### Moving Crushed Can Walls! Lab Book 2014_07_28

Summary:
I made the last few fixes on the can crusher code port from IDL to +Sage Mathematical Software System and the can wall is now moving in simulation.  For a refresher on what the can crusher does and why the wall moves in the first place, see the embedded can crusher video post below.  Graphs were created showing how the current through the driving coil varies with time when the can is allowed to move and when it is not.  The leak detector is still broken, work will continue tomorrow on finding the root cause.

For background on the experiment in general, please scroll to the end.

Can Crusher Video

Can Crusher code
The can moving does influence the current through the coils.  Here’s a graph with the can moving, red and another without it moving, blue superimposed on the same plot.  The current graphed is the current through the driving can crusher coil, as opposed to the current through the can.

The x-axis denotes microseconds, and the y axis is in kA of current.
The can movement code also looks good!  Here’s a graph of the can wall moving.  The horizontal line at the top is the can wall immediately before it begins to crush.  Each successive line as your eye moves down the y axis denotes the six segments of the can that are modeled, see picture at beginning of this entry.

The x axis is the segment index and the y axis is the radius of the segment.
Should this data be deposited somewhere even though it can be generated by the simulation? For the moment, I’ll just go with releases of the simulation on github:  https://github.com/hcarter333/cancrusher
Next:  Clean the code and make an initialization function.  Write up a simulation that captures the two curves shown above that uses the initialization function.

Leak Detector Work

It is still unclear that the diffusion pump path is being vacuumed well.  The next step will be to attach the thermocouple gauge in place of the leak detector’s gauge on the nitrogen trap wall.

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…

### 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…