Lesson #3 - Fundamental Radiation Field Variables
Reading Assignment: Section 2.2
In this section, the fundamental field constants that we will be using
throughout the course are introduced: fluence, flux ("fluence rate"), flow,
and current ("flow rate"). The terms in quotation marks are those
used in the book; the other term is the one I will use anyway (out of habit),
so I put it first.
It is interesting to note that the rate terms, flux/"fluence rate" and
current/"flow rate" are the terms that would conflict. For those
of us who learned transport theory in a reactor theory context, it was
POWER that we cared about, so the RATE terms (like power) were the ones
that got a word defined for them because of constant usage. In radiological
studies, it is cumulative effects that are important, so the time-integrated
terms, fluence and flow, have linguistic preference. But old
habits die hard, so you will have to be familiar with both sets of terms.
Contrast of flux and current
The greatest challenge of this section is in understanding the difference
between the difference between flux and current. Both of them have
the units of particles/cm2/sec (i.e., rate of particles crossing an area),
but the areas in question are different for the two concepts:
For the flux concept, the area is the projected area of
a sphere. In practice, this means that the area is the same no
matter what direction the particle is traveling.
For the current concept, the area is associated with a flat
area that has a particular, fixed position (i.e, an unchanging
normal vector). In practice this means that particles that approach
the area "flat on" (i.e., in the direction of the normal vector) will see
a larger area than particles that approach at a shallow angle (like an
airplane landing). In fact, particles travelling in planes that are
parallel to the flat area cannot see it, therefore cannot cross it.
An aspect of current that cannot fit into the rainy paper analogy is the
fact that one of the directions of crossing the area is considered positive
and the other negative. As far as current is concerned, no
matter how many particles are moving around, if just as many are crossing
in one direction as the other, the current is zero. (What
was I to do? Claim that the paper could stay dry if just as many
drops hit the back of the paper as hit the front?)
As an analogy, consider the situation where you left your basketball
out in the rain. If the basketball has a cross-sectional area
of 1 square foot and the rain is falling at a uniform rate of 100 raindrops/ft2/sec,
then 100 drops are going to hit the basketball every second. On the
other hand, if you leave a sheet of paper with the same area out in the
rain, then it might get wet at the rate of 100 drops/sec (if it
is lying flat) or it might even stay completely dry (if it is standing
on end). But the paper cannot get wetter than the basketball.
The basketball is getting wet at the flux rate; the paper is
getting wet at the current rate.
In fact, of course, if more particles are crossing in the negative direction,
we will have a negative current. Flux cannot be negative.
You need to be familiar with the symbols used for the four concept:
Both flow and current can have "+" or "-" superscripts if we want to only
consider particles crossing the fixed area segment in one direction only.
= net flow
= current = "net flow rate"
= flux = "fluence rate" (Note: The pattern is the same
-- upper case for time-integrated, lower case for rate)