Optimization of current leads for superconducting systems

An optimized current lead in the context of this paper is one cooled by many baffles which intercept heat at fixed refrigerated stages. The helium boil-off-gas from the lead does not cool the leads but is totally utilized via heat exchangers in the refrigeration cycle. Discrete cooling without gaseous heat exchange has the advantage of eliminating the possibility of voltage breakdown in gas near the input leads. A method is presented to optimize a baffle system of fixed temperature shields to intercept heat conducted into a dewar through and generated by the current lead. The refrigeration power required for 1,2,3...n shields is compared with that required for an infinite number of shields, which is the absolute minimum power,
P_{\min}
, and is given by
P_{\min} = 2I\sqrt{T_{H}} \int\min{T_{C}}\max{T_{H}}\sqrt{\frac{\rho k (T_{H}-T)}{T^{3}}}dT
, where T
C
and T
H
are the cold and hot-end temperatures, ρ is the resistivity,
k
is the thermal conductivity and
I
is the transport current. The value
P_{\min}/I
depends on ρ and
k
of the material and end point temperatures. Also given is the lead optimization procedure for the case of a load current which is constantly changing with time in some prescribed way. Similar optimization of gas cooled leads with respect to minimizing refrigeration power is given.