University of Groningen

Bachelor Thesis in PhysicsResearch performed at SRON

Design and characterization of a LTS fluxpump system for possible satellite

application

Author:Laurens Even

Supervisor:dr. ir. G. de Lange (SRON)

prof. dr. ir. R.A. Hoekstra (RUG)prof. dr. T. Banerjee (RUG)

July 8, 2016

l.even.1@student.rug.nl

student number 2315963

Abstract

In this bachelor project research is performed on the design of a prototypelow temperature superconducting (LTS) flux pump system. With such asystem a superconducting electromagnet can be charged to high currents,while only a low current power supply and cryogenic wiring is necessary.The flux pump could find potential as an application in the SAFARIinstrument for the SPICA satellite, but it can also be used for cryogenicenergy storage or for offsetting a magnetic field. As a satellite applicationthe flux pump can reduce parasitic heat load on the cold stages of thesatellite.

Within this thesis we continued the work on an existing flux pumpdesign from a previous bachelor project. This design had previouslyshown some essential performance characteristics of a flux pump system,but the actual flux pumping was not observed. In this thesis work weinvestigated the possible causes of this and implemented improvements.These improvements have resulted in a working flux pump system. Themain improvement (which was found in a late stage of the project)was the correction of the winding orientation of a secondary coil inthe transformer. Other improvements are: (1) the optimization of thetransformer cooling, such that higher critical currents in the primarytransformer superconducting wire could be achieved, and (2) the increaseof the self-inductance of the primary coil of the transformer by replacingthe original aluminum transformer core (that will induce eddy currents)by a Vespel polyamide core. For the characterization of the transformerperformance we have used a two-phase lock-in measurement technique todetermine the self-inductance and mutual inductance of the primary andsecondary coils as a function of frequency.

The final flux pumping system (V3.0) operates at 4 K, and consists of atransformer with a 4950 turn primary coil (Lp = 4,4 mH self-inductance),a 2 x 10 turn secondary coil (Ls = 0,5 µH, and a 900 turn load coil withan estimated self-inductance around 13,5 mH), all made with supercon-ducting wire. The current in the load coil is monitored by measuring themagnetic field that is generated by the coil with a fluxgate meter. Theprimary coil has been operated with a maximum current (ramp) of 0,5 A(500 mA/s). The measured and calculated current gain of the flux pumpare both around 0,16 mA per cycle for a 50 mA primary current. Withthis system a current of at least several amperes should be achievable inthe load coil (resulting in a magnetic field in the order of at least dozensof milliteslas), but we have limited ourselves to a maximum of 60 mA,because of limitations in the range of the flux gate sensor (not higherthan 590 µT).

The coupling factor (0 ≤ k ≤ 1) describes the coupling between theprimary and secondary side in a transformer, where a value close to 1would be ideal. For the final flux pumping system k is estimated to bearound 0,45.

AcknowledgmentsI would like to thank the following people who helped and supported me during my BachelorProject that I worked on at SRON:

3 SRON supervisor Gert de Lange for his help on understanding the basics of flux pump systems,its components and the measuring equipment involved in the measurements. Also for hisadvice on relevant research items and important items to look at.

3 Willem-Jan Vreeling for his help with the laboratory instruments, cryostat operations andhelping me understand the LabVIEW programming language to control the flux pump.

3 Axel Detrain for helping me to understand the basics of measuring and determining thecharacteristics of electromagnetic coils and also for his help in analyzing some of the data.

3 Duc van Nguyen, Rob van der Schuur and Jarno Panman for their help with fabricating partsneeded for the flux pump project. Extra thanks to Duc for his comprehensive work related tothe soldering of wires and attaching parts together.

3 RUG supervisors Prof. Dr. Ir. R.A. Hoekstra and prof. dr. T. Banerjee for supporting meduring my project.

3 Wim van den Berg for his continuous support related to questions I had about his formerresearch on the flux pump system. Special thanks for his one day revisit at SRON. Duringwhich he helped me put the improved system (V3.0) together and also at doing the first (andlast) measurements on the improvement flux pump system. This was almost at the end of mybachelor project, but luckily it was still in time.

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Contentsabstract i

Acknowledgments ii

1 Introduction 11.1 Origin of this research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Topic of this research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Research questions and aim of this research . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Research aim 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.2 Research aim 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.3 Research aim 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theoretical Background 52.1 Superconductivity in short . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Flux pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Half and full wave rectifier flux pump operation . . . . . . . . . . . . . . . . 82.2.2 Description of the flux pump system used in this research project . . . . . . 92.2.3 Flux pumping quantified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.4 Coupling factor, mutual inductance and stray fields . . . . . . . . . . . . . 122.2.5 Flux pump operation example . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Two and four terminal resistance measurement methods (sensors) . . . . . . . . . . 13

3 Experimental Methods/setup 153.1 Description of flux pump setup V2.0 and V3.0 . . . . . . . . . . . . . . . . . . . . . 153.2 Self-inductance values of the coils present in setup V2.0 and V3.0 . . . . . . . . . . 183.3 Expected relation between load coil current and measured magnetic field strength 193.4 Description of three self-made coils/transformers . . . . . . . . . . . . . . . . . . . 19

4 Results & Discussion 214.1 Measurements on self-made coils/transformers . . . . . . . . . . . . . . . . . . . . . . 21

4.1.1 General remarks about the measurements on coil 1 and 2. . . . . . . . . . . . 214.1.2 Coil 1 (aluminum) and coil 2 (Vespel) with air core . . . . . . . . . . . . . . 224.1.3 Coil 1 and coil 2 with iron material in core . . . . . . . . . . . . . . . . . . 224.1.4 Coil 1 and 2 put in liquid nitrogen . . . . . . . . . . . . . . . . . . . . . . . 224.1.5 Coil 3 with and without ferrite (high permeability) core . . . . . . . . . . . 224.1.6 Summary about test coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 Expected transformer coupling factor and (current) gain . . . . . . . . . . . . . . . 234.3 Repeated experiments on flux pump setup V2.0 . . . . . . . . . . . . . . . . . . . . 244.4 Lock-in amplifier frequency sweep measurements analysis and comparison with

LTspice IV simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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4.5 Flux pump cryostat measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.5.1 Persistent current test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.5.2 Trouble with the fluxgate meter . . . . . . . . . . . . . . . . . . . . . . . . 264.5.3 Calibration fluxgate meter (Bartington) output in µT with current magnitude 274.5.4 Heat switches & persistent current test (commutation) . . . . . . . . . . . . 284.5.5 Flux pumping fast to 60 mA (590µT) . . . . . . . . . . . . . . . . . . . . . 304.5.6 Flux pumping slow to 60 mA (590 µT) . . . . . . . . . . . . . . . . . . . . . 324.5.7 Critical temperature determination of the load coil during system warm up 33

5 Conclusions and recommendations for future work 345.1 Research aims and questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.1.1 Research aims 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.1.2 Research aim 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 Recommendations for future improvements . . . . . . . . . . . . . . . . . . . . . . 35

References 37

Appendices 39

A Measurements of test coil parameters 40A.1 Test coils 1 and 2 - inner air core left empty . . . . . . . . . . . . . . . . . . . . . . 40A.2 Test coils 1 and 2 and inner core filled with some magnetic iron material . . . . . . . 41A.3 Test coils 1 and 2 - in liquid nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . 41A.4 Test coil 3 - with & without an iron core/casing . . . . . . . . . . . . . . . . . . . . 42

B Results lock-in amplifier and simulation with LTspice IV 43

C LabVIEW control and instrument setup of the flux pump system 46

D Possible magnetic bearing setup for the FTS 47

E Primary coils V1.0, V2.0 and V3.0 48

F Pinout flux pump experiment (setup V3.0) 49

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Chapter 1

Introduction1.1 Origin of this research

SRON, Netherlands Institute for Space Research, focuses on building technology and advanced spaceinstruments for use in astrophysical, Earth science and exoplanetary research. SRON, together withESA (European Space Agency) and JAXA (Japanese Space Agency), is working on the SAFARIinstrument which is an infrared spectrometer. It is to be included in the SPICA satellite (SpaceInfrared Telescope for Cosmology and Astrophysics) and launched to space in 2028, on one ofJAXA’s launch vehicles [1][2].

The original plan for the SAFARI instrument on the SPICA satellite was to have the incominglight analyzed by a Fourier Transform Spectrometer (FTS). The FTS includes a movable mirrorwhich is suspended in magnetic bearings with a magnetic linear stage providing the ability for themirror to move (see appendix D for possible applications). In order to test this system on earth themagnetic bearings need to provide a stronger magnetic field than required in space due to the earthgravitational force. This is called ’1G-off-loading’ and it can be implemented such that the mirroris magnetically levitated and free to be controlled by the linear magnetic stage. The mirror willalso be cooled to almost absolute zero (cryogenic) temperature (−273 C) to minimize backgroundnoise (heat radiation) and to improve experimental results. Operating at these low temperaturesand a limited cooling capacity of system coolers in space require that parasitic heat sources need tobe managed well.

1.2 Topic of this research

The need for 1G-off-loading of the FTS mirror requires additional electromagnets (to obtain higheramperages) in order to obtain stronger magnetic fields as mentioned earlier, but this also requiresextra wiring. This and higher amperages give rise to more parasitic heat flow between the cryogenicand ’hot’ environments in the system. To minimize this heat flow high resistive wiring will be usedto connect these environments, but this will increase resistive heating and thus also increase theheat load on the system. The allowed 4 K heat load in a space system is of order mW (much lowerthan commercial pulse tube coolers or laboratory He cooled cryostats). The required current isof order 1 A. Since the electrical conductivity and the thermal conductivity of metals are linkedwith the Wiedeman-Franz law, one cannot have wires that have both a low electrical resistanceand a high thermal resistance (except for superconducting wire). One therefore has to balancethe dissipation in the wire due to Joule heating with the parasitic thermal heat flow (from highertemperature stages) due to thermal conductivity.

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In the end, a higher current from the ’hot’ (at around 300 C) to the cryogenic environment (4 C)means an increase in the parasitic heat load and as a consequence a larger part of the coolingcapacity is taken up. However, the cooling capacity has a certain threshold (total allowed heatload) which may not be exceeded for the system to remain at a temperature of almost zero Kelvin.

Unfortunately because of the logistics involved in satellite development, additional magnets andwiring are difficult if not impossible to be removed from the instrument before it is launched intospace. Hence additional parasitic heat load will be present in space when the satellite is operating.Thus to not reduce the mission duration of SAFARI the parasitic heat load needs to be minimized.In a previous bachelor project BSc. Wim van den Berg’s worked on a system that could in principleobtain high currents in an electric circuit to dive an electromagnet while using a low power supplyin a different circuit resulting in low parasitic heat load. This system is called a ’flux pump’ andthe use of the principle goes back a long time and many articles have been published on this topic[3–16].

During his bachelor thesis the principles of ’flux pumping’ were studied. Though the studied articleswere mainly about high current applications (of order kA), the operating principle also holds forthe mA ranges that are of interest for this specific satellite application. Eventually a flux pumpsystem prototype was built and this, and its components, were tested thoroughly and had multipleoptimizations and revisions [17]. Unfortunately the flux pumping operation was not working asintended. The problem was not clearly identified, but had something to do with the coupling ofthe electromagnetic coils in the transformer part of the system and/or the wiring of these coils.A constant primary current ramp up or down (dI/dt = C) in the primary side needs to inducea current in the secondary circuit, via an induced electromotive force (emf), which subsequentlyneeded to generate a magnetic field with sufficient strength to be measurable. Unfortunately thefield strength could not be determined, because Wim van den Berg could not distinguished thesignal from noise during measurements.

This research focuses on the design and further characterization of a low temperature supercon-ducting (LTS) flux pump system that can be used as a basis for 1G-off-loading of a certain mass.Although a change was made in the FTS mission design, a flux pump system is still of interest andcan also be applied on other field. When the system as a whole proves itself to be functioning, it isalso usable in satellite applications similar to the FTS and/or for offsetting magnetic fields or evenfor superconducting magnetic energy storage called SMES.

1.3 Research questions and aim of this research

This research project follows up on the work done by BSc. Wim van den Berg. The prototype thathe made will be updated where necessary. My main research aim is to improve the existing systemand to get it fully operational including the flux pumping itself.

1.3.1 Research aim 1

Obtaining a better understanding of the operating principles of (superconducting) coils andtransformers (in electric circuits), especially related to the flux pump system. To do so, thetransformer behavior will be analyzed with a LCR measurement equipment and with a two phaselock-in amplifier. With a lock-in measurement technique we can measure the frequency behaviorof the transformer up to frequencies of 100 kHz and we will be able to measure small emf signalswith a high signal to noise ratio. With the obtained knowledge it may be possible to find problems

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in the current flux-pump setup and improve the parts that are involved and possibly apply moreoptimizations.

Hypothesis: Bad coupling between the primary and the secondary side of the transformer ismainly the result from (large) Eddy currents present in the aluminum core of the primary coilsegments, which has a high electrical conductivity. Another possible problem could be shortagesbetween turns in the primary coil.

1.3.2 Research aim 2

Improve the thermal design of the flux pump to allow higher (critical) currents in the system.

Hypothesis: With the existing flux-pump design the critical current in the primary coil is relativelylow (< 100 mA) while the wire itself should at least be able to carry several amperes. This indicatespoor thermal contact with the copper ground plate which is cooled to 4 K. Improving this willfacilitate a higher current ramp in the primary coil, and thereby a larger current in the secondarycoil.

1.3.3 Research aim 3

Research question: Show that a flux pump system can operate more efficiently than a systemwithout a transformer and where instead a current is driven directly though the 1G-off-loading coil.

1.4 Thesis outline

First of all literature was studied related to superconductivity and flux pump systems to get a basicunderstanding of the research topics, including but not limited to: superconductivity, magneticfields, operation of transformers and the characteristics of the individual coils in a transformer. Asa next step experience was gained with the graphical programming language LabVIEW in order toget a feeling on how to build a Virtual Instrument (VI) and how to use this to control equipmentwith it. This is needed to get a general understanding of the LabVIEW program that Wim van denBerg developed, which controls and monitors the flux pump system. During the research there isalso focus on how to measure the different parameters of coils and transformers, this includes theuse of a LCR-meter.

Measurements with a LCR-meter were first performed on factory made transformers and sub-sequently on self-made test coils which should resemble the characteristics of the flux pumptransformer, albeit on a different scale (see section 4.1). The intention is to use these coils to studydifferent effects on the coupling of two coils together forming a transformer and to extrapolate itto the used flux pump transformer. Some experiments with the unchanged system that Wim vanden Berg built are repeated to get a feeling for how the system reacts to certain inputs and whatis important to keep in mind such as the maximum allowed currents (see section 4.3 for some ofthe results). With a Lock-in amplifier AC frequency sweeps measurement are performed on (test)transformers in order to study the characteristics of the primary and secondary coils. An attemptis made to determine the coupling between the primary and secondary side of the transformer.Section 4.4 sh

An important part of the bachelor project is the development and fabrication of new componentsfor the flux pump system, especially a new primary coil (and transformer), called version 3.0. Forprimary coil V3.0 roughly 4800 turns of superconducting wire is wound around six identical coresegments made of Vespel polyamide core instead of an aluminum core as was used in V1.0 and

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V2.0. The thermal contact of the transformer with the cryostat will also be improved to try toincrease the primary critical current. The winding direction and connections of the secondary coilleads is also thoroughly looked at and corrected. The new transformer and setup will from here onebe called ’setup V3.0’.

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Chapter 2

Theoretical Background2.1 Superconductivity in short

Superconductivity is a phenomenon that occurs in some materials when they are cooled belowa critical temperature. The result is an absolutely zero electrical resistance (see figure 2.1) andexpulsion of magnetic fields in the material interior (possibly originating from external fields). Thisis called superdiamagnetism or perfect diamagnetism. Thus a superconducting coil is a perfectdiamagnet and characterized by the complete absence of magnetic permeability.

Figure 2.1: In this graph the resistivity ρ is plotted against the temperature for a normalmetal and a superconductor.(figure from simpliphy page about ”Superconductivity” [18].

These characteristics are described by the brothers Fritz London and Heinz London. They developeda theory with two important equations, being:

E =∂

∂t(ΛJs) (2.1)London equation 1:

h = −c curl (ΛJs) (2.2)London equation 2:

Λ =4πλ2

c2=

m

nse2(2.3)where

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is a phenomenological parameter. Js is the superconducting current density, λ the Londonpenetration depth, m electron mass, e electron charge, ns the number density of superconductingelectrons and h the value of the flux density on microscopic scale.[19]

The first London equation (2.1) describes perfect conductivity since any electric field acceleratesthe superconducting electrons rather than simply sustaining their velocity against resistance asdescribed in Ohm’s law in normal conductor. The second London equation (2.2) when combinedwith the Maxwell equation curl h = 4πJ/c gives:

∆2h =h

λ2. (2.4)

This describes the exponential expulsion of magnetic fields from the interior of a sample withpenetration depth λ, this is called the Meissner effect and can be seen in figure 2.2. Circulatingcurrents will be induced in a thin boundary layer at the surface of the superconducting materialin such a way that the flux through a superconducting coil stays constant. During a materialtransition from normal to superconducting state electrons have the tendency to ’condensate’ byforming Cooper pairs. Cooper pairs or BCS pairs are described in the BCS theory (being thefirst microscopic theory of superconductivity), named after its theory creators John Bardeen, LeonCooper, and John Schrieffer. The cooper pairs ’make’ electrons behave like bosons and they therebyenter the ground state. The coupling between the electrons partly has to do with electron-phononinteractions. For more information on this theory take a look at ”Introduction to Superconductivity”by Michael Tinkham [19] or other literature.

Figure 2.2: This figure shows the Meissner effect expelling the magnetic fields (indicated bythe black arrows) out of a superconductor [20].

2.2 Flux pump

What is a flux pump? What is flux pumping? and why use a flux pump in the first place?

The most important property of superconducting flux pumps is their ability to build up a persistentcurrent and maintaining the current even when there is no external power source connected orpresence of changes in magnetic flux. In particular superconducting rectifying flux pumps can

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induce a persistent current by electromagnetic induction, by periodical flux pumping, and whenstopped after some time t the current can be maintained even when there is no induction takingplace at that moment.

According to an article by Van de Klundert and Ten Kate [3] flux pumps can be divided in threeclasses, namely flux compressors, DC dynamos and transformer rectifiers. Only the transformerrectifier flux pump is relevant for this research project. The other two classes will not be discussedhere.

A rectifier flux pump consists of two separate electric circuits. An essential part of this type of fluxpump system is the transformer which magnetically couples the electric circuits via electromagneticcoils. One of the circuits contains a power source and a primary coil and the other circuit containsat least one secondary coil and two heat switches. From here on the circuits will be convenientlyreferred to as primary circuit and secondary circuit respectively. The use of the word switch isfor convenience, but in this context it actually does not describe a physical switch. In this reportthe word switch describes a piece of superconducting wire which can be heated so that it reachesits critical temperature and breaks superconductivity making it resistive. The heating is done bysending a ’heater current’ through a thermally connected wire. The switch has a cool-down time tobecome superconducting again, which depends on its thermal contact with the copper ground plate.

The basic operating principle of a flux pump is a time varying primary current which generates atime varying changing magnetic flux which consecutively induces an emf or voltage in the secondarycircuit according to Faraday’s law of induction. When the change of the primary current in time isconstant the emf will also be constant. The emf will generate a secondary current, which magnitudedepends on the magnitude of the emf which again depends on the slope of the primary current.The secondary current also increases with time which depends on the induced emf that is relatedto the maximum primary current divide by the slope of the current as

Ist ∝ emf ∝Ip max

dIp/dt. (2.5)

The direction of the induced current can be derived from Lenz’ Law, which says ”Nature abhors achange in flux”. In the case of an increasing flux a current will be induced of which its direction isso to oppose the change in flux. In circuit diagrams the dot marking convention can be used toindicate in which direction the induced current will flow (this is explained in figure 2.3 and again insection 2.2.2).

Figure 2.3: The dot convention for four different situations. The figure is quite self-explaining,because it can be quickly seen that a certain instantaneous or changing primary current (I1)will induce a current (I2) in the secondary circuit with the currents directions as indicatedby the dots [21].

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2.2.1 Half and full wave rectifier flux pump operation

Rectifier flux pumps can be split into half wave and full wave rectifiers. The former only induces acurrent during primary current ramp up OR ramp down, while the latter induces a current duringboth primary ramp up AND ramp down.

Figure 2.4: Flux pump operation of a half wave rectifier [17].

In figure 2.4 the flux pump op-eration of a half wave rectifier isshown with four steps. (1.) Dur-ing the first step switch 1 is closed(superconducting) and switch 2 isopen (resistive). A primary cur-rent ramp up will induce a constantemf or voltage over the secondaryloop which induces a CCW currentthrough switch 1 and the load coil.(2.) The primary current is keptconstant and no currents will be in-duced. Switch 2 is closed making itsuperconducting. The current willremain in the outer loop becauseof its inductive property. (3.) Theprimary current remains constant,while switch 1 is opened which forces the secondary current from the outer loop to the inner loop(through switch 2). This is called commutation. (4.) The primary current is ramped down inducinga negative voltage over the outer loop, but this will not induce a current because switch 1 is open.

After step 4 switch 1 is closed followed by the opening of switch 2 forcing the secondary current tothe outer loop. Now the steps as described above can be repeated periodically to build up a largerpersistent current.

Figure 2.5: Flux pump operation of a full wave rectifier [17].

In figure 2.5 the flux pump opera-tion of a full wave rectifier is shownwith four steps. (1.) During thefirst step switch 1 is open (resistive)and switch 2 is closed (supercon-ducting). A primary current rampwill induce a constant emf over bothsecondary loops which induces aCW current in both loops whichare in different directions throughthe load coil, but due to the resis-tance in switch 1 the current in theupper loop will be very low relativeto the current in the bottom loop.(2.) The primary current is keptconstant and no currents will be in-duced. Switch 1 is closed makingboth secondary loops superconduct-ing. The current will remain in thebottom loop.

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(3.) The primary current remains constant, while switch 2 is opened forcing the secondary currentfrom the bottom loop to the upper loop. The current direction through the load coil remains thesame, because of its inductive property. (4.) The primary is ramped down inducing a current withdifferent direction than in step 1, but increasing the secondary current.After step 4 switch 2 can be closed followed by the opening of switch 1 forcing the current fromthe upper loop to the lower loop. Again the steps described above can be repeated periodically tobuild up a larger persistent current.

2.2.2 Description of the flux pump system used in this research project

In this research project a superconducting rectifier flux pump is used where both the primary andsecondary sides are placed in a cryogenic environment (cryostat). The flux pump system as built byWim van den Berg is a full wave rectifier with one primary coil and two secondary coils similar tofigure 2.5, but the secondary coil is physically split in two coils though practically it is connected inthe same way. The complete flux pump circuit with the full wave rectifier included can be seen infigure 2.6. Also indicated are the locations of two (superconducting) joints that are needed to makea closed loop. The secondary circuit is completely superconducting and only magnetically coupledto the primary circuit by means of electromagnetic coils. The primary coil is also superconducting,but the rest of the primary circuit is not since it includes a current power source which is locatedin the ’hot environment’.

Figure 2.6: Circuit diagram of the flux pump system with a full wave rectifier with oneprimary coil on the left, two secondary coils, one load coil, two superconducting joints andtwo heat switches indicated with the number 1 and 2 [17].

In the figure the dot convention is used which indicates the direction of the induced current. Inthis case an increasing primary current in the CW direction (or decreasing in CCW) will induce aCW current in both secondary loops and a decreasing primary current in the CW direction (orincreasing in CCW) will induce a CCW current in both secondary loops. When the switches areclosed and opened as in the previous section for a full wave rectifier a persistent current can bebuild up.

When a current is sent to the cryogenic environment it encounters high resistive wiring (Rp) duringthe entering of the cryostat.a When the power source is on during the operation of the fluxpump, the primary current will cause extra inflow of heat into the cryogenic environment whichis generated due to the high resistive wiring. The secondary side has zero resistance by beingcompletely superconducting (which means no current dissipation) and has no power source. Thusthere is no source of parasitic heat in the secondary circuit (internal generation or external inflow of

aHigh resistive wiring reduce the inflow of parasitic heat into the (cold environment of the) cryostat, but on theother hand result in more Joule-heating. It is a trade-off between these two factors and this will be discussed inmore detail later (section 3.1).

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heat). However, during flux pump operation commutation of the persistent current takes place inthe secondary circuit. When using resistive commutationb some fraction of the persistent current isdissipated and converted into heat.

With a flux pump system as described above, there can only be (extra) external heat flowing intothe system and heat generated within the system during the operation of the flux pump. Thus aftera persistent current is built up, it can be maintained and remain constant while no heat is generatedin the cryogenic environment. This makes it possible to generate a constant magnetic field with asuperconducting electromagnet which remains constant when the power source is disconnected andalso minimizes the heat load on the cooling system.Unfortunately this only holds for the ideal case in which a persistent current in a superconductingcircuit always stays constant because of zero resistance. Although this is true, in practice thesecondary circuit always has some small resistance originating from the presence of at least twojoints. This finite resistance makes the persistent current decay over time, but the joints can’t beavoided since they are needed to make the secondary loop a closed loop. A circuit that containstwo secondary coils, a load coil and two heat switches while being made out of one piece of wire isjust too hard to make and then still one joint comes into existence.

2.2.3 Flux pumping quantified

In this section formulas will be used to quantitatively describe the increase of the persistent currentin the secondary circuit based on the work of T. P. Bernat, D. G. Blair, and W. O Hamilton (1975)about an automatic superconducting (4,2 K) high current flux pump (∼ 1000 A) [5]. Though thisarticle is about a high current application it should also be applicable to low currents (∼ 1 A),because the flux pump principle is exactly the same at these different scales.

During the first flux pump step

i10 = −ipkps√LpLs

Ls + Ll(2.6)

is induced in one of the secondary loops, where the minus sign indicates a current in oppositedirection so to counteract the changing magnetic field generated in the primary loop. kps is thecoupling between the primary and secondary coils. The coupling factor between two coils is alwaysa value between 0 and 1, with the former being no coupling and the latter being perfect coupling.During the fourth flux pump step

i20 = i10Ll − k12Ls

Ll + Ls= α i10 (2.7)

is induced in the other secondary loop adding to the already present persistent current.k12 is thecoupling between the secondary coils and α is defined as α ≡ (Ll − k12Ls)/(Ll + Ls) which isthe fraction of the current transferred from one loop to the other. The induced current after onecomplete cycle is

i(1) = i10(α+ α2). (2.8)

Each cycle of the flux pump operation is the same as the first. The persistent current inducedduring step one and step four and the factor α are all independent of the initial current flowing in

bResistive commutation is a process where the non-zero current through the switch during the switching isdissipated and converted into heat. A different process is called inductive commutation, which does not generateheat in the switches. For a more detailed explanation about the two processes you can look up the second article ofVan de Klundert and Ten Kate about flux pumps (1981)[4].

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both secondary loops. When the cycle repeated n times the persistent current through the loadcoil will be

i(n) = i10(α+ α2 + ...+ α2n) = i10α

(α2n − 1

α− 1

). (2.9)

From equations 2.6 and 2.9 the maximum load circuit current that can be obtained after infiniteflux pump cycles is

i(∞) = −ip√Lp

Ls

αkpsk12 + 1

. (2.10)

Equation 2.10 can be used to rewrite the persistent current after n cycles to

i(n) = i(∞)(1− α2n). (2.11)

The maximum current amplification or gain (G) after infinite cycles can be written as (if k12 = 0)

G =∣∣∣I(∞)

s /Ip

∣∣∣ = αkps

√Lp/Ls. (2.12)

This limit in the persistent current exists due to the dissipation of a certain fraction of the currentduring the current transfer from one loop to the other. The dissipation is due to the ’on time’ ofthe heat switches and occurs in the normal regionc of the secondary wire which is the part of thesecondary circuit that is heated by the switches [5]. At one point after a certain number of fluxpump cycles the fraction of the total persistent current which is not transferred from one loop tothe other and the induced current during a half flux pump cycle (1− α)ipers. = i10 become equallylarge since the current decay is proportional to the total persistent current.d

The ideal gain is obtained when α = 1, /(k12 = 0andLl/Ls = inf) and kps = 1, but actually α cannever become The current gain is just the primary current magnitude multiplied by the gain factor,so this limits the current gain to the maximum allowed primary current and the self-inductanceratios.

A high gain factor (G > 100) means that the persistent current in the secondary circuit can reacha high multiple of the primary current magnitude (×100), which allows a large current through theload coil (depending on the primary current magnitude) to generate a strong magnetic field. Thusit is important that the ratio of the self-inductances of the primary and secondary coil(s) in a fluxpump transformer is high (so Lp Ls, which follows from the relation given in equation 2.12) inorder to have a high current gain in the system.Secondly the ratio between the load coil self-inductance and the secondary coil(s)needs to be high(Ll Ls), so α is as close as possible to 1, which will also improve the gain (as can be seen inequation 2.12).

Note from equations 2.10 and 2.12 that the (current) gain is independent of the current ramp. Ahigher current ramp will induce a secondary current with the same magnitude in a shorter timesimply by inducing a larger emf. Unless there are materials with magnetic properties nearby thetransformer that exhibit hysteresis effects and/or generate eddy current, because these effect dodepend on the operating frequency (current ramp). Also note that from the equations just describedin this section one can conclude that the rate of generating a certain persistent mainly depends on

cThe normal region is the region of the secondary circuit which is not superconducting and thus has a non-zeroresistance.

dThe current fraction which is dissipated is independent of the normal resistance [5].

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the magnitude of the primary current, the ratio between primary and secondary self-inductanceand the coupling between the coils. Unfortunately the self-inductance ratio that is beneficial fora high current gain per step (quick charging) is unfavorable for the total (current) gain and viceversa. So has to choose what is favorable and balance the two aspects accordingly.

2.2.4 Coupling factor, mutual inductance and stray fields

What is the relation between the coupling factor (k) between coils, mutual inductance (M) andleakage (or stray) inductance?

The coupling factor (k), a value between 0 and 1, indicates the ratio of the ’leakage’ flux to theenclosed magnetic flux (Φleakage/Φenc) of one coil to the other coil. An ideal transformer has k = 1,which means that all magnetic flux of a primary coil is completely enclosed by the surroundingsecondary coil(s). The coils in a transformer with k = 0 have no mutual coupling. The couplingfactor with the primary and secondary coil self-inductance relate to the Mutual inductance as

M = k√Lp/Ls. (2.13)

An indication for the coupling factor is given by

k =

√1− Lp stray

Lp, (2.14)

where Lp stray and Lp can be experimentally determined.

The self-inductance of a long solenoid (a straight coil with a single winding layer) with a lowpermeability core (µr ≈ 1 soµ ≈ µ0) has a self-inductance of

L =µ0N

2A

l, (2.15)

where µ0 is the vacuum permeability, N the number of turns, A the area of the solenoid perpendicularto the longitudinal axis and l the length of the coil. For coils with a higher permeability coreequation 2.15 can give higher deviations from reality. The magnetic field in the core of a solenoid is

B =µNI

l, (2.16)

where µ is the magnetic permeability and I the current through the wire in the coil.

The magnetic permeability (µ) is the product of (µ0) the vacuum permeability and the relativepermeability (µr). The core (material) of a coil thus has influence on its self-inductance andmagnetic field but can also have an effect on the coupling factor. A magnetic core concentrates amagnetic field so this can improve the coupling of could by reducing the leakage flux and likewiseincrease the enclosed flux. High permeability cores also introduce non-linear effects, especiallyat high frequency operation and also have hysteresis and residual magnetic fields (see figure 2.7).Hysteresis is an effect whereby the internal magnetic fields in a magnet does not directly align witha changing magnetic field. Figure 2.7 describes the relationship between the magnetic flux density(B) and magnetic field strength (H) for a particular material, and in this case the shape couldmatch with a ferromagnetic material such as iron. The residual magnetic field is the remaining fieldstrength inside a material when the external field is removed. The coercive force is the negativemagnetic field strength needed to demagnetize the material completely.

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Figure 2.7: This figure shows the relationship between the magnetic flux density (B) and themagnetic field strength (H) for a particular material. The enclosed area is proportional tothe energy loss when the material is magnetized with varying polarity (AC power) [22].

2.2.5 Flux pump operation example

With a flux pump system one can obtain for example a 10 A persistent current through the loadcoil while only needing a 100 mA power source. This will require at least a primary to secondaryself-inductance ratio of 10000, which when square-rooted gives a factor of 100 (see equation 2.12).The rate of achieving this maximum gain depends on the self-inductance ratio of the primary andsecondary coil and likewise does the gain.

2.3 Two and four terminal resistance measurement methods(sensors)

The resistance of a Device Under Test (DUT) can be determined by supplying a known current,measuring the voltage drop over the DUT and dividing the voltage over the current R = V

I . In orderto get accurate resistance readings from sensors used at low-voltage/low-resistance applications,four terminal sensing is used instead of the ’normal’ two terminal sensing. Figure 2.8 shows aschematic with both methods set up to measure the resistance R.

Figure 2.8: A schematic showing two terminal sensing on the left and four terminal sensingon the right [23].

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In two terminal sensing one pair of wires is used to supply a current and to measure the voltageover a DUT. In this way the DUT’s resistance is not the only component of the measured voltagedrop. The resistance of wire contacts and the wires itself (Rlead) also result in voltage drops. As aresult the measured voltage is higher than the actual voltage over the DUT. The deviation fromthe actual voltage becomes even larger when there is a relatively high series resistance present inthe circuit.

Four terminal sensing solves this problem by using two separate wire pairs. One pair is connectedto the current source supplying current through the DUT (force connections) and the other pair isused to measure the voltage over the DUT (sense connections). Since a Voltmeter has a very highimpedance there will be almost no current flowing through the instrument and thus the voltagedrop over the sense leads is negligible. This means the voltage drops occurring over the force leadsand contacts will not be present in the voltage measurement over the DUT provided that the senseleads are precisely at the DUT leads. Thus only the voltage drop over the DUT is measured andtogether with the known current the resistance can be accurately calculated.

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Chapter 3

Experimental Methods/setup3.1 Description of flux pump setup V2.0 and V3.0

The flux pump system consists of the following components: LabVIEW Virtual Instrument and computer setup (see appendix C) 2 stage cryostat with two separate chambers (outer: liquid nitrogen and inner: liquid helium)

2x D-sub DB-25 connectorManganin wire ~(42,0± 0,6) Ω @ 297 K

Primary coil (V2.0: 6120 turns, V3.0: 4950 turns) Secondary coil split into two coils (total V2.0; 6 turns, V3.0: 20 turns) Load coil V2.0 (900 turns, also used in setup V3.0) Two heat switches (with a resistance around 1,025 kΩ each) Two aluminum pressure joints Sensors (all using 4 wire sensing):

Cernox thin film resistance cryogenic temperature sensor (CX-1010)Bartington MAG-01H Single Axis Fluxgate Magnetometer (range ±0,1 nT to ±2 mT)Unused Hall effect sensor (magnetic field sensor) (SIEMENS KSY10)

(disconnected in setup V3.0)

The components as placed in the cryostat can also be seen in figure 3.1. All components areattached to a copper ground plate which is screwed to the cryostat. The primary coil with the twosecondary windings are located in the center underneath an aluminum plate with two pressurejoints on top of the plate (setup V2.0). The load coil can be seen in the upper part of the figure andthe heat switches are located on the black vertical stripes at the sides of the copper ground plate.

The cryostat has two female DB25 25-pin connectors on the inside and two male DB25 connectors onthe outside and each pin is connected with Manganin wire between the outer and inner connectors.These wires have a resistance of roughly 40 Ω per wire and have a lower thermal conductivity thanplain copper wire. Although this high resistive wiring increase the dissipation in the wire dueto Joule heating, a balance must be made between the Joule heating and the parasitic thermalheat inflow from the ’hot environment’ which needs to decrease the heat flow into the cryogenicenvironment. It is trade-off resulting from the fact that there are no wires that have both a lowelectrical resistance and a high thermal resistance.

Two DB25 male solder type connectors are placed on the inner cryostat connectors on which allsense and current leads are attached. One male connector has 20 pins used for current input intothe primary coil which gives an effective resistance of around 8 Ωa. Four pins are used for the

aThe parallel wires used for the primary current enables a higher current, but also means more heat can flow intothe system. As a proof of concept a low resistance is beneficial, but it is unwanted in a real application because of

15

fluxgate meter of which the probe is placed in the middle of the load coil. The other connectoris used for the Cernox temperature sensor, of which the probe is place on top of the aluminumplate covering the primary coil in setup V2.0. Also several voltage and current leads (12 wires, 4x2voltage and 2x2 current for setup V2.0 and 14 wires for setup V3.0 with 1x2 extra voltage leads)are attached for measuring and testing of the system (power supply/heater currents), see appendixF for the complete overview of the connections.

Figure 3.1: Flux pump setup V2.0, top view of cryostat.

The heat switches contain two 0,5 kΩ resistors that are ’glued’ together with the superconductingwire by stycast. This is efficient and results in fast heating, or high response in breaking thesuperconductivity.

Note that many of these wires are added and used for flux pump diagnostic purposes. In a bareflux pump system one would only need 4 wires for the heater currents and 2 wires for the primarycurrent. This could even be reduced to 6 when using a common ground for the heat switches andprimary current. Extra wires could be needed when its is required to include a magnetic fieldsensor (4 wires) inside the cryogenic environment and/or a resistance temperature detector (RTD)(4 wires).

The importance of the earlier mentioned four terminal resistance measurement method (section2.3), as applied in the RTD sensors, becomes clear when the relatively high resistance cryostatwiring is considered. By using the four wire method these extra (series) resistances don’t have aneffect on the measurement outcome.

In figure 3.2 the new setup can be seen with the improved primary coil (V3.0) completely castin a trench of stycast, which is a thermally conductive epoxy encapsulant. It can be identifiedby its black color and it is well suited for improving the transformer thermal contact with thecopper ground plate to enable a higher maximum primary current. For this setup the location

the extra heat inflow.

16

of the pressure joints were also removed for convenience even as the load coil to make room forthe pressure joints. The Cernox temperature sensor was placed in between the load coil and thebottom right pressure joint. Transformer V3.0 has 20 secondary turns instead of 6 turns. SetupV3.0 also includes a third extra secondary coil made of 0,2 mm diameter copper wire which is opencircuited. This extra coil is included to perform emf measurements and to have more verificationpossibilities to test the transformer function of the flux pump.

Figure 3.2: Flux pump setup V3.0 before installation in the cryostat; included a new primarycoil and new secondary coils.

The primary coils (V1.0-3.0) consists of six identical solenoid-like segments that have 30° angledends and when put together they form a hexagonal ring which resembles a toroidal coil (see figure3.3 and in appendix E all primary coil versions are shown).

Figure 3.3: A photo of version 1.0 of the hexagonal primary coil consisting of six identicalsegments with 4800 turns in total. The type of wire that is used on the primary coil in thisfigure is Niomax-CN A61/05 (NbTi) with a diameter of 70 µm [17].

The primary coil V2.0 (V1.0) core is made of aluminum and the length of a segment is between 21and 29 mm, but the effective length for the (primary) wire winding is 21 mm. The outer diameterof the segments is 5 mm, but the ends of the segments are raised to become 6 mm in diameter. Theheight difference between the middle and the sides keeps the wire better in place during productionand the sides offer some protection against potential wire damaging. The segments have an innerair core which is 3 mm in diameter which is needed in production. Primary coil (V2.0) has roughly1020 turns per segment wound in multiple layers which brings the total turn count to around 6120.

17

For this primary winding a superconducting wire is used with a diameter of 100 µm. The roomtemperature resistance of the primary coil is 11,33 kΩ.

For primary coil V3.0 the core is made of Vespel polyamide and the same wire is used as for primarycoil V1.0 (70 µm Niomax-CN A61/05 (NbTi). The coil has about 4950 turns, or a little more than800 per segment on average. The room temperature resistance of the coil is 17,45 kΩ.

The secondary wire type is mono-filament copper-cladded superconducting Niobium with 25% Zrwire with a diameter of 0,36 mm for setup V2.0 and Load coil V2.0, and 0,23 mm for setup V3.0(same wire type). The smaller diameter secondary wire was used to allow the wire to wind moreeasily around the primary coil since the wire type is quite stiff. This also should have made ita bit easier to get the secondary wires in the pressure joints, which are basically two sets of twoaluminum parts, one with a slit and the other giving pressure within the slit (see figure 3.4). The(small) secondary wire should be capable of sustaining a current up to at least its critical current of27 Ab as indicated by the manufacturer Supercon, Inc. .

Figure 3.4: A photo of the mechanical pressure joints used in setup V2.0 and V3.0 [17].

For the pressure joints the ends of the secondary wires have their isolation stripped and their coppercladding removed. Per joint three wires plus an extra dummy wire are ’cold-welded’ together by themechanical force of six socket screws tightened with a torque wrench at 60 N cm. The dummy wireis included to make sure the surface contact between the wires is optimal, especially since setupV3.0 uses a smaller secondary wire type while still using the same pressure joints. The pressurejoints should only add a very small resistance when used correctly (in the order of nanoohms).Both secondary wires should at least support several amperes as indicated by the manufacturer.The voltage leads and heater current wires inside the cryostat are around 0,34 mm with isolationand 0,30 mm without isolation. Some long wires are partly made up of 0,2 mm copper wire insidethe cryostat to allow better thermal contact with the cryostat walls (better cooling), just as theprimary current leads (connector → primary coil leads) are completely copper wired.

3.2 Self-inductance values of the coils present in setup V2.0and V3.0

The self-inductances of the coils are not experimentally determined, except for the primary coil. Theself-inductances of the other coils will be estimated by using an online self-inductance calculator forsingle- or multi-layer round coils [24]. The calculator seems reasonably accurate based on experiencewith real -self-inductance values and calculated values (Vespel test coil segment and Vespel primarycoil V3.0), roughly said with an error margin of ±10 %.

Primary coil self-inductance is determined during superconducting state and by using the currentleads (with 2x10 parallel wires to minimize series resistance) and a LCR-meter.

bThe critical current is determined with a magnetic field of 1 T perpendicular to at a temperature of 4,2 K

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The measured self-inductance of coil V2.0 (aluminum core) is 1,119 mH.c The measured selfinductance of coil V3.0 (Vespel core) is 4,449 mH.d The calculator from reference [24] gives aself-inductance of around 4,9 mH when the coil segments are assumed to be in line with each otherand around 4,5 mH when assuming six ’independent’ segments.e

The load coil self-inductance is estimated to be around 13,5 mH.f

The secondary coils self-inductance of setup V2.0 (6 turns) is estimated at around 0,13 µH and ofsetup V3.0 (20 turns) at around 0,5 µH.g

3.3 Expected relation between load coil current and mea-sured magnetic field strength

When using the simple equation for the magnetic field strength inside a (single-layer) solenoid(equation 2.16), assume a relative magnetic permeability of 1, the load coil has 900 turns in multiplelayers but for the calculation it is assumed that all turns are next to each other (not physical, butfor convenience) and the coil has a length of 11 mm. A current of 10 mA should then generate amagnetic field strength of 100 mT in the middle of the solenoid. The magnetic field just scaledlinearly with the current so a ten times stronger current will also generate a ten times strongermagnetic field inside the solenoid.

Of course the load coil in the flux pump system is not a single layer solenoid but consist out ofmultiple layers and its length/radius ratio fis not large enough for the approximation to hold, butat least some simple estimation can be made. For the real solenoid the magnetic field is probablylower especially resulting from the just mentioned length/radius ratio.

3.4 Description of three self-made coils/transformers

Shown in figure 3.5 are the three self-made coils/transformers. They all have two windings with adifferent number of turns that are magnetically coupled to form little transformers. The design ofcoils 1 and 2 is based on the six identical segments of the hexagonally-shaped primary flux pumpcoil and are made so to reasonably resemble its properties, but there are some important differenceswhich will be discussed shortly. Coil 1 has an aluminum core and coil 2 a Vespel polyamide coreallowing a comparison to be made between the difference core materials. The first having a highelectrical conductivity, and the second having a negligible electrical conductivity. This is to checkthe hypothesis that induced eddy currents in the transformer core counteract a changing magneticfield and thereby substantially worsen the coil coupling in a transformer with an aluminum core.

cAt a measuring frequency of 100 kHz giving the highest phase shift of 67,4 °and with impedance 761,5 Ω and 7,876 Ω DC resistance.

dAt 20 kHz measuring frequency with the highest phase shift at 89,1 °and with impedance 559,3 Ω and 7,924 Ω DC resistance.

eFor both calculations using 3 layers with 275 turns per layer, inner diameter of 5 mm and segment length of 21 mm [24].fAssuming a 30 layers of 30 turns, an inner diameter of 14 mm and 11 mm length [24].

gFor both calculations an inner diameter of 5.4 mm is taken and a length of respectively 7,5 mm for 3 turns and 10 mm for 10 turns and

then the self-inductance is multiplied by two for two secondary coils [24].

19

Figure 3.5: From left to right: coil 1 (aluminum core), coil 2 (Vespel core) and coil 3 (hereshown with iron casing).

Further differences between the test coils and primary coil segments are: 1) the layer depth,eight instead of three to five layers resulting from a different wire thickness, 2) the type of wire,copper (0,2 mm in diameter) instead of superconducting wire (70 to 100 µm in diameter) and 3) thenumber of secondary turns is increased to 20 turns per segment (while the primary turns remainat 800/segment which is the same as the primary coil segments) resulting in a turn ratio betweensecondary and primary side of 20:800 instead of 6:4800. This will increase the secondary voltagebut lower the secondary current. For a flux pump with a high current requirement this is bad, butfor characterizing the coils it is actually an advantage for doing measurements, because its easier tomeasure a higher voltage.

Coil 3 is a simple transformer with a 90 and a 30 turn winding made of copper wire. A MnZnferrite core with high permeability encloses the windings as can be seen in figure 3.5, but the corecan also be removed. This will give information about the influence of the core permeability on theself-inductance of the coils.

20

Chapter 4

Results & Discussion4.1 Measurements on self-made coils/transformers

Most parameters are measured with the Agilent (nowadays Keysight) 4263B LCR meter with testsignal frequencies from 100 Hz to 100 kHz. An LCR-meter measures the voltage over and thecurrent through a DUT. With these vales the instrument can determine the impedance and phaseshift and use that to subsequently determine the value of the DUT inductance or capacitance. Inthe following experiment the following values are measured/determined: Impedance, phase shift,self-inductance, stray inductance and DC resistance for both the primary and secondary winding ofthe coils. Also the coupling capacity, with the impedance and phase shift, between the windings isdetermined separately for each coil (except for the nitrogen experiment). See appendix A for adetailed description of the measurement method and an overview of the measurement results.

4.1.1 General remarks about the measurements on coil 1 and 2.

As mentioned earlier the coils have 800 primary turns and 20 secondary coils and there dimensionsare roughly equivalent, but there is a difference in the outer diameter of the windings. The aluminumhas tighter wound turns resulting in a lower outer winding diameter 7,5 vs 9 mm.

The turn ratio (n) can experimentally be determined by

n =√Lp/Ls. (4.1)

This can be easily shown by filling in the formula for the self-inductance, for example for a solenoid(equation 2.15: L = (µ0N

2A)/l). Assuming the area and length is the same, each parameter cancelsexcept the number of turns so we get n = Np/Ns. The turn ratio is 40 in all measurements so itshould also be 40 (or at least close) when calculating the turn ratio by using equation 4.1 and themeasured values for the primary and secondary self-inductance values. The calculated turn ratio’sshow different values: the aluminum core coil has a turn ratio between 16,3 and 17,6 and the Vespelcore coil has a turn ratio between 25,3 and 28,6. The differences between real and calculated turnratio is substantial.

The difference may originate from the coil having less (effective) turns, for example caused byshortages. Also in case of the aluminum coil the outer diameter (7,5 mm) is too low to fit eightlayers of 0,2 mm on a 5 mm diameter core, because a close wound coil would at least have 8,2 mmouter diameter. This indicates the coil has less turns from the start. Other causes could be a largedeviation in the measurement of the self-inductances but at least for the Vespel core the primaryself-inductance seems to match quite OK with the online calculator [24].

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4.1.2 Coil 1 (aluminum) and coil 2 (Vespel) with air core

The Vespel core coil has a significantly higher primary impedance (692,4 Ω vs. 227,7 Ω) and alsohigher primary self-inductance (1101,0 µH vs. 347,5 µH) while the wiring, turn ratio and dimensionsare the same. The coupling factor of coil 1 is 0,388 and 0,561 of coil 2. This could indicate thepresence of eddy currents in the aluminum core coil.

4.1.3 Coil 1 and coil 2 with iron material in core

When the aluminum and Vespel core coils have their inner core filled with some iron material, theVespel coil shows an increase in its primary impedance and self-inductance. This effect cannotbe seen for the aluminum core coil, whereby the change in the primary impedance is negligible(∼ 0,5%) self-inductance. The primary stray inductance of the Vespel coil also increases with thepresence of an iron core, but here the aluminum coil shows a decrease. Still the coupling factor ofboth coils increases with 19% (to 0,669) and 27% (to 0,493) respectively, which should be expectedwhen a magnetic material is inserted.

4.1.4 Coil 1 and 2 put in liquid nitrogen

The coils were also put into liquid nitrogen (77 K) for a self-inductance measurement. At lowertemperatures the copper and aluminum have a higher conductivity or lower resistivity. Lowerresistivity of the copper wire won’t change the self-inductance, but lower resistive aluminum cansustain larger eddy currents which could mean higher stray fields.

The nitrogen cooling of the coils shows a reduction of the impedance for the aluminum coil as well asthe Vespel coil, which is explained by the fact that the copper wiring becomes less resistive at lowertemperatures. The DC resistance of both coils drops from around 9 Ω at room temperature to a littleover 1 Ω at liquid nitrogen temperature. At first sight also the self-inductance of both coils 1 and 2looks to be decreasing (234,7 µH and 995,4 µH respectively), but when the test signal frequency ischanged (from 100 to 20 kHz) about the same self-inductance values are measured as compared tothe room temperature experiment (air core), namely 356,2 µH and 1065,9 µH respectively.

Unfortunately no stray inductance measurement was performed, and thus also no coupling factorcan be calculated.

4.1.5 Coil 3 with and without ferrite (high permeability) core

The primary impedance of coil 3 increases tremendously by a factor of almost 60 and the self-inductance with a factor of almost 300 (to 36,52 mH) when a magnetic ferrite core is placed aroundthe primary and secondary wiring. It also shows the reduction of the magnetic stray field as theratio of the self-inductance and the stray inductance decreases drastically when encasing the coilwith a high permeability material. The coupling factor increases from below 0,4 to almost unity.

4.1.6 Summary about test coils

The aluminum coil has a significant lower self-inductance than the Vespel coil indicating eddycurrent is the aluminum reducing the self-inductance.

Real turn ratio and calculated turn ratio don’t match for both coils. The measurements on coil 3 clearly show a large effect of the presence of a high permeability

core, such as a MnZn (ceramic) ferrite core on the the properties of an electromagnetic coil.

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4.2 Expected transformer coupling factor and (current) gain

By using the self-inductance values mentioned in section 3.2, the equations of section 2.2.3 and themeasurement results of the test coils (section 4.1) calculations can be done give estimations of somevalues describing the system characteristics of the used flux pump system. Important values arethe (current) gain of one cycle, of n cycles and the maximum obtainable secondary(/persistent)current gain (after infinite cycles).

Made assumptions for the calculationsThe secondary coils are quite far apart thus their mutual coupling will be very low. Based on thisfact the assumption is made that the coupling between the secondary coils is negligible and setto zero (k12 = 0), which will be convenient for the calculations. The coupling factor kps (betweenprimary and secondary coils) is estimated to be at least 0, 3 , but could possibly also be as highor higher than 0, 6. The former is based on the worst coupling between the aluminum core coils,but the lower bound is even set below that for it to be a safe margin (k = 0, 3 vs k = 0, 39). Lesssecondary turns (around 6 turns in total) could in practice mean less mutual coupling resultingfrom the imperfect geometric orientation of the windings. So for coil V2.0 this is reasonable. A kfactor higher than 0, 6 could be possible because the hexagonal (Vespel) toroid-like transformer inprinciple should have less stray fields, because the magnetic field in a toroid is more constrained tostay and to be concentrated within the toroid. Also for coil V3.0 no eddy currents can be generatedin the Vespel core which increases the coupling.k = 0, 45 will be chosen as a final estimate for the coupling factor of the transformer in flux pumpsetup V3.0 .

Estimated valuesFor the primary current (Ip) a (peak-peak) magnitude of 50 mA is chosen in the calculations forthe estimated operating values of the flux pump (current gain).

If setup V2.0 would have a working flux pump the following values would indicate estimations ofthe pumping characteristics. The ideal gain is 113, the minimum ’real gain’ is 51 and the maximumobtainable current gain (after infinite cycles) is 2,54 A (ideal max current gain 5,64 A). The currentgain per flux pump cycle is 33,1 µA and the current gain after for example 400 cycles is 13 mA.

Setup V3.0 has an estimated ideal gain of 93, minimum ’real gain’ of 42 and a maximum currentgain of 2,09 A (ideal max current gain 4,65 A). The current gain per cycle is 159 µA and after 400cycles the current gain is 63 mA which is already 13 mA more than the primary current.

Effect of higher coupling factor and/or higher primary currentFor example, when the coupling factor is doubled from 0, 3 to 0, 6 all values are simply multipliedby 2, except the ideal gain which only depends on the number of turns and the geometry of thetransformer. Thus a higher coupling factor brings the real current gain values closer to the idealvalues.And when for example the primary current is increased with a factor of 10, then the current gainper cycle, after n cycles and after infinite cycles also increase with a factor of 10.

Conclusions about estimationsAlthough primary coil V2.0 has roughly a 75% lower self-inductance than primary coil V3.0, theideal and minimum real gain of setup V2.0 and V3.0 is not very different. This is because the lowerprimary self-inductance is accompanied by a lower secondary self-inductance (since the secondarycoil has 6 turns instead of 20 as in setup V3.0) which results in roughly the same gain. Still setupV2.0 has a slightly higher Lp/Ls ratio and thus more time is required to built up a certain persistentcurrent (when keeping the flux pump time and primary current constant). On the other hand V2.0has a higher (current) gain. Both differences can be seen in the calculations; when setup V2.0 has

23

built up a persistent current of ’only’ 11,0 mA after 500 cycles, setup V3.0 has already built upfivefold of that (52,1 mA). For a real application the primary coil of setup V3.0 and the secondarycoil of setup V2.0 is desired, but as a proof of concept both setups would be fine for the first step;to get a working flux pumping system.

4.3 Repeated experiments on flux pump setup V2.0

Some experiments on the existing flux pump setup were repeated to test its functionality andpossibly determine the coupling between the primary and secondary side of the transformer. Thefollowing performed tests will be shortly discussed here: persistent current test and critical currenttest of the load coil.

See figure 4.1 for a persistent current test on the unchanged flux pump system. The left part of thegraph shows some change actions playing with the primary current and a heater while an externalpower is connected to the load coil circuit. At the end of the first part and during the first half ofsecond part it can be seen that the flux pump works as intended when it comes to maintaining apersistent current, albeit a small current in this case.The weird spike and drop of the magnetic field halfway the second part of the graph happenedbecause the battery of the magnetic field sensor (Bartington fluxgate meter) ran out of power.

The critical load coil current was found by trial and error. When inserting a current of 65 mA afterhaving inserted a current of 62 mA the fluxgate meter jumps from a very large value (out of range)to almost zero. This means the secondary circuit superconducting state is broken, so the criticalcurrent lies between 62 and 65 mA.

Figure 4.1: Plot of persistent current experiment repetition on flux pump setup V2.0.

24

4.4 Lock-in amplifier frequency sweep measurements analy-sis and comparison with LTspice IV simulations

Lots of frequency sweep (or frequency response) measurements have been done with the lock-inamplifier. These were done with the intention to study the coupling of the primary and secondarysides. But there were some distractions regarding strange peaks in the measurement results whichtook a lot of time to discover. The cause was really hard to find, and in the end the exact causewas still not found but it also turned out to not be necessarily relevant to the research in this thesis.A thorough sorting needs to be done to see what is useful related to this report, but because oftime constraints when writing this report this research cannot be discussed thoroughly. A briefdescription of the setup, some measurements and simulations will be shown in appendix B.

4.5 Flux pump cryostat measurements

This section describes experiments done with the improved flux pump system, that includes a newtransformer with the core material being Vespel instead of aluminum and the secondary windingsoriented in the correct way. The Vespel core ensures the absence of (possible) eddy currentsoccurring in the transformer core. Because of the long manufacturing time of the new primary coiland other complications during the project, results for this section came only until recently, that isat the end of the research project. But finally the system was proven to be working and so a lotof different tests could be performed. The most important results will be discussed here. Also abrief description will be given about the wrong configuration of the secondary wiring of transformerV2.0 which turned out to be the main culprit of the nonfunctional transformer in setup V2.0.

In setup V2.0 one side had its turns in the clockwise direction while the other was in the counter-clockwise direction (see figure 4.2). When the bottom secondary ends are connected together andthe upper ends likewise no flux could be built up because of the opposite direction of the inducedsecondary currents which would cancel the already persistent current and result in a net current ofzero in the secondary circuit.

Figure 4.2: Correct and incorrect orientation of secondary windings to primary winding.

For transformer V3.0, their topside ends are connected together and their bottom side ends areconnected together. The latter connection makes the two secondary sides to configured as if theyare one coil.

25

4.5.1 Persistent current test

In this experiment a persistent current is externally induced through the load coil. This is done byconnecting an Agilent E3631A power source to the load coil voltage leads and than set the desiredcurrent while the switches are still closed (superconducting). No current will go through the loadcoil at first because it has a higher impedance compared to the switches, but when the switches areopened all current will go through the load coil and the power source can be turned off. Because ofthe load coil inductive property the current will keep going through the load coil.

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Figure 4.3: This graph shows a persistent current test during more than 12 hours. Themagnetic field strength is shown as a function of time, but the fluxgate meter (Bartington)out of range so the ’measured’ value is not physical.

In figure 4.3 the magnetic fields strength at the position of the load coil is plotted against time withon top shown the temperature. The magnetic field unfortunately is too big to be measured by thefluxgate meter (saturated), but the inserted current was 150 mA as set on the power source. Afterthe insertion all power sources were disconnected. This was done just before 22:00 as is indicatedon the figure.

The ’measured’ magnetic field strength remains above the measuring thresholds during at leastmore than 12 hours (graph stops around 10:49) meaning that at least some persistent current ismaintained. Unfortunately because of the saturation of the fluxgate meter this experiment doesn’tgive much information about the rate of current decay in the secondary circuit.

4.5.2 Trouble with the fluxgate meter

There was originally a problem with the fluxgate meter (Bartington) pin connection. The 4sense/force wires were not connected correctly in order to measure magnetic field strength inmicroteslas. It has something to do with a wrong polarity of the sense/force connections. Thesolution turned out to be swapping pins 1 and 2 as well as pins 14 and 15. After the correctiona background magnetic field strength of around −40 µT was measured instead of a value around−0,7 µT. The former seems more reasonable since the earth’s magnetic field is in the range of25-65 µT. The original incorrect wiring of the fluxgate meter did give a response but (in retrospect)

26

in an erratic non-linear manner. Unfortunately this problem was not discovered until a lot ofmeasurements on setup V3.0 were already performed.

The measuring limit of the correct connection is determined to be around 590 µT, or roughly 59 mA.This relation will be explained in section ??).

4.5.3 Calibration fluxgate meter (Bartington) output in µT with currentmagnitude

Calibration of the fluxgate meter’s µT output is performed by external inputting a (persistent)current into the secondary circuit and reading out the value of the fluxgate meter. This turned outto be roughly 10µT per mA.

For example for the slow flux pumping experiment (see section ??) the flux pumping was stoppedat 516 µT. Than an estimation was made and an external current of 50 mA was inserted resultingin a drop of the magnetic field strength to 500,2 µT. 51 mA gave a value of 513,2 µT and a currentof 52 mA gave 523,6 µT. Inserting an external current of 60 mA into the load coil resulted in thefluxgate meter being out of range

27

4.5.4 Heat switches & persistent current test (commutation)

In this experiment the functionality of the heat switches is tested and also the warm up and cooldown temperature of the superconducting secondary wire is examined. The results are shown infigure 4.4 and give information about how effective the current commutation is from one secondaryloop to the other loop. The data is useful for an indication of the commutation-time and -losses.

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Figure 4.4: In this graph temperature, the magnetic field strength and the heater currentsare shown against time, during a current commutation test of a 50 mA persistent current.Each heater current peak means a switch is opened and breaking superconductivity of thecorresponding loop.

For this system test also an external current was inserted, first 60 mA (first spike), but later acurrent of 50 mA to be within a save margin of the measuring range limit of the fluxgate meter.After inserting an external current and removing the power source the system was given the timeto cool down a bit before starting the ’stress test’. Then the switches were alternately activatedand deactivated and controlled by the ’automatic flux pumping’ feature in the LabVIEW program,but without the connection of a primary current.

The switch opening time (heating time) was first set at 0,2 s and the switch closing time (coolingdown time) at 2,5 s. This was later reduced to 0,1 s and 1 s respectively and also the current rampwas increased reducing the period time and increasing the frequency.

The heater currents were set at 5 mA each but because of the accuracy limits at low currentsthe heater currents were actually around 3,5 to 4,0 mA and shown in the bottom graph of figure

28

4.4. With a heater resistance of 1,025 kΩ (+2 x 40Ω for the cryostat wiring), a current of 4 mA(rounded off for convenience) and a heater on time of 0,2 s the resulting power (in W) delivered tothe cryostat per switch is given by P = I2R = 0,0164 W or in terms of energy (E = Pt): 0,0033 Jper switch.

The switch period of a cycle was able to be reduced below ten seconds while maintaining thepersistent current. The current through the load coil shows no clear drop in its generated magneticfield, maybe 1 µT but not more. Also the monitoring of the temperature shows an increase, butthis seams to stabilize at around 5 K From this we can conclude that the commutation in systemsetup V3.0 can pe performed efficiently (fast) and also the losses are low (<1 µT/50 switches) andsystem temperature can stay low.

29

4.5.5 Flux pumping fast to 60 mA (590µT)

In figure 4.5 the results of flux pumping with a high primary current are shown. The bottom graphshows the periodical ramping up and down of the primary current. For this experiment the loadcoil current was zero from the start. This means the fluxgate meter starts around −40 µT (beingthe background value for the earth’s magnetic field). The primary current ramp is set to almost500 mA (peak-peak) and a dI/dt of 250 mA/s. The switch open time was first set to 0,1 s butquickly changed to 0,5 s and later to 0,2 s the closing time to 2,5 s. In about 7 minutes the magneticfield strength is increased from −40 to 590µT.

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Figure 4.5: Shown here is the flux pumping operation with a high primary current (500 mApeak-peak and starting at zero current. The temperature spikes originate from a programcontrol issue, that keeps one of the heaters on for too long.

There is a sudden increase in the temperature around 16:14 and later more than 5 in a row, this isheater 1 being ’stuck’ (left on heating) which explains the increases in temperature but also thedrops in the measured magnetic field. The loss per drop is the induced current from a half fluxpump cycle. This glitch in the heater current control is a software/programmatic problem. It mayresult from some manual fiddling with the automatic flux pump signal generator in the LabVIEWprogram and/or the happening of some kind of timing bug. The problem does sometimes also occur’on itself’ when there is no manual change in the controls.

During this experiment about 40 to 45 cycles were needed to obtain a magnetic field strength of

30

590 µT. The induced current per cycle adds a magnetic field strength of (16± 2) µT. When usingthe estimations of section ?? and converting µT to mA according to section 4.5.3 (10 µT ≈ 1 mA)the current per cycle comes down to (1,6± 0,2) mA. This is about the same compared to whatwas calculated in section ??. There a magnetic field increase of 0,159 µT per cycle was calculatedfor a 50 milliA primary current, but for this experiment a 500 mA primary current is used insteadso this results in an increase of 1,59 mT per cycle. Still the total built up current after 400 (40for Ip = 500 mA ) steps is shown to be 63 mA which is more than what is built up during theexperiment in 40 cycles. From this we can conclude that the coupling factor must be a little lowerthan 0, 45, namely around 0, 42 which would mean that in practice the current gain per cycle isaround 15 µT, which lies within the uncertainty margin for the magnetic field gain per cycle whichwas read out from the data shown in figure 4.5. The value of 0, 42 can of course only be accurate ifthe estimations of the self-inductances are also accurate, which of course can and probably havedeviations from the real situation.

This experiment shows that the flux pump is operating as it should be, namely stepwise inducingan additional current in the secondary circuit and also be able to maintain this persistent current.The analysis just performed shows the measurements have nice agreement with the estimationsdone earlier.

31

4.5.6 Flux pumping slow to 60 mA (590 µT)

For a final and possible flux pump application in a space satellite, low parasitic heat is importantthus the primary current needs to be low, but must obtain a much higher secondary current. In thisexperiment an attempt is made to build op a persistent current which is larger than the primarycurrent used during the flux pump operation.

During this experiment a 50 mA peak-peak primary current is used. From figure 4.6 we can againsee that the magnetic field strength increases nicely in time starting at −40 µT or zero current. Thebuilding up of a magnetic field strength of 516 µT took little over an hour (3800 s). Each flux pumpcycle period is around 9 and 10 sa so this results in roughly 400 cycles and thus 0,13 mA/period.The final magnetic fields strength corresponds with approximately 51,2 mA.

When using cycles steps and a coupling factor of 0, 42 from section 4.5.5 the estimated current gainper cycle is 14,9 mA and after 400 cycles is 58,6 mA. This again is in quite good agreement withthe measurement. The difference could partly be explained by the uncertainty in the cycle time.

This experiment shows flux pumping also works at a peak-peak primary current of 50 mA and thesystem is able to build up a persistent current which is larger than the primary current.

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Figure 4.6: This figure shows the automatic flux pumping process from zero current to thesaturation with a low primary current (50 mA peak-peak) with the aim to build up a largersecondary current.

aNOTE: During the flux pumping there was some playing around with the flux pump signal controls such aschanging the dI/dt and heater close and open times. This resulted in some variations in the signal as seen in figure4.6.

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4.5.7 Critical temperature determination of the load coil during systemwarm up

The load coil critical current can be nicely determined when the liquid helium is becoming depletedmaking the cryostat warm up very slowly. Before the load coil/secondary circuit reaches atemperature above its critical temperature of the wire (and breaking superconductivity), an externalpersistent current of 50 mA was inserted in the secondary circuit over the load coil and than theexternal power source was removed. Again a value that results is a measurable magnetic fieldstrength for the fluxgate meter.

At a temperature of 9,23 K the load coil suddenly ’loses’ its superconducting property and thepersistent current is dissipated within a few seconds as can be seen in the sudden drop of themagnetic field strength in figure 4.7.

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Chapter 5

Conclusions and recommendationsfor future workIn conclusion a working flux pump system is developed and which is capable of building up andmaintaining a persistent current in a superconducting load coil (circuit). The measured performanceof the flux pump system is in agreement with estimations based on the system properties andtheory (± 10%). The coupling factor of the transformer is determined to be around 0, 42 assumingthe measured and estimated values for the self-inductance of the coils are accurate. The currentgain per cycle is close to 0,16 mA for a 50 mA primary current.

The influence of different core materials is shown to be important related to the magnitude ofthe self-inductance of coils, but the trouble with the dis-functional flux pump transformer (V2.0)was (mainly) due to the wrong secondary winding direction of the secondary coils. The aluminumcore was not necessarily the problem in “system setup V2.0”, but by replacing it with Vespel intransformer V3.0 the self-inductance of the primary coil was increased which is still a good thing.

Improvements of the system with revised/renewed components are: Correct functioning of the flux pump transformer, by changing one of the secondary winding

direction so both windings are counterclockwise. Improvement critical current of primary coil, by better thermal conduction to the copper

ground plate. A maximal current ramp of 500 mA could be applied while previously fortransformer V2.0 this was limited at around 60 to 65 mA.

Another thing that’s replaced is the primary coil with an aluminum core by a coil with Vespelpolyamide material to prevent eddy currents in the core material.

5.1 Research aims and questions

5.1.1 Research aims 1 and 2

Research aims 1 and 2 are related to the understanding of the flux pump system, finding theproblem of the dysfunctional transformer (V2.0) and improving the thermal design of the setup toallow higher critical currents. These research aims are achieved and related actions how this wasdone were described above in the start of the conclusion section.

5.1.2 Research aim 3

Research question: Show that a flux pump system can operate more efficiently than a systemwithout a transformer and where instead a current is driven directly though the 1G-off-loading coil

34

The current flux pump setup (V3.0) and the performed measurements up to now show great success.Still some things can be improved, but already the system looks to be quite efficient in building upa persistent current and maintaining it. Especially for a proof of concept, the current flux pumpsystem has passed the test and paved the way for a future implementation. No calculations havebeen done to compare a flux pump with a directly driven electromagnet, but it is improbable thatthe latter case is more efficient in heat management since a power source needs to constantly delivera current into the cryogenic system to maintain the magnetic field. On the other hand the currentflux pump can maintain a persistent current while staying at a temperature below 5 K.

5.2 Recommendations for future improvements

The monitoring of the current in the secondary current is limited by the range of the Bartingtonfluxgate meter at around ∼60 mA or ∼590 µT . This limits flux pump testing to below the indicatedvalue and also the persistent current decay at higher currents couldn’t be analyzed. In order toimprove the monitoring of the persistent secondary current testing a different sensor should beused like the earlier used hall effect sensor. This sensor was not used anymore because of its highparasitic heat load on the load coil which caused the load coil to go out of superconductivity. Sofor setup V3.0 the sensor was not connected, also because of a tight time schedule. For futureimprovements the position of the hall effect sensor should be attached to the bottom of the copperplate instead of the load coil itself, which should enable the load coil to remain superconducting. Afluxgate meter outside the cryostat could also be considered.

Because of limited time for the measurements on setup V3.0 at the end of my bachelor project wedidn’t succeed in doing another persistent current test. A persistent current test of more than 24hours and a magnetic field within the measuring range would provide a nice approach to determinethe current decay in the load coil circuit and which can be translated to a value for the jointresistance in the secondary circuit.

The automatic flux pump function of the LabVIEW VI sometimes shows a problem with the currentof heater 1, namely being on too long which probably is some mind of timing error in the program.This prevents the potential current step-up of one period and generates an excess amount of heat.This problem should be resolved to optimize the flux pumping, because it can sometimes happentwo or three times in a row.

Also the VI can be improved by including some kind of failsafe to prevent system overheating whensuperconductivity is broken by ways of feedback from the measured magnetic field strength. Thiswill allow for automatic flux pumping without the need to constantly monitor the system and tomanually prevent overheating. Thus enabling the possibility of testing the flux pump during 24hour operation or more.

Another possible improvement can be made related to the measurement period of the LabVIEW.The time between each measured is now around one second, but by reducing this time, flux pumpingat higher frequencies could be performed and analyzed better. With the current program fast fluxpumping (above 1 Hz is probably not even possible because of timing error and mismatches.

35

36

References

[1] SRON. Mission and strategy. url: https://www.sron.nl/mission-and-strategy-about-sron-595/ (visited on 04/22/2016).

[2] SRON. SPICA/SAFARI. url: https://www.sron.nl/spica-safari-missionsmenu-2253/(visited on 04/22/2016).

[3] L.J.M. van de Klundert and H.H.J. ten Kate. “Fully superconducting rectifiers and fluxpumpsPart 1: Realized methods for pumping flux”. In: Cryogenics (Apr. 1981).

[4] L.J.M. van de Klundert and H.H.J. ten Kate. “On fully superconducting rectifiers and flux-pumps. A review. Part 2: Commutation modes, characteristics and switches”. In: Cryogenics(May 1981).

[5] T. P. Bernat, D. G. Blair, and W. O Hamilton. “Automated flux pump for energizing highcurrent superconducting loads”. In: Review of Scientific Instruments 46.5 (May 1975).

[6] Zhiming Bai et al. “A novel high temperature superconducting magnetic flux pump for MRImagnets”. In: Cryogenics 50.10 (2010). Ed. by Elsevier, pp. 688–692.

[7] H. L. Laquer. “An electrical flux pump for powering superconducting magnet coils”. In:Cryogenics 3.1 (Mar. 1963). Ed. by Elsevier, pp. 27–30.

[8] K.J. Carroll. “Behaviour of a flux pump using an automatic superconducting switch”. In:Cryogenics 13.6 (June 1973). Ed. by Elsevier, pp. 3530–360.

[9] Yong Soo Yoon (Member IEEE) et al. “Characteristics Analysis of a High-Tc Supercon-ducting Power Supply Considering Flux Creep Effect”. In: IEEE Transactions on AppliedSuperconductivity 16.3 (Sept. 2006). Ed. by IEEE, pp. 1918–1923.

[10] Hyun Chul Jo et al. “Experimental Analysis of Flux Pump for Compensating Current Decayin the Persistent Current Mode Using HTS Magnet”. In: IEEE Transactions on AppliedSuperconductivity 20.3 (June 2010). Ed. by IEEE, pp. 1693–1696.

[11] Christian Hoffmann, Donald Pooke, and A. David Caplin. “Flux Pump for HTS Magnets”. In:IEEE Transactions on Applied Superconductivity 21.3 (June 2011). Ed. by IEEE, pp. 1628–1631.

[12] H. Van Beelen et al. “Flux pumps and superconducting solenoids”. In: Physica 31.4 (1965).Ed. by Elsevier, pp. 413–443.

[13] Y. Iwasa. “Microampere flux pumps for superconducting NMR magnets Part 1: basic conceptand microtesla flux measurement”. In: Cryogenics 41.5-6 (2001). Ed. by Elsevier, pp. 385–391.

[14] V. Newhouse. “On minimizing flux pump heat dissipation”. In: IEEE Transactions onMagnetics 4.3 (Sept. 1968). Ed. by IEEE, pp. 482–485.

[15] S. P. Bernard and David L. Atherton. “Performance analysis of transformer-rectifier fluxpumps”. In: Review of Scientific Instruments 48.10 (Oct. 1977). Ed. by American Institute ofPhysics, pages.

[16] Sangkwon Jeong nd Sehwan In and Seokho Kim. “Superconducting micro flux pump using acryotron-like switch”. In: IEEE Transactions on Applied Superconductivity 13.2 (June 2003).Ed. by IEEE, pp. 1558–1561.

[17] Wim van den Berg. “Research and development of a flux pump system for satellite application”.bachelor. Saxion university Enschede, Sept. 2015.

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[18] Dwi Prananto. Figure from ’Superconductivity’. Ed. by Dwi Prananto. May 6, 2012. url:https : / / simpliphy . wordpress . com / 2012 / 05 / 06 / superconductivity/ (visited on07/06/2016).

[19] Michael Tinkham. Introduction to Superconductivity. second. 1996.

[20] Figure from ’Meissner effect’. last edit on 4 May 2016. Wikipedia. May 4, 2016. url: https://en.wikipedia.org/wiki/Meissner_effect (visited on 07/06/2016).

[21] Figure from ’Polarity (mutual inductance)’. last edit on 12 June 2016. Wikipedia. June 12,2016. url: https://en.wikipedia.org/wiki/Polarity_(mutual_inductance) (visited on07/06/2016).

[22] Walter Ditch. B-H Curve. Electronics and Micros. url: http://www.electronics-micros.com/electrical/b-h-curve/ (visited on 07/06/2016).

[23] Adam Daire. Low-Voltage Measurement Techniques. Tech. rep. Keithley Instruments, Inc.,Oct. 2005.

[24] Robert Weaver. Online Calculators. Jan. 3, 2016. url: http://electronbunker.ca/eb/Calculators.html (visited on 06/2016).

[25] Entechna Engineering. Magnetic bearing design for the FTS Mechanism in SPICA-SAFARI.Entechna Engineering. June 26, 2012. 12 pp.

[26] Entechna Engineering. Magnetic bearing design for the FTS Mechanism in SPICA-SAFARIUpdate. Entechna Engineering. Sept. 13, 2016. 66 pp.

38

Appendices

39

Chapter A

Measurements of test coil parametersIn this appendix the parameters of the three self-made coils are described in more detail, somebackground is given about the measurements and the results are shown in a series of tables below.

The coil/transformer parameters are measured with an Agilent 4263B LCR-meter that has attachedthe 16089B Medium Kelvin Clip Lead fixture. Each time before taking a series of measurementsthe LCR-meter is reset to its default setting using the system reset button. Then the test signalfrequency is set to one of the available values (100, 120, 1k, 10k, 20k or 100k Hz) and the test signalvoltage is set to 100 mVrms unless stated otherwise. There is also an option to set the length ofthe connector cables (at 0, 1, 2 or 4 m), which cancels the phase shift error caused by the lengthof the cable. The used fixture has connector cables with a total length of about 1 m. The defaultsetting after resetting is 0 m. During the first set of measurements this was forgotten a few timesso for consistency the set cable length was left at 0 m.

The ideal test frequency setting depends on the characteristics of the Device Under Test (DUT). Tomeasure the inductance of a coil the ideal frequency setting is the one where the measured θ (phaseshift) value is closest to 90°. Meaning the coil has the strongest induction characteristics at thistest frequency. For each coil this was roughly determined by measuring the phase shift at differentfrequencies beforehand. Most often this was found to be at 20 or 100 kHz. Subsequently at thechosen frequency an open & short circuit correction is performed to calibrate the used equipment,such as the fixture and connector cables.

The design of coils 1 and 2 is based on the six identical segments as was mentioned earlier in section3.4. Here they will be described in a bit more detail, especially its dimensions. The (segment-)lengthof the coils is roughly the same, namely (21,6± 0,1) mm which is a bit more than the primary coilsegments. The primary wire is wrapped around a cylindrical core with a diameter (5,5± 0,5) mmand divided in eight layers of about 100 turns per layer. In this way the primary self-inductance ofcoil 1 and 2 is comparable to a primary coil segment. The secondary windings consists of 20 turnsaround the primary winding. The secondary wire type is copper with a diameter of 0,73 mm.

Coil 3 has roughly 30 and 90 turns wrapped around a small plastic holder with a removable MnZnferrite casing/core. In figure 3.5 coil 3 is shown with this casing.

A.1 Test coils 1 and 2 - inner air core left empty

The inner air core of 3 mm is left empty during the first measurements of which the results areshown in table A.1.

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Table A.1: LCR-meter measurement at 100 kHz test signal frequency.

Aluminum (air)core Vespel (air)corePrimary Secondary Primary SecondaryZ (Ω) 227,7 Z (Ω) 0,7634 Z (Ω) 692,4 Z (Ω) 1,033θ (°) 73,52 θ (°) 80,19 θ (°) 87,4 θ (°) 84Lp (µH) 347,5 Ls (µH) 1,1970 Lp (µH) 1101,0 Ls (µH) 1,635Rd (Ω) 8,683 Rd (Ω) 0,03132 Rd (Ω) 10,018 Rd (Ω) 0,03598Lsprim (µH) 295,1 Lssec (µH) 0,6995 Lsprim (µH) 754 Lssec (µH) 0,7381

Coupling capacityZ (kΩ) 74,8

Coupling capacityZ (kΩ) 86,5

θ (°) -89,4 θ (°) -88Cww (pF) 21,25 Cww (pF) 18,4

A.2 Test coils 1 and 2 and inner core filled with some mag-netic iron material

For the measurements shown in table A.2 the air core of the coils (3 mm in diameter) is filled witha magnetic hex key that exactly fits in the core so almost all of the core is filled.

Table A.2: LCR-meter measurement at 100 kHz test signal frequency

Aluminum (iron)core Vespel (iron)corePrimary Secondary Primary SecondaryZ (Ω) 228,90 Z (Ω) 0,7241 Z (Ω) 1261,1 Z (Ω) 1,4107θ (°) 73,72 θ (°) 80,2 θ (°) 66,03 θ (°) 74,03Lp (µH) 349,7 Ls (µH) 1,135 Lp (µH) 1768,8 Ls (µH) 2,158Rd (Ω) 8,7404 Rd (Ω) 0,03120 Rd (Ω) 10,084 Rd (Ω) 0,03599Lsprim (µH) 264,6 Lssec (µH) 0,6344 Lsprim (µH) 976,4 Lssec (µH) 0,8277

Coupling capacityZ (kΩ) 69,5

Coupling capacityZ (kΩ) 76

θ (°) -89,7 θ (°) -89,7Cww (pF) 22,91 Cww (pF) 21,03

A.3 Test coils 1 and 2 - in liquid nitrogen

For the measurements shown in table A.3 the coils are put in liquid nitrogen and cooled to 77 K.The top results are measured with the test signal frequency set at f=100 kHz and for the bottomresults set at f=20 kHz except for the primary side of the Vespel air core which is set to f=10 kHz.The coupling capacity was not determined in this measurement setup.

Table A.3: LCR-meter measurement at 100 kHz test signal frequency for upperpart and 20 and 10 kHz for the lower part.

Aluminum (air)core Vespel (air)corePrimary Secondary Primary SecondaryZ (Ω) 169,8 Z (Ω) 0,5908 Z (Ω) 628,6 Z (Ω) 0,9260θ (°) 60,2 θ (°) 70,56 θ (°) 83,57 θ (°) 78,93Lp (µH) 234,65 Ls (µH) 0,8880 Lp (µH) 995,4 Ls (µH) 1,447Rd (Ω) 1,1785 Rd (Ω) 0,00655 Rd (Ω) 1,3743 Rd (Ω) 0,00895R (Ω) 8,422 R (Ω) 0,1960 R (Ω) 70,6 R (Ω) 0,178

Z (Ω) 47,24 Z (Ω) 0,1478 Z (Ω) 66,96 Z (Ω) 0,2100θ (°) 71,33 θ (°) 78,30 θ (°) 87,7 θ (°) 83,34Lp (µH) 356,18 Ls (µH) 1,15 Lp (µH) 1064,9 Ls (µH) 1,660Rd (Ω) 1,18 Rd (Ω) 0,00659 Rd (Ω) 1,3796 Rd (Ω) 0,00904R (Ω) 15,12 R (Ω) 0,0300 R (Ω) 2,673 R (Ω) 0,0249

41

A.4 Test coil 3 - with & without an iron core/casing

The measurement results in table A.4 shows the properties of coil 3 having or not having a highpermeability core. The test signal frequency is set to f=100 kHz for coil 3 containing the MnZnferrite core and to f=20 kHz for coil 3 without this core. The differences really show the impact onthe characteristics of the electromagnetic coil.In this setup the test cable length correction is set to 1 m instead of 0 m.

Table A.4: My caption

Coil 3 (with MnZn ferrite core) Coil 3 (only the bobbin alone)Primary Secondary Primary SecondaryZ (Ω) 4536 Z (Ω) 571,52 Z (Ω) 78,085 Z (Ω) 8,888θ (°) 89,86 θ (°) 89,83 θ (°) 87,83 θ (°) 86,97Lp (µH) 36520 Ls (µH) 4170 Lp (µH) 124,18 Ls (µH) 14,129Rd (Ω) 0,9750 Rd (Ω) 0,3041 Rd (Ω) 0,97902 Rd (Ω) 0,30474Lsprim (µH) 392 Lssec (µH) 43 Lsprim (µH) 107,05 Lssec (µH) 12,027

Coupling capacityZ (kΩ) 764

Coupling capacityZ (kΩ) 260

θ (°) -89,8 θ (°) -89Cww (pF) 10,4 Cww (pF) 6,1

42

Chapter B

Results lock-in amplifier and simulation withLTspice IVWith a lock-in amplifier frequency sweeps were performed to look at the behavior of the electro-magnetic coils in the flux pump setup. This was done to study setup V2.0 and with the intentionto possibly find what was wrong with transformer V2.0. In the end this was not very successful,but large amounts of frequency sweeps were performed and so a lot of data was gathered. There isuseful information in all of it, but due to irrelevancy of a large amount of data (a lot of data comesdown to the same thing) and time constraints during the writing of this report, only a few graphswill be shown here. It is very time consuming to study everything thoroughly. In the end the newsetup (V3.0) was shown to work anyway, so this also made these results a bit less relevant. Stillsome results will be discussed here in short.

The following electrical diagrams (in figure B.1 and B.2) shows the circuits used in the measuringsetup with a Stanford Research System 830 lock-in amplifier. This device was controlled by aself-made LabVIEW program that could perform frequency sweeps with an adjustable number oflog steps between an adjustable start and stop frequency.

Figure B.1: This is the lock-in setup with only the primary coil connected and in series acapacitor and resistor. The voltage response is determined over the resistor.

Figure B.2: This is the lock-in setup to determine the coupling of the transformer coils. Theinduced emf is measured over a resistor in series with the secondary coil.

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When measuring the frequency response of circuit 1 (figure B.1) by performing the lock-in frequencysweep the measurement results (see figure B.3) seem to match quite good with the frequency sweepsimulation of LTspice (see figure B.4), although the scales are not exactly the same. For examplethe phase shift scale of the simulation spans a larger range. This example shows that there can bea good accordance between measurements and simulation related to the flux pump setup.

-80

-60

-40

-20

0

20

40

60

80

100

-70

-60

-50

-40

-30

-20

-10

01kHz 10kHz 100kHz

Phase

shift (t

heta

)

Am

plitu

de (R

in d

B)

Frequency (f, log scale)

4K measurement Primary coil series capacitor and series resistor 1-100kHz (50 steps)

Amplitude (R) prim 100nF 100 ohmAmplitude (R) prim 10nF 100 ohmAmplitude (R) prim 1nF 100 ohmPhase (Theta) prim 100nF 100 ohmPhase (Theta) prim 10nF 100 ohmPhase (Theta) prim 1nF 100 ohm

Figure B.3: Lock-in frequency sweep measurement of the coupling between both sides oftransformer V2.0 at 4 K.

Figure B.4: LTspice IV frequency sweep simulation of the coupling between both sides oftransformer V2.0 at 4 K.

In the case of figure B.5, however, strange things are happening. One could also say things arenot happening. The figure should show the frequency response of transformer V2.0, but a ’strange’frequency peak/response can be seen. For different external capacitor values parallel connected

44

in the primary circuit the response is very similar. Normally as the (external parallel) capacitorvalue is changed in a LCR circuit the self resonance frequency (SRF) should also change (a highercapacitor, a lower SRF via the relation SRF = 1/(2 ∗ π

√LC)), but it does not, at least not the

peak which is the most prominent and shows the largest phase shift. This is probably some parasiticproperty of the setup.

-200

-150

-100

-50

0

50

100

150

200

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

010kHz 100kHz

Phase

shift (t

heta

)

Am

pltitude (R

in d

B)

Frequency (in Hz)

4K measurement Coupling Primary-Secundary coils - parallel capacitor in primary circuit 10-100 kHz (25 steps)

Amplitude (R) 1nF

Amplitude (R) 10nF

Amplitude (R) 100nF

Amplitude (R) 1000nF

Phase (Theta) 1nF

Phase (Theta) 10nF

Phase (Theta) 100nF

Phase (Theta) 1000nF

Figure B.5: Coupling measurement test of the primary and secondary coils in transformerV2.0. Shown is a remarkably constant phase shift and amplitude response around 39 kHz.

Later a lot of exclusions are done by performing different experiments to find the cause of thisstrange frequency response. It first seem to be mainly happening when an external capacitor isexternally connected and not when a series capacitor was connected. A changing value of the seriescapacitor did actually show a change of the SRF most of the time. Later it was found that thisdoes not has to be the case, but the real cause was never exactly found.

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Chapter C

LabVIEW control and instrument setup ofthe flux pump systemThis appendix shows a figure (C.1) with the instrument setup, used cable types and the devices thatare controlled by LabVIEW for the flux pumping operation. The DAQ and amplifier control theprimary current, one Power Supply controls the heater currents and the other Power Supply controlsthe Hall sensor in Setup V2.0 and in setup V3.0 it is only used for inserting an external current inthe secondary circuit. All voltage leads and control currents (primary and heaters) are measuredby the Data Logger. The breakout boxes are an intermediary between the DB25 connectors andthe connection with the Data Logger. It splits up the connector cable in 25 individual pins to beconnected as desired.

Figure C.1: LabVIEW control and instrument setup of the flux pump system [17].

For a more enhanced description of the control setup see the report by Wim van den Berg [17].

46

Chapter D

Possible magnetic bearing setup for theFTSThis appendix includes two figures showing possible applications of the magnetic bearing in theFTS for the SAFARInstrument. Design and development of the setups shown in figures are doneby Entechna Engineering [25, 26].

Figure D.1: Possible FTS magnetic bearing setup, indicated are two coils with poleshoes. Asmall coil for normal movement (also in space) and a large coil for 1G-off-loading and testingon earth.

Figure D.2: Another possible magnetic bearing application setup for the FTS.

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Chapter E

Primary coils V1.0, V2.0 and V3.0In the top left of figure E.1 primary coil V1.0 with an aluminum core and around 4800 turns(∼800/segment with wire properties: (70 µm Niomax-CN A61/05 (NbTi).

In the bottom, primary coil V2.0 with roughly 6120 turns or ∼1020 turns/segment. The roomtemperature resistance of the primary coil is 11,33 kΩ and superconducting self-inductance of1,098 mH (measured with an LCR-meter at f=100 kHz and phase shift θ = 68,16°. In the figureprimary coil V2.0 is still placed on the copper ground plate with the secondary windings attachedand aluminum tape for thermal conductivity.

On the top right primary coil V3.0 is shown, having a Vespel polyamide core and 4950 turns(∼820/segment) of (70 µm Niomax-CN A61/05 (NbTi) superconducting wire. Primary coil V3.0has a room temperature of 17,45 kΩ and a superconducting self-inductance of 4,45 mH (measuredwith an LCR-meter at f=20 kHz and phase shift θ = 89,09°).

Figure E.1: In the top left corner is primary coil V1.0, in the bottom, primary coil V2.0 andin the top right corner primary coil V3.0

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Chapter F

Pinout flux pump experiment (setup V3.0)

Channel 34970 Sensor type Type of measurement Connection type Connector 1 Con.2 => Box 1 (37 pins) Mod.1 => Box 2 (50 pins) Mod.2 => Box 3 (50 pins

I+ - 11 1 -

I- - 23 2 -

V+ - 12 24 -

V- - 24 25 -

V+ - 9 3 -

V- - 21 4 -

V+ - 3 5 -

V- - 15 6 -

V+ - 6 7 -

V- - 18 8 -

V+ - 7 9 -

V- - 19 10 -

V+ - 8 11 -

V- - 20 12 -

V+ 1/2 => Bar - 13 -

V- 14/15 => Bar - 14 -

V+ - 13 15 -

V- - 25 16 -

I+ 3:13 - 48 (A meas with 49)* -

I- 16:25 - 49 (A meas with 48)* -

I+ - 4 => 47-box 3 - Pow. Sup. 2 (+25V) <= 46 (A meas with 47)

I- - 16 => Pow. Sup. 2 com - 4-box 1 <= 47 (A meas with 46)

I+ - 5 => 49-box 3 - Pow. Sup. 2 (-25V) <= 48 (A meas with 49)

I- - 17 => Pow. Sup. 2 com - 5-box 1 <= 49 (A meas with 48)

Not used in current setup (V3.0)

Not used in current setup (V3.0)

222 Heater 2 Current-2w

108 Primary coil leads Voltage-2w

121 Hall sensor Current-2w

106 Heater 2

122 Primary Current Current-2w

221 Heater 1 Current-2w

*48/49 naar coax con. /

naar weerstanden

107 Bartington Voltage-2w

104 Load coil leads Voltage-2w

105 Sec. coil 1 Voltage-2w

Voltage-2w

102 Gr200 Ω-4w

103 Hall sensor Voltage-2w

101 Cernox cx1010 Ω-4w

102Extra secondary

copper coil leadsVoltage-2w

Figure F.1: This table shows the Pinout of setup V3.0

49