0 Quantum Field Theory of the Laser Acceleration

After the historical background concerning the pressure of light, we derive the quantum field theory force of the laser radiation acting on electron. Numerically, we determine the velocity of an electron accelerated by laser beam, after acceleration time ∆t = 1s. 1 Why laser acceleration ? The problem of acceleration of charged particles by the laser field is, at present time, one of the most prestigeous problem in the accelerator physics. It is supposed that, in the future, the laser accelerator will play the same role in particle physics as the linear or circle accelerators working in today particle laboratories. The acceleration effectiveness of the linear or circle accelerators is limitied not only by geometrical size of them but also by the energy loss of accelerated particles which is caused by bremsstrahlung during the acceleration. The amount of radiation, following from the Larmor formula, emitted by accelerated charged particle is given generally as follows (Maier, 1991): P = 2 3 r0m c (γ6a2|| + γ 4a2⊥); γ = 1 √ 1− β ; β = v/c (1) where v is the velocity of a particle, c is the velocity of light in vacuum, a|| is parallel acceleration of a particle and a⊥ is the perpendicular acceleration of a particle in the accelerator, m is the rest mass of an electron. The quantity r0 = 1 4πε0 e mc (2) is the electron classical radius in SI units. In terms of momenta ṗ|| = Ė βc ; ṗ⊥ = mγv̇⊥, (3) the radiated power can be written as