let’s just say, *if* the exit beam pulse were 1 ns long, and the coil’s transducer diameter is on the order of one wavelength, that’s 30 cm; for a 5 MW reactor producing 3000 pulses per second, we’re asking for 1.66 kilojoules per pulse; this is about 12.9 MV and 129 kA, for 1 ns.
the more turns of coil, the higher the voltage but the lower the current, and they are inversely related. so if you want high voltage from this, then you’d have lots of turns and a narrower gauge wire; but lower voltage would imply fewer turns and larger gauge wire. you want to minimize the resistance of the coil and the inter-turn capacitance, and there is a skin effect to consider, as a 1 ns pulse can penetrate only 2 micrometers into copper. effective resistance on ordinary awg 10 copper wire (2.6 mm dia) would be 1 ohm / m. (losses are I^2R, so to get these below 10% we need R < .01 ohm/m. i think that makes a good argument for superconducting wire. but there are other problems: critical current density of YBCO is high, but in thin films this yields nominal 300 A/cm width of tape, causing us to increase tape width or number of layers, which increases inter-loop capacitance. see http://www.ornl.gov/sci/oetd/documents/aug04_intro.pdf for more on this.)
let’s imagine there are 1000 turns of the above size; each turn would be collecting 40.8 kV and running 40.8 kA current, for each 1 ns pulse. i expect dielectric strength of the chamber gases at 40 torr to be greater than those at atmospheric pressure, but if not, then each turn would need to be over 2 cm apart at closest point. this implies 6.4 m inner diameter. outer diameter is then 7.0 m. this coil’s inductance is 5.38 mH.
at 10x the dielectric strength, the inner diameter could be 1.6 m, outer diameter 2.2 m; this coil’s inductance is 19.1 mH.
some thoughts and calculations lead me to believe that
(a) the exit pulse is probably on the order of 10 ns;
(b) the inductance of the coil should be about 30 uH overall;
(c) the rogowski coil should use superconducting YBCO tape in a liquid N2 bath. each 1cm wide YBCO wire can support 300 A current; (though i have not yet made allowance for the magnetic field)
(d) transducer diameter is 3 m, coil inner diameter is 0.955 m, outer diameter is 6.955 m;
this alters the design to 2.22 MV and 75 kA for 10 ns, or 250 coils of 5 turns each, in parallel. (total 1250 turns).
i expect efficiency to be above 88%, so long as the coils are tightly coupled magnetically (> 0.999), and the parallel capacitance is below 20 pF.
it seems that i have been working with assumptions belonging to the lumped element model, and that since the rogowski coil is operating at sizes where a single turn is on the same order as a wavelength, only a fully electromagnetic model will suffice. so please treat my above remarks as early guesses, and there is still much engineering to do.