There is no bibliography, but similar ideas are described in:
Lawrence Livermore National Laboratory has been studying the transverse gas guns for a few years and tried to build a spiral gas gun accelerating 1 gram projectiles to 15 km/s. Ray Finucane supervised the project.
Hydrogen gas flows in two dimensions. Precise timing of the gate valves is critical; a 10-meter long glider calls for 1 millisecond tolerance. The need for a large number of precisely timed gate valves is the only fault of the spiral gas gun.
The vortex gun can be called an improved spiral gas gun. The main advantage of the vortex gun is fewer gate valves releasing the hydrogen gas. Fins located inside the gun force a helical flow of the gas. Interaction between five rows of short wings secured to the sabot and the helical flow of the gas, propels and stabilizes the sabot.
The passage of the projectile compresses the hydrogen gas and momentarily heats it up to 660 K, thus raising the speed of sound in the hydrogen to 2 km/s. Some of the drag produced by the nose cone is offset by the forward thrust produced by the tail cone.
The two identical parts of the projectile are joined together by a streamlined crossbar which houses telescoping tubes. A spring twists the two parts slightly when the projectile leaves the gun. The aerodynamic forces produce a torque spinning the projectile about its center of mass. Outside the atmosphere the centrifugal force twists the parts to a position that releases the telescoping tubes, extends the crossbar, and changes the moment of inertia enough to stabilize an apogee rocket motor mounted inside the projectile. See details in umbrella projectile.
To reduce drag, the helical fins may be replaced with pivoting blades.
High performance applications utilize pure hydrogen compressed by the two stage light gas gun and offset injector proposed by Andrew J. Higgins.
Andrew Nowicki proposed a sabot with six rows of wings. Andrew J. Higgins likes this idea because the vortex can pump gas away from the central tube, provided that the slits in the tube are narrow. Unfortunately, it is impossible to avoid physical contact between the narrow slits and the wings.
It is possible to combine the powder vortex ram accelerator with the vortex gun. The contraption is called vortex accelerator. Its simplicity makes it the cheapest member of the vortex gun family. A mixture of hydrogen and a fine powder of ammonium nitrate is pumped through the accelerator. Helical ribbons produce vortex flow of the mixture and prevent premature detonation. The vortex generates centrifugal force which keeps most of the powder away from the center of the accelerator. A thin, hot boundary layer forms on the nose cone of the projectile and its wings. Powder in the center of the tube burns in the boundary layer before impinging on the nose cone. Density of the mixture is lower in the center of the tube, so the aerodynamic forces may be strong enough to keep the projectile away from the walls of the tube. To prevent fast rotation of the projectile, the vortex alternates between clockwise and counterclockwise direction. The projectile compresses the mixture to the point of ignition and is propelled by vortex flow of the burning mixture. Several rows of flexible wings are attached to the projectile. They are feathered unless gas pressure deflects them.
Military application of this contraption must be short, so it must utilize dense mixture of hydrogen, powdered fuel, and powdered oxidizer.
The ability to store energy in the gas vortex enables the gun to compete against the orbital coilgun. A glider loaded with cargo enters the gun and generates vortex flow. The energy of the vortex is then used to fire empty glider back to the Earth.