Abstract
Using a relativistic plasma with an isotropic monoenergetic distribution of electrons and positrons as an example, we show that in the maser regime the maximum possible amplification of synchrotron radiation at a distance of one wavelength is achieved in a medium where the magnetic energy density is of the order of the particle energy density. This ratio of the energy densities corresponds to a (Harris-type) current sheet. We have obtained an electron Lorentz factor of 350 and a magnetic field strength of 10 kG in the maser radio emission region for the Crab pulsar. Our estimate suggests that the optical and coherent radio emissions of the object originate from one synchrotron source in the form of a current sheet. The diameter of the source must exceed the light-cylinder radius approximately by a factor of 6 for the maser wave field to interact with particles in the linear regime, in particular, to keep its phase velocity higher than the speed of light in a vacuum—a necessary condition for the synchrotron instability.
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Notes
In the case of synchrotron absorption of a photon \(\hbar\omega\), the relativistic electrons from the energy interval \(\textrm{d}E\ll\hbar\omega\) pass into a larger volume of momenta \(4\pi(E+\hbar\omega)^{2}\textrm{d}E/c^{3}\) than in the case of induced emission with a reduction in the occupied volume to \(4\pi(E-\hbar\omega)^{2}\textrm{d}E/c^{3}\). These volumes are proportional to the number of quantum states in which an electron ends up in the corresponding radiation process. The maser regime requires that the decrease in the probability of spontaneous emission with increasing particle energy be faster than the increase in the number of quantum states of the electron per unit interval of its energy.
The values of \(R_{\perp}\), \(k_{\perp}\), and \(\Delta\Phi\) are the same in the laboratory frame and the frame moving with the longitudinal velocity of the electron.
In the optical range a relativistically strong laser field was achieved in experiments in the late 1990s on the amplification of linearly-frequency-modulated laser pulses, where the flux density of the focused radiation exceeded \(10^{18}\textrm{ W}\textrm{cm}^{-2}\); see the reviews by Di Piazza et al. (2012) and Danson et al. (2019) and the description of the experiment by Ginzburg et al. (2010).
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This work was supported by the Russian Foundation for Basic Research (project no. 20-02-00104a).
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Translated by V. Astakhov
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Koryagin, S.A. Current Sheet as an Optimal Synchrotron Maser on a Radio Pulsar. Astron. Lett. 49, 811–817 (2023). https://doi.org/10.1134/S1063773723120046
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DOI: https://doi.org/10.1134/S1063773723120046