Concerning the arcing quaestion
-Arc discharge in a gas is governed by a complex relationship between pressure , voltage and separation distance between electrodes. My basic understanding is that a gas- due to partial to nearly full ionization to a plasma, will become a conductor. At high pressures- near atmospheric, it takes a lot of voltage to generate enough plasma, that is free mobile charge carriers, to allow for significant current flow. This would often be called an arc. Best examples may be lightning, or static shocks delivered to your friend. The gas composition also plays a role. Coronal discharge and arcing both play a role. The Van Degraf (sp?) generator is another example. As voltage deepens the voltage needed to 'arc' decreases. Once the arc or conduction path is established, the current flow is dependent mostly on the density/ pressure of the ionized gas. Th current can become impressive if there are enough charge carriers. Again, lightning is a good example of this. As the pressure falls further, the number of free mobile charge carriers decrease and the resultant current decreases, even as the voltage necessary to initiate the arc decreases. There is a point though where the voltage trend reverses. This probably is due to a handful of considerations like Debye shielding, aviable charge carriers, etc. At pressures of around 0-10 Microns, the necessary voltage necessary to initiate and sustain a conductive plasma reverses and increases in an exponential fashion. The voltage you can maintain is such a system is dependent on the density (and type) of gas pressent. At high pressures, the voltage necessary to jump a gap is considerable. Once the gap is bridged though, the amount of ionization, up to the limit of 100 % ionization of a given density of gas, determines the amount of current flowing through the system- gap. Power equals voltage times current, Watts= V * A. Generally a power supply is limited by it's power rating. If the voltage is high, the current has to be low and visa versa. If a power supply can deliver 1000 Watts, then at 100 V , 10 A can be delivered. If the current is increased to 100 A, the Voltage can only be 10 V. This voltage droop is a common aspect of electrical engineering. To control the system you have to control either the voltage, and/ or the current.
Note that arc discharge and glow discharge are sometimes defined differently, but basically is is a matter of degree. Glow discharge can place considerable restraints on the maintainable voltage, though an arc discharge is even more limiting.
http://www.glow-discharge.com/?Physical ... ge_Regimes
https://en.wikipedia.org/wiki/Electric_arc
So, basically, if the gas pressure is too high (the sustainable voltage drops) The potential well depth or magnitude is directly related to the input voltage, so if the sustainable voltage from the power supply drops, so does the potential well.
In the Polywell, it is the electron current that is of most interest for several reasons. Normally, the current travels from a cathode outside the Magrid, to the magrid surface which is grounded or maintained at high positive voltage. You can have a high negative voltage cathode with a low voltage (grounded) magrid or a low negative voltage cathode and a high positive voltage magrid surface voltage, or any combination in between. The difference in potential is what drives the electron acceleration. As advertized, the Polywell is an amplifier when talking about the sustained current of electrons within the magrid. Optimally, the electrons shoot into the machine and bounce back and forth (don't confuse this with magnetic mirror bouncing, which may be somewhat different in details, at least at high Beta. If the electrons bounce around inside 100,000 times before completing their journey to the anode/ ground, then the contained density is the equivalent of ~ 100,000 times greater, This recirculating current within the magrid gives internal densities similar to what a noncontained (one pass directly to the magrid surface) current would if the emitter/ cathode current was increased a 100,000 fold. Instead of perhaps 100 A, you would need 10,000,000 Amps. And, of course a power supply that could maintain the thousands of volts at this current drain. In an operational D-D Polywell,instead of ~ 100,000 volts at 100 A or 10 MW, you would need 100,000 V at 10,000,000 A or 1 TW . Adequate confinement is needed not only for the Q consideration, but also from an engineering perspective of a realistic power supply. For steady state the relationship is straight forward. For pulsed or startup conditions, where the confinement may not be nearly as good, time considerations apply, the difference between Joules and Watts.
With high voltage, some of the electric current may overcome the magnetic shielding and flow directly to the magrid; without the intervening 100,000 passes within the machine. You might be able to maintain a voltage/potential well, but only at reduced voltage.
Also, with sufficient voltage and density the current may arc to other structures- like the grounded vacuum vessel wall, and bypass the magrid entirely. This is completely useless, and drains the power supply as well as screwing up your efforts at reaching a Q greater than one.THere is some leakage of current through the magnetic shielding, or the gap shielding effect (separation distance}at any voltage, but this increases, perhaps exponentially, with increasing voltage at any given density of plasma (or gas that can be ionized to plasma). So, to maintain a target voltage, you need to manipulate the insulation chariteristics, and the tolerable density in the chamber. The magrid should have smooth, gently curving surfaces to avoid electromagnetic field buildup at points, and also, have sufficient magnetic insulation to seriously retard any available low resistance path to grounded or positively charged magrid. Because of these considerations, the voltage* current conditions inside the magrid can be pushed to high levels. This is much more difficult to apply to all of the structures outside of the magrid, so here the density must be kept well below some limit. It turns out that this limit is around 1-10 microns (~ 1-10 millionths of an atmosphers- Using Pascals would be better, but...) Above this density, voltages of interest could not be maintained due to current external structures. The density outside may need to be maintained below 10^19 particles / M^3. With an advertised operating internal density of 10^22 particles/ M^3, the internal magrid volume, can tolerate ~ 1000 times greater densities before insulation breaks down. As the fusion scales as ~ density squared, this concentrating ability (Wiffleball trapping factor) and tolerance of the Polywell volume inside the Magrid allows for ~ 1 million times the fusion rate.Without this concentrating consideration, a Polywell would need to be many times larger than a Tokamak in order to produce useful amounts of fusion, and reaching a Q> one would be very much more difficult. As it is, the sustainable density within the Polywell may result in fusion rates in a given volume to be ~ 60,000 times greater. This is according to Nebil and gives a a general estimate of the size comparison between a Polywell and a Tokamak. This is ~ 60,000 times less volume,or ~ 40 times less diameter. Other considerations may eat into this ratio some, but there is an obvous advantage.
Any of this also applies to P-Boron11 fusion, just the numbers need to be changed some.
In an amatuer Fusor, efforts to push the voltage past a few thousand volts requires the pressure to be in the region of ~ 5-15 Microns. Then the power supplies available can push the voltage up to 10's of KV. For reasonable and detectable D-D fusion to occur this competing relationship needs to be balanced. The fusion cross section goes up with increased voltage (within limits) and the fusion rates goes up with increased density, but the ability to maintain the target voltage goes down with increased density. This is where the Polywell changes the game somewhat. With it's hoped for resistance to higher density voltage drains, and its containment efficiency it is potentially capable of not only reasonably profitable Q's, but also economical scaling of power plants. How this applies to FRC or DPF approaches is uncertain, but it is a tremendous challenge for Tokamaks. The physics may work, but the design must also be economical to build and operate, or it is useless.
Dan Tibbets