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