Employing the two-fluid model, a generalized Sagdeev equation governing solitary kinetic Alfvén waves (SKAWs) and the criterion for the existence of SKAWs, which are valid for different ranges of plasma pressure parameter β, are presented. In the limit cases of β≫me/mi and β≪me/mi, the present results correspond, respectively, with conclusions obtained by Hasegawa et al. [Phys. Rev. Lett. 37, 690 (1976)] and by Shukla et al. [J. Plasma Phys. 28, 125 (1982)], that is, SKAWs accompanied by, respectively, hump and dip density solitons for β≫me/mi and β≪me/mi. However, for the case of β∼me/mi, the present results show that SKAWs accompanied by both hump and dip density solitons are possible, and lead to KdV solitons in the small amplitude limit. In addition, the possibility for applying these results to electromagnetic spikes observed by the Freja scientific satellite is discussed [detailed information about the Freja satellite experiments can be found in serial papers presented in Space Sci. Rev. 70, Nos. 3/4 (1994)].
In the free-boundary case, the extremum of the potential functional is found from the variational principle. Thereby the equation and boundary conditions required for plasma equilibrium are derived. The Euler equation of the relevant functional is the magnetic surface function equation with the condition of free boundary. A variational functional suitable for numerical computation is given. This functional corresponds to a boundary value problem with an equal-value surface boundary condition. For the case of a conducting wall of simple geometry (i.e., a rectangular wall), numerical computation has been carried out by using the Ritz method.
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