Abstract
Photon emission by an ultrarelativistic charged particle in extremely strong magnetic field is analyzed, with vacuum polarization and photon recoil taken into account. Vacuum polarization is treated phenomenologically via refractive index. The photon emission occurs in the synergic (cooperative) synchrotron–Cherenkov process [J Schwinger et al 1976 Annals of Physics 96 303] which is similar to the synchrotron emission rather than to the Cherenkov one. For electrons, the effect of vacuum polarization on the emission spectrum is not evident at least below the probable onset of non-perturbative quantum electrodynamics (QED). However, the effect of vacuum polarization on the emission spectrum can be observable for muons already at γB/BS ≈ 30, with γ the muon Lorentz factor, B the magnetic field strength and BS the critical QED field. Nevertheless, vacuum polarization leads to only 10% enhancement of the maximum of the radiation spectrum.
Highlights
Quantum electrodynamics (QED) predicts nonlinear dielectric properties of the vacuum in strong magnetic field caused by virtual electron-positron pairs
The general formula which describes the photon emission by an ultrarelativistic electron in a strong magnetic field can be found in the framework of the quasiclassical theory of Baier and Katkov [32]
Baier–Katkov formula can be extended to the case of a constant non-unity refractive index n, |n − 1| 1 [see equation (30)]
Summary
Quantum electrodynamics (QED) predicts nonlinear dielectric properties of the vacuum in strong magnetic field caused by virtual electron-positron pairs. The field of the order of 10−3 × BS will be available which results the vacuum refractive index n such that δn = n − 1 ∼ 10−10 for photons with energy 1 GeV [21], with BS = m2c3/eh the Sauter–Schwinger critical QED field [22], m and e > 0 the electron mass and charge magnitude, respectively, c the speed of light andh the reduced Plank constant Despite such small value of δn, the Lorentz factor γ ∼ 105, available for electrons nowadays, is enough to reach the speed of a charged particle greater than the phase speed of the photons, the Cherenkov emission may occur.
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