Optimization of single-stage x-ray laser coherence

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Abstract
The effect of smoothly varying transverse gain and refraction profiles on x-ray laser coherence is analyzed by modally expanding the laser electric field within the paraxial approximation. Comparison with a square transverse profile reveals that smoothly varying profiles generally lead to a greatly reduced number of guided modes and a consequent improvement in transverse coherence length. However, the refractive defocusing responsible for enhanced coherence can also significantly degrade the coherent power of plasma x-ray lasers based on amplified spontaneous emission. A critical value of the Fresnel number is indicated, below which the coherent power rapidly decreases as refractive defocusing is increased. A parameter study of transverse coherence for current or planned x-ray laser experiments is provided. Comparison with ray-optics scaling laws for transverse coherence length and coherent power is made. An optimal coherent energy output of nearly 0.5 mJ in 100 psec is determined in Ni-like Ta at a wavelength of 45 Å for a saturated single-stage x-ray laser. A favorable comparison with coherent energy requirements for holographic imaging of biological samples is indicated.