This work is focused on numerical modeling of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{ArF}^\ast$</tex-math> </inline-formula> laser operating on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Electra</i> electron beam (e-beam) facility at the Naval Research Laboratory. The results are based on a suite of codes that includes electron kinetics derived from the electron Boltzmann equation, plasma chemistry, lasing amplification, and 3-D radiation transport. The mechanisms of formation and destruction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{ArF}^\ast$</tex-math> </inline-formula> molecules have been investigated. Time-dependent laser parameters, such as small signal gain, nonsaturable absorption, saturation intensity, and amplified spontaneous emission (ASE) and their dependence on e-beam power deposition in the range of 0.5–1 MW/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{3}$</tex-math> </inline-formula> , gas pressure of 0.8–1.4 atm, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{F}_{2}$</tex-math> </inline-formula> concentration of 0.1%–3.0%, are investigated. The modeling results show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{ArF}^\ast$</tex-math> </inline-formula> laser is an efficient and coherent light source at 193 nm ultraviolet wavelength.