Dimensional Analysis II

Discuss how polywell fusion works; share theoretical questions and answers.

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mattman
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Joined: Tue May 27, 2008 11:14 pm

Dimensional Analysis II

Post by mattman »

Picking the variables is the hardest part about applying this method to experimentation. You need to pick variables which directly affect the phenomenon you are interested in and you need to pick variables that are independent of one another. Below are variables related to the potential well and the ion injection voltage.


1. The voltage of the ion source – Voltage – (kilogram * meter^2/ second^2 * Amp)]
2. The net charge in the center of the device – Amps
3. The distance from the gun to the center – [meters]
4. The permittivity of free space –[(Amp^2 * Second^4)/(Meters^3 * kilograms)]
5. Pi – [dimensionless]

These variables predict that there is 1 dimensionless group that can be formed. This group is shown below. It is the ratio of the voltage created by the charge in the center of the device and the voltage of the ion beam injected into the center. The bottom part of the equation comes out of the formula for electric potential equation for a point charge.

Group = voltage from Ion Beam/ Potental well Voltage = Ion Beam voltage/ (Net charge inside whiffleball /( 4*Pi*permittivity*distance gun to center))


This group maybe very useful; imagine an experiment where we vary the voltage of the ion source against the voltage inside the well. We could run through dimensionless quantities of 0.1 to 10 and see what this does to our fusion rate.

happyjack27
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Post by happyjack27 »

why no mag field?

D Tibbets
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Post by D Tibbets »

Why voltage on the ion beam?

The goal is to inject (or create from neutral gas) ions with as low a potential as possible when they reach the edge of the wiffleball border. This can be done by having the end of the ion gun located in a cusp near the wiffleball border at low voltage, or by having an ion gun further out with a voltage just slightly greater than the voltage on the magrid, so that the ions can enter but only have a minimal KE left when they reach the Wiffleball border. The interactions with the magnetic fields , electrons in the cusps, etc make for a complex interaction and I suspect the need for much tweaking to reach the best compromise. A neutral gas puffer is much simpler and and has advantages, and disadvantages.

As for the central attractive potential well, for a simulation, placing a negative charge in the center may serve for a simple model. But realize that the shape of the potential well may be very complex. The shape may be square initially, then elliptical once ions are added. Local variations may occur and be very important. The most obvious variation is the formation of a central virtual anode. This virtual anode is relative (less negative than other regions , but still well below ground).

For a simulation placing a central point charge may serve, but the results would have to be interpreted with caution.

As for the amount of charge (Coulombs) it could be assumed by calculating average ion density and then adding one part per million more electrons. This is approximately the maximal difference that can be achieved without going to massive and untenable voltages.

As for magnetic fields, the ions interact with them, and it does effect central focus/ confluence. But for a simple simulation the magnetic field could be ignored from the ions perspective. The majority of the confinement (90% to 99.99999% ?) is by electrostatic/ electrodynamic forces. You could assume the electrons are contained without going into how they are contained. Thus only a partial picture could be obtained, but it might still be useful.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Post by D Tibbets »

Without worrying about the method or difficulty of achieving the conditions, you could set the voltage of the new ion to zero and the location at the Wiffleball border. Assume this current of ions equals the current of electrons/ differences in relative confinement times . Of course you do not know the ion confinement time with any precision. You have to make assumptions. The easiest is that piratically all of the ions are contained till they fuse. This rate can be calculated from the density, temperature (with some assumptions about the degree of thermalization) and fusion cross section. I have read that ~ 20 ms dwell time is adequate for most of the ions to fuse. This is a rough number and may vary by 1-2 orders of magnitude depending on multiple considerations such as degree of convergence, volume, average density, etc.

The potential well depth could be arbitrarily set at ~ 85% of the electron injection voltage (potential on the magrid) as this seems to be a reasonable condition that has been found in experiments (WB6). This would be the KE of the ion as it approached the center of the machine in this simplistic construct.

A few rough numbers that I keep in mind is that the electron confinement time (with recirculation) must be greater than ~ 100,000 passes or several milliseconds. he ion confinement time must be ~ 20 milliseconds or ~ 10 times that of the electrons. This suggests that the ion lifetime in terms of passes (distance traveled) must be similar to the electron passes. The ions travel slower at the same KE so the longer dwell time (~1-2 orders of magnitude) fits. Note though that this confinement time (distance traveled) by the ions is set by their survival till fusion, not the time to escape. If an inert ion was used (helium in this example/ KE range) it's dwell time may be much longer.

My rambling may seem unnecessary, but it does emphasize the extreme complexity of the system and why it is difficult to model the system with any degree of precision or accuracy on a computer. The Polywell looks simple in design, but the interacting processes are extremely complex and the variables (knobs) can be adjusted over a wide range of interacting settings.

Dan Tibbets
To error is human... and I'm very human.

hanelyp
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Post by hanelyp »

I'd suggest replacing distance for the ion source with radius of the magrid. The former has no clear relation to conditions inside the wiffleball, while the latter has a clear relation to charge inside the device for a given well depth.

replace "voltage of the ion source" with "potential between electron injector and magrid".

D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Post by D Tibbets »

hanelyp wrote:I'd suggest replacing distance for the ion source with radius of the magrid. The former has no clear relation to conditions inside the wiffleball, while the latter has a clear relation to charge inside the device for a given well depth.

replace "voltage of the ion source" with "potential between electron injector and magrid".
These are numbers that would be usable, but injecting the ions at the Wiffleball border is better than the mid plane of the magrid. There are consequences to injecting at a higher level (this would also apply to my mention of injection from outside the magrid) but if very low energy the ion gun injected ions may not be penalized too much. The point is that the potential well base for the ions should be at the Wiffleball border. Higher locations results in more magnetic effects on the ions and confluence suffers. Bussard mentions that this is significant for up scattered ions, but in this case it would apply to all ions (except those down scattered. This is an advantage of the neutral gas puffer. Ionization occurs very near (depending on the size of the machine) the Wiffleball border due to the sudden increased in density dependent ionizing collisions. Also, no tube penetrating a cusp and causing potential problems with confinement. The mouth of a gas puffer could be outside the cusp (and even off axis to the cusp) and so long as the gas flow is fairly well columated, the vast majority will enter the Wiffleball. The problem with WB6 was that some of the gas would transit the machine and exit the opposite side befor it was ionized. Larger machines would have less problems with this (ionization is time dependent, and larger size equates to longer transit times and thus higher percentage of ionization. From an external arching viewpoint this is important. Also, I suspect the ions created closer to the Wiffleball border ( as a proportion to total Wiffleball diameter), thus perhaps some in the monoenergetic distribution of the ions.

As far as electron energy. The potential well voltage is not the injection energy but a fraction of it., perhaps ~ 80-90%. It depends on how you setup the model. If you account for this injection inefficiency then you could use the injection voltage (difference between E-gun and magrid potentials, otherwise you should use the potential well potential as the electron energy within the magrid.

Dan Tibbets
To error is human... and I'm very human.

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