Calculating temperature distributions for gradient coils

The operation of gradient coils typically requires large currents to be driven in resistive copper wires. A major problem in gradient coil design is therefore the correspondingly large Ohmic heating that results, which can severely impact image quality or lead to system failure. Of particular concern is the location and extent of temperature hot spots in the coil system. In this article, a model is presented for predicting the spatial temperature distribution of a gradient coil. The model includes axial and azimuthal dissipation of heat via conduction throughout a copper layer, radial conduction of heat through an insulating former, and radial convection and radiation to the environment. Two steady-state solutions for the temperature distribution are presented, involving Green's functions and Fourier series. In addition, an approximate time-dependent solution is sought describing the hot spot temperature as a function of time, which demonstrates that the steady-state solutions are likely to be reached within a typical scanning scenario. The impact on the temperature distribution of a great number of coil properties may be investigated using the model and examples are given for different coil geometries, thermal material properties, and cooling mechanisms, such as convective air, forced air, and forced water cooling. (C) 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 146-159, 201