The development of a new-generation hypersonic vehicle is constantly breaking through the boundary of flight speed and cruising space, experiencing high enthalpy shock wave/boundary layer interaction (SWBLI) during flight, which poses a serious threat to the vehicle's flight safety. The kinetic energy is transformed into internal energy because of the strong shock wave and viscous retardation that is created by high enthalpy SWBLI. These thermochemical non-equilibrium conditions can greatly impact the flow structure and surface properties of the vehicle, which needs further investigation. Flow control technology is an important way to improve the comprehensive performance of hypersonic vehicles. Under the local thermal ionization condition of the high enthalpy SWBLI flow field, the conductivity around the flow field is high, which provides a direct working environment for the application of magnetohydrodynamic (MHD) control technology. An expansion tube is one of the few qualified test facilities on the ground to simulate the hypervelocity high-temperature flow environment. Numerical simulations based on the multicomponent thermochemical non-equilibrium MHD model are adopted to analyze the double-cone standard model flow in an expansion tube under high enthalpy conditions. The influences of alkali metal "seed particles" on the control effect were discussed. Results demonstrate that the developed numerical calculation method accurately predicts the complex SWBLI flow field of a double-cone under different enthalpy incoming flow conditions. Near the triple point and the downstream of shock-shock interference, the intensity of the thermochemical non-equilibrium effect is the strongest here, and the conductivity of the flow field in related areas reaches the peak. In the high enthalpy operation state of expanded tube wind tunnel, adding alkali metal particles to the driven section to assist ionization can significantly enhance the MHD control effect. Under the action of 0.1% "seed particles", the separation zone is increased, and there is a decrease in the peak heat flux by about 50%, which meets the engineering application requirements. Moreover, there exists a saturation effect in the seeding amount for the MHD control effect.