ELECTROMAGNETIC ENERGY DEPOSITION IN AN INHOMOGENEOUS BLOCK MODEL OF MAN FOR NEAR-FIELD IRRADIATION CONDITIONS I. Chatterjee, M. J. Hagmann, and O. P. Gandhi Department of Electrical Engineering University of Utah Salt Lake City, Utah 84112 Summary The plane wave spectrum approach is used to cal- culate the electromagnetic energy absorption and its distribution in a 180-cell, inhomogeneous model of man for a prescribed vector electric field generated by RF sealers and other electronic equipment. The whole- body-averaged absorption density increases approxi- mately as (A/A)2 to the asymptotic plane wave value where A/a is the width in wavelengths of $he best-fit half-cycle cosine function to prescribed E-values. Introduction A great deal of progress has been made in the quantification of electromagnetic absorption by humans under plane wave irradiation conditions. However, to date, little work has been done with near-field expo- sure conditions which are of greater concern to workers involved in the operation of electromagnetic radiation equipment for communications, radar, and industrial and biomedical applications. Electromag- netic fields near several pieces of high-power in– dustrial equipment have been measured and found to be fairly intense, with electric fields as high as 500- 2000 V/m for 27.12 MHz RF sealers. In many near-field problems, the sources are loosely coupled to the human operator, and it is this class of problems that we have solved in the first instance. Important examples of this are the leakage fields from RF sealers and microwave ovens. Procedure The 180-cell block model of manl illustrated in Fig. 1 has been used for all calculations. Anatomical z Block model of man Fig. 1. Coordinate system and geometrical arrange- ment. drawings2, 3 were used to determine the contents of each cell and its volume-weighted complex permittivity was calculated using measured values for various tissue types. 4-6 Input required for the computations is the calcu- lated or measured leakage electric fields over a plane (Y-Z plane in Fig. 1) just in front of the intended location of the target. The prescribed incident elec- tric fields (E and Ez) can then be used to calculate the rsmaining ‘field components in the case of N-polar– ization (~, Ey, Hz nonzero) or P-polarization (Ex, Hy, Ez nonzero). The plane wave spectrum a preach of Booker and c~emow7,8 used earlier by us ! with 10SSY semi-infinite slab models is used here with the block model. In order to use plane wave decomposition based on Fourier analysis, the prescribed fields are repeated with a spatial period that is considerably larger than the 1 widths over which the fields are prescribed and also larger than 2-3 wavelengths to prevent interference from the fictitious sources. Implementation of the computationally-efficient fast Fourier transform and inverse fast Fourier transform has allowed usage of as many as 212 or 4096 component plane waves. Many of these plane waves are evanescent (decaying with dis- tance from the Y-Z plane). The incident electric field at each cell centroid is calculated by allowing for propagation of the plane waves from the Y-Z plane. The method of momentsl~l” is used to calculate the electric fields in the various cells of the model from the incident electric fields. At each frequency, for both N- and P-polarizations, it is only necessar to perform one expensive L-U matrix factorization. 11 Thereafter the stored factors may be used to obtain in- expensive solutions for different incident fields. Results of Numerical Calculations A 1-D field variation is assumed and fields are taken to be invariant for the y-direction. This limitation will be avoided in future calculations. Most of the calculations performed to date pertain to the c~se of P-polarization at 27.12 I@z. The fields measured by BRH/OSHA personnel for an RF sealer have been used for a realistic example. The measured values of the magnitude of Ez are plotted in Fig. 2 along with a piecewise cubic spline fit to the data points. Fig- ure 3 shows measured values of Ex as well as values generated from Ez in our computations. Zero phase dif- ference was assumed between the various measured values of Ez in preparing Fig. 3. Figure 4 was obtained by assuming a phase difference in Ez (less than 37°) based on difference in retarded time for propagation from the center of the prescribed distribution. A closer agree- ment of calculated and measured values of Ex is evident in Fig. 4, suggesting that phase measurement is re- quired (as well as a larger number of data points) in future field specifications. The calculated values of energy deposition for the fields with and without phase information are shown in Figs. 5 and 6, respectively. Also shown in these figures are the values calculated for a free-space plane wave field with a peak electric field of 826.8 V/m corresponding to the maximum elec- tric field measured from this sealer. A whole-body- X Robert Curtis, OSHA -- personal communication. 337