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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. 

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.

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?)

In fact, of course, if more particles are crossing in the negative direction, we will have a negative current.  Flux cannot be negative.

Symbols used

You need to be familiar with the symbols used for the four concept: 
  •  wpe19.gif (882 bytes) = net flow
  • wpe1A.gif (882 bytes) = current = "net flow rate" 
  • wpe1F.gif (886 bytes) = fluence
  • wpe23.gif (883 bytes) = flux = "fluence rate"    (Note: The pattern is the same -- upper case for time-integrated, lower case for rate)
Both flow and current can have "+" or "-" superscripts if we want to only consider particles crossing the fixed area segment in one direction only.

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