Parameters for Vortex Formation - Charge Sheath and Ball Lightning

Vortex formation is controlled by a number of factors - which makes the process difficult to simulate!
The process is determined by the velocity and path of  individual electrons. Any calculation based on bulk charge or current  flow will not provide useful results.

The particle species involved in the process are:

• molecules with neutral charge
• ionised molecules
• neutral molecules forming dipoles in response to an external electric charge field
• extra electrons attached to otherwise neutral molecules.
• free electrons.

• neutral molecules form dipoles that are attracted to the negative charge. Electrons attach to neutral molecules, which are then repelled from the origin, and from each other. (Faraday wind).
• electrons ejected from charge source, move as free electrons before attaching to neutral molecules, repelled from each other.
• electrons ejected from charge source with greater energy, collide with other molecules but continue as free electrons for some distance before attaching to neutral molecules. The region of free electrons may appear as a glowing sheet under blackout conditions. Electromagnetic attraction and electrostatic repulsion may be in balance. 
• electrons ejected with sufficient velocity for electromagnetic attraction to be greater than electrostatic repulsion. These electrons pinch into a lightning discharge.
• quasi-neutral electron flow. This is similar to the electron flow in a wire, where a population of electrons is moving through the plasma or gas cloud, but the cloud itself is close to neutral
  

•  the magnetic field produced by the velocity of the free electrons and the mean free path between collisions with other particles.(Collisions here is taken to be the events that make a significant change to the velocity or direction of the electron).
• the charge of surrounding particles.
• the magnetic field through which the electron is moving.
  

• a charged particle will move directly away from a similar high charge towards a region of lower charge.
  
• a charged particle will be repelled by any similar charge - at rest, this is the dominant force.
• a moving electron produces a circular electromagnetic field round the direction of movement. 
• any charged particle moving through an external magnetic field will experience a force ( but not along a magnetic field)
  
• charge in a neutral molecule can form a dipole that will be attracted to another charge.
• in a charge field, neutral dipoles can be attracted to each other.
• in a quasi-neutral flow, the moving electrons produce electromagnetic fields that attract other electrons in the moving flow, but there is no overall electrostatic repulsion initially in the cloud. As the moving electrons try and move closer, then the electrostatic forces will keep them apart.

1. A group of electrons moving through a gas cloud or plasma will produce electromagnetic fields that mutually attract each other. They also have the same electrostatic charge that repel each other.
2. If the velocity of the free electrons is low, or only a small proportion of the non-neutral electrons is a free electron at any one time, then the electromagnetic attraction will be small compared to the electrostatic repulsion, and the electrons will follow paths that are held apart by these forces.
3. As the velocity of the free electrons increases, and the time spent as a free electron also increases, then the balance of electromagnetic attraction and electrostatic repulsion will ensure that the electrons follow closer paths through the gas or plasma.
4.  If the velocity of the free electrons between collisions is sufficiently high, and the proportion of electrons in the non-neutral population of electrons that is moving as a free electron at any one time, is also sufficiently high, then the electromagnetic forces of attraction will be greater than the electrostatic repulsion, and the electrons will follow paths that are much closer together - they will pinch. Such pinching can also accelerate the electrons and intensify the electromagnetic fields that cause attraction, so once initiated it is self stable until the source of electrons is removed.
5. Along the direction of electron flow, there is no electromagnetic attraction, but the electrostatic repulsion remains at full strength. Electrons cannot accumulate - they must keep moving. However, adjacent strands of flow will attract.
   

• The electromagnetic field will intensify and the electron will experience an electromagnetic force that will turn it further into the kink.
• The electrostatic field that is driving the electron from left to right will continue to drive these electrons- and will oppose the kinking. ( This is what we see in a normal lightning type discharge where vortices are rare.)
• Should the electromagnetic forces produced as the kink starts to form be sufficient to overcome the electrostatic field, and maintain the kink, then the kink can start to develop into a helix, as adjacent strands attract each other. This will decrease the voltage difference between the high voltage source and the kink, and increase the voltage difference between the kink and the low voltage sink to the right. This kinking will still be opposed  by the electrostatic forces between the electrons in adjacent loops, which increase as these loops get closer together. (The voltage differences may result in the kink formation moving rapidly towards the source and straightening of the kink on the side of the sink.)
• In a quasi-neutral electron flow, because each strand is electrostatically closer to neutral for the same electron current, there will not be the same electrostatic repulsion between adjacent strands, and a vortex forms much more readily.
  

• An externally applied magnetic field should only be considered in relation to the path of a single electron.
• The external field should be designed to combine with the fields of all the electrons in a vortex to force a single electron to follow the desired path round the vortex.

1. In a charge cloud, each non-neutral electron ( electrons not matched by a proton) experiences a force that repels it from the region of the same charge and attracts it to a region of lower charge, or of the opposite charge.
2. When the field strength is sufficient to start some electrons moving as free electrons down this electric charge gradient, collisions with other charged molecules can knock further non-neutral electrons free and produce a cascade of free electrons travelling in roughly parallel directions down the charge gradient.
3. As these free electrons accelerate in the charge field, they produce electromagnetic fields that attract them together. Provided that the voltage gradient is sufficiently high, these free electrons experience stronger attractions as they move closer together and pinch into a narrow lightning discharge. Collisions in this discharge path heat up neutral molecules which glow brightly.
4. This discharge path is highly negatively charged and attracts two species of charged particle from the surrounding air. Positive ions are drawn towards the discharge path and neutral molecules form dipoles that are also attracted strongly towards the discharge path. The result is a violent pressure wave moving inwards and compressing the discharge path. This also increases the heating effect on the discharge path and the cylinder of air immediately surrounding it.
5. As soon as the initial electron discharge has passed, the highly positive charge of the pressure wave now also very hot, expands back outwards and propagates as the loud sound waves that we hear.

1. Maximise the number of free electrons
2. Maximise the velocity and free paths of electrons
3. Constrain free electrons to follow the desired vortex path
4. Minimize the electric charge gradient accross the vortex

• Add extra molecule species to the air in the chamber that readily provide an extra source of free electrons 
• I have considered that mercury vapour may provide these conditions.

• Initialise vortex formation by physical means - this will also initialise the magnetic field.
• I have considered the tubular rail gun would meet this requirement.
• a problem with using external magnetic fields is that the equipment also creates an electron sink.
• an alternative is to create a 'smoke ring' type vortex, and for the vortex to brush the surface of a charged van-de-Graf dome.
  

• Use a very high voltage discharge into the initialised vortex to maximise free electrons
• (into it rather than through it - keep the electrons in the vortex)

• Separate the electron source from the vortex as quickly as possible

• Keep all electrostatic earth points as far as possible from the vortex formation zone
• Use a room lined with polythene sheet that removes all 'points' that encourage the vortex to discharge.
• make sure there are no discharge points on the apparatus that creates the vortex.