Design, modification and test of the conduction cooled high-current current leads for the superconducting magnet

•Conduction cooled current leads are used in a 2.1K, 31mbar cryogenic system.•Comsol multiphysics are used for temperature profiles and heat load simulation.•Impregnated epoxy improved the heat conductivity, increase mass density.•A horizontal cryogenic test stand verifies the simulation results.