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This paper discusses the causes of and some solutions to the commonly observed problem of DC field offsets in finite-difference time-domain (FDTD) simulations. DC electric and magnetic field offsets are shown to be valid calculated responses of the modeled systems, resulting from interaction between the turn-on characteristics of the source and the properties of the models. The DC offsets may be avoided in the time domain by tailoring the source waveforms or in the frequency domain by post-processing the FDTD output.

A geometrical-optics approximation was used to calculate the mass-normalized rate of RF energy absorption (the specific absorption rate or SAR) in cylindrical models of man and in experimental animals irradiated by an electromagnetic (EM) plane wave at high radio frequencies. Comparison of these results with corresponding geometrical-optics calculations for prolate spheroidal models showed that the relative absorptive cross section of the prolate spheroidal and cylindrical models of man are essentially the same at frequencies above 20 GHz. The exact solution for the SAR in a lossy, infinitely long homogeneous circular cylinder exposed to an electromagnetic plane wave, for perpendicular incidence and with the incident E field both perpendicular and parallel to the axis, is also given. Although the formal solution is in the literature, data showing SARs for very lossy cylinders have apparently not been calculated. Curves showing SAR versus frequency for cylindrical models of man and animals in comparison with composite curves obtained from prolate spheroidal calculation are presented. It is shown that the exact solution for SARs in cylindrical models of animals and human beings appears to be a good approximation in the frequency range just below the geometrical-optics limit, thus providing an important method for extending the calculation of SARs into a range of frequencies where calculations were not available previously.

Analysis of the near-field irradiation of prolate spheroidal models of humans and animals by a small coaxial loop antenna is described. The near fields of the antenna are known exactly and hence are used to identify the suitable field parameters involved in the near-field absorption in the spheroidal model. An integral equation is formulated in terms of the transverse dyadic Green's function, and the fields radiated by the current loop are expanded in terms of the vector spherical harmonics. The extended boundary condition method is then employed to solve the integral equation. The power distribution and the average specific absorption rate (SAR) are calculated and plotted, for different human and animal models, as a function of the separation distance from the loop. It is shown that for distances less than 5λ the average SAR values oscillate about the far-field value. In particular, for d/λ < 0.4 an increase in the average SAR values was generally observed. It is also shown that in spite of the complicated nature of the near fields the absorption characteristics can still be explained in terms of the incident radiation. Furthermore, from the calculated SAR distributions at different frequencies it is shown that at all frequencies, excessive heating occurs at the surface of the spheroid while a limited absorption occurs in the central region around the major axis. This result is of particular importance in hyperthermia, where extensive efforts are being directed toward achieving deep-tissue heating by a coaxial coil carrying RF power at about 27 MHz.

The electric fields and power deposition patterns generated in two-dimensional inhomogenous models exposed to the axially directed uniform magnetic fields of an infinitely long solenoid are calculated numerically. The fields are calculated using the method of moments (Galerkin procedure) with linear basis and weighting functions. This low-frequency analysis is useful for studying the power deposition patterns attributable to solenoidal inductive applicators operated at frequencies up to 13.56 MHz. For the models we have studied, the ratio of power per volume deposited into the tumor to power per volume deposited into the immediately surrounding tissue is largest for tumors in the lung, although the power per volume deposited into the outermost layer is still much larger than the power per volume deposited into the tumor; it may be possible, however, to cool this region adequately from the body surface. When the complex permittivity of the tumor model is similar to that of the region in which it is embedded, the currents in the torso and tumor circulate primarily around the center of the body, as has been previously calculated for concentric cylinders. When the complex permittivity of the tumor is much greater than the region in which it is embedded, the currents in the tumor circulate primarily around the center of the tumor.

Analysis of the near-field irradiation of prolate spheroidal models of humans and animals by a short electrical dipole is described. The method of solution involves an integral equation formulation of the problem in terms of the transverse dyadic Green's function and expanding the fields irradiated by a short dipole in terms of the vector spherical harmonics. The extended boundary condition method (EBCM) is employed to solve the integral equations. The power distribution and the average specific absorption rate (SAR) are calculated and plotted as a function of the separation distance. It is shown that for a dipole placed along the major axis of the spheroidal (k-polarization), and for a very short separation distance, d= 0.15 lambda, the relative power values at both ends of the spheroid are about 40 compared with the ratio of 15 in the planewave exposure case. Furthermore, the calculated average SAR values as a function of the separation distance were found to oscillate around the constant value obtained from the planewave irradiation case. Differences between the near-and far-field exposure cases occurred only at separation distances shorter than 0.5 lambda where the magnitudes of the electric and magnetic energy densities are higher than the time-average radiation power density.

The power absorption characteristics of the prolate spheroidal model of an average man have been studied when the model is exposed to the near fields of an arbitrarily located small loop antenna. An integral equation is formulated and the fields radiated by the loop are expanded in terms of the vector spherical harmonics. This equation is then solved using the extended boundary condition method (EBCM,). For three different loop-spheroid configurations, the power distribution and the average SAR have been calculated as a function of the frequency and the separation distance. It is shown that the results obtained for separation distances larger than lambda /2 agree well with those obtained from the plane wave exposure case. Furthermore, the average SAR value calculated as a function of separation distance for the case where the magnetic dipole moment is aligned parallel to the major axis of the spheroid are found to oscillate around the constant value obtained from the H-polarized plane wave exposure case. On the other hand, the average SAR values for the E-polarization case (magnetic dipole is parallel to the spheroidal minor axis) are found to increase monotonically with the decrease in separation distance. It is also shown that despite the complicated nature of the near fields, the absorption characteristics can still be explained in terms of the variations of the incident radiation. These loop results, together with those obtained from other simple soures, can be used as building blocks in arriving at a qualitative understanding of the near-field absorption characteristics for more general exposure cases.

A surface integral equation (SIE) method is used to calculate the specific absorption rate (SAR) in spherically capped cylindrical models irradiated by an axially incident electromagnetic plane wave (K polarization) in a frequency range for which calculations previously have not been available (80-400 MHz for man models). In the SIE method, the electromagnetic (EM) field relations are formulated in terms of electric and magnetic currents on the surface of the model. The average SAR is calculated from the far scattered EM fields by means of the forward scattering theorem. SAR data calculated by the SIE method agree with data calculated by the extended boundary condition method (EBCM) for frequencies up to 80 MHz (the upper frequency limit of the EBCM) for man models. For rat models exposed to 1-3 GHz radiation, reasonable agreement was also obtained with the limited experimental data available.

Using the mathematical field analysis of a companion paper in this issue, solutions are found for the wave interactions occurring in several different configurations of drifting electron beams in a longitudinal magnetic field. First, wave interactions are found for both single and double beams of infinite extent. Next, single and double beams completely filling a cylindrical waveguide are analyzed. Finally, examination is made of single and double beams which only partially fill the waveguide. The resulting wave interactions are described with ω-β (dispersion) diagrams. Since only the small-signal approximation is made, space-charge waves, cyclotron waves, and waveguide waves are all present in this analysis.

Of all the many kinds and sizes of tumors, the deep lying tumor offers the greatest challenge in hyperthermia. It is not only more difficult to get the energy to the deep lying tumors than to superficial tumors, but it is also more difficult to measure temperatures in the internal tumors, which is significant because controlling the temperature requires measuring the temperature.

It is shown that the average specific absorption rates (SAR's) in a prolate spheroidal model of man are essentially the same as those for a block model of man irradiated by a short electric dipole at 27.12 MHz, even in the near fields. For purposes of average SAR, this allows use of the simpler and less expensive prolate spheroidal calculations.

Expressions are derived for the induced internal electric fields and average specific absorption rate (s.a.r.) in prolate spheroidal models of man and experimental animals irradiated by electromagnetic (e.m.) fields having arbitrary orientation and arbitrary impedance. These expressions are of value in estimating the s.a.r. in man and test animals exposed to e.m. near fields when the wavelength is long compared to the dimensions of the body.