The Linac Coherent Light Source (LCLS) is the world's first x-ray free electron laser. It is a scientific user facility operated by the SLAC National Accelerator Laboratory, at Stanford, for the U.S. Department of Energy. As beam time at LCLS is extremely valuable and limited, experimental efficiency -- getting the most high quality data in the least time -- is critical. Our overall project employs cognitive engineering methodologies with the goal of improving experimental efficiency and increasing scientific productivity at LCLS by refining experimental interfaces and workflows, simplifying tasks, reducing errors, and improving operator safety and stress. Here we describe a multi-agent, multi-scale computational cognitive interaction model of instrument operations at LCLS. Our model simulates aspects of human cognition at multiple cognitive and temporal scales, ranging from seconds to hours, and among agents playing multiple roles, including instrument operator, real time data analyst, and experiment manager. The model can roughly predict impacts stemming from proposed changes to operational interfaces and workflows. Example results demonstrate the model's potential in guiding modifications to improve operational efficiency. We discuss the implications of our effort for cognitive engineering in complex experimental settings, and outline future directions for research. The model is open source and supplementary videos provide extensive detail.