So we have an RL DC circuit. If the inductor L1 has a high core permeability, there will be a high inductance and thus a long L/R time constant. So the circuit takes a long time to charge. Would putting a second inductor L2 in parallel with L1 help reduce this time constant at all, if L2 has a much lower core permeability (but is otherwise the same as L1)? If not, is there another way to reduce it other than decreasing L1 or increasing R?
Schematic below. Dotted lines to indicate L2 being added to the circuit.