An inductively coupled plasma torch could operate at atmospheric pressure without consumables. An initial seed plasma is provided by a glow discharge, a short-lived conventional arc, or (if we permit consumables) a conventional oxidation flame; then it is advected into the center of an induction coil, where inductively-coupled power transfer brings it to a high temperature and propagates it opposite from the advection direction to sustain it in a constant position. In addition to conventional water cooling, the coil can be separated from the plasma by low-permittivity, non-ferrimagnetic, insulating refractory ceramics; for example, magnesia, lime, silicon nitride, alumina, urania, thoria, or boron nitride; the ceramic itself might be actively cooled as well. (Refractories unusable due to high conductivity include graphite, amorphous carbon, silicon carbide, tantalum carbide, zirconia, and the diborides and nitrides of hafnium, titanium, and zirconium; and silica is probably too low-melting, although fused quartz does have an attractively low TCE.)
The electrodeless plasma thruster article suggests further possible ways to initiate plasma formation, including electron guns and laser ionization, and I suppose in theory a sufficiently powerful ultrasound wave converging on a point ought to heat it enough to produce plasma too, as in sonoluminescence, but doing that without a liquid seems like it would be hard.
The problem remains of how to limit the damage to the ceramic walls from the plasma, since plasma-ceramic contact would surely ablate the surface fairly rapidly; under uniform conditions the outer plasma will tend to shield the inner plasma from receiving inductively-coupled energy, so the natural tendency is for the plasma zone to grow. Even under adverse applied magnetic field conditions, by establishing a gas-flow profile within the induction ring in which the flow near the walls is much faster than the flow in the center, it should be possible to adjust the induction power so that the plasma is self-sustaining only in the center, while being blown away faster than it can form around the outside. (Of course, if the plasma were to reach the ceramic wall it would also be self-sustaining there, since in contact with the wall it would be stationary, but the plan is to avoid this.)
It might be possible to manipulate the magnetic field conditions instead of the gas flow conditions to keep the plasma away from the walls, for example by making the induction coil smaller than, and axially displaced from, the ceramic aperture. I think this would imply that the field would get stronger axially into the torch body, creating a strong tendency for the plasma to propagate into unprotected areas of the torch, but this could be countered by a stronger negative advection divergence: all the gas closer to the induction coil would be moving too quickly for the plasma to spread into it. I’m not sure if this is feasible.
In this scenario there is still radiative transfer of heat from the plasma to the ceramic walls, but this can easily be kept low enough to avoid wear to the ceramic. If an arc between conventional graphite electrodes is used to initially ignite the plasma, the electrodes will erode somewhat, but if we’re talking about one spark every 20 minutes of use or something like that, it should be easy to make the electrodes big enough to last the life of the rest of the torch.
Such a plasma is of course easier to sustain in gases like argon or at lower pressures, but air plasma has the great advantage of not requiring any consumables, just an air compressor.
Probably the frequency required to efficiently couple into the plasma would be on the order of a megahertz for human-hand-tool-sized torches, hundreds of kilohertz for larger torches, and several megahertz for smaller ones.
The torch might require active electronic control at submillisecond timescales to stabilize the plasma and keep it from either blowing out or flashing back. Both the complex impedance of the induction coil and the blackbody radiative flux from the hot plasma could provide crucial feedback information.
Operating such a torch in a pulsed mode might be feasible and simplify the process further: the induced current in the plasma tends to Z-pinch it into a toroidal plasmoid while repelling it from the induction coils, and hence from the torch. Sakharov reportedly took this to the logical extreme by vaporizing a small aluminum ring with eddy currents into a self-contained plasmoid traveling at 100 km/s, powered by an EPFCG.