Lightning Tunnel
An artificial lightninglike discharge collinear with the nose of the launch sled can drastically reduce heating and drag with a surprisingly low amount of power in the electric arc.
The main launchloop acceleration track is at 80 km equatorial altitude, with sled velocities ranging from 7.5 km/s to 11 km/s tangential to the Earth's surface. According US Standard Atmosphere 1976, the atmosphere at 80 km is cold and about 15 ppm pressure and density. While the real atmosphere is turbulent, frisky, and varies with time of day and weather conditions, for the following simplified analysis we will use these conditions:
altitude, km 
0 
40 
50 
60 
70 
75 
80 
density kg/m³ 
1.2250e+0 
3.9957e3 
1.0269e3 
3.0968e4 
8.2829e5 
3.9921e5 
1.8458e5 
pressure Pa 
10132.5 
287.14 
79.779 
21.958 
5.2209 
2.3881 
1.0524 
temperature K 
288.150 
250.350 
270.650 
247.021 
219.585 
208.399 
198.639 
Number dens. n/m³ 
2.5470e25 
8.3077e22 
2.1351e22 
6.4387e21 
1.7222e21 
8.3003e20 
3.8378e20 
particle speed m/s 
458.94 
427.78 
444.79 
434.93 
400.64 
390.30 
381.05 
Collision freq. Hz 
6.9189e+9 
2.1036e+7 
5.6210e+6 
1.6195e+6 
4.0839e+5 
1.9175e+5 
8.6559e+4 
mean free path m 
6.6332e8 
2.0336e5 
7.9130e5 
2.6239e4 
9.8102e4 
2.0354e3 
4.4022e3 
sound speed m/s 
340.39 
317.19 
329.80 
315.07 
297.06 
289.40 
282.54 
Kinematic viscosity m²/s 
1.460735 
4.0066e3 
1.6591e2 
5.1141e2 
1.7357e1 
3.4465e1 
7.2557e1 
Breakdown voltage proportional to density (or pressure? TBD), 3MV/m at ground level 

Blunt Drag power 2m² 
na 
na 
8 MW 
8 MW 
10 MW 
17 MW 
22 MW 
Breakdown V/m 
3M 
9800 
2500 
760 
200 
100 
45 
Shock energy per meter to accelerate 2 meter radius cylinder of air to mach 3 

Shock energy J/m 
8M 
23K 
6300 
1700 
413 
190 
90 
Vehicle velocity m/s WAG 
na 
na 
2000 
3000 
5000 
7500 
10640 
Shock power Watts 
na 
na 
13 MW 
5.1 MW 
2.1 MW 
1.4 MW 
1.0 MW 
Acceleration 30 m/s², 7000 kg vehicle plus sled, hence acceleration power is velocity times 210KN 

Acceleration power Watts 
na 
na 
420 MW 
630 MW 
1050 MW 
1600 MW 
2200 MW 
I should compute arc voltage and current with Paschen's law  I must estimate arc length, too 

Arc voltage V/m WAG 
1000 






Arc current amp WAG 







Arc mass kg WAG 







I can probably guesstimate the arc voltage from upper atmosphere sprites, though the power density for a lightning tunnel will be much higher.
Lorentz force should push the arc current away from the counter current in the track in order to intercept the nose. This will of course be a function of speed, which is a fixed function of distance along the track. The basic geometry can be baked into the track and the windings, diodes, connections, etc, with some secondorder tweaks to accomodate atmospheric variation.