Tuesday, December 30, 2014

Qualitative Superconductor Hysteresis Monitoring: Lab Book 2014_12_30

Lab Book 2014_12_30

Today I worked on getting a qualitative susceptometer up and running.  By qualitative I mean that we won't be attempting to analyze the returned data to accurately determine any characteristics of the superconducting materials that are to be studied, only the state of the materials, and the existence, or not of a hysteresis curve for the material.

The why of it all
I’m experimenting with a quick and dirty susceptometer that can be used with the hray experiment to determine when we’ve quenched the superconductor.  Today’s work is using a ferromagnetic core, not a superconductor.  The responses are similar and I don’t have to worry about cooling a superconductor.

Experimental Setup
Something old and something new
I’m pressing a General Radio 1311-A audio oscillator and a Tektronix TDS 210 into service together.


The general radio signal generator is being used to drive the coil surrounding the iron core.  The oscilloscope is measuring both the signal from the General Radio source and the pickup coil on the iron core as shown below






Voltage vs. time vs. frequency
In the following waveforms, the driving voltage is on channel 1 and the response voltage from the pickup coil is shown on channel two.  Channel one is a cleaner signal than channel two.  There’s a 180 degree phase difference between the signal just as you’d expect from Lenz’s law and the output on the pickup coil increases with frequency as you’d expect from Faraday’s law.
400 Hz
500 Hz
1000 Hz
2000 Hz
5000 Hz
10000 Hz









X-Y data vs. frequency
The expected hysteresis loop began to appear once the frequency of the generator was brought sufficiently high.  The following data table illustrates this.
400 Hz
500 Hz
1000 Hz
2000 Hz
5000 Hz
10000 Hz

The final data point at 10,000 Hz is shown below with bandwidth limiting on the scope enabled to cut down on the signal noise:


What we’re seeing
As the frequency of the oscillator is increased, the loop is opening up because the ferromagnetic response of the core can’t track quickly enough with the driving current.  Consequently there’s a phase difference between the two signals and this appears in the x-y display mode as a gradually opening loop.
It should be noted that the signal isn’t large enough to cause the iron core to saturate.  If it was, we’d see horizontal flat extensions at either corner of the loop.  A power amplifier may be added to the arrangement tomorrow to cause saturation.

Here’s a set of hysteresis curves that depend on frequency[1].  Notice that the enclosed loop becomes wider as the frequency increases, just as in the data shown above.


How Ferromagnets and Superconductors are Alike, (well, one way anyway)
I mentioned that ferromagnets behaved in a similar manner to superconductors when subjected to a magnetic field.  It’s because their hysteresis curves don’t look too much different.  Here’s a hysteresis curve[2] measured for superconducting Pb.  The square is the theoretically ideal response.  The curved lines are the actual response of the superconductor.


References:

1.  Jiles, J.C., “Frequency dependence of hysteresis curves in conducting magnetic materials
”, Journal of Applied Physics 76, 5849 (1994) http://dx.doi.org.lib-ezproxy.tamu.edu:2048/10.1063/1.358399

2. Rjabinin, Shubnikow, “Dependence of Magnetic Induction on the Magnetic Field in Supraconducting Lead”, Nature, 134, (1934), 286-287

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