Particle Motion In Electromagnetic Fields Research Articles

Exploring exponential time integration for strongly magnetized charged particle motion

A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical stiffness arising from the wide separation in time scales between highly oscillatory gyromotion and overall macroscopic behavior of the system. In contrast to conventional finite difference schemes, we investigated exponential integration techniques to numerically simulate strongly magnetized charged particle motion. Numerical experiments with a uniform magnetic field show that exponential integrators yield superior performance for linear problems (i.e. configurations with an electric field given by a quadratic electric scalar potential) and are competitive with conventional methods for nonlinear problems with cubic and quartic electric scalar potentials.

Modeling of Beam Transport, Secondary Emission and Interactions With Beam-Line Components in the ITER Neutral Beam Injector

The injection of high energy beams of neutral particles is a fundamental method for plasma heating to ignition in the advanced fusion devices. The requirements of the heating neutral beam to be installed on ITER Tokamak and of the full scale prototype megavolt ITER injector and concept advancement represent a large extrapolation from existing devices. An extensive work on numerical modeling is required to optimize the final design and the injector performances. As the power and charge deposition onto components originates from several sources (primary beam, co-accelerated electrons, and secondary production by beam-gas, beam-surface, and electron-surface interaction), the beam propagation along the beam line is simulated by a comprehensive 3-D model of the beam transport and power deposition phenomena along the injector. The code calculates the particle motion in electromagnetic fields, including the secondary production, the reionization of the beam, and the interactions with the surfaces. The preliminary calculations here reported are focused on the phenomena occurring in the residual ion dump.

Charged particle motion in electromagnetic fields varying moderately rapidly in space

Electromagnetic fields are considered which vary on the space scale of the geometric mean of the Larmor radius and the much larger scale length of variation of the magnetic field lines. It is first shown that the magnetic moment is an adiabatic invariant, even though the usual arguments for its existence fail. The motion of the guiding center is then examined. For perpendicular drifts in magnitude comparable with the particle speed, the subsequent motion is dominated by electrostatic effects. The motion of particles along the field lines occurs on a much slower time scale than the perpendicular drift time scale. When the guiding center motion is approximately periodic in time, a second adiabatic invariant exists, the magnetic flux enclosed by the almost periodic orbit. When the perpendicular drift is small compared with the particle speed, the parallel motion and the perpendicular drift occur on the same, slow timescale.

Electrodynamics of Magnetoactive Media

`Electrodynamics of Magnetoactive Media' is an unusual book in that it cuts across conventional physics discipline boundaries. The unifying theme allowing this is, quite simply, the physics of magnetic fields in various media. I believe the authors are correct in stating that the book is unique in specifically covering electrodynamic phenomena associated with magnetic fields, though of course some of the more elementary aspects are covered in the classical textbooks on electromagnetism, which are duly acknowledged. This interdisciplinarity makes the book very interesting to people with a range of backgrounds. For example, as a plasma physicist, I was familiar with most of the material on plasmas, but liquid crystals and superconductors were entirely new territory for me. These chapters were indeed both accessible and interesting, and it was surprising for me to see how much commonality there is in the physics of these various media. The first part of the book covers some fundamentals of electrodynamics and magnetostatics, and of electromagnetic waves. Most of this material is covered in textbooks on electromagnetism, and some of it is very basic (for example, LRC circuit theory, surely covered in most first year physics courses, is included) but it is perhaps a useful prelude for what is to come. The generic topic of charged particle motion in electromagnetic fields is well covered. Three main magnetoactive media are then discussed: plasmas (focusing on waves), liquid crystals and superconductors. It is all too easy to criticise a book on the grounds of omitted material, but I do feel that a chapter on magnetostatics in plasmas would have been very helpful, covering force-free fields and so on. Some interesting analogies could then have been exploited. For example, I was intrigued to discover an equation for magnetic fields in superconductors (equation (9.36)) which, apart from a change of sign, is identical to the Helmholtz equation used to\newpage\noindent model linear force-free fields in plasmas. Even more intriguingly, the mathematical solution then developed for a junction between a normal conductor and a superconductor is then almost identical to a solution I once published for the equilibrium of expanding plasma loops in the solar corona! The book is clearly written, and the level of mathematics is very appropriate for an advanced undergraduate or postgraduate text: the authors do not fall into the trap of superficially simplifying the description by omitting steps of mathematical arguments. It is a pity, however, that there are no examples or problems, ideally with solutions, which would have been very helpful if the book were to be used for teaching purposes. Nevertheless, because of the interdisciplinarity and the emphasis on fundamental physical principles unifying diverse applications, this book would be a very good basis for a course. Perhaps academics will be encouraged to introduce new lecture courses on this interesting topic. Every library should have a copy of this book, and it would be of interest to many individual researchers who would like to broaden their knowledge outside their own research fields.

Krylov–Boholiubov Methods and Gyrokinetics

The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov–Boholiubov averaging method. The correspondence between the general asymptotic methods, elaborated by M Krylov and M Boholiubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed.

Computing the Particle Paths in an Open-Trap Sharp-Point Geometry

The article presents simulation results for the motion of electrons in two different regions: a high-current vacuum diode and an open trap. The entire system is immersed in an external magnetic field with sharp-point geometry. The electrons are continuously injected from a part of the cathode into the diode region, where they are accelerated to relativistic velocities. In this region, the self-consistent problem of particle motion in electromagnetic fields is solved by the “large” particle method. In the magnetic trap region, the particles experience only the external magnetic field, and their paths are computed by the test particle method. The simulation efficiency is improved by partitioning the problem into two: separate simulation of the high-voltage diode and integration of the particle paths in the trap. Calculations show that the bulk of the particles leave the trap through the side walls, moving along the magnetic forcelines, and only a small part of the particles undergo multiple reflections and remain longer inside the trap.

Long Time-Step Particle Pushing in Drift Approximation without Orbit Averaging

An alternative way to utilize the well known drift approximation for particle motion in electromagnetic fields is proposed. Contrary to the traditional approach, in which the motion of the guiding center of a particle is considered, in the suggested algorithm the coordinates and velocities of the particle itself are evaluated. This approach is found to give accurate results provided that the characteristic scales of the change of fields both in time and in space are large compared to the corresponding micro-scales of the particle motion in these fields (e.g., wavelength of radio wave is large compared to the particle gyroradius in the magnetic field of that wave). Under this condition an approximate analytical solution for the Newton–Lorentz Law, accurate within many characteristic micro-timescales of the particle motion, is derived. This approximation is exploited to advance a particle substantially within a single elementary step of the algorithm, which can extend for as long as ∼mi/me≃ 2000 times the traditional one for certain astrophysical plasmas. Utilization of this approach can give a boost of productivity for the existing and new PIC codes, in which substantial computational time is spent solving the Newton–Lorentz Law for superparticles. In the present work the approach is implemented for the ultrarelativistic case, with the magnetic field prevailing over, although being not necessarily much higher than the electric field. The relevant computer code is developed and used to simulate the motion of a particle in an electromagnetic field with a complicated profile. The results exhibit a good agreement with those, obtained by direct integration of the Newton–Lorentz law, using a conventional ODE solver.

Second-order adiabatic invariant of particle motion in electromagnetic fields

The second-order adiabatic invariant of particle motion in electromagnetic fields is found within the context of the quasi-particle description. Macroscopic invariants for the magnetized plasma are derived, and the constraints on stable plasma states which follow from them are discussed.