### Experimental Estimates and Deconstruction: Lab Book 2015_01_16

Took apart the apparatus at the bottom of the proposed Dewar stick.  This is stick that will eventually support all the required apparatus in liquid helium.  Pictures follow.  Per normal, if this is your first day on the site, scroll to the bottom for the experimental background.

The inside of the Dewar measure out at 1 and 1/8 inches.  That works out to about 1.25 cm.  Then, plugging that into an expression for the size of cylinder we can get to fit

 Working with square cylinders Inscribe a square inside a circle circle radius 0.5625 1.42875 cm square side 0.795495129 1.010279 cm Square radius 1.010278814

The above distances are to the wall of the Dewar.  If we back off of this a little bit and give ourselves  an 1/8 of an inch clearance at all the corners, we get
 Working with square cylinders Inscribe a square inside a circle circle radius 0.5 1.27 cm square side 0.707106781 0.898026 cm Square radius 0.898025612

a radius of 0.89 cm.  That gives a maximum energy of about 290 keV and a total flux of 10,000 events per quench.  How does this jive with the sensitivity of the NaI detector?  This fits well within the range of the signals the detector is sensitive to:
 Source Peak Channel Energy eV Cd109 am241 110 26344 Cs 137 121 32000 Am241 221 59541 Cd109 Cs 137 2118 662000

For reference, here’s what the Cs137 spectrum looked like in the fiberglass Dewar

As it turns out, the brass disc at the bottom of the stick is too wide to fit in the Dewar.  It will b removed soon.

To Do:
·         Characterize the detector response with the glass Dewar
·         Calculate the solid angle with the detector much closer to the source
·         Characterize the background response in the basement
Attempt to do a 90 degree rotation of the sample between runs.  This should help to account for any directionality issues due to the sample being a cylinder and not a sphere.

A possible source for the sample

Back to spheres?
The extruded version of this might work fine

Background
Hirsch's theory of hole superconductivity proposes a new BCS-compatible model of Cooper pair formation when superconducting materials phase transition from their normal to their superconducting state[1].  One of the experimentally verifiable predictions of his theory is that when a superconductor rapidly transitions, (quenches), back to its normal state, it will emit x-rays, (colloquially referred to here as H-rays because it's Hirsch's theory).

A superconductor can be rapidly transitioned back to its normal state by placing it in a strong magnetic field.  My experiment will look for H-rays emitted by both a Pb and a YBCO superconductor when it is quenched by a strong magnetic field.
This series of articles chronicles both the experimental lab work and the theory work that’s going into completing the experiment.

The lab book entries in this series detail the preparation and execution of this experiment… mostly.  I also have a few theory projects involving special relativity and quantum field theory.  Occasionally, they appear in these pages.

Call for Input
If you have any ideas, questions, or comments, they're very welcome!

References
1.  Hirsch, J. E., “Pair production and ionizing radiation from superconductors”, http://arxiv.org/abs/cond-mat/0508529

### 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…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…