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

Tuesday, September 30, 2014

Finding Quenching Field Magnitude Using Levitation Force: Lab Book 2014_09_29

Summary:  Working more on using the superconductor to detect its own quenching field.  The initial setup is shown below.  The quenching test is described in the following.  A YBCO superconductor is placed between the poles of a very uniform magnet and then cooled into its superconducting state.  The field frozen into the sample at the state transition opposes the fringing fields on the magnet.  However, had the magnetic field been strong enough to quench the superconductor, the results would have been the pendulum swinging freely beyond the pole pieces' diameter until it encountered a field less than its critical field at which point, it would have re-entered the superconducting state and frozen in those field lines, suspending itself.  There's another realization of this process that will be tested today.  The pendulum is again suspended in a uniform field and the field is slowly increased.  It is suspected the sample will be deflected until the quenching field is reached at which point, the pendulum will fall back to its equilibrium vertical position.  By measuring the angle of the pendulum, the levitation field could also be determined.

The superconductor is placed in a Styrofoam cup supported on a wood plank wedged between the two poles of the magnet.   The magnet gap was set at 2 and 9/16 inches.  This could be much smaller for the sample used here, I just need to find a smaller reservoir.

There are two movies.  The first contains the cooler alarm going off.  After the alarm went off, the magnet current supply was slowly ramped down, and water was added to the reservoir after the cooler was switched off.  The cooler alarm did not start again after it was turned back on, nor when the magnet supply was ramped up to 49 amps.

The second movie detailed the superconductor not moving while the reservoir slipped out from underneath it.
We’re measuring the magnetic field with a F. W Bell 5180 Hall Effect Gauss meter.
7.32 – 7.35 kG at a 2 and 9/16 inch gap.

12.8 kG at the gap setting, 1 and 1/8 inch gap setting.
A small Dewar was carved from blue Styrofoam to fit in the smaller gap space, see the first picture below.  The Dewar was suspended as a pendulum between the poles of the magnet as shown in the second picture below.  Dental floss was used to support the Dewar pendulum from the upper yoke of the electromagnet.

The quenching test was as follows:
A YBCO superconductor is placed between the poles of a very uniform magnet and then cooled into its superconducting state.  The field frozen into the sample at the state transition opposes the fringing fields on the magnet.  However, had the magnetic field been strong enough to quench the superconductor, the results would have been the pendulum swinging freely beyond the pole pieces' diameter until it encountered a field less than its critical field at which point, it would have re-entered the superconducting state and frozen in those field lines, suspending itself.  There's another realization of this process that will be tested today.  The pendulum is again suspended in a uniform field and the field is slowly increased.  It is suspected the sample will be deflected until the quenching field is reached at which point, the pendulum will fall back to its equilibrium vertical position.  By measuring the angle of the pendulum, the levitation field could also be determined.

The fringe field produced at the edge of the electromagnet pole, mentioned above, is shown in the diagram below from Lawrence's cyclotron patent application.  Note that the 'magnetic lines of force' become less uniform as the edge of the pole piece is approached.

The small YBCO sample did not quench at this gap and field setting.
Note in the video that at 35 amps during the ramp down, the sample seems to be drawn to the pole piece .  At 10 amps, the lower right corner of the Dewar relaxes.

Friday, September 19, 2014

Writing Activity Metric Tracking

I'm playing around with tracking metrics on my writing activities today.  Clearly I need to enhance my charting presentation skills, but the information here is kind of interesting to me.  It's about me, so of course it is, but it's interesting to think about in terms of why a writing log is useful as well.  Here's what I learned  As the semester has ramped up, I've been doing more writing on EM homework and less on EM notes in preparation for class.  That's not a sustainable model.  Work on the hray presentation an proposal has been ramping up nicely.  I need more detail on what aspects of each project I'm working on and more tracking towards defined goals.

Tuesday, September 9, 2014

Proper Velocity!!! and Getting Index Notation Worked Out: EM II Notes 2014_09_09

Summary:  It looks like I'll finally get a good understanding of the gamma notation for moving proper velocities to lab velocities and back.  It'll be nice to know it inside and out, but a little irksome given all that can be done with the hyperbolic notation we're not using.  I want to maintain my fluency in both.

There may be a subtle second notation for inverted Lorentz transforms.  As it turns out, the subtle notation difference of moving around indices in the top and the bottom with spaces is meant to keep track of which index comes first when you go back to side by side notation.

First, we cover Lorentz transforms, (which are not in fact tensors), and contractions and arrive at the interesting result in equation 1.99:

$\Lambda^\mu_\rho \Lambda^\sigma_\mu T^\rho_\sigma = \delta^\sigma_\rho T^\rho_\sigma$

Which indicates the transpose of the Lorentz transform times itself follows a sort of orthogonality rule making use of contravariant indices.

Q:  Does this obviate the need for the $\eta$ metric?

A:  But wait!  There's so much more!  This is a way to write things without the $\eta$ cruising through everywhere, but it also explains the oddball spacing of the indices.  Maybe I just don't remember this from MacConnel?  First, the Lorentz transform is not a tensor.  Now, we hve that down.  The next bit is how to arrive at the above expression.

$\eta_{\mu\nu} \Lambda^\mu_{\;\rho} \Lambda^\nu_{\;\sigma} = \eta_{\rho\sigma}$

The next step is to plow the $\eta$ on the l.h.s. in and lower the $\nu$ on the second transform.

$\Lambda^\mu_{\;\rho} \Lambda_{\mu\sigma} = \eta_{\rho\sigma}$

We then raise the sigma

$\eta^{\sigma\lambda} \Lambda^\mu_{\;\rho} \Lambda_{\mu\sigma} = \eta^{\sigma\lambda}\eta_{\rho\sigma}$

$\eta^{\sigma\lambda} \Lambda^\mu_{\;\rho} \Lambda_{\mu\sigma} = \eta_\rho^\lambda = \delta_\rho^\lambda$

$\Lambda^\mu_{\;\rho} \Lambda^{\;\lambda}_\mu = \eta_\rho^\lambda = \delta_\rho^\lambda$

Now, since we can see that the first two indices are $\mu$s, we can call the above statement a transpose.  The index locations matter to get the transpose to be a transpose, making sure the rows and columns are handled properly.

NOTE:  This doe arise in MacConnel.  His notation is slightly different.  Instaed of $\Lambda^\mu_{\;\rho}$, he writes $\Lambda^\mu_{.\rho}$

We're going to need the delLambertian soon and it's important to note that it is

$\Box = -\partial_0\partial_0 + \partial_i\partial_i = \partial^\mu \partial_\mu$

A few notes follow on why the D'Alambertian is written with one index up and one down.  It has to do with the negative sign in the first entry of the Minkowski metric.  As it turns out, the index up version of the Kronecker delta is the same as the index down version, but not so for $\eta$ because of the $-1$ $00$ entry.  This is all much simpler if you never start writing your indices in the 'wrong' location in the first place.

OK, now for the interesting stuff.  First, with the choice of signature for the Minkowski metric here, we wind up having to write down $d\tau$ as \

$d\tau = -ds^2 = dt^2 - dx^2 - dy^2 - dz^2$

Given $d\tau$ we define the four velocity to be

$U^\mu = \dfrac{dx^\mu}{d\tau}$

Which is technically mixing frames, but then, that's what proper velocity does.  Intersting that we're starting with four velocity, proper velocity here.  It's really nice to get this out of the way early on and benefit from it.

Picture of the Day
Presenting the Takeno metric line element.  Hopefully one of the payoffs of all this will be understanding this more fully, and possibly using it to explain the circular Unruh effect.  However, a far more productive use is in explaining the Thomas Precession.