Initial Track Accelerator
Most of the velocity transformer track, from 17 km to 1900 km, will use pitch-ratioed windings to match sled magnets to the motor rotor core. However, over the first 17 km ( to 1000m/s ), the pitch ratios will be larger than 12.5, and suboptimal, the exciter/de-exciter ratios in particular. The velocity transformer method will be modified for pitch management in the latter part of this region, and the "zeroth" portion of the track, up to 100 m/s or so, will use an electrically-switched coil gun for initial acceleration and release testing.
Zero Track - Coil Gun Accelerator
The Zero Track will use electronically switched drive coils to push the payload and briefly test the payload release from the rotor. The sled and payload acceleration will ramp from 0 to 30 m/s² (3.06 gees) over three seconds, a "jerk" of 10 m/s³. The velocity at three seconds will be 45 m/s, 45 meters down the zero track. Then the fun part - the sled will be abruptly decelerated from 3 gees to 0 gees over 3 seconds, then an additional 80 milliseconds of negative jerk, resulting in a negative sled acceleration of 0.8 m/s². Sled jerk switches back to positive 10 m/s³ and sled acceleration resumes in another 80 milliseconds. This drops the sled behind the vehicle by 1 centimeter, mimicking the first centimeter of payload release at the end of the track, perhaps 6 minutes later.
This tests the release mechanism; if it isn't working properly, and doesn't reseat properly when acceleration resumes, something is wrong and launch is aborted. If anything jars loose in the vehicle, launch is also aborted. Abort is discussed below.
This test occurs at T+06 seconds, at a velocity of 90 m/s, 270 meters down the track. Acceleration ramps up to to a full 30 m/s² (at T+09.16) seconds for the remainder of the launch. At T+10, the end of the zero track, the sled/vehicle velocity is 160 m/s, and the elapsed distance is 726 meters. If the sled and vehicle acceleration force is 200kN, the acceleration power peaks at 32 MW. If the exciter and the de-exciter are each 5 meters long (which the coil gun does not use), the thrust section of the sled is 40 meters and the thrust power supplied by the track is 800 kW/meter. The entire zero track will need perhaps 1.7 GW of switching devices, active for a fraction of a second; presumably drawing power from the rotor and rectifying it. This may be reduced with a faster start/stop jerk, or lower peak acceleration.
An abort begins at T+06 seconds, and is the reverse of acceleration, ending at T+12 seconds, 540 meters down the track. 27 MN of kinetic energy is dissipated into resistors. The vehicle is switched aside, and slides back to a pressurized silo for emergency crew extraction, and vehicle/sled return to the surface for diagnostics and repair.
Remaining First Track
Between T+10 and T+38, the vehicle accelerates from 160 m/s to 1000 m/s: v = 30 t - 140 (m/s), and d = 15 t² - 140 t + 626 (m). At T+38, the vehicle has travelled approximately 17 km.
A direct velocity transformation between the 12.5 km/s rotor and a 160 m/s 10cm wavelength vehicle requires a transformation ratio of nearly 80 to 8 meters; that is only 5 wavelengths in 40 meters of rotor. That will not provide enough acceleration power, nor will it allow enough space for the exciter to preload the rotor plenum with high magnetic flux. However, over this stretch of first track, we can add extra weight to the path, and spread the vehicle flux and exciter flux over a much longer distance along the rotor, perhaps 1000 meters rather than 40 meters for the thrust motor section driving the rotor.
MoreLater - I must convert this from wild handwaving to a defensible design.