A guiding-center Fokker-Planck collision operator for nonuniform magnetic fields

On the validity of the guiding-center approximation in a magnetic dipole field

The problem of the charged-particle motion in an axisymmetric magnetic-dipole geometry is used to assess the validity of Hamiltonian guiding-center theory, which includes higher-order corrections associated with guiding-center polarization induced by magnetic-field nonuniformity. When a magnetically-confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when guiding-center polarization ef…

交叉电场和磁场中的粒子与引导中心轨道

Particle and guiding-center orbits in crossed electric and magnetic fields

该研究评估了引导中心近似在交叉电磁场中的有效性，针对非均匀径向电场提出了哈密顿引导中心理论，并在线性电场下给出实例。

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal…

On the validity of the guiding-center approximation in the presence of strong magnetic gradients

The motion of a charged particle in a nonuniform straight magnetic field with a uniform magnetic-field gradient is solved exactly in terms of elliptic functions. The connection between this problem and the guiding-center approximation is discussed. It is shown that, for this problem, the predictions of guiding-center theory agree very well with the orbit-averaged particle motion and hold well beyond the standard guiding-center limit $ε\equiv ρ/L \ll 1$, where $ρ$ is the gyromotion length scale and $L$ is the magnetic-field gradient length scale.

Monte Carlo method and High Performance Computing for solving Fokker-Planck equation of minority plasma particles

This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the transformation of the collision operator. Even within the guiding-center formalism, the fast particle simulations can still be very CPU intensive and, therefore, we introduce the reader also to the world of high-performance computing. The paper is concluded with a few examples where the presented method has been applied.

向自洽求解ICRH波方程和福克-普朗克方程

Towards solving the ICRH wave and Fokker-Planck equations self-consistently

本文提出了一种自洽求解ICRH波方程和福克-普朗克方程的框架，并展示了如何计算任意分布函数的介电响应。

Improved accuracy in degenerate variational integrators for guiding center and magnetic field line flow

First-order accurate degenerate variational integration (DVI) was introduced in C. L. Ellison et. al, Phys. Plasmas 25, 052502 (2018) for systems with a degenerate Lagrangian, i.e. one in which the velocity-space Hessian is singular. In this paper we introducing second order accurate DVI schemes, both with and without non-uniform time stepping. We show that it is not in general possible to construct a second order scheme with a preserved two-form by composing a first order scheme with its adjoint, and discuss the conditions under which such a composition is possible. We build two classes of se…

Enhancement of Pressure Perturbations in Ablation due to Kinetic Magnetised Transport Effects under Direct-Drive ICF relevant conditions

We present for the first time kinetic 2D Vlasov-Fokker-Planck simulations, including both self-consistent magnetic fields and ablating ion outflow, of a planar ablating foil subject to nonuniform laser irradiation. Even for small hall parameters ($ωτ_{ei} \lesssim 0.05$) self-generated magnetic fields are sufficient to invert and enhance pressure perturbations. The mode inversion is caused by a combination of the Nernst advection of the magnetic field and the Righi-Leduc heat-flux. Non-local effects modify these processes. The mechanism is robust under plasma conditions tested; it is amplitude…

什么导致磁曲率漂移？

What causes the magnetic curvature drift?

本文探讨了带电粒子在弯曲磁场中运动时磁曲率漂移的原因，指出传统解释假设粒子沿磁场线运动，但实际上粒子会偏离，导致洛伦兹力使其速度矢量周期性对齐，从而产生曲率漂移。

Self-Organization and Heating by Inward Diffusion in Magnetospheric Plasmas

Through the process of inward diffusion, a strongly localized clump of plasma is created in a magnetosphere. The creation of the density gradient, instead of the usual flattening by a diffusion process, can be explained by the topological constraints given by the adiabatic invariants of magnetized particles. After developing a canonical formalism for the standard guiding center dynamics in a dipole magnetic field, we complete our attempt to build a statistical mechanics on a constrained phase space by discussing the construction principles of the associated diffusion operator. We then investig…