Electron thermalization time versus confinement time.
Posted: Sun Dec 13, 2009 11:48 am
This topic is presented to hopefully consolidate various arguments into one thread.
A. Carlson has recently commented on the EMC2 target of matching the electron confinement time to the thermalization time. I would rephrase it to suggest that they recognize there is no advantage to have electron confinement times longer that the thermalization times within the Polywell system.
What is the thermalization time? I posted in the past a study that gave thermalization time of ~25 ms for a small low voltage mirror machine. A. Carlson shot that down as it was evidentially not applicable.
So some questions:
1) what is a reasonable electron thermalization time in a WB6 type Polywell? For that matter what degree of thermalization will the machine tolerate- 20%, 90% ?
If there was a pulse of radial mono energetic electrons injected once, how long would it take for them to thermalize. How would the continuous injection of new mono energetic electrons to replace the more thermalized escaping electrons modify the process? Where would these competing processes reach an energy loss limit (for the system to work)? ie- How much electron current is needed to replace the thermalizing and escaping electrons such that some needed thermalization limit is not exceeded? Is that compatible with breakeven?
2) What knobs can be used to modify this competition? Some possibilities- microwave resonate heating of selected cold electrons, increased loss rates for hot electrons. What are the energy penalties incurred ?
3) Which should be considered as the balance point? Is it the Wiffleball confinement time versus the thermalization time, or is it the Wiffleball confinement time x the recirculation factor?
In the WB6 I estimate that the Wiffleball trapping for the electrons resulted in a confinement time of ~ 0.5 ms or less*. How does that compare with the expected thermalization time under those conditions?. With recirculation added, the confinement time effectively increases to 5.0 ms. But, I believe these 9 out of 10 electrons that are recirculated match the mono energetic and near radial directions of new injected electrons (without the energy cost). Ideally those 1 out of 10 electrons that escape recirculation are upscattered electrons (electrons spreading into the hot side of the thermalization graph) so there is some advantageous bias in the resulting thermalization curve.
Also, consider that the upscattered electrons that do escape give back a portion of their energy to the magrid, so there is less of an energy penalty for removing them from the system .
I'm guessing that the recirculation increases the effective confinement time while maintaining (or even improving) the limiting thermalization time.
This would represent a 10 fold gain or more in the energy balance (input energy needed to maintain a desired condition).
There are a lot of complex tradeoffs and dynamic considerations that need to be accounted for to derive a final answer.
To confuse the issue even more, with increasing size and magnetic field strength I'm assumeing the confinement times will increase. If there is indead a favorable balance in the small machines, will scaling to larger sizes and strengths crowed the limits ? Or do the +/- effects scale equally?
* Electron confinement time derived from some numbers and assumptions. Bussard said the electrons traveled ~ 1 billion cm per second in WB6. I don't know if this was the injection speed or the average speed. I think it is the injection speed (10,000 eV) so I took an average speed of 500 million cm/s. I assume the Wiffleball diameter is ~ 20 cm (or less?), so there would be ~ 25 million passes per second (assuming the electrons retain most of their radial directions, some limited thermalization would blur this number some). WB trapping was reported as ~ 10,000 passes. 10,000 passes divided by 25 million passes per second = 0.5 ms
Dan Tibbets
A. Carlson has recently commented on the EMC2 target of matching the electron confinement time to the thermalization time. I would rephrase it to suggest that they recognize there is no advantage to have electron confinement times longer that the thermalization times within the Polywell system.
What is the thermalization time? I posted in the past a study that gave thermalization time of ~25 ms for a small low voltage mirror machine. A. Carlson shot that down as it was evidentially not applicable.
So some questions:
1) what is a reasonable electron thermalization time in a WB6 type Polywell? For that matter what degree of thermalization will the machine tolerate- 20%, 90% ?
If there was a pulse of radial mono energetic electrons injected once, how long would it take for them to thermalize. How would the continuous injection of new mono energetic electrons to replace the more thermalized escaping electrons modify the process? Where would these competing processes reach an energy loss limit (for the system to work)? ie- How much electron current is needed to replace the thermalizing and escaping electrons such that some needed thermalization limit is not exceeded? Is that compatible with breakeven?
2) What knobs can be used to modify this competition? Some possibilities- microwave resonate heating of selected cold electrons, increased loss rates for hot electrons. What are the energy penalties incurred ?
3) Which should be considered as the balance point? Is it the Wiffleball confinement time versus the thermalization time, or is it the Wiffleball confinement time x the recirculation factor?
In the WB6 I estimate that the Wiffleball trapping for the electrons resulted in a confinement time of ~ 0.5 ms or less*. How does that compare with the expected thermalization time under those conditions?. With recirculation added, the confinement time effectively increases to 5.0 ms. But, I believe these 9 out of 10 electrons that are recirculated match the mono energetic and near radial directions of new injected electrons (without the energy cost). Ideally those 1 out of 10 electrons that escape recirculation are upscattered electrons (electrons spreading into the hot side of the thermalization graph) so there is some advantageous bias in the resulting thermalization curve.
Also, consider that the upscattered electrons that do escape give back a portion of their energy to the magrid, so there is less of an energy penalty for removing them from the system .
I'm guessing that the recirculation increases the effective confinement time while maintaining (or even improving) the limiting thermalization time.
This would represent a 10 fold gain or more in the energy balance (input energy needed to maintain a desired condition).
There are a lot of complex tradeoffs and dynamic considerations that need to be accounted for to derive a final answer.
To confuse the issue even more, with increasing size and magnetic field strength I'm assumeing the confinement times will increase. If there is indead a favorable balance in the small machines, will scaling to larger sizes and strengths crowed the limits ? Or do the +/- effects scale equally?
* Electron confinement time derived from some numbers and assumptions. Bussard said the electrons traveled ~ 1 billion cm per second in WB6. I don't know if this was the injection speed or the average speed. I think it is the injection speed (10,000 eV) so I took an average speed of 500 million cm/s. I assume the Wiffleball diameter is ~ 20 cm (or less?), so there would be ~ 25 million passes per second (assuming the electrons retain most of their radial directions, some limited thermalization would blur this number some). WB trapping was reported as ~ 10,000 passes. 10,000 passes divided by 25 million passes per second = 0.5 ms
Dan Tibbets