MR gradient coil heat dissipation.

The temperature responses of five different gradient coil designs were modeled using simplified engineering equations and measured. The model predicts that the coil temperature approaches a maximum as an inverse exponential, where the maximum temperature is governed by two parameters: 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 controlled by (1) providing forced cooling, (2) having a coil former with high thermal conductivity and thin walls, and (3) varying the emissivity of the coil surfaces. For a given gradient strength, the average temperature rise is minimized by designing a coil with a small radius and thick copper. The model predicted the local temperature rise, which is also dependent on the current density, to within 5 degrees C of measured values.