Inertial fusion energy promises nearly unlimited, clean power if it can be achieved. However, the design and engineering of fusion systems requires controlling and manipulating matter at extreme energies and timescales; the shock physics and radiation transport governing the physical behavior under these conditions are complex requiring the development, calibration, and use of predictive multiphysics codes to navigate the highly nonlinear and multi-faceted design landscape. We hypothesize that artificial intelligence reasoning models can be combined with physics codes and emulators to autonomously design fusion fuel capsules. In this article, we construct a multi-agent system where natural language is utilized to explore the complex physics regimes around fusion energy. The agentic system is capable of executing a high-order multiphysics inertial fusion computational code. We demonstrate the capacity of the multi-agent design assistant to both collaboratively and autonomously manipulate, navigate, and optimize capsule geometry while accounting for high fidelity physics that ultimately achieve simulated ignition via inverse design.