Demokan O., Mirnov V. V.
Department of Physics, Middle East Technical University, Ankara, Turkey.
Chaos. 1997 Sep;7(3):387-391. doi: 10.1063/1.166211.
In the first part, the equations of motion in a weakly corrugated, periodic magnetic field are linearized and solved by using paraxial approximation, to describe the model and the associated resonance condition. In the second part, the nonlinear evolution of the magnetic moment of resonant particles, in connection with their axial displacement is investigated analytically by using the multiple scale method. It is seen that the linear evolution is converted into a slow and periodic oscillation around the unperturbed value, with a considerable amplitude. The analytic expressions for the period and amplitude of the oscillations are derived and compared with the numerical simulations, which are also presented. Finally, the limitations of the paraxial approximation are concluded by investigating the numerical simulations, with actual field expressions. (c) 1997 American Institute of Physics.
在第一部分中，通过使用傍轴近似将弱波纹周期性磁场中的运动方程线性化并求解，以描述该模型及相关的共振条件。在第二部分中，利用多尺度方法对共振粒子磁矩的非线性演化及其轴向位移进行了分析研究。可以看出，线性演化转变为围绕未受扰动值的缓慢且周期性的振荡，且振幅相当大。推导了振荡周期和振幅的解析表达式，并与所给出的数值模拟结果进行了比较。最后，通过使用实际场表达式研究数值模拟，得出了傍轴近似的局限性。（c）1997美国物理研究所。
