## How does a fusor scale with size?

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
Calmarius
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### How does a fusor scale with size?

I read in this article that discharge properties depend on the product p*d. If we keep pd and the voltage constant we'll get a similar discharge.

So a twice larger device on half pressure would have a similar discharge. One can even make a nice glow discharge even on atmospheric pressures that's several mm long if you can choose the right series resistance.

So if you keep the voltage constant and the product pd constant in a fusor. How does other numbers change?

Is there a sweet spot in size that maximizes the efficiency for a given input power?

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While I did my 45 minute walk into work I thought about this.
So if you build a 2 times larger device you'll have 8 times larger volume 2 times smaller pressure and density, thus 4 (=8/2) times more particles.
Due to the smaller number density, collisions 2 times less likely, thus 2 times less chance for fusion, but there are 4 times more particles, so I'd expect 2 (=4/2) times more fusion. Since there are 4 times more particles the electric field is potentially moving 4 times more charge carriers so the current is 4 times higher. 4 times more power consumption (since we assumed voltage is constant) for 2 times more gains, 2 times worse. So this would suggest that a tiny device would be better...

But I don't want to go too far, as my train of thought could be downright wrong... I'm curious what are your thoughts on this.
Last edited by Calmarius on Thu Jun 12, 2014 8:07 am, edited 1 time in total.

Dan Tibbets
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### Re: How does a fusor scale with size?

I think you are confused, or at least I am. What is the product of P*D. They are the same thing, only expressed differently.
P= pressure(?). A pressure of 1 atmosphere or about 760 Torr or about 1024 Bar, or whatever Pascals is the same of saying you have a density of ~ 10^25 gas particles per cubic meter.
A pressure of 1 Micron (1 micro Torr or ~ 1/760,000 of an atmosphere is the same as saying you have ~ 10^19 particles per cubic meter.

You may be thinking of the fusion scaling as the square of the density. You could mix pressure units and density units and it is saying the same thing, but keeping tract of the unit conversions would be a nightmare.

Fusion may scale as density squared, at least theoretically, but piratically it is a different matter as you also have to account for resultant variation in temperature of the interacting particles, the beam- beam interactions, the beam - background interactions, and the beam- target interactions (beam- wall). All are occuring at different rates, and the interaction is complex. Some think that most of the fusion occurring in a Fusor is of the Beam- target type. Some studies have shown this dominance while others have shown beam- background or beam - beam dominance. The relations ships are complex and variable. At lower pressures beam- beam may become more dominate, provided you can limit beam target opportunities. This is the idea of magnetically shielding surfaces/ wires. By halving the density, while increasing the volume two fold may increase fusion, or decrease it depending on these complex interactions.
You can probably say that increasing the density and/ or the volume (with associated increased surface area) increases the fusion rate, but the details are variable and elusive.

Here the consensus seems to be that increasing amperage and density within limits increases fusion in a mostly linear fashion in amateur fusors. There are all sorts of manipulations that may modify this somewhat and is what amateur fusioneers work at.

One general theoretical scaling law for fusion in that at constant voltage, fusion scales as the Density squared * the radius cubed. While losses scale as the radius squared. So theoretically if you built the machine big enough you could breakeven eventually (we are talking really big). But, this ignores many complexities of which only a few has been mentioned above.

This does not imply that Fusors are only a toy or educational tool only. You can make enough neutrons for use in diagnostic machines such as for geology, weapons detection, possible medical scanning and treatment. Also, a modified fusor may make a better rocket engine than current Hall effect ion thrusters. You just have to have a separate power supply just like the Hall thrusters.

The Polywell is a greatly modified fusor approach that may have some potential to be a useful power source, but again, while the theory is promising, the application is complex and fraught with complexities and uncertainity.

Dan Tibbets

Calmarius
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### Re: How does a fusor scale with size?

I must clarify. On P*D I meant the paschen law, or the similitude of discharges in general. P is the pressure, D is the distance between the electrodes (grid, wall distance for example), or simply the fusor size.

So if you want similar running conditions you should keep this number constant: bigger fusor must run on lower pressures to remain in the same discharge regime.

Calmarius
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### Re: How does a fusor scale with size?

One general theoretical scaling law for fusion in that at constant voltage, fusion scales as the Density squared * the radius cubed. While losses scale as the radius squared.
Hmmm...

p: pressure, proportial to density
d: chamber size (assume single grid setup with chamber wall anode).

C = p*d = constant.

L = d² = losses
F = p²*d³ = (C²/d²)*d³ = C²*d = fusion rate

F/L = C²*d / d² = C²/d

Maybe my in-the-mind calculation on the first post doesn't downright wrong...

A bigger machine produces more neutrons but less efficient. Looking forward to see a mm sized device...

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### Re: How does a fusor scale with size?

Dan Tibbets wrote:One general theoretical scaling law for fusion in that at constant voltage, fusion scales as the Density squared * the radius cubed. While losses scale as the radius squared. So theoretically if you built the machine big enough you could breakeven eventually (we are talking really big). But, this ignores many complexities of which only a few has been mentioned above.
This doesn't apply to a fusor. In fact, it doesn't apply to a magnetically confined plasma either, AFAIK. Sounds like theorising on a different device.

Fusor is not a thermal-plasma device. Forget any notions of 'plasma density' and the physics of thermonuclear plasmas. Statistically speaking, there is virtually no plasma in there.

In regards the central point of the question, you can look up my discussions on 'small fusor' sizes to understand my position on it. If you make the fusor very small, the 'pd' will drift onto the lower side of the Paschen curve which means you need higher densities and high currents to create a discharge at moderate voltages. This appears to be problematic because you end up well into viscous flow pressures which seem to suppress the 'beaming' phenomenology of the fusor. If you make the fusor large, the pd drifts high and you need very low pressures which in turn mean very low currents.

Consequence appears to be that there is a Goldilocks region where current is high and the potential is at 'fusible' levels, and this tends to be around units to teens of microns, and in turn this appears to set a working fusor's dimensions to around 6cm to 40cm diameter for those voltages to lead to a glow discharge.

This is the way I will see it, until I see DD fusion done in substantially larger or smaller chambers.

Calmarius
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### Re: How does a fusor scale with size?

'pd' will drift onto the lower side of the Paschen curve which means you need higher densities and high currents to create a discharge at moderate voltages.
But isn't the whole rationale behind this pd product that the mean free path inversely proportional to the pressure? So if you compensate the smaller mean free path by smaller spacing of the electrodes, you have a similar discharge. Hence the Paschen function depends on pd.

After further reading. My main concern about small fusors is the field emission of electrons which usually happens when field strength reaches the magnitudes of 1GV/m. There is a stronger electric field between the electrodes if they are closer together. So this would make it harder to make a glow discharge (it would arc instead).