Determination of the bulk emittance of a laser plasma in the x-ray wavelength range

An analysis is made of a method for numerical determination of the bulk emittance of a laser plasma from experimental results obtained by contactless diagnostic methods (such as camera obscura, x-ray crystaldiffraction microscope, etc.). The main problem in an analysis of the experimental results obtained using such diagnostic apparatus is to find a stable solution of the Abel equation since it represents an incorrectly posed problem for a pair of naturally used classes of functions (metric spaces), in particular in the space of continuous functions with a uniform metric. The attention is concentrated on the problem of selection of regularizing counting parameters. It is desirable to use a counting scheme with a regularizing parameter variable over a grid of values of the required function. The results are given of test calculations and, by way of illustration, an analysis is given of experimental results.