Here is a working link to Burns' original paper:

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20190029294.pdf
Sorry, but it is garbage.

He accelerates his ions almost sideways but also slightly forwards, pointing out the net forward momentum gain on them after multiple cycles. But he quite forgets that all the while the equal and opposite reaction experienced by the accelerating magnets is not just sideways the other way but also slightly backwards, leading to an equal and opposite momentum change on the engine after those same multiple cycles. Net thrust after recovering the ion momentum at the far end: zero.

Like all these perpetual motion ideas, he buries the obvious in some dark technical corner hidden behind jargon-riddled smoke and mirrors.

I haven't looked that closely, but one effect which can be overlooked by the inexperienced is that at relativistic speeds, the particle rest mass ceases to be relevant. Its momentum is its velocity times its relativistic mass,

*not its rest mass*. For example a force doubling its momentum might increase its velocity by only a few percent but would nearly double its relativistic mass. But it takes the same doubling of momentum, and the same accelerating force x time, as does a non-relativistic doubling of speed for constant mass. You do not get the relativistic mass increase without the accompanying reaction force. It may be that this is why he failed to notice the reaction in his analysis.

The absolutely one and only way to accelerate yourself in a Relativistic inertial reference frame is to exert a force on something external, even if you have to throw it out the back yourself.