Analysis of a soft-x-ray laser with charge-exchange excitation

A soft-x-ray laser utilizing electron pickup by a stripped nucleus is proposed. A particular example using electron exchange between hydrogen and an $\alpha$ particle is analyzed and is shown to produce inversion between the ${\mathrm{He}}_{2p}^{+}$ and ${\mathrm{He}}_{1s}^{+}$ levels giving stimulated emission at 304 Å. In this scheme the $\alpha$ particles are swept along the target at the speed of light. The cross sections involved in the electron pickup in a hydrogen target and subsequent collisional deexcitation are analyzed to ascertain the optimum target thickness for population inversion. Also the effects of atomic collisions on the stimulated-emission cross section are estimated (Doppler broadening). The dynamics of the beam including focusing and space-charge effects are discussed. The stimulated-emission cross sections for a gas and a solid thin-film target are calculated. For a 30-mA $\alpha$-particle current and a 10-cm lasing length, we estimate gains of 1.1 and 50, respectively.