where Pin is the incident power density and M is the mass of the object exposed to EM fields.
Calculated average SAR in a prolate spheroidal model of an average man, as a function of frequency for several values of permittivity. m is the permittivity of muscle tissue.
Relative absorption cross section in prolate spheroidal models of an average man, a rabbit, and a medium-sized rat--as a function of frequency for E polarization.
Comparison of relative scattering cross section (RSC) and relative absorption cross section (RAC) in a prolate spheroidal model of a medium rat--for planewave irradiation, E polarization.
E1p = E2p (Equation 5.28)
1E1n = 2E2n (Equation 5.29)
where Elp and E2p are components parallel to the boundary, and Eln and E2n are component, perpendicular to the boundary, as shown in Figure 5.10. It is important to remember that Equations 5.28 and 5.29 are valid only at a point on the boundary. From Equation 5.29, we can see that E2n = 1 Eln /2; and if 2 >> 1, then E2n << E1n. Thus if Eln is the field in free space and E2n is the field in an absorber, the internal field at the boundary will be much weaker than the external field at the boundary when 2 > > 1 and the fields are normal to the boundary. Also, from Equation 5.28, we see that the external field and the internal field at the boundary are equal when the fields are parallel to the boundary. These two results will be used extensively in explaining relative energy absorption.
Field components at a boundary between two media having different complex permittivities, 1 and 2.
For the very special case of a lossy dielectric cylinder in a uniform H-field Equation 5.30 can be solved by deducing from the symmetry of the cylinder and fields that E will have only a component that will be constant around a circular path, such as the one shown dotted in Figure 5.11. For E constant along the circular path, and H uniform, Equation 5.30 reduces to
Thus, Equation 5.30 shows that E is related to the rate of change of the magnetic flux intercepted by the object; and Equation 5.31 shows that for the very special case of Figure 5.11, the E-field circulates around the H-field and is directly proportional to the radius. For this example the circulating E-field (which produces a circulating current) would be larger for a larger cross section intercepted by the H-field. The generalized qualitative relation that follows from Equation 5.30 is that the circulating field is in some sense proportional to the cross-sectional area that intercepts the H-field. This result is very useful in qualitative explanations of relative energy absorption characteristics; however, this qualitative explanation cannot be used indiscriminantly.
A lossy dielectric cylinder in a uniform magnetic field.
Ein = E e+ Eh (Equation 5.32)
Ee is stronger when Einc is mostly parallel to the boundary of the object and weaker when Einc is mostly perpendicular to the boundary of the object.
Eh is stronger when Hinc intercepts a larger cross section of the object and weaker when Hinc intercepts a smaller cross section of the object.
Qualitative evaluation of the internal fields based on qualitative principles QPl and QP2. Ee is the internal E-field generated by Einc, the incident E-field, and Eh is the internal E-field generated by Hinc,the incident H-field.
Average SAR in a prolate spheroidal model of an average man as a function of normalized impedance for each of the three polarizations. (a = 0.875 m, b = 0.138 m, f = 27.12 MHz, = 0.4 S/m, incident E-field is 1 V/m.)
Ratio of (SAR)e, to (SAR)h of a 0.07-m3 prolate spheroid for each polarization as a function of the ratio of the major axis to the minor axis of the spheroid at 27.12 MHz, = 0.4 S/m.
Go to Chapter 5.2
Return to Table of Contents.
Last modified: June 14, 1997
© October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 78235-5301