They propose to burn D-³He fuel, which according to Rider, can yield
energy if burnt in thermal equilibrium
Just barely.
Does the reactor approach of Helion count as maintaining a
thermal-equilibrium reaction ?
Yes. The plasma is thermalized in bulk during the reaction time. The reactions will mostly take place during the brief period of maximum compression. The now-hot(ter) plasma then relaxes against the field for energy recovery.
This is similar to a car's engine, where the reaction is fired somewhere near the top-dead-center and then allowed to expand against the piston (at a much slower rate) for power recovery. If you look at one entire cycle of the engine you would be confused why it is considered thermal, but if you consider just the period of the reaction is clearly is.
Rider's work involving non-thermal plasmas is referring to devices like the fusor, where the ions have a non-thermal distribution and the reactions take place between these particles. These are vanishing in the thermal case.
Two things to note:
The otherwise similar-looking TAE device is a non-thermal FRC system (or at least it was, when proposed).
The Helion design does not aim to have appreciable fusion burn, their proposed levels of fusion are not unlike existing older devices like JET. The entire concept hinges on the power recovery system, which they claim will allow them to produce net energy even operating below Q = 1.
