Derivation of electrostatic Korteweg–deVries equation in fully relativistic two-fluid plasmas

Lee, Nam C.
August 2008
Physics of Plasmas;Aug2008, Vol. 15 Issue 8, p082301
Academic Journal
A second order Korteweg–deVries (KdV) equation that describes the evolution of nonlinear electrostatic waves in fully relativistic two-fluid plasmas is derived without any assumptions restricting the magnitudes of the flow velocity and the temperatures of each species. In the derivation, the positive and negative species of plasmas are treated with equal footings, not making any species specific assumptions. Thus, the resulting equation, which is expressed in transparent form symmetric in particle species, can be applied to any two-fluid plasmas having arbitrarily large flow velocity and ultrarelativistically high temperatures. The phase velocity of the nonlinear electrostatic waves found in this paper is shown to be related to the flow velocity and the acoustic wave velocity through the Lorentz addition law of velocities, revealing the relativistic nature of the formulation in the present study. The derived KdV equation is applied to some limiting cases, and it is shown that it can be reduced to existing results in nonrelativistic plasmas, while there are some discrepancies from the results in the weak relativistic approximations.


Related Articles

  • Linear and nonlinear ion-acoustic waves in very dense magnetized plasmas. Khan, S. A.; Mahmood, S.; Saleem, H. // Physics of Plasmas;Aug2008, Vol. 15 Issue 8, p082303 

    Obliquely propagating linear and weakly nonlinear ion-acoustic waves in a magnetized quantum plasma are investigated by employing the quantum hydrodynamic formulation. A linear dispersion relation is presented and the nonlinear Korteweg–de Vries equation is derived using the reductive...

  • Nonlinear Korteweg–de Vries–Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions. Saeed, R.; Shah, Asif // Physics of Plasmas;Mar2010, Vol. 17 Issue 3, p032308 

    The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg–de Vries–Burger equation has been derived by reductive perturbation technique, and its...

  • On dust ion acoustic solitary waves in collisional dusty plasmas with ionization effect. Shalaby, M.; El-Labany, S. K.; El-Shamy, E. F.; Khaled, M. A. // Astrophysics & Space Science;Apr2010, Vol. 326 Issue 2, p273 

    The propagation of solitary waves in an unmagnetized collisional dusty plasma consisting of a negatively charged dust fluid, positively charged ions, isothermal electrons, and background neutral particles is studied. The ionization, ion loss, ion–neutral, ion–dust, and...

  • The effects of Bohm potential on ion-acoustic solitary waves interaction in a nonplanar quantum plasma. Sheng-Chang Li // Physics of Plasmas;Aug2010, Vol. 17 Issue 8, p082307 

    The interaction of ion-acoustic solitary waves (IASWs) in a nonplanar unmagnetized quantum plasma consisting of electrons, positrons, and ions are studied by employing the quantum hydrodynamic model and the Korteweg–de Vries description. We provide the theoretical predictions about the...

  • Linear and nonlinear dynamics of a dust bicrystal consisting of positive and negative dust particles. Kourakis, I.; Shukla, P. K.; Morfill, G. E. // Physics of Plasmas;Nov2005, Vol. 12 Issue 11, p112104 

    A dusty plasma crystalline configuration consisting of charged dust grains of alternating charge sign (.../+/-/+/-/+/...) and mass is considered. Both charge and mass of each dust species are taken to be constant. Considering the equations of longitudinal motion, a dispersion relation for linear...

  • A High-Order Nonlinear Envelope Equation for Gravity Waves in Finite-Depth Water. Slunyaev, A. V. // Journal of Experimental & Theoretical Physics;Nov2005, Vol. 101 Issue 5, p926 

    A third-order nonlinear envelope equation is derived for surface waves in finite-depth water by assuming small wave steepness, narrow-band spectrum, and small depth as compared to the modulation length. A generalized Dysthe equation is derived for waves in relatively deep water. In the...

  • Electrostatic shocks and solitons in nonuniform dusty plasmas. Saleem, H. // Physics of Plasmas;Sep2005, Vol. 12 Issue 9, p094505 

    The Korteweg–de Vries–Burgers equation for the nonlinear dust drift wave is obtained which admits solutions in the form of solitons, monotonic shocks, and oscillatory shocks in different limits. The relevance of this investigation to laboratory and space plasmas is pointed out.

  • Nonlinear evolution of kinetic Alfvén waves and the turbulent spectra. Sharma, R. P.; Kumar, Sachin; Singh, H. D. // Physics of Plasmas;Aug2008, Vol. 15 Issue 8, p082902 

    This paper presents the model equation governing the nonlinear dynamics of the kinetic Alfvén wave (KAW) in the low-β plasmas (β≪me/mi) and intermediate-β plasmas (me/mi≪β≪1), where β is thermal pressure to background magnetic pressure ratio, me/mi is the...

  • Preliminary Observations of Z-pinch Plasma Formation within a Conducting Coil. Wyndham, E.; Favre, M.; Pernas, A. // AIP Conference Proceedings;2006, Vol. 875 Issue 1, p461 

    We present preliminary experimental results on an attempt to produce a single component X-ray emitting Titanium pinch plasma. The salient features are a thin wall Titanium coil, with similar physical dimensions to capillary loads used in previous experiments. The coil forms the load of a small...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics