Lab Book 2014_05_08
Hamilton Carter
Summary: A lot of work was done on the YBCO side of the experiment. YBCO superconducts at 90 degrees Kelvin or so. If it can be used, then part of the experiment can be done using liquid nitrogen which is much cheaper than liquid hydrogen. YBCO produces far fewer x-rays than Pb though, and at a far lower energy. The fiberglass Dewar I hope to use for the pulsed magnetic field experiments was measured and it compares favorably to the originally proposed Pb sample size. In the event that the pulsed magnetic coil is placed insside the fiberglass Dewar, it's going to evaporate some of the liquid helium. Calculations were performed to find out how much and what the pressure build up due to this helium would be. The pressure number seems suspiciously low and needs to be checked.
I’m catching up on some of the to do items from the last two
days.
YBCO Experiments
The plan here would be to look for the critical field using the yoke magnet. If we can find it, then experiments using liquid nitrogen, which is much cheaper than liquid helium, can be performed using both the yoke magnet and the can crusher coil.
The plan here would be to look for the critical field using the yoke magnet. If we can find it, then experiments using liquid nitrogen, which is much cheaper than liquid helium, can be performed using both the yoke magnet and the can crusher coil.
Look into the AJP articles about how other people have added contacts. Re-read the four point contact strategy.
I found a rather
skeletal reference that states silver pain can be used to make contacts on
YBCO samples. The do provide contact
information for the supplier, however.
They also have a very nice diagram for the four contact resistivity measurement.
The supplier listed is: Silver
paint, cat. No. 16031, Ted Pella, Inc., P.O. Box 492477, Redding, CA 96049
The four point measurement works as follows. A current is sent through the superconductor
using the two outer leads. As long as
the superconductor is in its normal state, (resistive to electrical currents),
then there will be a measurable voltage created by the current travelling
between the two outer leads. The two
inner leads measure that voltage.
The question that still arises is whether or not we can
quench the YBCO superconductor using the iron yoke magnet. Hirsch’s
data table indicates we may be able to, but other tables contradict it. An article written by Tiernan
at the University of Massachusetts indicates that granular YBCO has a much
lower critical field than single crystal YBCO.
This is a good sign since we have granular
samples from CAN superconductor.
There’s another
article about measuring the critical current density that may be
useful. It looks like give a granular
sample, Hirsch’s number is believable.
The next step is to look at low energy x-ray samples since YBCO gives
much smaller energies than Pb.
As far as what energies can be detected using NaI
scintillation, the following data
is from 1952.
The available YBCO sample is 14 cm in diameter by 6 mm
thick. Assuming a maximal spherical size
of a 3 mm radius gives the following maximum energy and flux as predicted
by Hirsch’s formulas.
Maximum energy
(0.3/RCYBCO)*(eMass*c^2)*(1/evToJ)
6339.71 eV
(0.3/RCYBCO)*(eMass*c^2)*(1/evToJ)
6339.71 eV
Maximum flux
FluxYBCO[0.3]
FluxYBCO[0.3]
136.735 events
The maximum energy is in what Wikipedia calls the hard x-ray
region.
Pb and Liquid Helium
Work
The Pb sample may be placed into the fiberglass Dewar with the pulsing coil mounted either inside or outside the Dewar. By mounting the coil outside, we can use a larger Pb sample since we don’t have to account for the radius of the pulsing coil. DeSilva used a gap between the coils and the can to be crushed of minimally 0.5 mm. The coil was constructed with 3 turns of number 10 copper wire. The wire has a diameter of 2.588 mm. The down side of mounting the coil outside is that our maximum magnetic field for a given current though the coil will be reduced.
The Pb sample may be placed into the fiberglass Dewar with the pulsing coil mounted either inside or outside the Dewar. By mounting the coil outside, we can use a larger Pb sample since we don’t have to account for the radius of the pulsing coil. DeSilva used a gap between the coils and the can to be crushed of minimally 0.5 mm. The coil was constructed with 3 turns of number 10 copper wire. The wire has a diameter of 2.588 mm. The down side of mounting the coil outside is that our maximum magnetic field for a given current though the coil will be reduced.
Aside from the larger possible sample size, and the ease of
construction, there’s another advantage to mounting the pulser coil outside the
Dewar. Most of the heat created by the
coil pulses won’t wind up being deposited in the liquid helium.
The proposed Pb sample will fit easily into the fiberglass Dewar. The neck radius on the Dewar is 4.52 cm and
the specified sample radius is 3.8 cm.
These dimensions give almost 7 mm of clearance on either side of the
sample, which would seem to be enough room to fit the pulsing coil inside the
Dewar.
If the coil does go into the Dewar, then there will be
concerns about the amount of liquid helium evaporated per coil pulse and how
much pressure will build up. The
following is a diagram of the inside of the fiberglass Dewar used for volume
calculations.
Assuming only the tail is filled with liquid helium, that
gives us the volume of the large chamber and the neck to fill with evaporate liquid
helium. The volume available is
calculated below:
Fiberglass Dewar Dimensions (all in inches) | Actual | Scaled | |||
Neck Dia | 3.5625 | 0.890625 | 9.04875 | cm | |
Chamber Dia | 8.0625 | 2.015625 | 20.47875 | cm | |
Neck Depth | 12 | 3 | 30.48 | cm | |
Chamber Depth | 11 | 2.75 | 27.94 | cm | |
Tail Depth | 9.75 | 2.4375 | 24.765 | cm | |
Neck volume | 1960.117 | ||||
Chamber volume | 9202.868 | ||||
Total volume | 11162.98 |
This volume is to be substituted into the ideal gas state
equation,
where
m is the mass of helium in grams, E is the energy per
pulse in Joules, and Q is the latent heat of
liquid helium in J/gram.
All the parameters used and calculated results are shown in
the spreadsheet below.
Avagadros number | 6.02E+23 | molecues | |||
molar conversion for H | 4 | g/mole | He4 | ||
Empty volume above liquid helium | 11162.98 | cm^3 | |||
number of moles | 5.952380952 | mol | |||
R | 8.314 | cm^3 kPa/K mole | |||
T in Dewar above Li He | 8 | K | |||
Specific Heat of Liquid Helium at ~4 K | 3 | J/gm.K | |||
Latent Heat of Liquid Helium | 21 | J/gm | |||
Density of liquid helium | 125 | g/liter | |||
Energy from Pulser | 500 | J | |||
Evaporation per pulse | 23.80952381 | gm | 0.19048 | l | |
Pressure after pulse | 0.035465867 | kPa | 0.00514 | psi |
Table 1 Evaporation
and pressure buildup
The pressure seems a little low. I may have underestimated the temperature in
the Dewar above the liquid helium.
Experimental
Setups
Sample | Quench Speed | Dewar | Sample Size | Detector |
YBCO | Slow | Styrofoam LiNi replenished | 16mm x 6 mm | Film |
YBCO | Fast | Styrofoam LiNi replenished. Sample holder reinforced for Lorentz forces. | 16mm x 6 mm | Film |
Pb | Slow | Glass Dewar | ~1.74 cm radius | NaI |
Pb | Fast | Fiberglass Dewar | ~3.81 cm radius | NaI |
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