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The 2017 proposal is here: https://web.archive.org/web/20171017043638/https://www.elisa... This information-dense PDF got lost in the shuffle and its contents smeared across a hundred slides on the LISA website, because I guess PR people think only cell phone users exist.

Yes, solar. Laser power is only 5 watts. Total spacecraft power is 760 watts. They're downlinking a mere 334 megabytes a day, sampling at 3.3Hz.

how can the test masses remain in free fall, while each satellite is undergoing course corrections?

That's the hard part. The test mass floats in the middle of the spacecraft, which maneuvers around it, occasionally firing ultra low-impulse cold gas thrusters to counteract drag. They put up a spacecraft back in 2015 to test that concept: https://en.wikipedia.org/wiki/LISA_Pathfinder

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