Friday, August 29, 2014

Energy Considerations and a Magnet Test: Lab Book 2014_08_29

Summary:  The energy and flux calculations show that the maximum sample size for the fiberglass Dewar should have a maximum energy of 308 keV.  This energy can easily overcome the Dewar attenuation.  A bit of research into computing an accurate theoretical spectrum was done.  The detector was recalibrated to place 320 keV in the highest channel.  Source runs with this setup were performed with Am 241 and Cs 137.  Things look good in this direction so far, (the channels look linear).  The iron yoke magnet was tested at currents up to 40 amps, which yielded a field of 4.33 kGauss.  The cooling held with the water traveling through the magnet coils only heating a bit.

If you're new to the experiment, please scroll to the bottom for all the background info.

Sample and Dewar Considerations
The following are energy and flux numbers generated using Sage.  The solid angle flux is 1.4% of the total flux based on a calculation in the proposal.
 Radius Energy Flux Solid Angle Flux 1.5 inches (small dewar) 154835 45651 639.1230729 3.8 cm 308857 181646 2548

At the time of the proposal, we didn’t have the fiberglass Dewar, so I’m recalculating the solid angle percentage here.  The external radius of the Dewar neck is 2 9/16 inches.
 Neck radius Surface Area NaI Surface Area Rough Solid Angle Ratio 2.5625 20.62897364 7.068583471 0.342653183

This obviously gives a much higher flux ratio:
 Radius Energy Flux Solid Angle Flux 1.5 inches (small dewar) 154835 45651 15521 3.8 cm 308857 181646 61880

This is good because the attenuation may be higher than originally expected.  These numbers need to be generated based on counts from recent runs.

Check this book for details on the Bremsstrahlung spectrum.

Detector Work
 Bias 1500 V Gate Window 0.5 uS Threshold 1.5mV Attenuation 0 dB Data set HBC_00025 Source Am 241 Start Time 5:00 AM Stop Time ??? Date 2014_08_28 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-

The noise trace is left over from yesterday.  It’s left in the graph just for looking, not for any rational reason.

 Bias 1500 V Gate Window 0.5 uS Threshold 1.5mV Attenuation 3 dB Data set HBC_00026 Source Am 241 Start Time 12:28 PM Stop Time 1:38 PM Date 2014_08_28 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-
We won’t run at this attenuation level, so the data was not analyzed.
Configuring Attenuation for 320 keV spectral range
Taking readings of the Cs 137 662 keV peak with different attenuations to determine what attenuation to use to get 308 keV full scale with maximum gain.  Here’s the data in terms of dB of attenuation and gain.  The data turns out to be linear in gain.
The formula for gain from attenuation can be derived using
$dB = 20 log\left(gain\right)$
$gain = exp\left\{2.303 \dfrac{dB}{20} \right\}$,
Where 2.303 is the conversion factor using log base 10 instead of the natural logarithm.
 db gain 662 keV peak channel 10 0.31616217 925 11 0.281773985 825 12 0.251126119 750 13 0.223811746 660 14 0.199468291 600 15 0.177772613 545 16 0.158436721 480 17 0.141203947 410 18 0.12584554 390 19 0.112157628 303 20 0.099958518 275

Now, figure out what channel 662 keV should be in to give us 320 keV in channel 1023, assuming the channels are linear in energy.  Use a simple proportion ala high school:
$\dfrac{320}{1024} = \dfrac{662}{channel}$
Solving gives channel number 2118.4.
Finally, solve the equation shown in the graph above to determine the attenuation that will place 320 keV at channel 1023.  The solution is -2.99471 dB.  3 dB will be used in the lab.  For the numerical details, see the spreadsheet notes.

Now, with the 3 dB of attenuation calculated above, here’s an Am 241 spectrum
 Bias 1300 V Gate Window 0.5 uS Threshold 1.5mV Attenuation 3 dB Data set HBC_00027 Source Am 241 Start Time ??? Stop Time 7:36 PM Date 2014_08_28 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-

Plotting the two peaks above along with the desired location of the Cs 137 peak at channel 2118 gives the following

More points are needed, but it looks good so far.  Data is being collected on a Cs 137 run over night to add more points to the curve.
 Bias 1300 V Gate Window 0.5 Us Threshold 1.5mV Attenuation 3 dB Data set HBC_00028 Source Cs 137 Start Time 7:44 PM Stop Time Date 2014_08_28 x-y scope V/div 1, 0.5 Shielded? Yes Tube Harshaw B-

For the x-ray spectrum predicted by Kramer’s in a thick target, see
page 4.
Can I Monte Carlo the spectrum?
 82 Pb 72805.42(24) 74970.11(17)

Magnet High Current Results
 Time Current Field 4:09 10 A 4:12 20 A 4:14 25 A 2.647 kG 4:20 30 A 3.22 kG 4:25 35 A 3.81 kG 4:31 40 A 4.33 kG

Iron Yoke Magnet Turn-On Procedure

1.       Turn on cooler circuit A, the lest hand switch by the left hand RF room.
2.       Turn on the faucet and measure that the flow is 2 gallons per minute using bucket with tape at one gallon level.  Make sure it fills to bottom of tape level in 30 seconds
3.       Turn on three phase power at wall.
4.       Move all magnet power dials to minimum
5.       Turn on magnet supply breaker switch located on front panel of large box.
6.       Push DC Power On button
7.       Slowly adjust current as desired using the coarse and fine control knobs.

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