Several variations of a notional space based electrical laser power system architecture were evaluated with a general thermal systems analysis. The analysis and evaluations of technology options and feasibility were based on a baseline laser power system concept that incorporated an advanced solar array/battery power combination. Two closed-loop, dynamic cycle system concepts are of interest here, both using H2-O2 to fuel the combustor with the heat engine concept using a PEM fuel cell to regenerate fuel constituents. The first dynamic system is a turbo-generator based concept, and the second is a Brayton cycle based heat engine concept driven by an H2-O2 combustor. Each one of these power generation mechanisms has its own advantages and disadvantages. This first-order thermal analysis aims to compare these various options on a common footing such as system mass, in order to arrive at the most suitable configuration from the various options considered. Several technological enhancements were incorporated in the analysis for the H2-O2 system concepts with special emphasis and advocacy of the use of extremely efficient cryogenic super conducting generators and cryogenic power conditioning equipment as these components can be cooled with the cryogenic effluents before they are combusted. These systems would supply power to a 23.5% efficient electric laser (50% electric to optical power diode pump, and a 47% optical to optical high power laser) with >8 MWrf of output laser power in most cases. This is an extremely high power level, so we predict the systems to be somewhat massive and on the order of 40 metric tons (MT, 1000 kg) or more with high sensitivity to recharge time. For a one-day recharge time, the H2-O2 concept recycling all effluents is twice as massive as the baseline solar system. As the recharge time is extended from one day to more than five, the concept that reclaims the effluents begins to appear more attractive for the turbogenerator-based evaluations. For similar output power, the heat engine based evaluation appears to be more attractive at higher cycle temperatures.