Magnet Design and Sample Size

I've been looking lately at using an already constructed superconducting magnet instead of building my own for the upcoming experiment, (an Experimental Search for the Bremsstrahlung Radiation Predicted by the Hole Theory of Superconductivity)[1]. The issue at hand is that the bore isn't large enough to accept the originally planned 3.8 cm radius spherical Pb sample. I took a look this morning at what reducing the sample size would do to the energy of the predicted radiation in electron volts as well as what the dependency of the radiation flux would be with respect to sample size. The two formula for the energy and the flux (pictures 1 and 2) are:

See the aforementioned proposal as well as reference 2 for more details.

Plotting each of these versus R, the radius of the sample gave the following plots, (pictures 3 and 4). If the radius is reduced all the way down to 2 cm, the fall off in energy isn't unacceptable. It still lands in the ballpark of 160 keV which should light up the NaI detector just fine. Where I run into trouble is in the flux. Because of the R squared dependency it goes down by a factor of three.

For the moment, it looks like a better choice to build a magnet. That gets us to the fun part! Superconducting magnets are awesome! With 153 turns of .0018 in. diameter superconducting wire, I should be able to get approximately, (using the infinitely long solenoid approximation), 1300 Gauss. The approximation isn't quite valid since my solenoid will be pretty far from being significantly longer than it is wide, however, the required field strength is only 800 Gauss. For a first cut, things are looking pretty good.

Apologies for the xkcd style graphs. It occurred to me this morning, that the xkcd package is the only one I know how to label plots in.

References:
1. Experimental proposal and such
http://copaseticflow.blogspot.com/2013/03/open-science-is-cool-in-concept-but.html

2. Paper on radiation predicted by the hole theory of superconductivity
http://dx.doi.org/10.1103%2FPhysRevB.68.184502
Hirsch J. (2003). Charge expulsion and electric field in superconductors, Physical Review B, 68 (18) DOI: 10.1103/PhysRevB.68.184502

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