# Does magnetic geometry determine the scaling of a Polywell fusor?

Does magnetic geometry determine the scaling of a Polywell fusor?

Forgive imprecise terminology here - by "magnetic geometry" I mean the configuration of the magnets, the configuration that creates the "Christmas star" geometry of the electron field in the fusor.

On to my question... I've read that the rate of fusion scales at $r^5$, with $r$ being the radius of the reaction chamber. Is this because of the aforementioned magnetic geometry? Or is it because of something more essential, like Bremsstrahlung, or something else?

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The scaling you refer to is derived (though not in great detail) in for instance papers [0], [1] and [2] below.

Since the polywell approach relies on a very particular kind geometry for its proposed operation, it could be said that the magnetic geometry is determining the scaling, but that would be circumventing the question.

Fusion power scales as $P_f \propto B^4R^3$. For the polywell type devices $B\propto R$, and hence $P_f \propto R^7$. One main difference between the polywell approach and regular magnetic confinement devices, is that the polywell mainly aims to confine the electrons magnetically. The electrons then create a confining electrostatic potential to capture the ions. This means that much smaller magnetic fields are needed, and that the main loss of energy is assumed to be through electron losses, which scales as $P_l \propto R^2$, the area of the device. This gives a total fusion gain scaling of $G = P_f/P_l \propto R^5$.

As for the particular polywell design used, the most common so far is the cubic, but some of papers have mentioned octahedral and dodecahedral configurations. It is believed that a more spherical configuration will yield better stability, as well as a larger "active" core region compared to the overall size of the device, but the scaling does not rely on the particular polyhedral geometry employed.

It should be stressed that this scaling relies on a lot of as yet unproven assumptions, based on very little (so far) empirical experience from operating this kind of device.

References:

[0]: Bussard, R. W., "Some Physics Considerations of Magnetic Inertial Electrostatic Confinement," Fusion Technology, vol. 19 (1991)

[1]: Bussard, R. W., "Inherent Characteristics of Fusion Power Systems," Fusion Technology, vol. 26 (1994)

[2]: Bussard, R. W., "The Advent of Clean Nuclear Fusion," 57th International Astronautical Congress (2006)

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"the polywell mainly aims to confine the electrons magnetically" I thought it confined them by electrostatically charging the spherical grid, and the magnets in the grid just coaxed the electrons to go through the holes in the electrode instead of hitting it. Am I misunderstanding? –  endolith Aug 2 at 18:26