General classical theory of spinning particles in a Maxwell field

Radiation reaction effects on electron nonlinear dynamics and ion acceleration in laser–solid interaction

For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution ${j}_{a}$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the difference between the final and initial electromagnetic self-energy of the charge distribution, (ii) the net electromagnetic energy radiated to infinity (and/or into a black hole or white hole), and (iii) the total work done by the electromagnetic field on the charge distribution via the Lorentz force. A similar conservation theorem can be proven for linearized gravitational fields off of a stationary, asymptotically flat background, with the second order Einstein tensor playing the role of an effective stress-energy tensor of the linearized field. In this paper, we prove the above theorems for smooth sources and then investigate the extent to which they continue to hold for point particle sources. The ``self-energy'' of point particles is ill defined, but in the electromagnetic case, we can consider situations where, initially and finally, the point charges are stationary and in the same spatial position, so that the self-energy terms should cancel. Under certain assumptions concerning the decay behavior of source-free solutions to Maxwell's equations, we prove the vanishing of the sum of the net energy radiated to infinity and the net work done on the particle by the DeWitt-Brehme radiation reaction force. As a byproduct of this analysis, we provide a definition of the ``renormalized self-energy'' of a stationary point charge in a stationary spacetime. We also obtain a similar conservation theorem for angular momentum in an axisymmetric spacetime. In the gravitational case, we argue that similar conservation results should hold for freely falling point masses whose orbits begin and end at infinity. This provides justification for the use of energy and angular momentum conservation to compute the decay of orbits due to radiation reaction. For completeness, the corresponding conservation theorems for the case of a scalar field are given in an appendix.

In addition to the quantized molecular structure that constrains the kinematics of atom-molecule collision, constraints arising from energy and angular momentum (AM) conservation strongly influence the magnitude and probability distribution of rotational transfer due to collisions. However, once the nature of these constraints is established, it is possible to predict quantitatively, using quantized momentum mechanics, the outcome of inelastic and reactive collisions. The existence of these constraints is most clearly portrayed in plots of relative velocity versus final rotational AM . These represent channel opening under the conditions: (i) energy conservation, (ii) simultaneous energy and angular momentum conservation, the latter via a specified maximum effective impact parameter and (iii) angular momentum conservation via this same is generally set to be the half bond length (HBL) of the diatomic, as suggested by experimental and theoretical considerations. Each of these conditions may constrain the rotational transfer process. The plots also give indications of conditions under which backward or forward scattering will occur and when long-lived complexes will form. For sharply defined velocity distributions, scattering angle peaks are readily calculated and these agree well with experimental data. When energy constraints dominate, the value of may be less than HBL and this reduced value may be obtained from the kinematic equations. This permits wider usage of the AM theory of rotational transfer. AM constraints effectively reduce the number of channels that appear to be accessible from energetic considerations. The plots may also be used to analyse reactive collisions and inelastic processes in polyatomic molecules for data in which the angular momentum change is directed principally along one of the molecule's inertial axes.

Various different classical models of electrons including their spin degree of freedom are commonly applied to describe the coupled dynamics of relativistic electron motion and spin precession in strong electromagnetic fields. The spin dynamics is usually governed by the Thomas-Bargmann-Michel-Telegdi equation [1, 2] in these models, while the electron’s orbital motion follows the (modified) Lorentz force and a spin-dependent Stern-Gerlach force. Various classical models can lead to different or even contradicting predictions how the spin degree of freedom modifies the electron’s orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin induced relativistic Stern-Gerlach force acting on the electron. The Frenkel model [3, 4] and the classical Foldy-Wouthuysen model 5 are compared exemplarily against each other and against the quantum mechanical Dirac equation in order to identify parameter regimes where these classical models make different predictions [6, 7]. Our theoretical results allow for experimental tests of these models. In the setup of the longitudinal Stern-Gerlach effect, the Frenkel model and classical Foldy-Wouthuysen model lead in the relativistic limit to qualitatively different spin effects on the electron trajectory. Furthermore, it is demonstrated that in tightly focused beams in the near infrared the effect of the Stern-Gerlach force of the Frenkel model becomes sufficiently large to be potentially detectable in an experiment. Among the classical spin models, the Frenkel model is certainly prominent for its long history and its wide application. Our results, however, suggest that the classical Foldy-Wouthuysen model is superior as it is qualitatively in better agreement with the quantum mechanical Dirac equation. In ultra strong laser setups at parameter regimes where effects of the Stern-Gerlach force become relevant also radiation reaction effects are expected to set in. We incorporate radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin one-half particles. 1. Thomas, L. H., “I. The kinematics of an electron with an axis,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13), 1–22 (1927). 2. Bargmann, V., Michel, L., and Telegdi, V. L., “Precession of the polarization of particles moving in a homogeneous electromagnetic field,” Phys. Rev. Lett. 2(10), 435–436 (1959). 3. Frenkel, J., “Die Elektrodynamik des rotierenden Elektrons,” Z. Phys. 37(4–5), 243–262 (1926). 4. Frenkel, J., “Spinning electrons,” Nature (London) 117(2949), 653–654 (1926). 5. Silenko, A. J., “Foldy-Wouthyusen transformation and semiclassical limit for relativistic particles in strong external fields,” Phys. Rev. A 77(1), 012116 (2008). 6. Wen, M., Bauke, H., and Keitel, C. H., “Identifying the Stern-Gerlach force of classical electron dynamics,” Sci. Rep. 6, 31624 (2016). 7. Wen, M., Keitel, C. H., and Bauke, H., “Spin one-half particles in strong electromagnetic fields: spin effects and radiation reaction,” arXiv:1610.08951 (2016).

It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwell's field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.

By means of the scattering angles, we obtain an effective metric of spinless binaries with radiation-reaction effects up to fourth post-Minkowskian order, which is the foundation of the effective-one-body theory. We note that there are freedoms for the parameters of the effective metric because one equation corresponds to two parameters for each post-Minkowskian order. Accordingly, in order to construct a self-consistent effective-one-body theory in which the Hamiltonian, radiation-reaction forces and waveforms for the “plus” and “cross” modes of the gravitational wave should be based on the same physical model, we can fix these freedoms by requiring the null tetrad component of the gravitationally perturbed Weyl tensor Psi _4^B to be decoupled in the effective spacetime.

A model of three-body motion is developed which includes the effects of\ngravitational radiation reaction. The radiation reaction due to the emission of\ngravitational waves is the only post-Newtonian effect that is included here.\nFor simplicity, all of the motion is taken to be planar. Two of the masses are\nviewed as a binary system and the third mass, whose motion will be a fixed\norbit around the center-of-mass of the binary system, is viewed as a\nperturbation. This model aims to describe the motion of a relativistic binary\npulsar that is perturbed by a third mass. Numerical integration of this\nsimplified model reveals that given the right initial conditions and parameters\none can see resonances. These (m,n) resonances are defined by the resonance\ncondition, $m\\omega=2n\\Omega$, where $m$ and $n$ are relatively prime integers\nand $\\omega$ and $\\Omega$ are the angular frequencies of the binary orbit and\nthird mass orbit, respectively. The resonance condition consequently fixes a\nvalue for the semimajor axis of the binary orbit for the duration of the\nresonance; therefore, the binary energy remains constant on the average while\nits angular momentum changes during the resonance.\n

A new mechanism of harmonics generation is found in ultraintense laser interactions with plasmas, where radiation reaction effects dominate. The radiation reaction results in trapped electrons which oscillate in the laser field and emit high energy photons. Such emission event happens with a frequency spectrum containing double or high order components of the drive laser, inducing second and higher order harmonics emission. Although the intensity of such harmonics is too weak for practical applications, they could be used as a specific diagnostic to detect the radiation reaction effects in the upcoming experimental studies of the extremely intense laser pulse interacting with plasmas.

The effects of radiation reaction on the motion of charged particles are studied in strong electric and magnetic fields with special attention to the vacuum near-field region of an oblique rotator. For strong radiation damping a local velocity field is derived from the Lorentz-Dirac equation, which efficiently describes the motion of electrons and positrons in the whole range of typical pulsar parameters. The velocity field makes it possible to define regions in the inner magnetosphere, where particle trapping occurs due to the radiation losses. By numerical integration of particle trajectories from the pulsar surface, regions around the magnetic poles are found which are defined by particle emission into the wave zone. The shapes of the escape regions on the pulsar surface are determined to a considerable extent by the presence of the accumulation regions.

Effect of radiation reaction on the non-linear scattering of electromagnetic waves by free electrons

We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the magnitude of the total spin S and the effective spin ξ. This feature makes the entire dynamics qualitatively different compared to the generic unequal-mass case, where only ξ is constant while the variable S parametrizes the precession dynamics. For fixed individual masses and spin magnitudes, an equal-mass black-hole inspiral is uniquely characterized by the two parameters : these two numbers completely determine the entire evolution under the effect of radiation reaction. In particular, for equal-mass binaries we find that (i) the black-hole binary spin morphology is constant throughout the inspiral, and that (ii) the precessional motion of the two black-hole spins about the total spin takes place on a longer timescale than the precession of the total spin and the orbital plane about the total angular momentum.

We study the Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell's field.

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a vertical plate embedded in a uniform porous medium in the presence of thermal radiation and chemical reaction effects. The governing equations for this problem were developed and non-dimensionalized and the resulting equations were then solved numerically by an explicit finite-difference scheme. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in the graphical form to show the effects of material parameters including the thermal buoyancy, the solutal buoyancy, Reynolds number, the inverse thermal radiation parameter, the permeability parameter, Prandtl number, Schmidt number and the chemical reaction parameter on the skin-friction coefficient, the Nusselt number, the Sherwood number, the velocity profiles, the temperature profiles and the concentration profiles in the boundary layer.

The extreme laser intensity, IL>1023 W/cm2, will be made possible by Extreme Light Infrastructure. Such an ultra-intense and ultra-short laser pulse promises to promote laser-matter interaction into the exotic quantum-electro-dynamical regime. Electrons quivering in such a strong laser pulse experience a radiation reaction (RR) friction force by radiating high frequency photons. These extreme intensities will also make possible acceleration of heavy ions in new regimes. In this paper, the heavy ion beam generation based on ultra-intense and ultra-short laser foil interaction is systematically studied. Three-dimensional particle-in-cell simulations which include an energy conserving electrodynamics model for RR force and the corresponding γ-photons emission have been used. The energy partition into electrons, ions, and photons has been investigated in relation to efficient generation of heavy ion beams by linearly and circularly polarized (LP and CP) laser and for different foil thicknesses. It is found that the CP and LP cases each have an optimal foil thickness for efficient ion beam generation; the RR force has a stronger effect upon laser coupling to an opaque foil target for an LP laser than a CP laser; and the emitted photons are proven to be an efficient source of γ-ray emission with the peak frequency as high as 106∼108 times the laser frequency.

Maxwell's equations within a dielectric and/or a magnetic medium were first developed macroscopically and must be complemented by constitutive relations to obtain solutions. These relations connect D with E (and with B in optically active material) and H with B (and again with E in optically active material). The atomic and molecular theories of quantum mechanics allow a microscopic approach to derive these constitutive relations where the macroscopic electric and magnetic fields are averages of the microscopic fields e and b. In classical electromagnetic theory Lorentz [1] originally showed how to derive the Maxwell's macroscopic equations from electron theory using microscopic fields obeying the Maxwell's equations in vacuo but coupled to electronic and ionic sources. There are two distinct steps in this procedure. The first introduces microscopic polarization fields, both electric amd magnetic, p and m from which microscopic electric displacement vector field d and auxiliary magnetic field h are simply constructed. The resulting equations for the microscopic fields e, b, d, and h are called the atomic field equations. The second step is the statistical one where the macroscopic fields E, B, D, and H are defined as averages of the microscopic fields and these macroscopic fields are then shown to obey the phenomenological macroscopic Maxwell's equations. A historical appraisal may be found in the recent book by de Groot [2].