Biological Effects - RF/Microwave Interaction with Biological Tissues - page 146

3.4. (This problem addresses the reader familiar with Maxwell's equations.)
Frequency scaling (Section 2.5.2) is based on what is called the electro-
dynamic similitude theorem . The purpose of this problem is to establish
the theorem.
(a) Write Maxwell's equations for the curl of electric and magnetic fields
in the time domain for a e, m, s medium.
(b) Express all the quantities involved in the equations as a product of a
dimensional and a dimensionless quantity, such as, for the electric
field,

E e =

where is the a ctual electric field and e the scale factor in volts
per meter while is dimensionless. Such separation is to be done for
both the electric and magnetic fields, permittivity, permeability,
conductivity (writing permittivity for instance as e 0 e), and length
(included in the partial derivatives of the curls to be written, e.g., ∂ l 0 x )
and time (included in the time derivatives).
(c) Derive the two dimensionless curl equations for and . In these
equations, it is then possible to group all dimensionless quantities in
three factors. You now have the similitude theorem.
(d) Divide these factors by each other to eliminate e and h and obtain
two new dimensionless quantities: m 0 e 0 ( l 0 / t 0 ) 2 and m 0 e 0 l 2 t 0 . These must
remain constant for the same dimensionless curl equations to char-
acterize identical problems, for instance at different frequencies.
Observe what happens to the other parameters, in particular the
characteristic length, when frequency is multiplied, for instance, by a
factor 2. Observe that the simple rule for scaling frequency [Eqn.
(2.20)] is valid only when the conductivity is zero.

E

e

e h

3.5. The pattern of energy absorption in the body contributes to the
microwave effect, while inhomogeneities affect the local power absorp-
tion. This raises the question of whether the whole-body average SAR
can be used as the only determining factor in evaluating biological effects
of low-level microwaves. Discuss the advantages and disadvantages of
using a local SAR, for instance averaged over 10-g masses instead of over
the whole body.

3.6. The parameters of microwave exposure are important to consider when
investigating biological effects. For instance, pulsed-wave exposure with
the influence of duration, waveform, and peak versus average power can
lead to different biological effects than CW exposure. Discuss the influ-
ence of some parameters. More specifically, consider radar-type pulsed
microwaves, observe the relations between peak power and repetition
rate, and discuss possible consequences of a high peak power.