We study experimentally and theoretically the production of characteristic Ka x-rays during the interaction of intense infrared laser pulse with large N~10^4-10^6 atoms/ argon clusters. We focus on the influence of laser intensity and pulse length on both the total x-ray yields and the charge-state distributions of the emitting cluster argon ions. An experimental optimization of the x-ray yield based on the setup geometry is presented and the role of the effective focal volume is investigated. Our theoretical model is based on a mean-field Monte-Carlo simulation and allows identifying the effective heating of a subensemble of electrons in strong fields as the origin of the observed x-ray emission. Well-controlled experimental conditions allow a quantitative bench marking of absolute x-ray yields as well as charge state distributions of ions having a K-shell vacancy. The presence of an optimum pulse duration that maximizes the x-ray yield at constant laser energy is found to be the result of the competition between the single cluster dynamics and the number of clusters participating in the emission.