Coilin and coilex: A route for 100 T non-destructive magnets

This paper provides the missing formulae needed to set up a complete project of a coilin/coilex system. The expressions for the coilex's self-energy 1/2 L(.)I(0)(.2), of an A and B coilin, and the mutual energy MI(0)(.)I(0) are given together with the analytical resolution of the two differential equations coupled by M = k root LL(.) which govern the currents in each coil. The coilin capacitor bank is triggered at t(0)(.) - t(1) seconds after the coilex pulse generator (t(1) = t(0) root 1-k(2)). The delay setting ensures a perfect synchronism so that the total field B-o* is maximum when the coilin field is maximum and the coilex field is minimum so as to compensate for the energy MI(0)(.)I(0). Under that condition B-0* > B-o,i(.) + B-o,B-i, where B-o,i(.) and B-o,B-i are the individual fields given by the coilex and the coilin respectively when not coupled.