First and second order approximations of the first adiabatic invariant for a charged particle interacting with a linearly polarized hydromagnetic plane wave
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In the present paper the effect of a sinusoidal modulation of an electromagnetic field on the invariance of the magnetic moment is studied. Such a generalized invariant plays an important role in problems concerning the motion of charged particles in the non-uniform magnetic field of the magnetosphere or the solar wind. In order to find an adiabatic invariant J, a canonical transformation is introduced, and J is expanded in an asymptotic series in the relative modulation amplitude. We are studying the first and second order terms of this expansion. It is further shown that the curves J = constant closely fit the results obtained by a numerical integration of the system of differential equations governing the motion of the particles.
CitationVanclooster, R. (1977). First and second order approximations of the first adiabatic invariant for a charged particle interacting with a linearly polarized hydromagnetic plane wave. , Planetary and Space Science, Vol. 25, Issue 8, 765-771, DOI: 10.1016/0032-0633(77)90128-3.