Yes
There are several devices in existence that work based on similar principles as yours (with one or two adjustments). While they're used for plasma research, rather than weapons, they could presumably be adapted for your purposes. If you were to make a plasma cannon from scratch, you should probably model it at least in part after one of them.
The major issue remaining is containing the plasma once it leaves the barrel of the weapon; before then, it can be contained by magnetic fields applied by the weapon itself. After that, though, the plasma should expand in the atmosphere, where there's no significant residual field. The solution that seems to have been considered (at least by the US Air Force) is to simple rapidly increase the speed of the ejected plasma so that even if it dissipates quickly, it will still have traveled a significant distance.
The plasma gun down the hall from me
My physics department has the SSX lab, a group that studies how plasma structures called spheromaks form and evolve. Here's an image of the main part of their apparatus, the "gadget":
Image credit: Michael Brown/Swarthmore College.
The SSX group is interested in studying how magnetic reconnection in plasma works, and how particular structures (called Taylor states) form and evolve. They, too, have a plasma cannon of sorts, called a magnetized coaxial plasma gun, which works as follows:
- Hydrogen gas is "puffed" into a chamber (shown above in orange), which has to be extremely clean and must be at very low pressures - about one billionth the pressure at sea level on Earth.
- A pair of powerful capacitors (one of which is in the image above, in green) are brought to voltages of 5-10 kilovolts each; this is what's needed to ionize the gas.
- An electric current forms in the chamber and in the plasma itself; by interacting with magnetic fields, a Lorentz force arises and accelerates the plasma down the chamber of the gun. This is the major difference between their design and yours; pressure alone cannot bring plasma to these speeds.
After this, other parts of the assembly create the precise plasma structures the SSX lab is trying to form, but those are irrelevant for your purposes. The important things we can learn from the above mechanisms are:
- You can indeed turn normal (hydrogen) gas into plasma if you have strong enough capacitors, as you're trying to do.
- Magnetic fields and electric currents are needed to accelerate the plasma to high speeds (about 40 km/s).
- Instabilities can arise from impurities in the cannon or the chamber, as can leaks that let air in; because of this, the device needs to be regularly cleaned (with helium, I believe). This, I think, is the biggest issue with a portable plasma cannon; if you want to have an opening for the plasma to exit, you have to worry about stuff from outside coming inside.
- Magnetic fields are also needed to confine the plasma; in their absence (i.e. in your case, after the plasma exits the gun), the plasma would expand and become diffuse, making it a less effective projectile.
The whole assembly also fits in a normal-sized room (well, a pretty crowded and messy room), and should be transportable by a reasonably large vehicle.
MARAUDER
The main issue that would arise from just converting the SSX gadget to a weapon lies in confining the plasma after it leaves the barrel of your cannon. Inside, the hot plasma is confined by magnetic fields in a strong vacuum; outside, you have no magnetic fields (aside from ones arising from the plasma itself) and plenty of sources of turbulence in the atmosphere. This presents a problem, because it seems like it would be very easy for bursts of plasma to diffuse and lose compactness.
This problem might have been solved, though, back in the 1990s, with the start of MARAUDER, a US Air Force project. Its device worked similarly to the SSX lab's machine, with two key differences:
- Plasma acceleration happened via a slightly different design (a conducting probe inside the plasma, it seems).
- The device was explicitly meant to be adaptable as a weapon, rather than a pure research experiment.
After MARAUDER was classified in 1993, however, information about its development became unavailable. It was successful up to that point, and I assume they solved the problem of keeping the plasma projectile together (perhaps simply by shooting it at such high speeds - 3000 to 10000 km/s!).
Given that, I think your plasma cannon could work. Even if the plasma dissipates over some characteristic timescales $\tau\simeq1\text{ ms}$ (this is an enormous guess), in that millisecond, it will have traveled 3-10 km. That's not insignificant. - and if $\tau$ is even less than that, well, you've still got a range of probably several hundred meters. Plus, you don't need to have phenomenal accuracy, as the electromagnetic pulse from when the plasma hits something should do a good job of knocking out electronics in the enemy's vicinity.
At any rate, it appears that the Air Force considered the problem solved, considering that development went on for quite some time even before classified development began.
. . . Just please don't take ours. We still need it.