I'm investigating the idea of transporting gigawatts of electrical power to the first stage booster of an electrical rocket.
The first stage booster, like Falcon 9's recoverable first stage, stages at 70km altitude, 60km downrange, for a diagonal distance of 92km.
I'm using 100km for a nice, round figure.
If we use a 1000 Isp electro-thermal rocket to launch a 10 ton payload with 25 ton upper stage and 20 ton lower stage (ignoring engine and fuel tank masses), and assume a TWR of 1.2 at liftoff, we would need 3.17GW of power at liftoff.
How can this level of power be transported over a wire 100km long? Low mass is critical.