This thesis presents the iterative development of a table-top (TT) laser-produced plasma (LPP) light source optimised for high average radiance in the soft x-ray (SXR) region. The system employed a solid molybdenum target and exhibited peak emission within the water window (WW) region. Plasma generation was driven by a diode-pumped λ = 1064 nm Nd:YAG laser delivering 5 ns pulses (full width at half maximum, FWHM) with an energy of 37.5 mJ at a repetition rate of 1 kHz. Focusing these pulses with a 100 mm lens produced LPP SXR emission diameters (averaged over 100 shots) of approximately 22 μm and 13 μm (FWHM) along the horizontal and vertical axes, respectively, corresponding to an estimated radiance of 5×10¹⁰ photons/s/mm²/mrad² at 2.74 nm and 0.1% relative bandwidth (BW). This prototype addresses key challenges in solid target light-source development and paves the way for a design capable of achieving radiance up to two orders of magnitude greater. Realising this increase requires relatively straightforward improvements to the focusing optics and target stability. The compact design relies on helium buffer gas as the primary debris mitigation mechanism to protect nearby optical components. This approach necessitated the integration of a 100 nm thick silicon nitride membrane (SNM), positioned in close proximity to the LPP, to serve as a helium-vacuum interface transmissive to SXR radiation. To shield both the SNM and the laser focusing lens from particulate debris, a set of novel components was developed to manipulate particle trajectories through interaction with high-velocity gas flows. These components were designed using a three-dimensional (3D) particle drag force model, coupled with computational fluid dynamics (CFD) simulations of the surrounding environment. The final configuration demonstrated stable collection of SXRs from the LPP, transmitted through the SNM at a 2.7° collection angle, over a continuous 4 hour period. This duration represents a substantial fraction of the expected daily operational cycle for TT light sources intended for imaging, patterning, and spectroscopy applications
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