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Register a new userCovariant Worldline Numerics for Charge Motion with Radiation Reaction
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We develop a numerical formulation to calculate the classical motion of charges in strong electromagnetic fields, such as those occurring in high-intensity laser beams. By reformulating the dynamics in terms of SL(2,C) matrices representing the Lorentz group, our formulation maintains explicit covariance, in particular the mass-shell condition. Considering an electromagnetic plane wave field where the analytic solution is known as a test case, we demonstrate the effectiveness of the method for solving both the Lorentz force and the Landau-Lifshitz equations. The latter, a second order reduction of the Lorentz-Abraham-Dirac equation, describes radiation reaction without the usual pathologies.
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Abraham Lorentz (AL) formula of Radiation Reaction and its relativistic generalization, Abraham Lorentz Dirac (ALD) formula, are valid only for periodic (accelerated) motion of a charged particle, where the particle returns back to its original state. Thus, they both represent time averaged solutions for radiation reaction force. In this paper, another expression has been derived for radiation reaction following a new approach, starting from Larmor formula, considering instantaneous change (rather than periodic change) in velocity, which is a more realistic situation. Further, it has been also shown that the new expression for Radiation Reaction is free of pathological solutions; which were unpleasant parts of AL as well as ALD equations; and remained unresolved for about 100 years.
We discuss radiation reaction effects on charges propagating in ultra-intense laser fields. Our analysis is based on an analytic solution of the Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of a symmetry breaking parameter associated with the violation of null translation invariance in the direction opposite to the laser beam. As the Landau-Lifshitz equation is nonlinear the energy transfer within the pulse is rather sensitive to initial conditions. This is elucidated by comparing colliding and fixed target modes in electron laser collisions.
Cherenkov radiation (CR) generated by a charge moving through a hollow conical target made of dielectric material is analyzed. We consider two cases: the charge moves from the base of the cone to its top (``straight cone) or from the top to the base (``inverted cone). Unlike previous papers, a nonzero shift of the charge trajectory from the symmetry axis is taken into account which leads to generation of asymmetric CR. The most interesting effect is the phenomenon of ``Cherenkov spotlight which has been reported earlier for axially symmetric problems. This effect allows essential enhancement of the CR intensity in the far-field region by proper selection of the targets parameters and charge velocity. Here we describe the influence of charge shift on CR far-field patterns paying the main attention to the ``Cherenkov spotlight regime. Influence of variation of the charge speed on this phenomenon is also investigated.
We give an overview of the worldline numerics technique, and discuss the parallel CUDA implementation of a worldline numerics algorithm. In the worldline numerics technique, we wish to generate an ensemble of representative closed-loop particle trajectories, and use these to compute an approximate average value for Wilson loops. We show how this can be done with a specific emphasis on cylindrically symmetric magnetic fields. The fine-grained, massive parallelism provided by the GPU architecture results in considerable speedup in computing Wilson loop averages. Furthermore, we give a brief overview of uncertainty analysis in the worldline numerics method. There are uncertainties from discretizing each loop, and from using a statistical ensemble of representative loops. The former can be minimized so that the latter dominates. However, determining the statistical uncertainties is complicated by two subtleties. Firstly, the distributions generated by the worldline ensembles are highly non-Gaussian, and so the standard error in the mean is not a good measure of the statistical uncertainty. Secondly, because the same ensemble of worldlines is used to compute the Wilson loops at different values of $T$ and $x_mathrm{ cm}$, the uncertainties associated with each computed value of the integrand are strongly correlated. We recommend a form of jackknife analysis which deals with both of these problems.
Finding the exact equation of motion for a moving charged particle is one of the oldest open problems in physics. The problem originates in the emission of radiation by an accelerated charge, which must result with a loss of energy and recoil of the charge, adding a correction to the well-known Lorentz force. When radiation reaction is neglected, it is well known that the dynamics of a charge in a plane-wave laser field are inevitably periodic. Here we investigate the long-time dynamics of a charge in a plane wave and show that all current models of radiation reaction strictly forbid periodic dynamics. Consequently, we find that the loss of energy due to radiation reaction actually causes particles to asymptotically accelerate to infinite kinetic energy. Such a phenomenon persists even in weak laser fields and puts forward the possibility of testing the open problem of radiation reaction through long-duration weak-field precision measurements, rather than through strong-field experiments. Our findings suggest realistic conditions for such measurements through the asymptotic frequency shift and energy loss of a charge, which for example can be detected in electron energy loss spectrometers in electron microscopes.
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