A microsphere-based short-wavelength recombination x-ray laser

We describe a scheme for obtaining very short wavelengths ({lambda} {similar to} 10{Angstrom}) in recombination lasers. The rapid cooling rates necessary to achieve population inversion during recombination are attained by adiabatic expansion of sub micron spheres. The lasing region is made up of many such spheres. The spheres are heated impulsively by a powerful picosecond laser. First, they ionize, then as they expand, they cool and recombine. We have calculated the optimum sphere size and initial temperature for maximum gain in the n = 3 to n = 2 transition of hydrogen-like ions of elements with atomic numbers, Z, between 10 and 30. Gain of about 10{sup 3}cm{sup {minus}1} is calculated in aluminum at 38.8{Angstrom}. Gain rapidly decreases with Z so that gain in titanium at 13.6{Angstrom} is about 40 cm{minus}1. We have calculated the required pump laser intensity and found it to be attainable with current lasers. The propagation of the pump through the gas'' of spheres is considered and the problems arising from pump scattering by the spheres are discussed