shock strength is enhanced with the increase in the plasma density of the system. However, the increase in magnetic field strength decreases the amplitude of magnetosonic shock wave. The critical value of the dissipative coefficient to form oscillatory profile and monotonic shock is also discussed. The numerical results have also been plotted by taking the parameters from laboratory plasma experiments.

[1]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[2]  W. Masood,et al.  Two dimensional electrostatic shock waves in relativistic electron positron ion plasmas , 2010 .

[3]  J. Wilcox,et al.  Experimental Study of Alfvén‐Wave Properties , 1960 .

[4]  J. Bittencourt.  Fundamentals of plasma physics , 1986 .

[5]  B. Sahu,et al.  Quantum ion acoustic shock waves in planar and nonplanar geometry , 2007 .

[6]  J. Adam.  Viscous damping of nonlinear magneto-acoustic waves , 1975 .

[7]  A. P. Misra,et al.  ION-ACOUSTIC SHOCKS IN QUANTUM ELECTRON–POSITRON–ION PLASMAS , 2008 .

[8]  R. Lust,et al.  The Structure of Hydromagnetic Shock Waves , 1958 .

[9]  P. Shukla,et al.  Theory of dust-acoustic shocks , 1995 .

[10]  D. Swanson,et al.  EXPERIMENTAL STUDY OF COMPRESSIONAL HYDROMAGNETIC WAVES , 1964 .

[11]  R. Hazeltine,et al.  Radiation reaction in fusion plasmas. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  H. Shah,et al.  Effects of positron concentration, ion temperature, and plasma β value on linear and nonlinear two-dimensional magnetosonic waves in electron-positron-ion plasmas , 2005 .

[13]  Abdullah Al Mamun,et al.  Dust ion-acoustic shock waves in an adiabatic dusty plasma , 2007 .

[14]  K. Černý,et al.  Observations of double layers and solitary waves in the auroral plasma , 1982 .

[15]  Gustafsson,et al.  Characteristics of solitary waves and weak double layers in the magnetospheric plasma. , 1988, Physical review letters.

[16]  Stenzel,et al.  Force-free electromagnetic pulses in a laboratory plasma. , 1990, Physical review letters.

[17]  P. Shukla.  Dust ion-acoustic shocks and holes , 2000 .

[18]  J. Xue.  Cylindrical and spherical dust–ion acoustic shock waves , 2003 .

[19]  Y. Nakamura,et al.  Observation of Ion-Acoustic Shocks in a Dusty Plasma , 1999 .

[20]  C. B. Dwivedi,et al.  A new mathematical approach for shock-wave solution in a dusty plasma , 1997 .

[21]  Biswajit Sahu,et al.  Positron acoustic shock waves in planar and nonplanar geometry , 2010 .

[22]  R. Bingham,et al.  Shock waves in charge-varying dusty plasmas and the effect of electromagnetic radiation , 2000 .

[23]  Hiroaki Ono,et al.  Weak Non-Linear Hydromagnetic Waves in a Cold Collision-Free Plasma , 1969 .

[24]  P. Shukla,et al.  Magnetosonic shocks in nonlinear dispersive media , 1980 .

[25]  Abdullah Al Mamun,et al.  The role of dust charge fluctuations on nonlinear dust ion-acoustic waves , 2002 .

[26]  H. Hasegawa,et al.  Perpendicular nonlinear waves in an electron–positron–ion plasma , 2002 .

[27]  A. Dubinov,et al.  Cylindrical magnetoacoustic solitons in plasma , 2010 .

[28]  V. Karpman,et al.  Non-linear Waves in Weakly Dispersive Media , 1975 .

[29]  A. M. Mirza,et al.  A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas , 2010 .

[30]  M. Kivelson,et al.  Spatial correlation of solar-wind turbulence from two-point measurements. , 2005, Physical review letters.

[31]  S. Boldyrev.  Nonlinear magnetosonic waves in a multi-ion-species plasma , 1996, physics/9711002.