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This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
To calculate nonlinear transport of space charge dominated beam in 6D phase spaces, a computer code package LEADS-v5 (Linear and Electrostatic Accelerator Dynamics Simulations) has been developed. The codes calculate particle motions in the…
The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations…
We present a new algorithm for computing the electromagnetic fields of currents inside and outside of finite current sources, for arbitrary time variations in the currents. Unexpectedly, we find that our solutions for these fields are free…
Analysis of the original Feynman's formula for a moving point charge leads to the notion of a retarded time, which has to be treated as a field. The Lorentzian frame, the trajectory, and the retarded time field uniquely determine a system…
Practical expressions are derived for a rapid and accurate evaluation of electric and thermal conductivities and thermopower of degenerate relativistic electrons along quantizing magnetic fields in outer neutron star crusts. The electron…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…
We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion…
The electric field governing the dynamics of space charge produced by high intensity femtosecond laser pulses focused on a copper surface is investigated by time-resolved low-energy-electron-scattering. The pump-probe experiment has a…
We present a new methodology for calculating the electromagnetic radiation from accelerated charged particles. Our formulation --- the `endpoint formulation' --- combines numerous results developed in the literature in relation to radiation…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
Tracking calculations of charged particles in electromagnetic fields require in principle the simultaneous solution of the equation of motion and of Maxwell's equations. In many tracking codes a simpler and more efficient approach is used:…
We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we…
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional…
We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic…
We consider a bound system of particles interacting via electromagnetic forces in an external electromagnetic field, including leading relativistic corrections. Each particle has a definite mass, charge, spin, and charge radius. We…
We study the motion of charged particles constrained to arbitrary two-dimensional curved surfaces but interacting in three-dimensional space via the Coulomb potential. To speed-up the interaction calculations, we use the parallel compute…
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…