### Notation and Cryostat Design

I took the first look at the cryostat that is probably going to use for the hole theory of superconductivity experiment.  A cryostat is a vessel for holding a coolant or cooling system, (in our case, liquid helium), and the equipment/samples for an experiment.  Because helium transitions from a liquid to a gas at just over four degrees Kelvin, the cryostat has two walls separated by a vacuum space to insulate the liquid helium inside from the room level temperatures outside, just like a thermos.

Before I get to much further into the details of the cryostat, I'd like to coin a phrase.  As those of you who already read the proposal for the experiment[1] know, Dr. Hirsch of UCSD has proposed a new model for superconductivity[2], and one of the predictions made by that model is that superconductors will emit Bremsstrahlung radiation[3] when they are quenched back into their normal non-superconducting state.  It's getting to be a bit much to type Bremsstrahlung all the time, or the 'hole theory of superconductivity for that matter, so I'm going to coin a phrase with apologies to Dr. Hirsch.  From now on, to have less to type, I'll just call the project the experimental search for H-rays.  It's good to get the notation fixed.

Now, on to the cryostat!  The bore diameter of the cryostat is about 5 1/8 inches.  The planned size of the Pb sphere to be used is 3.8 cm which comes in at about 3 inches, so it should be a pretty comfortable fit.  The bore depth is roughly three feet, so there's plenty of room for the superconducting solenoid that will provide the required 800 Gauss to quench the superconducting Pb back to its normal state.  There are a few pictures of the cryostat shown below.

Looking into the top of the cryostat with the lid removed (picture 1)

The side view of the cryostat (picture 2)

Looking into the cryostat (picture 3).

I have to design an instrumentation header, (lid), for the cryostat.  At the moment, I know it needs the following

1.  Two ports to supply and exhaust first, liquid nitrogen and then liquid helium

2.  Either on or two ports for bringing supply leads to the superconducting magnet.  See below for more information.

3.  A port for the liquid helium level detector as well as the thermometer leads.

4.  Support structure for the superconducting solenoid.

5.  Support structure for the Pb sample.

More on Magnet Design
It was brought up today that while the superconducting solenoid could handle 50 amps, more heat would be created by the normal conducting leads that had to deliver the current into the cryostat.  More heat means more boiled liquid helium and less run time.  By upping the number of coils in the solenoid, I can reduce the current requirement, but then the inductance will go up it will be harder to change the magnetic field quickly.  There are trade-offs to be made before the final design is put in place.

References:
1.  Experiment proposal
http://copaseticflow.blogspot.com/2013/03/open-science-is-cool-in-concept-but.html

2.  Hirsch on the hole theory of superconductiivity
http://dx.doi.org/10.1103%2FPhysRevB.71.184521
Hirsch J. (2005). Spin currents in superconductors, Physical Review B, 71 (18) DOI:

http://dx.doi.org/10.1088%2F0953-8984%2F19%2F12%2F125217
Hirsch J.E. (2007). Ionizing radiation from superconductors in the theory of hole superconductivity, Journal of Physics: Condensed Matter, 19 (12) 125217. DOI:

4.  Ionizing Radiation from Superconductors on arXiv
http://arxiv.org/abs/cond-mat/0508529v2
J. E. Hirsch (2005). Pair production and ionizing radiation from superconductors, J. Phys. Cond. Matt. 19, 125217 (2007), arXiv:

### 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…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…

### 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…