I've been reading quite a bit about gas-core reactors, a theoretical reactor design where the fissioning of Uranium(along with Plutonium & possibly Thorium)occurs in gas phase. The result is that the heat of the reaction converts the gaseous nuclear fuel into plasma which can be contained in a magnetic bottle. The most feasible design for such a reactor is cylindrical metal reactor vessel with a magnetic solenoid where the electromagnets push inward radially; confining the plasma. I would imagine that such a reactor would need an inner lining of neutron reflecting material to deflect neutrons and bounce them back and forth across the chamber. But do to the chemical properties of Uranium Hexafluoride gas it might be more prudent to use a single, supercritical solid fuel rod assembled vertically inside of a vacuum solenoid. The fuel rod would then be bombarded by intense microwaves from directly above to convert it into plasma after the electromagnets are turned on. But the question remains if it is even possible to compress the plasma to a high enough density to initiate fission. Has this experiment ever been tried? If so, what were the results?
Yes, there were experiments both in USA and USSR, but as far as I know all actual criticality experiments used only 'cold' UF$_6$ gas, not plasma ( not venturing even close to thousand degrees K so no MHD stuff / first wall thermal load testing was done).
Let me present a report 'Spherical Gas Core Reactor Critical Experiment' that was conducted at ~1969-1971 with NASA sponsorship at National Reactor Testing Station in Idaho.
Summary of results:
Obviously, by varying wall moderator/reflector material, mixing in moderator (CF, He) in the gas phase the critical mass could be reduced somewhat, lowering enrichment degree will increase critical mass, but at least this should give an idea.
Raising temperature while keeping density constant should keep critical mass more or less constant (the effects of neutron thermalization at different T shouldn't change it much), but of course it will greatly increase the pressure.
So yes, from the neutronics point of view there is no obstacles for this type of reactor, and all comes down to confining hot gas / plasma and keeping it from melting containment vessel.
As for the magnetic confinement of such plasma I would like to note that at pressures around 100 bar and temperatures around 5000 K the degree of ionization of UF$_x$ gas is far from 100 %. For instance the paper 'Use of thermochemical modelling for the analysis of energy extraction in a gas-core fission reactor' lists 6% for 7000 K @ 100 bar. This means that magnetically confined plasma would 'leak' neutral molecules which would still inflict pressure on/ exchange heat with the containment vessel.