Here is a NASA report on Beamed Energy Propulsion.

https://ntrs.nasa.gov/archive/nasa/c...0150010986.pdf

I have a variation on this modality of rocket engine.
While the rocket is first climbing through the lower atmosphere
there will be significant air gas to run a Magnetohydrodynamic
(MHD) engine. The high power beam is focused on the ionization
chamber of the engine. The fuel becomes ionized air.

To drive the MHD magnet there is a simple solar cell electric
system.

As the rocket enters rarefied air level there needs to be
a change to a pressurized gas canister for fuel. Just use
something like CarbonDioxide.

It will obviously be a small rocket mass system, but it will work.