I havn't read all of the replies, so my apologies if I am redundant. At extremely simplified terms, with a cathode at high voltage an electron is freed from the metal and flies away from the wire at the accelerated energy from the voltage. As the wire heats up this electron emission increases dramatically due to thermionic effects. The electrons have <1/60 the momentum of the ions (or neutrals) in the wire so they escape much more rapidly. Ions, if they escape are quickly pulled back to the surface of the wire, where they are grounded/ neutralized. So for practical reasons electron emissions from the electrode dominate. With an anode the electrons that may have been emitted are mostly quickly pulled back provided they were at the surface of the electrode. A little distance such as with a passing electron changes things some. Because of this an anode will not create free charge carriers- electrons or positive ions as a general rule. Things can be manipulated to change this to a degree and now you have an ion gun.
When an electron boils off of the surface of a cathode, it flies away with KE equal to the voltage of the electrode. This KE is transferred in part to other electrons when another electron is encountered- such as with a neutral gas atom/ molecule. This will lead to ionization of that atom. The KE of the emmitted electron is great enough that it may lead to the ionization of hundreds of atoms. This is what leads to the profusion of negative and positively charged free charge carriers that are born away from the surface of the electrode. The positive ions are attracted to the negative grid so long as the ion is at a greater radius than the grid. Inside the grid Gauss Law changes things. If the ion hits the grid, two primary things happen. The ion transfers much of it's KE to the wire as heat, and the ion picks up a electron from the continually replaced electron supply in the wire to become neutral with some small retained KE. This might represent an average event, but a range of possibilities can occur, - lower energy transfer, total energy transfer with the ion embedding in the wire, sputtering of other neutrals , ions and electrons off of the wire, each with their own share of the KE, etc... The important point is that ions created away from the electrode due to cascading secondary ionizations from the high energy electrons, will then be accelerated by the negative voltage on the cathode grid towards the center (depending on the symmetry of the grid, the exact center may not be the result). As the ion approaches closer to a particular wire it will curve more towards that wire, and may hit it. This leads to the transparency term. If on a single pass the ion has a 1/10 to 20 chance of hitting a wire the transparency is referred to as ~ 90-95%.
I believe there are two loss mechanisms involved. If the KE of the ion is lost when it hits the cathode wire (or it is up scattered so that it can hit the shell). This is one loss mechanism. The other loss mechanism is the free electrons traveling outward hitting the wall. Basically for each ion created (in deuteriums case with a Z of one) there is one free electron created, plus the electrons emitted from the cathode. Because of the transparency issue, each ion lasts 10 to 20 times longer than the an electron (this in terms of passes or distance traveled, with the speed of the ions and electrons considered the time duration of the electrons and ions is further modified. So the total electron current - primary and secondary electron current, may be ~ 1000 times greater than the ion current. Thus it is the electron current that accounts for most of the losses.
You might insulate the cathode grids to increase the ion lifetimes in terms of ion passes. Note that insulation refers to magnetic insulation, not electrostatic insulation like with a rubber insulating coating. This is good in terms of ion losses, but as pointed out above, electron losses are already dominate.
The Elmore Tuck Watson Fusor concept reverses things, the electrons are now making multiple passes limited by the transparency of the anode grid, along with thermalization issues. In this situation the primary electrons are created with an independent E-gun located outside the anode grid. The electrons accelerate towards the anode grid, drift once inside the grid until they pass out the other side, then are again accelerated back towards the center. While inside the anode grid, the electrons build up a virtual cathode and this can become dominate over the electron emitting grid/ e-gun electrons as a source of the space charge, because each electron now has a lifetime of 10-20 or more passes instead of just 1. It can be viewed as the supplied electron current being 1/10 less for the same space charge effect (virtual cathode) or 10 times the virtual cathode strength at the same electron current. The ions are born or somehow injected at low energy inside the positive anode, so they are trapped by the virtual cathode just as they are trapped by the real cathode in they typical fusor. But, now the ions may have a lifetime of unlimited passes- except limited by thermalization issues. This is good for the ion lifetimes, the ion based current is decreased considerably, but the electron losses through hitting the anode grid is still a major problem. Again magnetically insulating this anode grid may mitigate the electron current losses.
The amount of gains necessary to push a Fusor's performance to the point where a Q greater than one might be obtained is tremendous (often a ~ one billion fold improvement in efficiency is given) , so the magnetic shielding of the anode grid has to be very good. Also, thermalization issues must be controlled to an uncertain extent. This is the approach claimed for the Polywell. Even then the goal is not met. Such things as recirculation while maintaining the magnetic shielding, density boosting mechanisms, and impedance of thermaliation need to be addressed. I should note that recirculation of electrons is the whole ETW purpose, the tricky part comes from needing to allow for this while also having good magnetic shielding of the grid, and especially the density boosting properties. Basically, the goal is that you can pump electrons in faster than they leak out (or hit the grid) to a higher limiting density and having this high density lead to increased fusion rates to useful levels- that exceed the electron losses and provides for meaningful excess power for utilization.
It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
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