Surpassing one x-ray photon per electron in nonlinear Thomson scattering in 180° geometry

Abstract

We have obtained the general analytical expressions of harmonic radiation for Thomson scattering (TS) of arbitrary polarized laser by virtue of generalized Bessel functions and derived the extremum conditions for backscattered harmonics. Especially, for the fundamental backscattered Thomson scattering x-ray yield, we have shown that at the same conditions, the circular polarization reaches maximum while the linear case minimum. This effect is significant when a 2 ! 1. With the assumption that the x-ray photon yield of a realistic focused pulse of energy E, wavelength k, and Rayleigh range z R is equivalent to a plane wave pulse containing N l cycles via the relation N l k ¼ pz R where the effective factor p is of order one, we applied the plane wave results to realistic laser pulses and deduced that the backscattered x-ray photon number N f per electron achieves its peak value when the average dimensionless laser intensity a 2 ¼ 0:677 and is irrelevant to the value of p. Since N f and its maximum N f max both scale with the square root of E=k, it is realizable to attain N f ! 1 using joule-scale laser pulses while a great challenge for N f > 10.