The charged sheath vortex:

The charge sheath vortex develops within a large spinning charge cloud where the repulsion between the charges is cancelled out, two stationary particles of the same electrical charge will repel each other, BUT two particles of the same electrical charge moving in parallel will develop a force of attraction.

 When we put these basic physical laws together we can predict a simple physical structure called the charged sheath vortex.
Imagine a thick walled cylinder spinning at high speed. The thick wall is a sheath of charged particles, all with the same charge. They are surrounded by a cloud of particles of similar charge, so there is no net force of repulsion between the particles. Because they are all moving rapidly they each produce an electromagnetic field that attracts the similar charged particles moving alongside. Any similar charged particle moving in parallel outside the cylinder wall is swept into the wall, and none can escape, provided the speed of rotation is maintained.
On the inside of the wall, the charge particles are attracted by the particles in the wall outside them, but repelled by the forces generated by the opposite wall, moving in the opposite direction. The centre of the charged sheath is therefore swept clear of the same charged particles. Because of the powerful dynamic nature and strong forces balanced in creating the charged sheath, the sheath develops almost parallel sides and a uniformly thick sheath, with a distinct central tube.

The charge sheath vortex is self confining – and the faster it spins, the more powerfully the particles are squeezed together.
There are several important differences between the forces created by the movement of electrons in a wire and the movement of electrons through mass flow of charged particles.
Electrons within a conductor are constrained to move within the conductor, but similar charged particles within a mass flow may move within the mass flow and cause movement of the body of mass flow within a surrounding uncharged region.
If we start with a smooth straight flow of similar charged particles, any slight turbulence can curve the flow and produce more intense magnetic fields on the inside of the curve. This results in positive feedback which will reinforce the curvature.
Unless the mass flow is strong enough to overcome these forces, any turbulent swirling mass flow of similar charged particles will tend to generate a coherent circular motion within the mass flow where the radius of curvature of the flow will be determined by the relative movement of the flow and the strength of the charge in the flow. Without any mass flow individual charged particles will tend to gyrate round the magnetic field lines.
Electrons within a conductor arranged as a helix to form a solenoid are constrained to follow the path of the conducting wire, but similar charged particles within a circular mass flow can move in response to the forces acting on them.
If we examine the effects of the standard electrical laws above, and consider what happens when charge particles are able to move within the circular mass flow.
The moving charged particles experience forces that attract them together, as well as forces that pull them more tightly into the curvature of the circular flow.
Together these forces act to pull a rotating mass of similar charged particles into a much tighter shell of circular flow.
The purely mechanical consideration of the conservation of rotational energy means that the rotational energy of the whole mass flow in a circular motion must be conserved.
Therefore as charged particles move within the rotating mass flow, they are drawn in towards the rotating shell, but in order to conserve angular momentum they must speed up. Think of the ice skater spinning, speeding up as she draws in her arms to her body.
The forces of attraction between the particles must increase as they speed up and the forces between the charged particles increase dramatically as the distances get smaller.
The forces created by an electrical current in a wire are produced in proportion to the speed of electrons through a wire. Because of collisions and random movements of electrons in the wire, the overall speed of the electrons, or drift speed is quite slow. (but the density is high). A 1 volt potential in a pure copper wire will produce a drift speed of 0.0043m/s This is less than half a centimetre in a second.
By contrast air flow in a tornado can exceed 1000 m/s.
The forces between moving electrons in a mass flow may be thousands of times greater than the forces between electrons in a wire. A mass charge flow is much more similar to a superconductor than copper wire.

The following important deductions are made from this discussion:
1 That any mass flow of similar charged particles will tend to produce circular eddies. Because of the reinforcing effect of attraction between the charged particles increasing as they speed up, and as the particles get closer together, turbulent circular motion of similar charged particles will tend to produce coherent circular motion of charged particles.
2. A large mass of similar charged particles rotating at low speed which is free to move will transform into a tube, or shell of rotation of similar charged particles rotating at high speed.
3. There is a maximum density gradient of charged particles possible in still air, above which the charge will discharge as a stream of electrons. (Lightning in air). All the forces described are acting directly on electrons, and indirectly on the particles to which they are attached. Within the rotating shell of deduction 2 above, the electrons are attracted strongly into the rotating shell, where the charge density gradient can greatly exceed the normal charge breakdown values of still air.
So this is the theory I applied to the tornado.

As well as analysing video of real tornados, we set out to recreate the tornado vortex in the lab. We were somewhat bemused to find how easy it was to create a charge sheath vortex in a cloud of salt dust!  Simply applying a large charge to the top and bottom of a container with a little salt dust resulted in a vortex developing. The electrical discharge seems to wrap round the vortex rather than discharging through it.

Miniature Whirlwinds Produced in the Laboratory by High-Voltage Electrical D...

Ryan and Vonnegut
Science 12 June 1970: 1349-1351
DOI: 10.1126/science.168.3937.1349
In experiments with electrostatic discharge from the surface of a CRT i've seen several types of vortices. There is good reason to consider these all these results to be scalable. A particular note of interest in natures tornados is the low hung clouds as a breakdown point approaches. 

Images from my experiments can be seen at  select backyard experimenter or larger images links.

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