Numerical approach to the semiclassical method of radiation emission for arbitrary electron spin and photon polarization

T N Wistisen,A Di Piazza

doi:10.1103/physrevd.100.116001

T N Wistisen, A Di Piazza

Open Access

https://doi.org/10.1103/physrevd.100.116001

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Abstract

We show how the semiclassical formulas for radiation emission of Baier, Katkov and Strakhovenko for arbitrary initial and final spins of the electron and arbitrary polarization of the emitted photon can be rewritten in a form which numerically converges quickly. We directly compare the method in the case of a background plane wave with the result obtained by using the Volkov state solution of the Dirac equation, and confirm that we obtain the same result. We then investigate the interaction of a circularly polarized short laser pulse scattering with GeV electrons and see that the finite duration of the pulse leads to a lower transfer of circular polarization than that predicted by the known formulas in the monochromatic case. We also see how the transfer of circular polarization from the laser beam to the gamma ray beam is gradually deteriorated as the laser intensity increases, entering the nonlinear regime. However, this is shown to be recovered if the scattered photon beam is collimated to only allow for passage of photons emitted with angles smaller than $1/\gamma$ with respect to the initial electron direction, where $\gamma$ is the approximately constant Lorentz factor of the electron. The obtained formulas also allow us to answer questions regarding radiative polarization of the emitting particles. In this respect we briefly discuss an application of the present approach to the case of a bent crystal and high-energy positrons.

Highlights

In view of recent and upcoming experiments involving radiation emission from relativistic electrons [1,2,3,4,5] and of high-intensity laser facilities under construction like the Extreme Light Infrastructure (ELI), it is fitting to investigate efficient approaches to calculating the high-energy radiation emitted when ultrarelativistic electrons collide with such an intense laser field with as much generality as possible
The latter would occur if the spin-flip radiation has a different yield for each of the possible initial spin states, i.e., a generalization of the Sokolov-Ternov effect [29] to fields other than that of a permanent magnetic field [30,31]. We briefly demonstrate this in the case of positrons channeling in a bent germanium crystal, where one has two kinds of motion superimposed—the oscillatory channeling motion between the bent planes, which in the unbent case would not lead to polarization, along with the motion along the bending arc, which leads to transverse polarization of the positrons
In conclusion we have presented a method to rewrite the semiclassical formulas of Baier, Katkov and Strakhovenko, which facilities their numerical implementation for arbitrary discrete quantum numbers of the particles

Summary

INTRODUCTION

In view of recent and upcoming experiments involving radiation emission from relativistic electrons [1,2,3,4,5] and of high-intensity laser facilities under construction like the Extreme Light Infrastructure (ELI), it is fitting to investigate efficient approaches to calculating the high-energy radiation emitted when ultrarelativistic electrons collide with such an intense laser field with as much generality as possible. The presented formulas allow us to find the polarization properties of the radiation depending on the spin of the initial and final electrons, which allows us to determine if the electrons become polarized The latter would occur if the spin-flip radiation has a different yield for each of the possible initial spin states (see e.g., [28]), i.e., a generalization of the Sokolov-Ternov effect [29] to fields other than that of a permanent magnetic field [30,31].

SEMICLASSICAL APPROACH

VOLKOV-STATE APPROACH

OF RESULTS

POLARIZATION IN A BENT CRYSTAL

CONCLUSION