Injector Rings for Medium Speed Bolt-style Rotors
( Note: the following is a first pass at some math. It is not optimized, perhaps not particularly accurate )
One of the challenges of dynamic structure towers is that the rotor changes length significantly during deployment. A 5600 km launch loop rotor gets longer by 34 km or 0.6% as the launch track rises to 80km. This is easily handled by rotor sections with reversing-pitch screw joints between meter-long sections, providing a continuous low-loss magnetic path. The rotor in a dynamic structure tower with 45 degree legs grows by 40%. This cannot be done with sliding sections, so Space-cable-style separated bolts should be used, at the cost of some drag and eddy current losses. It would be helpful to add sections to the rotor as it rises and grows in length.
We can use high speed robots on a long straight track to add (or repair) sections of launch loop rotor, see RotorRepair. Bolts do not need this complexity, and we do not have the long straight run in a dynamic structure where a repair robot can add them. Instead, we can use a shorter straight section on the surface where we can create a gap and add bolts from an injector ring.
Assume that a stream of 5 meter, 20 kg bolts move at 1200 m/s and are spaced by 40% of their length on a long run on the ground. The center to center spacing is 140% or 7 meters. Assume we are adding 0.5% more bolts to the stream, and reducing the spacing between then to 39.3%, and changing the center to center spacing to 6.97 meters. Thus, a "platoon" of 200 bolts becomes 201 bolts. We need to create a 6.97 meter gap, by slowing down the bolts at the head of the platoon and speeding up the bolts at the tail, then returning them to 1200 meters per second after creating a gap.
We are moving the head bolts back by 3.48 meters, and the tail bolts forward by 3.48 meters. If we do this in 1.167 seconds, the time it takes for a platoon to travel its length, then the acceleration for the lead and tail bolts is a = 4 \Delta L / t^2 = 10.2 m/s2, the peak velocity change is v = 2 \Delta L / t = 5.94 m/s , and the power (for the end bolts) is P = M a V_r = 245 kW . We will be subtracting power from 100 bolts, adding to 100 bolts, with the average bolt getting half the acceleration and power of the end bolts. So the total power flow per platoon ( front to back to get the bolts bunching, back to front to restore speed ) is 50*245 kW or 6.1 MW. We will be doing this over 1400 meters. The peak power handling of the track electronics is 245kW/5 meters, or 49kW per meter. 1400 meters of such electronics, and a 50% energy handling efficiency (some energy is going into building magnetic fields, not efficiently transferred to bolts), results in 137 MW of electronics, or about \$14M worth of power handling electronics at \$0.10 per peak watt.
Mass Drivers - not!
We are adding a new bolt every 700/1200 or 0.583 seconds. Accelerating a 20kg bolt to 1200 meters per second requires 14.4 MJ per bolt, or 24.7 MW of power for the stream of new bolts. If we tried to do this with a coil gun mass driver with a field switching length L_V of 10 meter ( and assuming a hypothetical "magnetic sabot", weighing 10kg, to create a higher field gradient ) then the accelerator power will be on the order of M V^3 / L_V or 30kg * (1200m/s)3 / 10M or 5.2 GW . That would be $520 M worth of power handling electronics.
Instead, let's plagiarize the smart high energy physicists who design particle accelerator rings. The folks at CERN do not darken Europe to make a burst of particles to inject into the main ring. They inject the particles from a relatively slow linear accelerator into a medium-sized circulating accelerator called an injection ring, where they are slowly brought up to speed to be injected into the main ring for further acceleration. This multistep process makes sure that each system in the chain is operated at high efficiency and high throughput, maximizing CERN's productivity (that is, a few $1.6M Nobel prizes per decade, CERN is not a cash cow, though they produce dandy music videos ).
Assume a pair of 200 meter diameter injector rings (A and B), each with a 15 MW (average power) circular linear motor, and each ring capable of holding 100 bolts. The rings are fed by ten 3MW (peak electronic power) mass drivers, short and slow versions of the mass driver (with magic sabots) already described. Each mass driver emits a stream of 20 bolts at 100 meters per second into ring A, perhaps 1 bolt per second from each (the mechanisms probably cannot feed them faster), for an average wall plug power rate of 15MW. Ring A fills in 10 seconds with 100 each 100 m/s 20kg bolts. We now feed the injector ring motor with 15MW, and accelerate the 100 bolts as a group to 1200 m/s in 96 seconds.
The circulating linear motors are more efficient because their power electronics are operated more smoothly and continuously, not in pulse mode, and each bolt makes 122 passes around the ring before it is injected, increasing the productivity of each section of motor. The motor electronics are not optimal; as the ring velocity changes from 100m/s to 1200m/s, the power to current ratio will change as well. Assume \$0.50 per watt for these non-optimal motors, or \$15M for both injector motors.
With the bolts up to speed, and circulating at 0.523 seconds per rotation, we start deflecting bolts one at a time ( 1 out of every 223, this should be relatively prime with the platoon size) into the platoon gaps in the main path, while ring B is loaded from the same mass drivers and brought up to speed. We alternate between injection rings to maintain a steady supply of bolts.
We can probably stack the injection rings under an ambit, as well as another load-leveling power storage ring so we do not stress the electric power plants with varying loads.
If we have 600 km of bolts in a 50 km dynamic structure tower system (the bolts at altitude more closely spaced, the average spacing is perhaps 6.5 meters and the average speed is perhaps 1100 m/s) then we can grow the total length by 1% every 20 minutes, and the extra density of bolts at altitude as well, deploying the tower in about 20 hours. This assumes we can build incline between deflectors and platform at about 1 meter/second, as we pull the upwards deflectors back from the center and towards the ambits. If 1 m/s is too fast, we can slow down our injection rate, lengthen our platoons, and reduce the power and cost of the injector rings.