Finally I checked what other Sapiens do already to transport electricity over continents
Very long powerful lines exist, they use DC, but with bare conductors at really tall towers. 12GW at ±1100kV over 3000km between Changji and Guquan hvdcnewschina.blogspot.com
almost what continental Europe needs to distribute windpower, except the vulnerability and aspect of the aerial line.
Most isolated lines are underwater. 2250MW at ±600kV over 422km between Hunterston and Wirral for 1.2Ggbp (1.46G€) assosubsea.com
The UK has links with many neighbours. 1400MW at ±515kV over 720km between Cambois and Kvilldal for 2G€ wikiwand.com
about the same with Denmark and next with Germany for 1.9G€ nsenergybusiness.com
Few HV lines are buried in continents. "Corridor A" will transport 2GW at ±525kV in Germany, comprising 300km "Corridor A-Nord" for 1G€ and 340km "Ultranet" nsenergybusiness.com
The usual dielectric is XLPE, cross-linked polyethylene. 1GW cables can make coils <3m wide. The central conductor is often multi-strand copper. The return current uses generally a separate cable, not the sheath, and generally at high voltage.
==========Can buried isolated cables of this technology transport 50GW over 2000km land?
According to the appended scaling factors, from 2250MW over 422km to 50GW over 2000km, identical radii need 105× as many cables, 499× as much conductor and insulator volume, and if it were proportional, 1.46G€ would extrapolate to 729G€. Even if the amount reduces the price by 40%, 437G€ are twice the cost of the wind turbines that produce the electricity, excluded. Or else if keeping two cables, with radii and voltage ×3.2 (that's ±1.9MV!), the volumes increase ×49 and a proportional price reaches 71G€, or much less
because the production cost doesn't increase like the cross area.
Cooling is a limit to flexible cables with plastic insulation (formula appended). Take a dissipation 30MW/300km = Q/L = 100W/m and R/r=2 in XLPE insulator, the drop is 29K there. In the soil, taking R≈1.5m r=0.1m, the drop is 108K if dry, 18K if wet, so favourable conditions leave little margin. Now if dissipating 1GW over 2000km = 500W/m, the insulator fails
. The design can be tweaked, uneasily.
An algebraic solution exists for the wave impedance, hence the lineic capacitance, of a round conductor over a ground plane. Adapting it to heat conduction would give a better formula than "taking R≈1.5m". Detail, I won't do it.