通过时间周期螺旋磁场的粒子扩散
Particle energization through time-periodic helical magnetic fields
摘要：
本文求解了带电粒子在螺旋形时间周期ABC（Arnold-Beltrami-Childress）磁场中的运动。系数为$A=B=C=1$的静止ABC场的磁场是混沌的，我们证明了带电粒子在这样一个场中的运动在后期也是混沌的，并且具有正的李雅普诺夫指数.我们进一步表明，在时间周期的ABC场，带电粒子的动能可以随时间无限增加。在后期，平均动能随时间以幂律增长，其指数接近1。对于粒子的初始分布，其动能在某个区间内均匀分布，动能的PDF在后期接近高斯分布，但具有较陡的尾部。
英文摘要：
We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the PDF of kinetic energy is, at late times, close to a Gaussian but with steeper tails.
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