Persistent Current in Type II Superconducting Loop

Transcription

1 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p.1 Persistent Current in Type II Superconducting Loop Badger, Bradon, Hayhurst, Brian, and Dr. Martin Madsen Department of Physics, Wabash College, Crawfordsville, IN (Dated: October 20, 2014) The goal of this experiment is to create and analyze persistent current in a superconducting loop. We created a persistent current in a superconducting loop and measured the magnetic field versus time. We found that the magnetic field would persist for ( ±.0060) 10 5 seconds (95% CI Gaussian pdf), with a maximum field of.3 mt.

2 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p.2 I. INTRODUCTION According to Lenz s Law: as flux changes through a loop, a current will be induced to oppose the change in magnitude of the magnetic field. An application of this is flux pinning through a superconducting loop. The defects in a type II superconductor effect the magnitude of the induced magentic field due to flux pinning [1]. As a superconductor reaches its critcal temperature (T c ) it will have little to no electrical resistance. Theoretically, if a current is induced in a superconductor and kept at or below T c, then the current should persist indefinitely[5]. This conclusion is not valid because there is a slight resistance in the soldered joint completing the loop. It is therefore of interest to explore the persistivity of the current in a superconducting loop as well as the properties of the induced magnetic field. II. MODEL First, a superconductor will only enter its superconducting state if: T < T c. (1) Where T is the temperature of the superconductor. Also, the current through the superconductor will only persist forever if: R Loop = 0. (2) Where R Loop is the resistance of the superconducting loop in its superconducting state[4]. However, we know R Loop > 0 because the soldered joint possesses a small trace of resistance[2]. Although there is a slight amount of resistance, one can still create an induced current over a long period of time. The creation of a quazi persistant current can be done via flux pinning; When a superconducting loop falls below its critical temperature, the flux through the loop will be locked in. To achieve a persistant current, flux through the loop must be present during the superconducting transition[1]. We want to pin flux through the loop (which we will explain here in a moment), then proceed to place the loop in an apparatus that allows us to measure magnetic field over a long period of time without the low temperatures influencing our magnetic field probes, all while still keeping the loop in its superconducting state. The apparatus we worked with was a 10 cm by 10 cm Styrofoam block. We used a soldering iron to melt a trench for the

3 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p.3 superconducting loop and liquid Nitrogen with a depth of h 6.5 cm and a width between walls of w 2 cm. This trench wraps around the center in a circle, so that the loop fits nicely around the unsoldered centerpiece of Styrofoam. Next, we hollowed out the top and bottom of the Styrofoam block in the center to fit two magnetic field probes to measure both sides of the superconducting loop. The hollowed areas extended to d.4 cm away from the center of the loop. A side view and overhead view of our apparatus can be seen in FIG 1. We induced current in the loop, then as quickly as possible, transferred it to its position in our Styrofoam apparatus. To pin flux in our loop, we first placed a magnet in the center of the loop. We then proceeded to engulf the superconductor with liquid nitrogen. Once the supercondutor fell below its critcal temperature, the magnet was removed from inside the loop to induce a current. The loop was then moved to our Styrofoam apparatus and two magnetic field probes were fixed a few millimeters away from the center of the loop (along the z-axis). We recorded magnetic field versus time while being careful to continually add liquid Nitrogen to keep the system under T c. It should be noted that our superconducting loop (SuperPower part number SCS12050: M ) had a radius of roughly 3 cm and a thickness of 1.1 cm. A step-by-step procedure of the described process can be seen in FIG 2. We observed that as a function of time, the magnitude of the magnetic field decreased slightly. Shortly after we let the liquid Nitrogen boil off, there was a drop in magnitude that signifies the loss of superconductivity. We can speculate that there is a steady decrease in magnetic field (as seen in FIG 4) as a result of the slight resistance of the soldered joint. As data collection continued, a sudden drop in the magnitude of the magnetic field occurred due to the transition out of the superconduting state. From here the resistance rapidly increases causing the current to decrease to zero. We can conclude that a current can persist for a long period of time, but due to the soldered joint, the current will not persist indefinitely. It would be of interest to explore methods of reducing the resistance by different soldering techniques and materials. Future work could entail exploration of techniques to increase the induced current while in the superconduting state[3]. Also as a side note, we created a Field Map of the magnetic field as a function of the distance from the center along the z-axis(fig 3), and found an observation of great interest. It appears that the magnetic field is one direction on one side of the

4 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p.4 z Top Probe y Styrofoam w w Hollow Area for Magnetic Probe h w d d Liquid Nitrogen Styrofoam Bottom Probe x Trench for Liquid Nitrogen x FIG. 1. Setup for measuring the magnetic field produced by the current in the loop. The two magnetic field probes in the figure on the left are at distance d.4cm from the center of the superconducting loop. The trench has depth h 6.5cm and width w 2cm. The figure on the right is the overhead view of the system. Holes for the magnetic field probes are present in the center of the top and bottom of the apparatus. The superconducting loop fits within the trench so that it is wrapped around the center. As the trench fills with liquid Nitrogen, the loop becomes engulfed and is able to sustain its superconducting state. Magnetic Field(~.3 mt) Magnet Induced Field(~.3 mt) 1.1 cm Radius= 3 cm Liquid Nitrogen Insulated Styrofoam Container Magnet pulled out from loop FIG. 2. The figures above show the process of flux pinning with our superconducting loop immersed in liquid Nitrogen in a Styrofoam container. The figure on the left shows the magnet inside the superconducting loop along with the dimensions of the loop. The magnet itself produces a field of approximately.3mt. The center figure depicts the magnet being pulled from the loop; the resulting induced field is appoximately.3mt, as shown by the figure on the right. loop, but antiparallel on the other side, suggesting evidence of a quadrupole field. undoubtedly creates grounds for future investigation of the reasons why this is occurring This

5 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p.5 magnetic field mt distance along z axis cm FIG. 3. The figure above shows the field map of the induced field produced by the superconducting loop. As one can see, at the center of the loop, the field is zero. The magnitude of the field becomes a maximum at approximately ±1.5cm from the center of the loop. This field map is consistent with a quadrupole field. and how to deal with this issue. [1] Cardwell, D. A., and N. Hari Babu. Improved Magnetic Flux Pinning in Bluk (RE)BCO Superconductore. AIP, 3 Mar [2] Gurtovoi, V, S Dubonos, A Nikulov, N Osipov, and V Tulin. Dependence of the Magnitude and Direction of the Persistent Current on the Magnetic Flux in Superconducting Rings. Journal of Experimental and Theoretical Physics (2007): [3] Mizutani, U., T. Oka, Y. Itoh, Y. Yanagi, M. Yoshikawa, and H. Ikuta. Pulsed-field Magnetization Applied to High-Tc Superconductors. Applied Superconductivity (1998): [4] Ohsaki, Hiroyuki, Tatsuya Shimosaki, and Naoyuki Nozawa. Pulse Field Magnetization of a Ring-shaped Bulk Superconductor. Superconductor Science and Technology 15.5 (2002): [5] Sander, M. Novel Pulsed Magnetization Process for Cryo-permanent Magnets. Physica C: Superconductivity (2003): ScienceDirect. Web. 28 Sept

6 WJP, PHY381 (2014) Wabash Journal of Physics v1.3, p magneticfield mt time s FIG. 4. Graph of magnetic field versus natural log of time. There is a small but steady decline in the magnetic field. This experiment was only run once, but the data suggests that the current will slowly fall to zero after t ( ±.0060) 10 5 seconds. This implies that there is a small resistance within the loop, most likely from its soldered joint.