The temperature responses of five different gradient coil designs were
modeled using simplified engineering equations and measured. The mode
l predicts that the coil temperature approaches a maximum as an invers
e exponential, where the maximum temperature is governed by two parame
ters: a local power density and a cooling term. The power density term
is a function of position and is highest where the current paths have
minimum widths and are closely packed. The cooling parameter consists
of convective, conductive, and radiative components which can be cont
rolled by (1) providing forced cooling, (2) having a coil former with
high thermal conductivity and thin walls, and (3) varying the emissivi
ty of the coil surfaces. For a given gradient strength, the average te
mperature rise is minimized by designing a coil with a small radius an
d thick copper. The model predicted the local temperature rise, which
is also dependent on the current density, to within 5 degrees C of mea
sured values.