Floating Wire Technique

Floating Wire Technique

Author: Tim

In his never-ending search on cyclotrons, their technology and history, Tim found this gem of a demonstration waiting to be re-discovered. Before the advent of numerical computers, accelerator builders pulled out their batteries, spools of wire, and ingenuity. Here is a paper by Lawrence Cranberg on Magnet Calibration by the Floating Wire Technique, a paper published by the US Atomic Energy Commission in 1951.  The floating wire technique was used to visualize the paths (orbits) of charged particles in magnetic fields.  A loop of wire, carrying a current will be drawn into a magnetic field (assuming the polarity is correct) and seek the center of the field, so as to include as many of the flux lines as possible.

If you find this particular experiment interesting, more detailed write ups include a paper Comparing Weak Focusing with AVF Focusing fields, and magnetic field mapping of cyclotron magnets.

The loop of wire is pulled into the magnet’s gap, outfitted with the weak focusing pole tips, The field is highest in the center and azimuthally symmetric about the center.
Using a height spacer, the loop of wire is held is supported in the mid-plane. Slowly slide the supporting block towards the magnet to let the loop find its center.
The magnetic field creates a tension in the wire, so it is as if you are supporting the wire from both end, and the wire will droop a little along the circumference according to a catenary, like a telephone wire between two telephone poles.
This is a 2-D vertical magnetic field map measurement of the good weak focusing pole tips, showing the peak field in the center, and dropping off with radius equally in any direction from center. Hence, if the field is truly symmetric, the loop of wire will seek to center itself about the center of the magnet.
And it does.
Interestingly, there there is a vertical field imbalance, the loop will raise and lower to find the median plane (where the field is purely vertical)
Things get more interesting in the AVF pole tip field, where there are sectors of higher and lower magnetic fields. (Such a field configuration has improved focusing properties)
Same data as shown above, but in a 2-D contour plot.
The three black paths are simulations showing the equilibrium orbits for three different energy (50, 200, 250keV) protons in this AVF cyclotron field. Note the pronounced “scalloping” in the the outer two orbits, bending harder in the high-field, and not as much in the lower field. Can we see this with the wire ?
Yes. For clarity, the upper radial sector pole tip has been removed, and the wire allowed to lay direction on the surface of the lower pole.
Two nested loops.
Finally, and even more interesting field configuration is the spiral sectored AVF poletips. The definition of and equilibrium orbit is the orbit an ion of a given momentum closes back on itself. Ions do not care the specific path taken, as long as the enclosed path has the right amount of magnetic field through it. You could imaging that in a complicated field, such as the spiral AVF, there might be several paths that encompass the same field.
The AKG270 spiral pole tips on the 12-Inch Cyclotron
The measured 2-D vertical magnetic field map of the AKG270 pole tips on the 12-Inch Cyclotron.
This plot, derived from a simulation, predicts the existence of five stable orbits. One about the center as we’d expect, but four more off center. Let’s see if the wire loop can find them.
Snap! Like a ouija board that actually works, if you slide the loop around a little, it snaps out of you fingers, and find the next equilibrium orbit. This composite photo shows the five orbits predicted by simulation.