|
Lesson 6 - General specifications of radiation sources
Types of sources
In this course, we will be working with four spatial layouts of sources.
In this lesson, we want to introduce them and get a little practice in
converting from one type to the other. The four are
-
Point sources,
-
Line sources,
-
Area (or surface) sources,
-
Volumetric sources,
NOTE: Notice that I have simplified the notation somewhat from
the book, taking out the spatial and angular dependence. This is
because we will be dealing almost exclusively with uniform, isotropic sources.
Point sources,
These are sources that denote particles that are spontaneously emitted
from a single point, with no physical source modeled:
This is a mathematical simplification, of course, of a physical source.
The book gives two general requirements for assuming this:
-
Volume of physical source sufficiently small in comparison with the dimensions
between source and detector; and
-
Negligible interaction of radiation with the matter in the source volume.
and then states that Requirement 2 can be relaxed if source characteristics
are modified to account for source self-absorption. This relaxation
is generally made by performing a stand-alone calculation of a physical
source, carefully collecting information about the number and energy profile
of particles (of all types) that escape the source, and then attributing
the escaping particles to the mathematical point source in a subsequent
calculation.
This allows the analyst to model the effects of the source without having
to model the source material in the calculation.
Line sources,
The line source, which has the addition dimension "per unit length," is
a similar mathematical simplification of a physical source, but one in
which all dimensions but one of the physical source are small in
comparison with the dimensions between source and detector. In other
words, it is long and skinny ("pencil-like"). We call the dimension
we keep the "length", L:
Notice that a differential length of the source emits  ,
therefore acts like a small point source. The total particle
emission rate from the line sources is  .
NOTE: If one is given a line source and -- either because
you think the length is really not significant or just to be conservative
in your analysis or just to get an approximate answer to save time -- you
can reduce the line source to a point source with this strength.
(You would probably want to locate the point source at the midpoint of
the line.)
Area (or surface) sources,
The analogy continues with the area source. If two dimensions cannot
be ignored, we model the source as a flat source and the dimension has
a "per unit area" in it. A differential area on the surface, then,
acts like a mini-point-source, and the total particle emission rate from
the area source becomes  .
Example: In two dimensions, we have an additional possibility
for reducing the complexity of the source. For example, as the detector
gets further away from the surface, the analysis might first decide that
the W dimension is no longer significant but the L dimension is
still significant; therefore, the analyst might approximate the area source
as a line source of length L (located, in the figure, vertically centered
left and right) with a strength
 .
Then, as the detector is withdrawn further and the analyst considers
the L dimension to be insignificant as well, the source might become a
point source located at the center of the originalsurface, with strength
 .
Volumetric sources,
The final, and most general, form of the source that we will use is a full
three dimensional source, where all three spatial dimensions are significant.
As an example, consider as a parallelepiped (i.e., block) shaped source:
A volumetric source can also be reduced to the previous, simpler forms:
area source, line source, and point source. The exercise at the end
of the lesson will give you practice doing this.
Curie vs. Becquerel
The standard, preferred unit of activity is the Becquerel (Bq), which
is 1 disintegration/sec. Us old guys still use the Curie (Ci), which
is  .
You are caught in the middle and have to know both.
Activity vs. particle production rate
Be sure to recognize the difference between these two. Sources are
often specified in terms of the disintegration rate of decaying isotopes;
it is up to the analyst to figure out the resulting particle source rate.
Appendix H in the book gives gamma and x-ray emission information for
selected radionuclides. This can be useful.
Example: What would be the source terms associated with
a 2 cm radius by 5 cm high cylindrical source of 90-day-old ruthenium-103
labeled as having an activity 0.1 microcurie on a date 90 days ago?
Answer: From the Appendix H data, the half-life of Ru103 is 36.4
days, which gives us a decay constant of:
The current activity will be:
 
Since Ru-103 decays with release of a 497.1 keV photon 90.9% of the
time and a 610.3 keV photon 5.73% of the time, the associated total gamma
production rate would be:
This would be the appropriate source strength if the source is represented
as a point source.
If the 62.83 cc volume of the source is modeled in the problem, then
the appropriate volumetric source terms are:
and
Use of Dirac delta function
When a given application calls for a distribution of a given variable (e.g.,
an energy source distribution in particles/sec/MeV), but the data is given
for particular values of the variable (e.g., 10.93 particles/sec at 0.4973
MeV), the mathematical tool to use is the Dirac delta,  ,
which is a special distribution with units of "per unit x" which
is infinite at  ,
and has the mathematical property that:
The dependent variables that we will see in this course are space, energy,
and direction.
Example: If we have an isotropic source that emits 10 particles/sec
of energy 100 keV at a particular point  ,
then the source distribution, written as a distribution in space and energy,
and direction, would be :
|
NE406 Radiation Protection and Shielding