H. Sanuki

J. Todoroki

National Institute for Fusion Science (NIFS-Repository)

§34. Modified K-dV Equation for Nonlinear Magnetosonic Waves 1n a Multi-lon Plasma Todoroki, J., Sanuki, H. Nonline_ar magnetosonic waves have been extensively studied because they play an important role in particle acceleration and heating of plasmas. Recently, the nonlinear behavior of both low -and high -frequency magnetosonic waves has been discussed by To ida and Ohsawa(ref.l ), who showed that these waves are described by K-dV equation, although the dispersion branch of high frequency mode has a finite cut-off frequency. We should note that we have to discuss very carefully the scaling and ordering in derivation of a nonlinear wave equation for this mode under the influence of finite cut-off frequency. Paying attention to this situation and applying a proper ordering and scaling with respect to amplitude and mass ratio involved in the present set of equations, we derive a nonlinear magnetosonic wave equation , which includes effects of the finite cut-off frequency. We here study a magnetosonic waves propa-gating in the direction(x) perpendicular to a magne-tic field(z) on the basis of following fluid equations with two ion-species: dn . a ( ) a: + dx njvrj = 0, dv . dv . q . ( 1 ) ___!L+v .___.!L=-1 E +-v B -:'\ X}-,. X VJ!' at ox m1 c · dv . dv . q . ( 1 J __!!_+v .__I!_=-1 E --v .B -,. X}'"\ V XJ:' at ox mj · c 146 dB d£v -' =-c-· dt dx ' In the following derivation, we apply the assumptions, m _e << 1, mi Then , using the conventional reductive pertur-bation method and introducing the following \ stretched variables and ordering ~ = £.112 (x- Vt), r = £ 312 t. we finally obtain a modified K-dY equation in a form where If we neglect the o -term, this equation reduces to the equation derived by Toida and Ohsawa. We note that the characteristics of this equation sensitively depends on the competing effect between y -and o -terms and is essentially different from the previous results( ref.l ). Detailed discussions is now under investigation. 1) M. Toida andY. Ohsawa: in Report of Plasma Science Center, Nagoya University PSC-33 N.ov. (1993). 

Modified K-dV Equation for Nonlinear Magnetosonic Waves in a Multi-Ion Plasma

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