HEAT-TRANSPORT ANALYSIS WITH ERROR CALCULATION

The problem of reliably determining the heat conductivity profile from measured profiles of temperature and power deposition is addressed. A new method is presented, which uses a Fourier decomposition of the measured profiles. By developing the profiles around a zero-order approximation of given shape, the heat conductivity profile is expressed as a cosine series. The coefficients of this series are bilinear combinations of the Fourier coefficients of the measured profiles. It is shown that this formulation allows the calculation of the error propagation. By truncating the Fourier series, the random error can be reduced at the expense of increasing the truncation error. The accuracy of the calculation of the heat conductivity can be optimized by proper truncation of the series. A truncation criterion is given that gives satisfactory results in a variety of test cases. In this paper it is assumed that the problem is one-dimensional and only the most simple form of the diffusion equation is considered. However, it is believed that, with little modification, the method presented here can be extended to more general cases. A simplified analysis of heat transport in a thermonuclear plasma is worked out as a detailed example and a comparison with a straightforward numerical differentiator is made. © 1990.