### Lab Outtakes: The 25 kHz AC Magnetic Field Superconductor Levitation Run

Not Very Educational, Just Pretty
I'm a little crunched for time since today's a travel day, so to get things started back off, here's a question.  What do the two pictures below have to do with each other?

Maglev trains like the one announced this week by Japan, (shown on the left), use pairs of superconductors and magnets to levitate.  Testing has to be done to ensure that the levitation won't become unstable because of mechanical vibrations or stray magnetic fields.  The picture on the right is a capture from the lab outtake video shown below.  The video is from a playday, but the apparatus was used in an experiment[1] that characterized the levitation of a superconductor by an alternating current magnetic field.

As quantitative data, the video is fairly useless because I'm changing way to many variables at once.  It's fun for me at least to see all the things going on.  Oh yeah, please excuse my super-classy super-scientific use of the phrase 'crappy signal'.

What you're looking at is a small pair of magnets levitated above a superconductor contained in the Styrofoam cup of liquid nitrogen.  The cup is sitting atop an electromagnet that's being driven with 25 kHz current.  As the current is increased, you'll see the magnet begin to lose stability as it's effected by the increasing field from the solenoid.  A while later, you'll see the liquid nitrogen begin to heat up and boil off because of the heat generated by the solenoid's iron core.  The boiling off utlmiately makes a pretty little dithered fog over the cup.  Finally, there's a surprise at the end.  I'll leave it at this, the superconductor itself isn't very sensitive to the 25 kHz magnetic field.  However, when I ramp down the current I'm superimposing  an apparent current that vibrates at only a few Hz.  The superconductor sees that and reacts.

References:

1.  Paper on levitation in an AC magnetic field
http://arxiv.org/abs/1208.1870

### 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…

### Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr.

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

### 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…