Adiabatic theory of charged particle motion.
Adiabatic theory of charged particle motion, considering first-order effects in radius of gyration and Alfven theory
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Adiabatic theory of charged particle motion, considering first-order effects in radius of gyration and Alfven theory
The motion of charged particles was examined in the case of a homogeneous magnetic field together with an orthogonal electric field which has a gradient opposing voltage parallel to the electric field. Two regimes result: in one of these, the particles' rate of gyration is changed from the conventional gyrofrequency; in the other, acceleration of the particle takes place. Applied to a plasma, the theory predicts new electric currents orthogonal to magnetic fields.
It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering difference between the temporal variation of gyrophase and that of the other phase space coordinates needs to be taken into account. Second, it is also important to note that the parametric limit of the derivative of a function is not equivalent to the derivative of the limit function. When these facts are taken into account, the near identity transformation rule for one form related to the Lagrangian is modified. With the modified near identity transformation rule, the drift motion of charged particles can be described in the first order, instead of the second order and beyond through a tedious expansion process as in the conventional formulation. Here, this resolves the discrepancy between the direct and Lie transform treatments in the Lagrangian perturbation theory for charged particle motion in a magnetic field.
First correction to second adiabatic invariant of charged particle motion in magnetic field
Second term obtained in asymptotic series for second adiabatic invariant of charged particle motion in static magnetic field and found to vanish at mirror points
The motion of charged particles is studied numerically and analytically using a test particle approach. Acceleration near the X-type neutral line is described in terms of adiabatic invariants and separatrix crossings. The relation between regular and chaotic properties of the process is discussed for a realistic source in the plasma mantle.
Charged particle motion in magnetic radiation shielding fields
Charged particle motion in the guiding center approximation is analyzed for models of the Jovian and Saturnian magnetospheric magnetic fields based on Voyager magnetometer observations. Field lines are traced and exhibit the distention which arises from azimuthally circulating magnetospheric currents. The spatial dependencies of the guiding center bounce period and azimuthal drift rate are investigated for the model fields. Non-dipolar effects in the gradient-curvature drift rate are most important at the equator and affect particles with all mirror latitudes. The effect is a factor of 10-15 for Jupiter with its strong magnetodisc current and 1-2 for Saturn with its more moderate ring current. Limits of adiabaticity, where particle gyroradii become comparable with magnetic scale lengths, are discussed and are shown to occur at quite modest kinetic energies for protons and heavier ions.
The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.
We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.
The motion of a charged particle in a 2-dimensional neutral sheet with linear magnetic field variation is analyzed by Hamiltonian methods. From the basic Hamiltonian formulation, results of Sonnerup are recovered and given intuitive interpretation. The transformed Hamiltonian is used to derive the correct frequency of oscillation and serves as the basis of analytical treatment of perturbed versions of the motion, e.g. with electric field added. For 2-dimensional fields with slightly differing configurations - in particular, with added small field component orthogonal to the sheet, with an X-type null or with a chain of null points - two alternative methods are developed, reducing the problem either to motion in a 2-dimensional potential or to a pair of coupled oscillators.
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single monopole, the solution was given long ago by Poincaré. In the case of a uniform distribution of monopoles, the solution can be expressed in terms of parabolic cylinder functions (essentially the eigenfunctions of an inverted harmonic oscillator). Further, this solution is relevant to recent studies of nonassociative star products, symplectic lifts of twisted Poisson structures, and fluids and plasmas of electric and magnetic charges.
If the Hamiltonian for the motion of a charged particle in a magnetic field has one or more cyclic coordinates it may often be viewed as representing the motion of a particle subject to a potential V. The use of V provides qualitative insight about the motion even in some cases where a solution of the motion cannot be obtained. Several examples using this concept are reviewed and discussed.
Charged particle motion in a geomagnetic field, including cosmic ray cutoffs, impact zones and cavity fields
The non-perturbative guiding-centre model provides an exact alternative to full-orbit simulations of charged particle dynamics in situations where traditional guiding-centre theory may fail. We demonstrate that the charged particle motion in a homogeneous, time-varying magnetic field is a solvable example of the non-perturbative guiding-centre model. This entails showing that the exact magnetic moment of Qin and Davidson can be constructed to be asymptotic to the adiabatic invariant series of Kruskal. In contrast to the perturbative invariant, the exact invariant contains information about parametric resonances. These resonances destroy the conservation of the usual magnetic moment over very long times. This refutes some previous claims about the all-time invariance of the magnetic moment.
We revisit the covariant formulation of a charged particle’s motion under the influence of a plane electromagnetic wave in classical picture. In the first case, we reproduce Meyer’s result by solving relativistic equation of motion ignoring radiation reaction in vacuum assuming zero mass approximation or null vector case ($k^µk_µ = k^2 = 0$). Then, we extend this approach to include the medium effects as perturbations in the propagation of electromagnetic wave (i. e. $k^2 ≠ 0$) and explore the effects of these perturbations in mass shift of the particle.
The dynamics of charged particles in electromagnetic fields is an essential component of understanding the most extreme environments in our Universe. In electromagnetic fields of sufficient magnitude, radiation emission dominates the particle motion and effects of quantum electrodynamics (QED) in strong fields are crucial, which triggers electron-positron pair cascades and counterintuitive particle-Trapping phenomena. As a result of recent progress in laser technology, high-power lasers provide a platform to create and probe such fields in the laboratory. With new large-scale laser facilities on the horizon and the prospect of investigating these hitherto unexplored regimes, this review explores the basic physical processes of radiation reaction and QED in strong fields, how they are treated theoretically and in simulation, the new collective dynamics they unlock, recent experimental progress and plans, and possible applications for high-flux particle and radiation sources.
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