## Saturday, November 15, 2014

### YBCO Four Point Measurements: Lab Book 2014_11_15

I was back in the lab this morning.  I’m working on getting the four point measurement to work on the YBCO sample.  In the grand scheme of things, this is low priority, but it’s important to know that we can successfully make these measurements here before we have a large bucket of liquid helium evaporating with a sample inside.  Here’s what the four point probe measurement looked like:

There are still no conclusive results.  With any luck this is a consequence of me not being able to interpret the results more than a bad experimental setup.  The table below details the four point probe readings in ohms as the superconductor cools

 Time Resistance kohm Comments 0 -0.35444 Negative reading is probably from swapped sense wires. 16 -0.36735 Immediately after nitrogen pour 59 -0.34466 Near minimum 101 -0.34359 Minimum immediately after new pour 280 -0.35815 Magnet in place beside superconductor in reservoir

I had expected more conclusive readings, a zero would have been nice for example.

## Wednesday, October 29, 2014

Here's today's special relativistic EM question.  Can the Thomas precession be shown to be a special case of the perihelion advance of relativistic elliptical orbits?  Any ideas?  Here's what's going on:

We've been deriving the special relativistic  orbit of a charged particles around another fixed charged particle.  At the end of the day, you wind up with a perihelion advance which is a fancy way to say that major axis of the elliptical orbit won't stay put.  It swivels around, (orbits), the charged particle as well.  The advance angle of the major axis winds up being\\

$\delta\phi = 2\pi\left[\left(1 - \dfrac{\kappa^2}{l^2}\right)^{-1/2} - 1\right]$

Which is very, very, similar to the Thomas angle for the spin precession, or gyroscopic precession along a circular orbit at special relativistic speeds:\\

$\delta\phi = 2\pi\left[cosh\left(w\right) - 1\right]$

$= 2\pi\left[\left(1 - \dfrac{v^2}{c^2}\right)^{-1/2} - 1\right]$

In the expression for the perihelion advance, $\kappa = eQ$ where $e$ is the charge of the orbiting particle and $Q$ is the charge of the fixed particle.  $l$ is the angular momentum and is written as $l = mr^2\left(\dfrac{d\phi}{d\tau}\right)$

Just a little more massaging of the above before I'm done for the day.  For a circular orbit, $\dfrac{d\phi}{d\tau} = \omega$ is constant and we can write $l = m\omega r^2$.  If we plug this in as to the Perihelion advance equation we wind up with

$\dfrac{\kappa^2}{l^2} = \dfrac{Q^2 e^2}{m^2v^2r^2}$ where $v = \omega r$

Here's where I get into trouble for playing fast and loose with things that migh actually be rapidities instead of velocities like $v$ above.  However, if you carry the simplificatins a bit further out, I believe you wind up with something that looks like an units of potential energy over momentum squared.

$\dfrac{Q^2 e^2}{m^2v^2r^2} = \dfrac{F}{m} \dfrac{1}{mv^2} \sim \dfrac{a}{E}$

Notes du jour:

## Tuesday, October 28, 2014

### EM Notes Part I: The visual bit of relativistic EM fields pointing at the observer

This is kind of cool from yesterday's EM notes.  Our professor pointed out that if you calculate the field from a relativistically moving electric charge, you'll always find that it's pointed straight at the point of observation.  Anyone have any idea why?  The argument could certainly be made that if you measure the field from a static charge that it will also be pointing straight at you.  Then, there's also the realization that the Lorentz transformation only affects the E and B fields in a frame that are perpendicular to the frame's tangential velocity.  I'm not sure that's either here or there since the point of observation can be anywhere.  Here's the associated diagram for the curious.

## Friday, October 24, 2014

### Day o' Videos: Presentation and Flying Superconductors

The lab book today was a bit sparse and a bit dry.  This is a bit odd considering I got to play lab yesterday...  You'll see.

First, here's an archival video of the presentation I did last Sunday for the TX APS section meeting here in College Station.  I fumble a few times, but the content is all there.  If you have any questions, they are very, very welcome!

The second video has some kind of cool stuff in it.  Not stuff that went the way I had hoped mind you, but cool nonetheless.  Here's the deal; we'd hoped to make a spiffy little superconductor visibly quenching video.  The idea was to suspend a superconductor as a pendulum in a magnetic field.  It was hoped that as the field increased, the superconductor would swing away from the pole of the magnet, (it did), and that as the field increased more, the superconductor would quench and fall from it's suspended state, (it didn't).  Our melt-texture growth superconductor from CAN just won't quench in 12.8 kG fields.  We already knew that.  Our next hope was to go with a low quality superconductor which should have quenched at a lower field strength.  I didn't consider the fact that quality also affects the force available for superconductor levitaiton, and so the lower quality superconductor did absolutely nothing.

In any event, it was educational and fun to watch the high quality superconductor as the field was ramped up.  Here's what you'll see.  As the field between the magnet poles is increased, the cylindrical superconductor which must have frozen in a bit of residual field when it was cooled will first orient it's magnetic moment perpendicular to the field to minimize the torque it feels.  As the field strength is increased, the superconductor will then begin to move itself out of the magnet altogether eventually swinging off the screen.  You'll also catch the odd snippet of extraneous lab conversations.

Picture of the Day:
New Mexico Mountains

## Thursday, October 23, 2014

### Pickup Coils, Faraday's Law and Back in the Lab! Lab Book 2014_10_23

As always, look to the bottom of the post for background on what's going on.

Finally, enough of theory and presentations!  I got back to the lab today!  Here’s the apparatus I built/used.

NOTE:   As always, look to the bottom of the post for background on what's going on.

No, the oscilloscope is not sticking its tongue out, that’s a floppy disc.  Remember those?

The small solenoid is what’s deemed a pickup coil.

It’s the first prototype, of the coil that will be used to measure the actual currents and magnetic fields produced by the can crusher magnet.  It’s exactly what it looks like, six complete turns made from a jumper wire.  The Styrofoam cup is to avoid abusing the small magnet block too much when it’s dropped.

The ‘scope pictured can capture a single waveform.  Here, it’s slowed way down to make a sweep over the course of several seconds.  It’s being used to look at the signal from the coil as the magnet is dropped through it.  Each set of spikes you see is created by dropping the boxy looking magnet through the solenoid.  Faraday’s law does the rest.

This is a very basic test run in preparation for measuring the changing magnetic field that will be generated by the pulsed magnetic field that’s to be used in the experiment.  Here’s a trace of a single magnet drop

Coil diameter  13.5 1/16ths
Number of turns 6
3178

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