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Showing posts from September, 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 …

### 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.

### 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 th…

### Stepping Back Up With Classes: Lab Book 2014_09_06

Summary: Classes started this week.  They're a lot of fun, but they take time.  Consequently, the lab work is moving a little more slowly.  I'm looking into what we can accomplish with a YBCO superconductor sample.  The advantage is that we can test our experimental techniques using relatively cheap liquid nitroogen intead of iquid helium.  The downside is that with the size of YBCO sample we have, the expected maximum energy is only 3 deV which is kind of low without a specialized detector.
For more background on the experiment, please scroll to the bottom of the post.
The percolator peak does not appear when the detector is initially turned on.  The attenuator does however appear to create a rather copious amount of noise.
Suppose we used YBCO as a sample.  The energy we could expect doing a back of the napkin calculation is 3.8 keV.  The flux is approximately 230 photons for our sample size.  For a 25 square mm detector that may be available, this gives a total flux of 57 p…

### Showing that SpaceTime Intervals are invariant: EM II notes 2014_09_03

Summary:  Continuing notes on the tensor version of the Lorentz tranform.  It's time to start on the second set of examples.

The interval in four space is invariant under Lorentz transforms and is called the Lorentz scalar.

The Lorentz transform also applies to differential distances as,

$dx^{\prime\mu} = \Lambda^\mu_\nu x^\mu$

We were asked in class to work out $x^2+y^2+z^2-t^2 = x^{\prime 2}+y^{\prime 2}+z^{\prime 2}-t^{\prime 2}$

The transforms we'll use are:

$x = \gamma\left(x^\prime + vt^\prime\right)$

$t = \gamma\left(t^\prime + vx^\prime\right)$

Substituting these into the l.h.s. gives

$\gamma^2\left(x^\prime + vt^\prime\right)^2 - \gamma^2\left(t^\prime + vx^\prime\right)^2 = x^{\prime 2} - t^{\prime 2}$

$= \gamma^2\left(x^{\prime 2} +2vtx + v^2t^{\prime 2}\right) - \gamma^2\left(t^{\prime 2} + 2vxt+v^2x^{\prime 2}\right)= x^{\prime 2} - t^{\prime 2}$

$= \gamma^2\left(x^{\prime 2} + v^2t^{\prime 2}\right) - \gamma^2\left(t^{\prime 2} + v^2x^{\prime 2}\right) = x^{\p… ### Tensor Based Special Relativity Begins! EM II Notes 2014_08_25 Summary: This one took awhile. I got busy in the lab These notes start with rotation matrix properties and the transpose products of matrices. special relativity via tensors also begins. Specifically, the Lorentz transformation tensor components are reviewed and the number of independent parameters are counted. Did a few concrete checks that a matrix times its transpose is symmetric. Sure enough, it is.$\begin{pmatrix}
a & b \\
c & d \\
\end{pmatrix}\begin{pmatrix}
a & c \\
b & d \\
\end{pmatrix} = \begin{pmatrix}
a^2 + b^2 & ca + bd \\
ca+bd & c^2+d^2 \\
\end{pmatrix}\begin{pmatrix}a & b & c\\
d & e & f \\
g & h & i \\
\end{pmatrix}\begin{pmatrix}
a & d & g\\
b & e & h \\
c & f & i \\
\end{pmatrix} = \begin{pmatrix}
a^2 + b^2 + c^2 & ad + be + cf & ag + bh  + ci\\
ad + be + cf & d^2 + e^2 + f^2 & gd + eh + fi \\
ga + hb + ic & gd + he + if & g^2 + h^2 +i^2 \\
\end{pmatrix}\$

Sure …

### Testing the Scintillator Near the Magnetic Field: Lab Book 2014_09_01

Summary:  The x-ray detector will be very near a rather large pulsed magnetic field in the experiment.  Tests were run today to determine how the scintillator reacts, if at all to the field. There were no visually available indications that the detector had behaved differently at all.  There is one channel that has a consistently higher count when the data is analyzed, however, this doesn't appear to be statistically significant though.
If you're new to the experiment, please scroll to the bottom for background material.
Took a background spectrum with the Dewar in place.  The percolator peak was not present when the spectrum was started, but had appeared by the time the spectrum was finished. Bias 1500 V Gate Window 0.5 Us Threshold 1.5mV Attenuation 3 dB Data set HBC_00029 Source background Start Time 8:35 AM Stop Time 12:43 PM Date 2014_09_01