Coherent phase control in laser-assisted radiative recombination and x-raygeneration

We investigate electron-ion recombination in a powerful bichromatic laser f ield of frequencies omega (L) and 3 omega (L) and consider the dependence o f the recombination probabilities on the relative phase phi of the two held components. During this process a certain number of laser photons can be a bsorbed or emitted, yielding a spectrum of harmonics of the form omega (x) = E-(p) over right arrow + nw(L) + I-io + U-p(tot), where E-(p) over right arrow is the initial electron energy, It the number of emitted or absorbed laser photons w(L), I-lo the ionization energy and U-p(tot) the total ponde romotive energy of the bichromatic laser field. This process is of interest for the generation of high=frequency fields during the laser heating of pl asmas. We shall evaluate the nonlinear recombination probabilities as a fun ction of the relative phase phi of the two field components using the inver se form of the Keldysh-Faisal-Reiss model, also taking into account in an a pproximate way the Coulomb effects of the ion on the recombining electron. Moreover, we shall compare our quantum mechanical results with those obtain ed from a classical theory of recombination, developed recently, based on B ohr's correspondence principle.