The launch loop rotor is mostly iron, and can be deflected magnetically. That means powering a small cross-section, large diameter, high field electromagnet at each end. That will consume on the order of 100 megawatts.
Plus a considerable amount of medium-power control electronics, computation, and measurement. <PERSON>'s theorem teaches us that magnetic levitation is unstable, but with environmental and spacing measurement, computational modeling, and medium power control electronics, the rotor can be kept on center. After all, we control the position of the mirrors at LIGO to 23 decimal places. An Nvidia graphics card can do thousands of floating-point multiply-adds in a nanosecond; the rotor moves 14 micrometers in a nanosecond.
Practically speaking, the "perturbation doubling" times are on the order of 100 microseconds, so class-D audio power amplifiers could be used for the control coils.
The Large Hadron Collider at CERN is a more challenging deflection problem, but it builds on decades of development and research. Launch loop will build on smaller scale, lower speed systems used for energy storage. Some Germans are pursuing this; Germany has room for tunnels, but not pumped storage.
A launch loop operating at full capacity can launch about 400 tonnes per hour to escape velocity, at high energy efficiency; that's a kinetic energy production rate of 6 GW. 284
That would cost terawatts if you launched the same tonnage with chemical propulsion. In 2018, with tonnages less than 2000 tonnes per year, such high rates make no sense.
OTOH, if a launch loop was launching 5kg/kW space solar power satellites, it could launch its own power supply in a week. But since we cannot even maintain the electrical grid we have in the US, much less pay for new generation, that won't happen here. If I could write Chinese, you would get a different answer.
There is plenty of information at http://www.launchloop.com, including an out-of-date paper from 2009 that replaces the original 1982 AIAA paper. Check "recent changes" for more; I'm drafting chapters for a book now, and have made some gratifying discoveries recently. As more engineers get involved, the pesky problems (and there are many, many, MANY more) are slowly being replaced by clever solutions.
I'm comfortably retired, and willing to share my almost-clever ideas, but the younger engineers want to earn their own nest-eggs and not support freeloading copycats. So, you won't get all the answers you want unless you contribute to their efforts. Standing back, asking questions you haven't bothered to research, and making claims that you can't support analytically, are amusing, but not contributions. Ah well, if everyone was a contributor, the world's problems would have been solved millenia ago. 284