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By Hamlet K. Avetissian

This publication is on diversified nonlinear schemes of unfastened Electron Lasers, Laser Accelerators, and Electron-Positron pair construction and covers the speculation of interplay of robust and large powerful laser fields with charged debris and vacuum. those subject matters may be within the heart of primary learn within the subsequent decade. the writer, who has over 30 years of expertise during this box, has constructed non-linear conception and new methods to unravel respective relativistic classical and quantum difficulties. The publication could be particularly precious for researchers, scholars and practitioners within the fields of Particle and Laser Physics.

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The relativistic parameter of intensity is taken to be ξ0 = 2 and γ = 10. be obtained utilizing the properties of the Bessel function. The argument of the latter in Eq. 63) reaches its maximal value αs max = ξ0 1 + ξ02 s 18 1 Interaction of a Charged Particle with EM Wave in Vacuum at the angle cos ϑm = v/c. Therefore, at ξ0 1 the harmonics with s ∼ αs >> 1 furnish the main contribution to the radiation power. At the angle θ = θm we have a peak in angular distribution of the radiation power. 69) 2/3 2 s − Js s 2 Ai (Z) , and taking into account that m∗ c2 E= 1− v2 c2 for the angular distribution of the radiation power we have e2 ωs2 1 − dP (s) dO × 2πc(1 − s2 − 1 − ξ0−2 αs2 s 2 v c v2 c2 cos ϑ) 2/3 2 s 4/3 Ai2 (Z) + Ai 2 (Z) .

119) where ϑ0 , ϑ are the incident and scattering angles of incident strong wave and radiated photon with respect to the direction of the particle mean velocity v = c2 Π/Π0 and ϑr is the angle between the incident wave and radiated photon propagation directions. 64) by the last term in the denominator ∼ s ω/Π0 , which is the quantum recoil of emitted photon. Making the integration over Π in Eq. 117) and multiplying by the photon energy we obtain the radiation power. In the case of circular polar2 ization of an incident strong wave (g = ±1) we have |Gs | = Js2 (α) and the radiation power is (s) dPk = × ω 2 e2 m2 c3 −Js2 (α) + ξ02 2πΠ0 Π0 s2 − 1 Js2 (α) + Js2 (α) α2 ×δ 2 2 1+ (kk ) 2 (pk) (p k) Π0 − Π0 + ω − sω dω dO, where the Bessel function argument α= eA0 ω k p p − pk p k .

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