Quasiadiabatic model of charged-particle motion in a dipole magnetic confinement system under conditions of dynamic chaos
Il'in V. D., Kuznetsov S. N., Yushkov B. Yu., Il'in I. V.
A model is constructed for the motion of nonadiabatic particles in a region of stochastic instability. This model differs from the standard adiabatic theory in that the particle spirals around a trajectory which passes through the center of the dipole (the "central trajectory"), rather than around a field line. There exists a constant of the motion, which is an analog of the magnetic moment in the adiabatic model. The equations for transforming from the coordinate system of the field line to that of the central trajectory are given. The transformations between coordinate systems are Euler rotations in the direction in which the particle revolves and drifts. These ideas are used to derive a simple Poincare mapping for the coordinate system of the central trajectory. This mapping describes the long-term evolution of the particles.
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![](/ps/1278/article_19326_800_head.png "A <b>model is constructed for the motion of nonadiabatic particles in a region of stochastic instability. This model differs from the standard adiabatic theory in that the particle spirals around a trajectory which passes through the center of the dipole (the "central trajectory"), rather than around a field line. There exists a constant of the motion, which is an analog of the magnetic moment in the adiabatic model. The equations for transforming from the coordinate system of the field line to that of the central trajectory are given. The transformations between coordinate systems are Euler rotations in the direction in which the particle revolves and drifts. These ideas are used to derive a simple Poincare mapping for the coordinate system of the central trajectory. This mapping describes the long-term evolution of the particles.</b>")