Magnetic circuit stupid formulae
Erice, September 2019.

This page is in the "junk" directory! Make sure you check some better material as well, on the main page :-)

Hi folks,
just a couple of random thoughts and images to keep at hand some basic magnetic circuit formulas. For my own reference. Right-click to enlarge them. Thanks to Arturo Popoli for kindly refreshing my mind! Still, any mistake is to attributed to me, not him. Ok? Good, let's start.

ALERT! THIS STUFF IS MORE THAN APPROXIMATED!

A magnetostatic circuit can be analyzed in analogy with an electrical one. First, a coil of N turns generates a magnetomotive force F = N I, where I is the current in the coil. This generates a flux PHI in the magnetic circuit, equal to F/R, where R is the reluctance. Pretty much like for the resistance, the reluctance is the sum of the reluctances of the series components of the magnetic circuit.

For small gaps, the reluctance can be computed like for the magnetic core, using the magnetic permeability of air. In the particular case of a Hall thruster, we have an axisymmetric configuration, like the one in the next figure. In this case the gap is large, and the reluctance can be computed using a sort of effective area. I made some super rough approximation in the next figure, just to have an idea of the field.

Following the formulas, one can assign a maximum magnetic field to be obtained in the channel centerline (at radius Rc), and this gives the magnetic flux PHI. The thickness of the magnetic structure can be obtained by assigning a value for the magnetic field B smaller than the saturation value. In this way, one has some room for increasing the current if the field in the centerline is to be increased due to the crappiness of my calculations.

From the area of the magnetic material one can design the thickness of every portion of the magnetic structure, the number of pylons holding the plates etc. Recall that near sharp corners you may have concentration of flux lines, meaning that the field may get larger locally, pretty much like an incompressible fluid flow.

Finally, the current times number of turns is easily found. Cheers!
-Stefano       -> BACK TO THE HOMEPAGE <-