Motion Of Relativistic Charged Particles Research Articles

Radiation reaction in higher-order electrodynamics

This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Landé–Thomas, and Podolsky. We rigorously derive a world line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. Our work thus gives a rigorous vindication of an expression for the self-force first proposed by Landé and Thomas, studied by Zayats for straight line motion, and, more generally, obtained by Gratus, Perlick, and Tucker on the basis of an averaging axiom.

Прямоточный релятивистский двигатель - гипотеза для обсуждения

In this paper, the engineering and scientific community is invited to consider and discuss the possibility of developing and constructing a ramjet engine for movement in the interstellar medium when the speeds of an aircraft are close to the speed of light. The idea is based on existing developments in high energy physics and accelerator technology. For interstellar flight, a motion scheme is proposed using accelerated relativistic high-energy protons to create efficient jet engines based on accelerating superconducting structures. The proposed scheme is based on the existing developments in the field of accelerator technology, using superconducting resonator systems, klystrons and high-frequency generators. The use of the impulse of the relativistic motion of charged particles is proposed as a hypothesis for discussing the design of a direct-flow engine for motion in the interstellar medium.

A Coupled Guiding Center–Boris Particle Pusher for Magnetized Plasmas in Compact-object Magnetospheres

Abstract We present a novel numerical scheme for simulating the motion of relativistic charged particles in magnetospheres of compact objects, typically filled with highly magnetized collisionless plasmas. The new algorithm is based on a dynamic switch between the full system of equations of motion and a guiding-center approximation. The switch between the two formulations is based on the magnetization of the plasma particles, such that the dynamics are accurately captured by the guiding-center motion even when the gyrofrequency is underresolved by the time step. For particles with a large gyroradius, due to acceleration in, e.g., reconnecting current sheets, the algorithm adaptively switches to solve the full equations of motion instead. The new scheme is directly compatible with standard particle-in-cell codes, and is readily applicable in curved spacetimes via a dedicated covariant formulation. We test the performance of the coupled algorithm by evolving charged particles in electromagnetic configurations of reconnecting current sheets in magnetized plasma, obtained from special- and general-relativistic particle-in-cell simulations. The new coupled pusher is capable of producing highly accurate particle trajectories even when the time step is many orders of magnitude larger than the gyroperiod, substantially reducing the restrictions of the temporal resolution.

Generation of megatesla magnetic fields by intense-laser-driven microtube implosions

A microtube implosion driven by ultraintense laser pulses is used to produce ultrahigh magnetic fields. Due to the laser-produced hot electrons with energies of mega-electron volts, cold ions in the inner wall surface implode towards the central axis. By pre-seeding uniform magnetic fields on the kilotesla order, the Lorenz force induces the Larmor gyromotion of the imploding ions and electrons. Due to the resultant collective motion of relativistic charged particles around the central axis, strong spin current densities of sim peta-ampere/hbox {cm}^{2} are produced with a few tens of nm size, generating megatesla-order magnetic fields. The underlying physics and important scaling are revealed by particle simulations and a simple analytical model. The concept holds promise to open new frontiers in many branches of fundamental physics and applications in terms of ultrahigh magnetic fields.

High-order integration scheme for relativistic charged particle motion in magnetized plasmas with volume preserving properties

A numerical algorithm for solving full gyro orbit of relativistic charged particle motion in magnetized plasmas is presented. The algorithm developed here achieves the following features simultaneously. (1) The time advancement is explicit, and (2) the integration is performed with respect to the observation time in a laboratory frame. (3) It is suitable for accurate long time integration with its volume preserving properties in the phase space. (4) The algorithm can properly treat the E×B drift velocity in electromagnetic fields for large relativistic factors, and (5) can be extended to arbitrary high orders with the aid of symmetric composition methods. Because our algorithm is formulated in the Lorentz covariant form, explicit conservation of the Minkowski norm is not assumed. Nevertheless, no secular growth of the numerical errors in the norm does occur, and its influence can be minimized up to the levels of round-off errors when a high-order scheme is applied. Numerical results are compared with explicit and implicit Runge–Kutta methods. The numerical accuracy and the computational efficiency are discussed for long time integration in toroidal magnetic field configuration.

Space–time characterization of ultra-intense femtosecond laser beams

Femtosecond lasers can now deliver ultrahigh intensities at focus, making it possible to induce relativistic motion of charged particles with light and opening the way to new generations of compact particle accelerators and X-ray sources. With diameters of up to tens of centimetres, ultra-intense laser beams tend to suffer from spatiotemporal distortions, that is, a spatial dependence of their temporal properties that can dramatically reduce their peak intensities. At present, however, these intense electromagnetic fields are characterized and optimized in space and time separately. Here, we present the first complete spatiotemporal experimental reconstruction of the field E(t,r) for a 100 TW peak-power laser, and reveal the spatiotemporal distortions that can affect such beams. This new measurement capability opens the way to in-depth characterization and optimization of ultra-intense lasers and ultimately to the advanced control of relativistic motion of matter with femtosecond laser beams structured in space–time. The complete spatiotemporal characterization of a 100-TW laser beam highlights distortions that must be taken into account for present and future generations of ultra-intense lasers.

Ptychographic measurements of ultrahigh-intensity laser–plasma interactions

The extreme intensities now delivered by femtosecond lasers make it possible to drive and control relativistic motion of charged particles with light1, opening a path to compact particle accelerators2, 3 and coherent X-ray sources4, 5. Accurately characterizing the dynamics of ultrahigh-intensity laser–plasma interactions as well as the resulting light and particle emissions is an essential step towards such achievements. This remains a considerable challenge, as the relevant scales typically range from picoseconds to attoseconds in time, and from micrometres to nanometres in space. In these experiments, owing to the extreme prevalent physical conditions, measurements can be performed only at macroscopic distances from the targets, yielding only partial information at these microscopic scales. This letter presents a major advance by applying the concepts of ptychography6, 7 to such measurements, and thus retrieving microscopic information hardly accessible until now. This paves the way to a general approach for the metrology of extreme laser–plasma interactions on very small spatial and temporal scales.

Effects of high energy photon emissions in laser generated ultra-relativistic plasmas: Real-time synchrotron simulations

We model the emission of high energy photons due to relativistic charged particle motion in intense laser-plasma interactions. This is done within a particle-in-cell code, for which high frequency radiation normally cannot be resolved due to finite time steps and grid size. A simple expression for the synchrotron radiation spectra is used together with a Monte-Carlo method for the emittance. We extend previous work by allowing for arbitrary fields, considering the particles to be in instantaneous circular motion due to an effective magnetic field. Furthermore, we implement noise reduction techniques and present validity estimates of the method. Finally, we perform a rigorous comparison to the mechanism of radiation reaction, and find the emitted energy to be in excellent agreement with the losses calculated using radiation reaction.

Motion of charged particles in a knotted electromagnetic field

In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce a mean quadratic radius of the energy density distribution in order to study some properties of this field. We study the classical relativistic motion of electrons in the electromagnetic field of the Hopf map, and compute their trajectories. It is observed that these electrons initially at rest are strongly accelerated by the electromagnetic force, becoming ultrarelativistic in a period of time that depends on the knot energy and size.

Hamiltonian theory of adiabatic motion of relativistic charged particles

A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space (which includes energy and time as independent coordinates) for all three adiabatic invariants. First, the guiding-center equations of motion for a relativistic particle are derived from the particle Lagrangian. Covariant aspects of the resulting relativistic guiding-center equations of motion are discussed and contrasted with previous works. Next, the second and third invariants for the bounce motion and drift motion, respectively, are obtained by successively removing the bounce phase and the drift phase from the guiding-center Lagrangian. First-order corrections to the second and third adiabatic invariants for a relativistic particle are derived. These results simplify and generalize previous works to all three adiabatic motions of relativistic magnetically trapped particles.

Analytical solution for relativistic charged particle motion in a circularly polarized electromagnetic wave

The relativistic motion of a charged particle in a uniform magnetic field and a circularly polarized electromagnetic wave propagating along the direction of magnetic field is studied. By manipulating the integrals of motion, some typical quantities of particle motion have been presented analytically in terms of explicit functions of three free parameters. The results may be of great importance for high-power microwave generation or particle acceleration.

Generalized Electrodynamics With Ternary Internal Structure

In Refs. [2]–[7] we suggested generalized dynamic equations of motion of relativistic charged particles inside electromagnetic fields. The dynamic equations had been formulated in terms of external as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, had been derived from evolution equations for internal momenta. In this paper, along with relativistic dynamics we generalize electromagnetic fields within the scope of ternary algebras. The full theory is constructed in 4D euclidean space. This space possesses an advantage to build ternary mappings from three vectors onto one. The dynamics is given by non-linear evolution equations with cubic characteristic polynomial. In polar representation the internal momenta obey the Jacobi equations whereas external momenta obey the Weierstrass equations for elliptic functions. The generalized electromagnetic fields are defined by the triple fields where the first one has properties of the electric field and the other two have properties of the magnetic field. The field equations for the triple fields analogous to the Maxwell equations are suggested.

Synchrotron radiation from a charge moving along a helical orbit inside a dielectric cylinder

The radiation emitted by a charged particle moving along a helical orbit inside a dielectric cylinder immersed into a homogeneous medium is investigated. Expressions are derived for the electromagnetic potentials, electric and magnetic fields, and for the spectral-angular distribution of radiation in the exterior medium. It is shown that under the Cherenkov condition for dielectric permittivity of the cylinder and the velocity of the particle image on the cylinder surface, strong narrow peaks are present in the angular distribution for the number of radiated quanta. At these peaks the radiated energy exceeds the corresponding quantity for a homogeneous medium by some orders of magnitude. The results of numerical calculations for the angular distribution of radiated quanta are presented and they are compared with the corresponding quantities for radiation in a homogeneous medium. The special case of relativistic charged particle motion along the direction of the cylinder axis with non-relativistic transverse velocity (helical undulator) is considered in detail. Various regimes for the undulator parameter are discussed. It is shown that the presence of the cylinder can increase essentially the radiation intensity.

Relativistic E x B acceleration.

The relativistic motion of charged particles is analyzed theoretically in electric and magnetic fields that are constant, uniform, and mutually perpendicular. In the relativistic regime where the magnitude of the electric field E is equal to or greater than that of the magnetic field B, i.e., |E| > or =|B|, the particle is effectively accelerated and gains energy indefinitely. This is quite different from the E x B drift motion in the nonrelativistic regime.

Relativistic Plasma Physics. Relativistic Motion of Charged Particles in Ultra-Intense Laser Fields.

Electron motions in laser fields are analyzed in cases when the laser field is non-relativistic and when it is relativistic. The typical eight-figure motion of an electron is obtained in weak laser field plane-polarized, while no such figure motion in circular-polarized case. Starting from the Lagrangian for an electron in a plane-polarized electromagnetic wave, constants of motions and the electron orbits are analytically obtained. It is demonstrated that the electron drifts with a constant velocity in the direction of wave propagation, and that the eight-figure motion is seen in the frame moving with the drift motion. In the case of the circular-polarize wave, the electron orbit is a spiral having the drift velocity same as does the plane-polarization.

Relativistic charged-particle motion in a constant field according to the Lorentz force law

A new and simple method is presented for integrating the equations of motion of a classical relativistic particle subject to a Lorentz force, given electromagnetic fields that are constant in space-time. This integration method leads naturally to a manifestly covariant form of solution.

Lifted transformations on the tangent bundle, and symmetries of particle motion

We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. Our aim is to develop tools for the study of kinetic/dynamic symmetries in particle motion. The new lift unifies and generalizes all the various existing lifted vector fields, with clear geometric interpretations. In particular, this includes the important but little-known “matter symmetries” of relativistic kinetic theory. We find the affine dynamical symmetries of general relativistic charged particle motion, and we compare this to previous results and to the alternative concept of “matter symmetry.”

Relativistic dynamics of charges in external fields: the Pauli algebra approach

The Pauli algebra is used to study the relativistic motion of charged particles in external electromagnetic fields. Plane-wave solutions to Maxwell's equations, in particular standing waves with electric and magnetic fields which are everywhere parallel, are easily represented and analysed in a gauge-independent treatment. The authors derive the 4-momentum of electromagnetic fields and show how the integrals for fields of a charged particle can be evaluated with integration limits specified in the rest frame of the moving charge. The general solution of the Lorentz force equation is shown to be a Lorentz transformation with time-dependent rotation and boost parameters which, in the case of parallel fields, are trivially related to the magnetic and electric fields, respectively. With the Pauli algebra, an earlier derivation in the Dirac algebra of the 4-velocity in constant uniform fields is greatly simplified and extended to arbitrary initial motion, and solutions are found to motion in a Coulomb fields and in the presence of arbitrarily polarised (monochromatic, directed) plane waves.

Analytic treatment of the relativistic motion of charged particles in electric and magnetic field

Using the Boris mover, or other standard methods, the error pile-up in the computation of the relativistic orbit of charged particles in electric and magnetic fields becomes quickly excessive, if one wants to keep reasonably limited the number of points employed to build the particle orbit. An analytical solution becomes, therefore, desirable and its construction is the subject of the present work.

Electric field effects on relativistic charged particle motion in Tokamaks

The authors consider the relativistic guiding center motion of charged particles (charge e, rest mass m0) in magnetic fields consistent with toroidal Tokamak equilibrium. The particle acceleration due to the toroidal electric field-essential to Tokamak operation-is taken into account. For the case of weak acceleration (eU/m0C2<<1, where U is the loop voltage), the poloidal locus of charged particle motion is found to be an envelope of closed drift orbits which, in the case of large aspect-ratio, are characterized by adiabatic invariance of their cross-sectional area. This allows, in the absence of collisions, a complete description of the motion and confinement of runaway electrons in Tokamaks. For peaked current distributions and sufficiently high energies drift separatices exist. They are calculated and their relevance to charge particle confinement and injection is considered.