The way to realize $\gamma$-ray lasers

Abstract

Essential ingredients for generating a laser are analyzed. Unified understanding on generation mechanisms for both usual lasers (with media composed of atoms, molecules or condensed matter) and free electron lasers are shown. It makes us understand the difficulties in generating a $\gamma$-ray laser. First of all, it is impossible to make a resonator in the $\gamma$-ray region by mirrors, like those made for optic instruments within or near the visible spectrum. The relation between the wavelength $\lambda_r$ of the emitted radiation, and the wiggler period $\lambda_w$ in a free electron laser is $\displaystyle\lambda_r\sim~\lambda_w/\gamma^2$, in which $\gamma$ is the Lorentz factor of the emitting electron.Requiring $\lambda_r$ falls into the $\gamma$-ray region, $\lambda_w$ has to be less than 1 mm.It seems impossible to be realized in a usual free electron laser either. We therefore propose a way to realize it by letting charged particles wiggle in an usual back ground laser. A circularly polarized plane wave laser distorts the electron wave in $x$-$y$ planes,periodically along the $z$ direction, andmodulates the periodicity along the $z$direction. It is the quantum correspondence of the classical wiggling of electrons. Since a laser is a coherentelectromagnetic wave, simple and clean, it is therefore anideal wiggler. To accurately and reliably analyze the whole process, we proposed Quantum Electrodynamics in a Laser. It is equivalent to the Quantum Electrodynamics in Vacuum, and is therefore the most reliable theory nowadays as well. Moreover we noticed that, emitted$\gamma$-photons moving with emitting electrons, itself is a favorable condition to make the stimulated emission easy. Its effect in some sense likethe effect of a resonator. The stimulated emissions amplify the $\gamma$-radiation and make it finally transit into a $\gamma$-ray laser under favorable conditions. In this sense, the generated $\gamma$-ray laser is aQuantum Free Electron Laser. Therefore we clearly concluded that in a head on collision between a suitable mono-energetic electron beam and a monochromatic plane wave laser, a $\gamma$-ray laser should be generated. For an electron beam of density $n_0~=~10^{18}$ m$^{-3}$and energy $E~=~307$ MeV, in the backgroundlaser with $\lambda~=785$ nm and $I~=~10^{19}$ W/m$^2$, theintensity of the output $\gamma$-ray laser is about$5~\times~10^{13}$ W/m$^2$. It is meaningful. Of course, this is a theoretical conclusion under ideal conditions. The competition and the balance between theemission and reabsorption of quanta byelectrons determine the evolution andtherefore the output intensity of the $\gamma$-raylaser. However, Synergetics tells us that there will be a critical point. When the real situation approaches the ideal condition and acrosses over this point, the positive feedback of stimulated emissions leads to a collapse of the created $\gamma$-photon beam into a coherent state. This is a phase transition of the produced $\gamma$-ray into a $\gamma$-ray laser, and is just what we want to search in experiments.