Bessel spatial profile of a soft x-ray laser beam

We report far-field profile measurements of an optical-field-ionized high-order harmonic-seeded soft x-ray laser. We show that the beam transverse profile can be controlled between a regular Gaussian shape and a Bessel profile exhibiting several rings via the infrared laser pump intensity. These experimental data are supported by a complete numerical modeling including a two-dimensional plasma amplifier simulation and a two-level soft x-ray amplification using a Maxwell-Bloch treatment. This model takes into account the experimental high-order harmonic wavefront and intensity before it is numerically amplified.