存在非高斯Lévy静电涨落的带电粒子动力学
Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
摘要：
采用Monte Carlo数值模拟方法研究了在$3$维螺旋磁场中，存在$α$稳定的Lévy静电涨落和线性摩擦力模型的碰撞库仑阻力时带电粒子的全轨道动力学.引入Lévy涨落来模拟间歇性静电湍流引起的速度空间分数扩散引起的非局域输运效应。计算了能量、粒子位移和拉莫尔半径的概率分布函数，并表明在高斯波动的情况下，能量的概率分布函数呈现出从指数衰减到Lévy波动的幂律衰减的过渡。幂律衰减指数的绝对值与Lévy指数$α$成线性比例。观测到的粒子拉莫尔半径的异常非高斯统计（由离群值输运事件引起）表明，当静电湍流波动表现出非高斯Lévy统计时，陀螺平均和引导中心近似可能面临限制，应考虑完整的粒子轨道效应。
英文摘要：
Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $α$-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the Lévy index $α$. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.
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