### Calculating x-ray Attenuation

I received detailed plans for the liquid helium Dewar that's going to be used in the h-ray experiment yesterday and spent some time calculating the amount of attenuation we can expect to the x-rays theoretically produced by our quenched Pb superconductor.  I'm making the assumption that most of the attenuation of x-ray flux will come from the aluminum walls and aluminum backed insulation, not from the plastic walls.  A cross-section of the walls is shown to the left, (picture 1).  The wall on the left of the cross-section is made of .125 inch thick aluminum.  The five sheets of insulation between the inner and outer walls are Mylar coated with .003 inch thick aluminum.The inner wall on the right hand side of the cross section is constructed of .1 inch of 'low thermal conductivity plastic'.  This gives me a grand total of 0.35 cm of aluminum between the source and the   detector.  The graph shown below (picture 2) is the amount of flux transmitted through the aluminum with respect to energy.  The attenuation values were taken from an online attenuation calculator[1]. The attenuation value without coherent scattering was used and was multiplied by the density of aluminum to arrive at a linear attenuation number mu.  The percent of transmitted flux was then calculated as

exp(-mu*thickness of material)

In addition to the attenuation due to the Dewar walls, I did two more calculations to get a ball park figure for how much attenuation I should expect from the superconducting solenoid magnet that will surround the sample and that is made from copper clad niobium alloy wire that is .045 cm thick.  The first graph is for copper of this thickness and the second graph is for Niobium, (pictures 3 and 4).

The theory predicts x-rays of about 382 keV energy.  If x-rays are produced at a much lower energy, say around 50 keV, it's conceivable that they could be missed with the detector outside the liquid helium Dewar.

Any thoughts, pointers, or questions are always welcome!

References:
1.  Aluminum attenuation
http://atom.kaeri.re.kr/cgi-bin/w3xcom?m=13

2.  Copper attenuation
http://atom.kaeri.re.kr/cgi-bin/w3xcom?m=29

3.  Niobium attenuation
http://atom.kaeri.re.kr/cgi-bin/w3xcom?m=41

4.  x-ray attenuation documentation
http://en.wikibooks.org/wiki/Basic_Physics_of_Nuclear_Medicine/Attenuation_of_Gamma-Rays

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Kids R Kapable

Just a little note to concerned ‘grownups’ everywhere.  If you look at a kid—and I mean really look—I don’t mean notice a person shorter than you, I mean make eye contact, notice their facial expression and observe their body language—If you look at a kid, don’t assume they need your help unless they’re obviously distressed, or ask for it.  You might think this is difficult call to make.  You might think, not having kids of your own, that you’re unable to make this determination.  You are.  You do in fact, already have the skills even if you’ve never been around kids  It’s a remarkably simple call to make, just use the exact same criteria you would for determining if an adult was in distress.  Because, guess what, kids and adults are in fact the same species of animal and communicate in the same way.  Honest.  If someone—adult or child—doesn’t need your help, feel free to say hello, give a wave, give a smile, but don’t—do not—try to force help on anyone that doesn’t want or need it.

Y…