University of Groningen

Bachelor Thesis in Physics Research performed at SRON

Design and characterization of a LTS flux pump system for possible satellite application

Supervisor: Author: dr. ir. G. de Lange (SRON) Laurens Even prof. dr. ir. R.A. Hoekstra (RUG) prof. dr. T. Banerjee (RUG)

July 8, 2016

[email protected] student number 2315963

Abstract In this bachelor project research is performed on the design of a prototype low temperature superconducting (LTS) flux pump system. With such a system 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 SAFARI instrument for the SPICA satellite, but it can also be used for cryogenic energy storage or for offsetting a magnetic field. As a satellite application the flux pump can reduce parasitic heat load on the cold stages of the satellite. Within this thesis we continued the work on an existing flux pump design from a previous bachelor project. This design had previously shown some essential performance characteristics of a flux pump system, but the actual flux pumping was not observed. In this thesis work we investigated the possible causes of this and implemented improvements. These improvements have resulted in a working flux pump system. The main improvement (which was found in a late stage of the project) was the correction of the winding orientation of a secondary coil in the transformer. Other improvements are: (1) the optimization of the transformer cooling, such that higher critical currents in the primary transformer superconducting wire could be achieved, and (2) the increase of the self-inductance of the primary coil of the transformer by replacing the original aluminum transformer core (that will induce eddy currents) by a Vespel polyamide core. For the characterization of the transformer performance we have used a two-phase lock-in measurement technique to determine the self-inductance and mutual inductance of the primary and secondary coils as a function of frequency. The final flux pumping system (V3.0) operates at 4 K, and consists of a transformer 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 with an estimated self-inductance around 13,5 mH), all made with supercon- ducting wire. The current in the load coil is monitored by measuring the magnetic field that is generated by the coil with a fluxgate meter. The primary 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 pump are both around 0,16 mA per cycle for a 50 mA primary current. With this system a current of at least several amperes should be achievable in the load coil (resulting in a magnetic field in the order of at least dozens of milliteslas), but we have limited ourselves to a maximum of 60 mA, because of limitations in the range of the flux gate sensor (not higher than 590 µT). The coupling factor (0 ≤ k ≤ 1) describes the coupling between the primary and secondary side in a transformer, where a value close to 1 would be ideal. For the final flux pumping system k is estimated to be around 0,45. Acknowledgments I would like to thank the following people who helped and supported me during my Bachelor Project 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 his advice on relevant research items and important items to look at. 3 Willem-Jan Vreeling for his help with the laboratory instruments, cryostat operations and helping 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 the characteristics 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 parts needed for the flux pump project. Extra thanks to Duc for his comprehensive work related to the soldering of wires and attaching parts together. 3 RUG supervisors Prof. Dr. Ir. R.A. Hoekstra and prof. dr. T. Banerjee for supporting me during my project. 3 Wim van den Berg for his continuous support related to questions I had about his former research on the flux pump system. Special thanks for his one day revisit at SRON. During which he helped me put the improved system (V3.0) together and also at doing the first (and last) measurements on the improvement flux pump system. This was almost at the end of my bachelor project, but luckily it was still in time.

ii Contents abstract i

Acknowledgments ii

1 Introduction 1 1.1 Origin of this research ...... 1 1.2 Topic of this research ...... 1 1.3 Research questions and aim of this research ...... 2 1.3.1 Research aim 1 ...... 2 1.3.2 Research aim 2 ...... 3 1.3.3 Research aim 3 ...... 3 1.4 Thesis outline ...... 3

2 Theoretical Background 5 2.1 Superconductivity in short ...... 5 2.2 Flux pump ...... 6 2.2.1 Half and full wave rectifier flux pump operation ...... 8 2.2.2 Description of the flux pump system used in this research project ...... 9 2.2.3 Flux pumping quantified ...... 10 2.2.4 Coupling factor, mutual inductance and stray fields ...... 12 2.2.5 Flux pump operation example ...... 13 2.3 Two and four terminal resistance measurement methods (sensors) ...... 13

3 Experimental Methods/setup 15 3.1 Description of flux pump setup V2.0 and V3.0 ...... 15 3.2 Self-inductance values of the coils present in setup V2.0 and V3.0 ...... 18 3.3 Expected relation between load coil current and measured magnetic field strength 19 3.4 Description of three self-made coils/transformers ...... 19

4 Results & Discussion 21 4.1 Measurements on self-made coils/transformers ...... 21 4.1.1 General remarks about the measurements on coil 1 and 2...... 21 4.1.2 Coil 1 (aluminum) and coil 2 (Vespel) with air core ...... 22 4.1.3 Coil 1 and coil 2 with iron material in core ...... 22 4.1.4 Coil 1 and 2 put in liquid nitrogen ...... 22 4.1.5 Coil 3 with and without ferrite (high permeability) core ...... 22 4.1.6 Summary about test coils ...... 22 4.2 Expected transformer coupling factor and (current) gain ...... 23 4.3 Repeated experiments on flux pump setup V2.0 ...... 24 4.4 Lock-in amplifier frequency sweep measurements analysis and comparison with LTspice IV simulations ...... 25

iii 4.5 Flux pump cryostat measurements ...... 25 4.5.1 Persistent current test ...... 26 4.5.2 Trouble with the fluxgate meter ...... 26 4.5.3 Calibration fluxgate meter (Bartington) output in µT with current magnitude 27 4.5.4 Heat switches & persistent current test (commutation) ...... 28 4.5.5 Flux pumping fast to 60 mA (590 µT) ...... 30 4.5.6 Flux pumping slow to 60 mA (590 µT)...... 32 4.5.7 Critical temperature determination of the load coil during system warm up 33

5 Conclusions and recommendations for future work 34 5.1 Research aims and questions ...... 34 5.1.1 Research aims 1 and 2 ...... 34 5.1.2 Research aim 3 ...... 34 5.2 Recommendations for future improvements ...... 35

References 37

Appendices 39

A Measurements of test coil parameters 40 A.1 Test coils 1 and 2 - inner air core left empty ...... 40 A.2 Test coils 1 and 2 and inner core filled with some magnetic iron material ...... 41 A.3 Test coils 1 and 2 - in liquid nitrogen ...... 41 A.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

iv Chapter 1

Introduction 1.1 Origin of this research

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

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

1.2 Topic of this research

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

1 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 cooling capacity is taken up. However, the cooling capacity has a certain threshold (total allowed heat load) 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 and wiring are difficult if not impossible to be removed from the instrument before it is launched into space. 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 principle obtain high currents in an electric circuit to dive an electromagnet while using a low power supply in a different circuit resulting in low parasitic heat load. This system is called a ’flux pump’ and the 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 articles were mainly about high current applications (of order kA), the operating principle also holds for the mA ranges that are of interest for this specific satellite application. Eventually a flux pump system prototype was built and this, and its components, were tested thoroughly and had multiple optimizations and revisions [17]. Unfortunately the flux pumping operation was not working as intended. The problem was not clearly identified, but had something to do with the coupling of the 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 induce a current in the secondary circuit, via an induced electromotive force (emf), which subsequently needed to generate a magnetic field with sufficient strength to be measurable. Unfortunately the field strength could not be determined, because Wim van den Berg could not distinguished the signal 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 and can also be applied on other field. When the system as a whole proves itself to be functioning, it is also usable in satellite applications similar to the FTS and/or for offsetting magnetic fields or even for 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 that he made will be updated where necessary. My main research aim is to improve the existing system and 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 and transformers (in electric circuits), especially related to the flux pump system. To do so, the transformer behavior will be analyzed with a LCR measurement equipment and with a two phase lock-in amplifier. With a lock-in measurement technique we can measure the frequency behavior of the transformer up to frequencies of 100 kHz and we will be able to measure small emf signals with a high signal to noise ratio. With the obtained knowledge it may be possible to find problems

2 in the current flux-pump setup and improve the parts that are involved and possibly apply more optimizations. Hypothesis: Bad coupling between the primary and the secondary side of the transformer is mainly the result from (large) Eddy currents present in the aluminum core of the primary coil segments, which has a high electrical conductivity. Another possible problem could be shortages between 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 relatively low (< 100 mA) while the wire itself should at least be able to carry several amperes. This indicates poor thermal contact with the copper ground plate which is cooled to 4 K. Improving this will facilitate a higher current ramp in the primary coil, and thereby a larger current in the secondary coil.

1.3.3 Research aim 3 Research question: Show that a flux pump system can operate more efficiently than a system without 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 basic understanding of the research topics, including but not limited to: superconductivity, magnetic fields, operation of transformers and the characteristics of the individual coils in a transformer. As a next step experience was gained with the graphical programming language LabVIEW in order to get a feeling on how to build a Virtual Instrument (VI) and how to use this to control equipment with it. This is needed to get a general understanding of the LabVIEW program that Wim van den Berg developed, which controls and monitors the flux pump system. During the research there is also focus on how to measure the different parameters of coils and transformers, this includes the use 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 pump transformer, albeit on a different scale (see section 4.1). The intention is to use these coils to study different effects on the coupling of two coils together forming a transformer and to extrapolate it to the used flux pump transformer. Some experiments with the unchanged system that Wim van den Berg built are repeated to get a feeling for how the system reacts to certain inputs and what is important to keep in mind such as the maximum allowed currents (see section 4.3 for some of the 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 attempt is 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 components for the flux pump system, especially a new primary coil (and transformer), called version 3.0. For primary coil V3.0 roughly 4800 turns of superconducting wire is wound around six identical core segments made of Vespel polyamide core instead of an aluminum core as was used in V1.0 and

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

4 Chapter 2

Theoretical Background 2.1 Superconductivity in short

Superconductivity is a phenomenon that occurs in some materials when they are cooled below a critical temperature. The result is an absolutely zero electrical resistance (see figure 2.1) and expulsion of magnetic fields in the material interior (possibly originating from external fields). This is called superdiamagnetism or perfect diamagnetism. Thus a superconducting coil is a perfect diamagnet 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 normal metal and a superconductor.(figure from simpliphy page about ”Superconductivity” [18].

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

∂ London equation 1: E = (ΛJ ) (2.1) ∂t s

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

4πλ2 m where Λ = 2 = 2 (2.3) c nse

5 is a phenomenological parameter. Js is the superconducting current density, λ the London penetration depth, m electron mass, e electron charge, ns the number density of superconducting electrons 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 accelerates the superconducting electrons rather than simply sustaining their velocity against resistance as described in Ohm’s law in normal conductor. The second London equation (2.2) when combined with the Maxwell equation curl h = 4πJ/c gives:

h ∆2h = . (2.4) λ2 This describes the exponential expulsion of magnetic fields from the interior of a sample with penetration depth λ, this is called the Meissner effect and can be seen in figure 2.2. Circulating currents will be induced in a thin boundary layer at the surface of the superconducting material in such a way that the flux through a superconducting coil stays constant. During a material transition from normal to superconducting state electrons have the tendency to ’condensate’ by forming Cooper pairs. Cooper pairs or BCS pairs are described in the BCS theory (being the first microscopic theory of superconductivity), named after its theory creators John Bardeen, Leon Cooper, and John Schrieffer. The cooper pairs ’make’ electrons behave like bosons and they thereby enter the ground state. The coupling between the electrons partly has to do with electron-phonon interactions. 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 by the 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 persistent current and maintaining the current even when there is no external power source connected or presence of changes in magnetic flux. In particular superconducting rectifying flux pumps can

6 induce a persistent current by electromagnetic induction, by periodical flux pumping, and when stopped after some time t the current can be maintained even when there is no induction taking place at that moment. According to an article by Van de Klundert and Ten Kate [3] flux pumps can be divided in three classes, namely flux compressors, DC dynamos and transformer rectifiers. Only the transformer rectifier flux pump is relevant for this research project. The other two classes will not be discussed here. A rectifier flux pump consists of two separate electric circuits. An essential part of this type of flux pump system is the transformer which magnetically couples the electric circuits via electromagnetic coils. One of the circuits contains a power source and a primary coil and the other circuit contains at least one secondary coil and two heat switches. From here on the circuits will be conveniently referred to as primary circuit and secondary circuit respectively. The use of the word switch is for convenience, but in this context it actually does not describe a physical switch. In this report the word switch describes a piece of superconducting wire which can be heated so that it reaches its critical temperature and breaks superconductivity making it resistive. The heating is done by sending a ’heater current’ through a thermally connected wire. The switch has a cool-down time to become 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 a time varying changing magnetic flux which consecutively induces an emf or voltage in the secondary circuit according to Faraday’s law of induction. When the change of the primary current in time is constant the emf will also be constant. The emf will generate a secondary current, which magnitude depends 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 related to the maximum primary current divide by the slope of the current as

Ip max Ist ∝ emf ∝ . (2.5) dIp/dt

The direction of the induced current can be derived from Lenz’ Law, which says ”Nature abhors a change in flux”. In the case of an increasing flux a current will be induced of which its direction is so to oppose the change in flux. In circuit diagrams the dot marking convention can be used to indicate in which direction the induced current will flow (this is explained in figure 2.3 and again in section 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 indicated by the dots [21].

7 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 a current during primary current ramp up OR ramp down, while the latter induces a current during both primary ramp up AND ramp down.

In figure 2.4 the flux pump op- eration of a half wave rectifier is shown with four steps. (1.) Dur- ing the first step switch 1 is closed (superconducting) and switch 2 is open (resistive). A primary cur- rent ramp up will induce a constant emf or voltage over the secondary loop which induces a CCW current through switch 1 and the load coil. (2.) The primary current is kept constant and no currents will be in- duced. Switch 2 is closed making it superconducting. The current will remain in the outer loop because of its inductive property. (3.) The Figure 2.4: Flux pump operation of a half wave rectifier [17]. primary 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 inducing a 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 to the outer loop. Now the steps as described above can be repeated periodically to build up a larger persistent current.

In figure 2.5 the flux pump opera- tion of a full wave rectifier is shown with four steps. (1.) During the first step switch 1 is open (resistive) and switch 2 is closed (supercon- ducting). A primary current ramp will induce a constant emf over both secondary loops which induces a CW current in both loops which are in different directions through the load coil, but due to the resis- tance in switch 1 the current in the upper loop will be very low relative to the current in the bottom loop. (2.) The primary current is kept constant and no currents will be in- duced. Switch 1 is closed making both secondary loops superconduct- ing. The current will remain in the Figure 2.5: Flux pump operation of a full wave rectifier [17]. bottom loop.

8 (3.) The primary current remains constant, while switch 2 is opened forcing the secondary current from the bottom loop to the upper loop. The current direction through the load coil remains the same, because of its inductive property. (4.) The primary is ramped down inducing a current with different 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 from the upper loop to the lower loop. Again the steps described above can be repeated periodically to build 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 and secondary sides are placed in a cryogenic environment (cryostat). The flux pump system as built by Wim van den Berg is a full wave rectifier with one primary coil and two secondary coils similar to figure 2.5, but the secondary coil is physically split in two coils though practically it is connected in the same way. The complete flux pump circuit with the full wave rectifier included can be seen in figure 2.6. Also indicated are the locations of two (superconducting) joints that are needed to make a closed loop. The secondary circuit is completely superconducting and only magnetically coupled to 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 located in the ’hot environment’.

Figure 2.6: Circuit diagram of the flux pump system with a full wave rectifier with one primary coil on the left, two secondary coils, one load coil, two superconducting joints and two 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. In this case an increasing primary current in the CW direction (or decreasing in CCW) will induce a CW current in both secondary loops and a decreasing primary current in the CW direction (or increasing in CCW) will induce a CCW current in both secondary loops. When the switches are closed and opened as in the previous section for a full wave rectifier a persistent current can be build up.

When a current is sent to the cryogenic environment it encounters high resistive wiring (Rp) during the entering of the cryostat.a When the power source is on during the operation of the flux pump, the primary current will cause extra inflow of heat into the cryogenic environment which is generated due to the high resistive wiring. The secondary side has zero resistance by being completely superconducting (which means no current dissipation) and has no power source. Thus there 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 the other hand result in more Joule-heating. It is a trade-off between these two factors and this will be discussed in more detail later (section 3.1).

9 heat). However, during flux pump operation commutation of the persistent current takes place in the secondary circuit. When using resistive commutationb some fraction of the persistent current is dissipated and converted into heat. With a flux pump system as described above, there can only be (extra) external heat flowing into the system and heat generated within the system during the operation of the flux pump. Thus after a persistent current is built up, it can be maintained and remain constant while no heat is generated in the cryogenic environment. This makes it possible to generate a constant magnetic field with a superconducting electromagnet which remains constant when the power source is disconnected and also minimizes the heat load on the cooling system. Unfortunately this only holds for the ideal case in which a persistent current in a superconducting circuit always stays constant because of zero resistance. Although this is true, in practice the secondary circuit always has some small resistance originating from the presence of at least two joints. This finite resistance makes the persistent current decay over time, but the joints can’t be avoided since they are needed to make the secondary loop a closed loop. A circuit that contains two secondary coils, a load coil and two heat switches while being made out of one piece of wire is just 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 current in 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 this article 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 p kps LpLs i10 = −ip (2.6) Ls + Ll is induced in one of the secondary loops, where the minus sign indicates a current in opposite direction so to counteract the changing magnetic field generated in the primary loop. kps is the coupling between the primary and secondary coils. The coupling factor between two coils is always a value between 0 and 1, with the former being no coupling and the latter being perfect coupling. During the fourth flux pump step

Ll − k12Ls i20 = i10 = α i10 (2.7) Ll + Ls is induced in the other secondary loop adding to the already present persistent current.k12 is the coupling between the secondary coils and α is defined as α ≡ (Ll − k12Ls)/(Ll + Ls) which is the fraction of the current transferred from one loop to the other. The induced current after one complete cycle is

(1) 2 i = i10(α + α ). (2.8) Each cycle of the flux pump operation is the same as the first. The persistent current induced during 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 is dissipated and converted into heat. A different process is called inductive commutation, which does not generate heat in the switches. For a more detailed explanation about the two processes you can look up the second article of Van de Klundert and Ten Kate about flux pumps (1981)[4].

10 both secondary loops. When the cycle repeated n times the persistent current through the load coil will be α2n − 1 i(n) = i (α + α2 + ... + α2n) = i α . (2.9) 10 10 α − 1

From equations 2.6 and 2.9 the maximum load circuit current that can be obtained after infinite flux pump cycles is r (∞) Lp αkps i = −ip . (2.10) Ls k12 + 1 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) q (∞) G = Is /Ip = αkps Lp/Ls. (2.12) This limit in the persistent current exists due to the dissipation of a certain fraction of the current during the current transfer from one loop to the other. The dissipation is due to the ’on time’ of the heat switches and occurs in the normal regionc of the secondary wire which is the part of the secondary circuit that is heated by the switches [5]. At one point after a certain number of flux pump cycles the fraction of the total persistent current which is not transferred from one loop to the other and the induced current during a half flux pump cycle (1 − α)ipers. = i10 become equally large 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 can never 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-inductance ratios. A high gain factor (G > 100) means that the persistent current in the secondary circuit can reach a high multiple of the primary current magnitude (×100), which allows a large current through the load coil (depending on the primary current magnitude) to generate a strong magnetic field. Thus it is important that the ratio of the self-inductances of the primary and secondary coil(s) in a flux pump transformer is high (so Lp  Ls, which follows from the relation given in equation 2.12) in order 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 in equation 2.12). Note from equations 2.10 and 2.12 that the (current) gain is independent of the current ramp. A higher current ramp will induce a secondary current with the same magnitude in a shorter time simply by inducing a larger emf. Unless there are materials with magnetic properties nearby the transformer that exhibit hysteresis effects and/or generate eddy current, because these effect do depend on the operating frequency (current ramp). Also note that from the equations just described in 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-zero resistance. dThe current fraction which is dissipated is independent of the normal resistance [5].

11 the magnitude of the primary current, the ratio between primary and secondary self-inductance and the coupling between the coils. Unfortunately the self-inductance ratio that is beneficial for a high current gain per step (quick charging) is unfavorable for the total (current) gain and vice versa. 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) and leakage (or stray) inductance? The coupling factor (k), a value between 0 and 1, indicates the ratio of the ’leakage’ flux to the enclosed 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 surrounding secondary coil(s). The coils in a transformer with k = 0 have no mutual coupling. The coupling factor with the primary and secondary coil self-inductance relate to the Mutual inductance as q M = k Lp/Ls. (2.13)

An indication for the coupling factor is given by s L k = 1 − p stray , (2.14) Lp 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 low permeability core (µr ≈ 1 soµ ≈ µ0) has a self-inductance of

µ N 2A L = 0 , (2.15) l where µ0 is the vacuum permeability, N the number of turns, A the area of the solenoid perpendicular to the longitudinal axis and l the length of the coil. For coils with a higher permeability core equation 2.15 can give higher deviations from reality. The magnetic field in the core of a solenoid is

µNI B = , (2.16) l 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 relative permeability (µr). The core (material) of a coil thus has influence on its self-inductance and magnetic field but can also have an effect on the coupling factor. A magnetic core concentrates a magnetic field so this can improve the coupling of could by reducing the leakage flux and likewise increase the enclosed flux. High permeability cores also introduce non-linear effects, especially at 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 with a 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 could match with a ferromagnetic material such as iron. The residual magnetic field is the remaining field strength inside a material when the external field is removed. The coercive force is the negative magnetic field strength needed to demagnetize the material completely.

12 Figure 2.7: This figure shows the relationship between the magnetic flux density (B) and the magnetic field strength (H) for a particular material. The enclosed area is proportional to the 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 load coil while only needing a 100 mA power source. This will require at least a primary to secondary self-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 and secondary 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, V measuring the voltage drop over the DUT and dividing the voltage over the current R = I . In order to 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 a schematic 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 sensing on the right [23].

13 In two terminal sensing one pair of wires is used to supply a current and to measure the voltage over a DUT. In this way the DUT’s resistance is not the only component of the measured voltage drop. The resistance of wire contacts and the wires itself (Rlead) also result in voltage drops. As a result the measured voltage is higher than the actual voltage over the DUT. The deviation from the actual voltage becomes even larger when there is a relatively high series resistance present in the circuit. Four terminal sensing solves this problem by using two separate wire pairs. One pair is connected to the current source supplying current through the DUT (force connections) and the other pair is used to measure the voltage over the DUT (sense connections). Since a Voltmeter has a very high impedance there will be almost no current flowing through the instrument and thus the voltage drop over the sense leads is negligible. This means the voltage drops occurring over the force leads and contacts will not be present in the voltage measurement over the DUT provided that the sense leads are precisely at the DUT leads. Thus only the voltage drop over the DUT is measured and together with the known current the resistance can be accurately calculated.

14 Chapter 3

Experimental Methods/setup 3.1 Description of flux pump setup V2.0 and V3.0

The flux pump system consists of the following components: ˆ LabVIEW Virtual Instrument and computer setup (see appendix C) ˆ 2 stage cryostat with two separate chambers (outer: liquid nitrogen and inner: liquid helium) 2x D-sub DB-25 connector Manganin wire ~(42,0 ± 0,6) Ω @ 297 K ˆ Primary coil (V2.0: 6120 turns, V3.0: 4950 turns) ˆ Secondary coil split into two coils (total V2.0; 6 turns, V3.0: 20 turns) ˆ Load coil V2.0 (900 turns, also used in setup V3.0) ˆ Two heat switches (with a resistance around 1,025 kΩ each) ˆ Two aluminum pressure joints ˆ 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 are attached to a copper ground plate which is screwed to the cryostat. The primary coil with the two secondary windings are located in the center underneath an aluminum plate with two pressure joints on top of the plate (setup V2.0). The load coil can be seen in the upper part of the figure and the 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 on the 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 than plain copper wire. Although this high resistive wiring increase the dissipation in the wire due to Joule heating, a balance must be made between the Joule heating and the parasitic thermal heat inflow from the ’hot environment’ which needs to decrease the heat flow into the cryogenic environment. It is trade-off resulting from the fact that there are no wires that have both a low electrical resistance and a high thermal resistance. Two DB25 male solder type connectors are placed on the inner cryostat connectors on which all sense and current leads are attached. One male connector has 20 pins used for current input into the 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 into the 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 connector is used for the Cernox temperature sensor, of which the probe is place on top of the aluminum plate covering the primary coil in setup V2.0. Also several voltage and current leads (12 wires, 4x2 voltage 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 appendix F 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 superconducting wire by stycast. This is efficient and results in fast heating, or high response in breaking the superconductivity. Note that many of these wires are added and used for flux pump diagnostic purposes. In a bare flux pump system one would only need 4 wires for the heater currents and 2 wires for the primary current. This could even be reduced to 6 when using a common ground for the heat switches and primary current. Extra wires could be needed when its is required to include a magnetic field sensor (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 (section 2.3), as applied in the RTD sensors, becomes clear when the relatively high resistance cryostat wiring is considered. By using the four wire method these extra (series) resistances don’t have an effect on the measurement outcome.

In figure 3.2 the new setup can be seen with the improved primary coil (V3.0) completely cast in a trench of stycast, which is a thermally conductive epoxy encapsulant. It can be identified by its black color and it is well suited for improving the transformer thermal contact with the copper 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 for the pressure joints. The Cernox temperature sensor was placed in between the load coil and the bottom right pressure joint. Transformer V3.0 has 20 secondary turns instead of 6 turns. Setup V3.0 also includes a third extra secondary coil made of 0,2 mm diameter copper wire which is open circuited. This extra coil is included to perform emf measurements and to have more verification possibilities 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 primary coil and new secondary coils.

The primary coils (V1.0-3.0) consists of six identical solenoid-like segments that have 30° angled ends and when put together they form a hexagonal ring which resembles a toroidal coil (see figure 3.3 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 identical segments with 4800 turns in total. The type of wire that is used on the primary coil in this figure 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 21 and 29 mm, but the effective length for the (primary) wire winding is 21 mm. The outer diameter of the segments is 5 mm, but the ends of the segments are raised to become 6 mm in diameter. The height difference between the middle and the sides keeps the wire better in place during production and the sides offer some protection against potential wire damaging. The segments have an inner air core which is 3 mm in diameter which is needed in production. Primary coil (V2.0) has roughly 1020 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 room temperature 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 primary coil V1.0 (70 µm Niomax-CN A61/05 (NbTi). The coil has about 4950 turns, or a little more than 800 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% Zr wire 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 more easily around the primary coil since the wire type is quite stiff. This also should have made it a bit easier to get the secondary wires in the pressure joints, which are basically two sets of two aluminum 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 of 27 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 copper cladding removed. Per joint three wires plus an extra dummy wire are ’cold-welded’ together by the mechanical force of six socket screws tightened with a torque wrench at 60 N cm. The dummy wire is included to make sure the surface contact between the wires is optimal, especially since setup V3.0 uses a smaller secondary wire type while still using the same pressure joints. The pressure joints 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 isolation and 0,30 mm without isolation. Some long wires are partly made up of 0,2 mm copper wire inside the cryostat to allow better thermal contact with the cryostat walls (better cooling), just as the primary current leads (connector → primary coil leads) are completely copper wired.

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

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

18 The measured self-inductance of coil V2.0 (aluminum core) is 1,119 mH.c The measured self inductance of coil V3.0 (Vespel core) is 4,449 mH.d The calculator from reference [24] gives a self-inductance of around 4,9 mH when the coil segments are assumed to be in line with each other and 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 of setup 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 multiple layers but for the calculation it is assumed that all turns are next to each other (not physical, but for convenience) and the coil has a length of 11 mm. A current of 10 mA should then generate a magnetic field strength of 100 mT in the middle of the solenoid. The magnetic field just scaled linearly with the current so a ten times stronger current will also generate a ten times stronger magnetic field inside the solenoid.

Of course the load coil in the flux pump system is not a single layer solenoid but consist out of multiple layers and its length/radius ratio fis not large enough for the approximation to hold, but at least some simple estimation can be made. For the real solenoid the magnetic field is probably lower 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 a different number of turns that are magnetically coupled to form little transformers. The design of coils 1 and 2 is based on the six identical segments of the hexagonally-shaped primary flux pump coil and are made so to reasonably resemble its properties, but there are some important differences which will be discussed shortly. Coil 1 has an aluminum core and coil 2 a Vespel polyamide core allowing a comparison to be made between the difference core materials. The first having a high electrical conductivity, and the second having a negligible electrical conductivity. This is to check the hypothesis that induced eddy currents in the transformer core counteract a changing magnetic field and thereby substantially worsen the coil coupling in a transformer with an aluminum core.

c At 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. d At 20 kHz measuring frequency with the highest phase shift at 89,1 °and with impedance 559,3 Ω and 7,924 Ω DC resistance. e For both calculations using 3 layers with 275 turns per layer, inner diameter of 5 mm and segment length of 21 mm [24]. f Assuming a 30 layers of 30 turns, an inner diameter of 14 mm and 11 mm length [24]. g For 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 (here shown 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) the number of secondary turns is increased to 20 turns per segment (while the primary turns remain at 800/segment which is the same as the primary coil segments) resulting in a turn ratio between secondary and primary side of 20:800 instead of 6:4800. This will increase the secondary voltage but lower the secondary current. For a flux pump with a high current requirement this is bad, but for characterizing the coils it is actually an advantage for doing measurements, because its easier to measure a higher voltage. Coil 3 is a simple transformer with a 90 and a 30 turn winding made of copper wire. A MnZn ferrite core with high permeability encloses the windings as can be seen in figure 3.5, but the core can also be removed. This will give information about the influence of the core permeability on the self-inductance of the coils.

20 Chapter 4

Results & Discussion 4.1 Measurements on self-made coils/transformers

Most parameters are measured with the Agilent (nowadays Keysight) 4263B LCR meter with test signal frequencies from 100 Hz to 100 kHz. An LCR-meter measures the voltage over and the current through a DUT. With these vales the instrument can determine the impedance and phase shift and use that to subsequently determine the value of the DUT inductance or capacitance. In the 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 of the coils. Also the coupling capacity, with the impedance and phase shift, between the windings is determined separately for each coil (except for the nitrogen experiment). See appendix A for a detailed 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 dimensions are roughly equivalent, but there is a difference in the outer diameter of the windings. The aluminum has tighter wound turns resulting in a lower outer winding diameter 7,5 vs 9 mm. The turn ratio (n) can experimentally be determined by q n = Lp/Ls. (4.1)

This can be easily shown by filling in the formula for the self-inductance, for example for a solenoid 2 (equation 2.15: L = (µ0N A)/l). Assuming the area and length is the same, each parameter cancels except the number of turns so we get n = Np/Ns. The turn ratio is 40 in all measurements so it should also be 40 (or at least close) when calculating the turn ratio by using equation 4.1 and the measured values for the primary and secondary self-inductance values. The calculated turn ratio’s show different values: the aluminum core coil has a turn ratio between 16,3 and 17,6 and the Vespel core coil has a turn ratio between 25,3 and 28,6. The differences between real and calculated turn ratio is substantial. The difference may originate from the coil having less (effective) turns, for example caused by shortages. Also in case of the aluminum coil the outer diameter (7,5 mm) is too low to fit eight layers of 0,2 mm on a 5 mm diameter core, because a close wound coil would at least have 8,2 mm outer diameter. This indicates the coil has less turns from the start. Other causes could be a large deviation in the measurement of the self-inductances but at least for the Vespel core the primary self-inductance seems to match quite OK with the online calculator [24].

21 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 also higher primary self-inductance (1101,0 µH vs. 347,5 µH) while the wiring, turn ratio and dimensions are the same. The coupling factor of coil 1 is 0,388 and 0,561 of coil 2. This could indicate the presence 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, the Vespel coil shows an increase in its primary impedance and self-inductance. This effect cannot be 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 the presence of an iron core, but here the aluminum coil shows a decrease. Still the coupling factor of both coils increases with 19% (to 0,669) and 27% (to 0,493) respectively, which should be expected when 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 lower temperatures the copper and aluminum have a higher conductivity or lower resistivity. Lower resistivity of the copper wire won’t change the self-inductance, but lower resistive aluminum can sustain 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 as the Vespel coil, which is explained by the fact that the copper wiring becomes less resistive at lower temperatures. The DC resistance of both coils drops from around 9 Ω at room temperature to a little over 1 Ω at liquid nitrogen temperature. At first sight also the self-inductance of both coils 1 and 2 looks to be decreasing (234,7 µH and 995,4 µH respectively), but when the test signal frequency is changed (from 100 to 20 kHz) about the same self-inductance values are measured as compared to the 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 factor can 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 around the primary and secondary wiring. It also shows the reduction of the magnetic stray field as the ratio of the self-inductance and the stray inductance decreases drastically when encasing the coil with a high permeability material. The coupling factor increases from below 0,4 to almost unity.

4.1.6 Summary about test coils ˆ The aluminum coil has a significant lower self-inductance than the Vespel coil indicating eddy current is the aluminum reducing the self-inductance. ˆ Real turn ratio and calculated turn ratio don’t match for both coils. ˆ 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.

22 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 the measurement results of the test coils (section 4.1) calculations can be done give estimations of some values describing the system characteristics of the used flux pump system. Important values are the (current) gain of one cycle, of n cycles and the maximum obtainable secondary(/persistent) current gain (after infinite cycles). Made assumptions for the calculations The secondary coils are quite far apart thus their mutual coupling will be very low. Based on this fact the assumption is made that the coupling between the secondary coils is negligible and set to zero (k12 = 0), which will be convenient for the calculations. The coupling factor kps (between primary and secondary coils) is estimated to be at least 0, 3 , but could possibly also be as high or 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). Less secondary turns (around 6 turns in total) could in practice mean less mutual coupling resulting from the imperfect geometric orientation of the windings. So for coil V2.0 this is reasonable. A k factor higher than 0, 6 could be possible because the hexagonal (Vespel) toroid-like transformer in principle should have less stray fields, because the magnetic field in a toroid is more constrained to stay and to be concentrated within the toroid. Also for coil V3.0 no eddy currents can be generated in 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 pump setup V3.0 . Estimated values For the primary current (Ip) a (peak-peak) magnitude of 50 mA is chosen in the calculations for the 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 of the pumping characteristics. The ideal gain is 113, the minimum ’real gain’ is 51 and the maximum obtainable current gain (after infinite cycles) is 2,54 A (ideal max current gain 5,64 A). The current gain 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 current gain of 2,09 A (ideal max current gain 4,65 A). The current gain per cycle is 159 µA and after 400 cycles 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 current For example, when the coupling factor is doubled from 0, 3 to 0, 6 all values are simply multiplied by 2, except the ideal gain which only depends on the number of turns and the geometry of the transformer. Thus a higher coupling factor brings the real current gain values closer to the ideal values. And when for example the primary current is increased with a factor of 10, then the current gain per cycle, after n cycles and after infinite cycles also increase with a factor of 10. Conclusions about estimations Although primary coil V2.0 has roughly a 75% lower self-inductance than primary coil V3.0, the ideal and minimum real gain of setup V2.0 and V3.0 is not very different. This is because the lower primary self-inductance is accompanied by a lower secondary self-inductance (since the secondary coil has 6 turns instead of 20 as in setup V3.0) which results in roughly the same gain. Still setup V2.0 has a slightly higher Lp/Ls ratio and thus more time is required to built up a certain persistent current (when keeping the flux pump time and primary current constant). On the other hand V2.0 has 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 up fivefold of that (52,1 mA). For a real application the primary coil of setup V3.0 and the secondary coil 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 and possibly determine the coupling between the primary and secondary side of the transformer. The following performed tests will be shortly discussed here: persistent current test and critical current test of the load coil. See figure 4.1 for a persistent current test on the unchanged flux pump system. The left part of the graph shows some change actions playing with the primary current and a heater while an external power is connected to the load coil circuit. At the end of the first part and during the first half of second part it can be seen that the flux pump works as intended when it comes to maintaining a persistent current, albeit a small current in this case. The weird spike and drop of the magnetic field halfway the second part of the graph happened because 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 after having 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 critical current 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-in amplifier. These were done with the intention to study the coupling of the primary and secondary sides. But there were some distractions regarding strange peaks in the measurement results which took a lot of time to discover. The cause was really hard to find, and in the end the exact cause was 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 of time constraints when writing this report this research cannot be discussed thoroughly. A brief description 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 new transformer with the core material being Vespel instead of aluminum and the secondary windings oriented in the correct way. The Vespel core ensures the absence of (possible) eddy currents occurring in the transformer core. Because of the long manufacturing time of the new primary coil and other complications during the project, results for this section came only until recently, that is at the end of the research project. But finally the system was proven to be working and so a lot of different tests could be performed. The most important results will be discussed here. Also a brief description will be given about the wrong configuration of the secondary wiring of transformer V2.0 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 and the upper ends likewise no flux could be built up because of the opposite direction of the induced secondary currents which would cancel the already persistent current and result in a net current of zero 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 are connected together. The latter connection makes the two secondary sides to configured as if they are 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 by connecting an Agilent E3631A power source to the load coil voltage leads and than set the desired current while the switches are still closed (superconducting). No current will go through the load coil at first because it has a higher impedance compared to the switches, but when the switches are opened all current will go through the load coil and the power source can be turned off. Because of the load coil inductive property the current will keep going through the load coil.

29-6-2016 22:00 30-6-2016 10:49:00 4,75 Cernox (K) 4,73

4,71

4,69

Temperature (K) Temperature 4,67

4,65 Time -8,E+25 ) T Magnetic field (μT) μ -2,E+41

-4,E+41

-6,E+41

-8,E+41

-1,E+42

-1,E+42 Time Magnetic field strength ( strength field Magnetic 29-6-2016 22:00 30-6-2016 10:49:00

Figure 4.3: This graph shows a persistent current test during more than 12 hours. The magnetic 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 with on top shown the temperature. The magnetic field unfortunately is too big to be measured by the fluxgate meter (saturated), but the inserted current was 150 mA as set on the power source. After the insertion all power sources were disconnected. This was done just before 22:00 as is indicated on the figure. The ’measured’ magnetic field strength remains above the measuring thresholds during at least more than 12 hours (graph stops around 10:49) meaning that at least some persistent current is maintained. Unfortunately because of the saturation of the fluxgate meter this experiment doesn’t give 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 4 sense/force wires were not connected correctly in order to measure magnetic field strength in microteslas. It has something to do with a wrong polarity of the sense/force connections. The solution turned out to be swapping pins 1 and 2 as well as pins 14 and 15. After the correction a 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 of 25-65 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 of measurements 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 current magnitude 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 out to be roughly 10 µT per mA. For example for the slow flux pumping experiment (see section ??) the flux pumping was stopped at 516 µT. Than an estimation was made and an external current of 50 mA was inserted resulting in a drop of the magnetic field strength to 500,2 µT. 51 mA gave a value of 513,2 µT and a current of 52 mA gave 523,6 µT. Inserting an external current of 60 mA into the load coil resulted in the fluxgate 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 cool down temperature of the superconducting secondary wire is examined. The results are shown in figure 4.4 and give information about how effective the current commutation is from one secondary loop to the other loop. The data is useful for an indication of the commutation-time and -losses.

5,5 Cernox (K) 5,4 5,3 5,2 5,1 5 4,9

4,8 Temperature(K) 4,7

7004,6 ) T Magnetic field (μT) μ 4,5 600 15:04:02 15:06:55Persistent current 15:09:48 Time15:12:40 15:15:33 15:18:26 500

400

300 Adjustments of switching time and flux 200 pump cycle time 100

0 Magneticfield( Strength -100 NO Persistent current Heater 1 current (A) Heater 2 current (A) 15:04:02 15:06:55 15:09:48 15:12:40 15:15:33 15:18:26 4,0E-03 Time 3,0E-03

2,0E-03

1,0E-03

0,0E+00

-1,0E-03

-2,0E-03 Heater(A)currents -3,0E-03

-4,0E-03 15:04:02 15:06:55 15:09:48 15:12:40 15:15:33 15:18:26 Time

Figure 4.4: In this graph temperature, the magnetic field strength and the heater currents are 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 the corresponding loop.

For this system test also an external current was inserted, first 60 mA (first spike), but later a current 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 time to cool down a bit before starting the ’stress test’. Then the switches were alternately activated and 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 (cooling down time) at 2,5 s. This was later reduced to 0,1 s and 1 s respectively and also the current ramp was 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 currents the 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 to the cryostat per switch is given by P = I2R = 0,0164 W or in terms of energy (E = P t): 0,0033 J per switch. The switch period of a cycle was able to be reduced below ten seconds while maintaining the persistent current. The current through the load coil shows no clear drop in its generated magnetic field, maybe 1 µT but not more. Also the monitoring of the temperature shows an increase, but this seams to stabilize at around 5 K From this we can conclude that the commutation in system setup V3.0 can pe performed efficiently (fast) and also the losses are low (<1 µT/50 switches) and system temperature can stay low.

29 4.5.5 Flux pumping fast to 60 mA (590 µT) In figure 4.5 the results of flux pumping with a high primary current are shown. The bottom graph shows the periodical ramping up and down of the primary current. For this experiment the load coil current was zero from the start. This means the fluxgate meter starts around −40 µT (being the background value for the earth’s magnetic field). The primary current ramp is set to almost 500 mA (peak-peak) and a dI/dt of 250 mA/s. The switch open time was first set to 0,1 s but quickly changed to 0,5 s and later to 0,2 s the closing time to 2,5 s. In about 7 minutes the magnetic field strength is increased from −40 to 590 µT.

5,3 Cernox (K) 5,2

5,1

5,0

4,9

Temperature(K) 4,8

4,7 70016:10:25 16:11:51 16:13:18 16:14:44 16:16:11 16:17:37 16:19:03

) Time Magnetic field (μT) T

μ 600

500

400

300 200 Heater 1 ‘stuck’ / switch 1 remains open 100

0

Primary current Magnetic fieldMagnetic( Strength -100 magnitude 16:10:25 16:11:51 16:13:18 16:14:44 16:16:11 16:17:37 16:19:03 0,3 (peak-peak) Time Primary current (A)

0,2

) A 0,1

0,0

-0,1

Primary current ( Primarycurrent -0,2

-0,3 16:10:25 16:11:51 16:13:18 16:14:44 16:16:11 16:17:37 16:19:03 Time

Figure 4.5: Shown here is the flux pumping operation with a high primary current (500 mA peak-peak and starting at zero current. The temperature spikes originate from a program control 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 is heater 1 being ’stuck’ (left on heating) which explains the increases in temperature but also the drops in the measured magnetic field. The loss per drop is the induced current from a half flux pump cycle. This glitch in the heater current control is a software/programmatic problem. It may result from some manual fiddling with the automatic flux pump signal generator in the LabVIEW program 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 using the 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 what was calculated in section ??. There a magnetic field increase of 0,159 µT per cycle was calculated for a 50 milliA primary current, but for this experiment a 500 mA primary current is used instead so this results in an increase of 1,59 mT per cycle. Still the total built up current after 400 (40 for Ip = 500 mA ) steps is shown to be 63 mA which is more than what is built up during the experiment in 40 cycles. From this we can conclude that the coupling factor must be a little lower than 0, 45, namely around 0, 42 which would mean that in practice the current gain per cycle is around 15 µT, which lies within the uncertainty margin for the magnetic field gain per cycle which was read out from the data shown in figure 4.5. The value of 0, 42 can of course only be accurate if the estimations of the self-inductances are also accurate, which of course can and probably have deviations from the real situation. This experiment shows that the flux pump is operating as it should be, namely stepwise inducing an 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 estimations done 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 important thus the primary current needs to be low, but must obtain a much higher secondary current. In this experiment an attempt is made to build op a persistent current which is larger than the primary current used during the flux pump operation. During this experiment a 50 mA peak-peak primary current is used. From figure 4.6 we can again see that the magnetic field strength increases nicely in time starting at −40 µT or zero current. The building up of a magnetic field strength of 516 µT took little over an hour (3800 s). Each flux pump cycle 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 gain per cycle is 14,9 mA and after 400 cycles is 58,6 mA. This again is in quite good agreement with the 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 the system is able to build up a persistent current which is larger than the primary current.

7,5 Cernox (K) 7,0

6,5

6,0

5,5

Temperature (K) Temperature 5,0

6004,5 ) 17:44:10 17:51:22 17:58:34 18:05:46 18:12:58 18:20:10 18:27:22 18:34:34Magnetic field (μ18:41:46T) 18:48:58 T μ 500 Time 400

300

200

100

0 Magnetic field strength ( field strength Magnetic -100 3,0E-0217:44:10 17:51:22 17:58:34 18:05:46 18:12:58 18:20:10 18:27:22 18:34:34 Primary current18:41:46 (A) 18:48:58 Time 2,0E-02

1,0E-02

0,0E+00

-1,0E-02

Primary(A) current -2,0E-02

-3,0E-02 5,0E-0317:44:10 17:51:22 17:58:34 18:05:46 18:12:58 18:20:10 18:27:22 18:34:34 18:41:46 18:48:58 Time Heater 1 current (A) Heater 2 current (A)

3,0E-03

1,0E-03

-1,0E-03

Heater currents (A) currents Heater -3,0E-03

-5,0E-03 17:44:10 17:51:22 17:58:34 18:05:46 18:12:58 18:20:10 18:27:22 18:34:34 18:41:46 18:48:58 Time

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

aNOTE: During the flux pumping there was some playing around with the flux pump signal controls such as changing the dI/dt and heater close and open times. This resulted in some variations in the signal as seen in figure 4.6.

32 4.5.7 Critical temperature determination of the load coil during system warm up The load coil critical current can be nicely determined when the liquid helium is becoming depleted making the cryostat warm up very slowly. Before the load coil/secondary circuit reaches a temperature above its critical temperature of the wire (and breaking superconductivity), an external persistent current of 50 mA was inserted in the secondary circuit over the load coil and than the external power source was removed. Again a value that results is a measurable magnetic field strength for the fluxgate meter. At a temperature of 9,23 K the load coil suddenly ’loses’ its superconducting property and the persistent current is dissipated within a few seconds as can be seen in the sudden drop of the magnetic field strength in figure 4.7.

9,26 Cernox (K) 9,25 300 9,24 9,23 Cernox (K) 250 9,22 9,21

Temperature(K) 9,2 200 700 20:02:50 Magnetic field20:03:24 (μT)

) 600

T 500 μ 150 400 300 200

100 100 Strength(

Magneticfield 0 Temperature (K)Temperature -100 50 20:02:50 20:03:24 Time 0 30-6-2016 18:14:24 30-6-2016 20:09:36 30-6-2016 22:04:48 1-7-2016 0:00:00 1-7-2016 1:55:12 1-7-2016 3:50:24 1-7-2016 5:45:36 1-7-2016 7:40:48 1-7-2016 9:36:00 700 Axis Title Loss of persistent Magnetic field (μT) T) 600 μ current 500

400

300

200

100

0 Magnetic fieldMagnetic( Strength -100 30-6-2016 18:14:24 30-6-2016 20:09:36 30-6-2016 22:04:48 1-7-2016 0:00:00 1-7-2016 1:55:12 1-7-2016 3:50:24 1-7-2016 5:45:36 1-7-2016 7:40:48 1-7-2016 9:36:00 Time

Figure 4.7: This graph shows a persistent current test lasting over 12 hours. The Magnetic field strength value is not physical, because the fluxgate meter is out of range (saturated).

33 Chapter 5

Conclusions and recommendations for future work In conclusion a working flux pump system is developed and which is capable of building up and maintaining a persistent current in a superconducting load coil (circuit). The measured performance of the flux pump system is in agreement with estimations based on the system properties and theory (± 10%). The coupling factor of the transformer is determined to be around 0, 42 assuming the measured and estimated values for the self-inductance of the coils are accurate. The current gain 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 of the 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 aluminum core was not necessarily the problem in “system setup V2.0”, but by replacing it with Vespel in transformer 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: ˆ Correct functioning of the flux pump transformer, by changing one of the secondary winding direction so both windings are counterclockwise. ˆ 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 for transformer V2.0 this was limited at around 60 to 65 mA. ˆ Another thing that’s replaced is the primary coil with an aluminum core by a coil with Vespel polyamide 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 the problem of the dysfunctional transformer (V2.0) and improving the thermal design of the setup to allow higher critical currents. These research aims are achieved and related actions how this was done 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 system without 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 up a persistent current and maintaining it. Especially for a proof of concept, the current flux pump system has passed the test and paved the way for a future implementation. No calculations have been done to compare a flux pump with a directly driven electromagnet, but it is improbable that the latter case is more efficient in heat management since a power source needs to constantly deliver a current into the cryogenic system to maintain the magnetic field. On the other hand the current flux 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 Bartington fluxgate meter at around ∼60 mA or ∼590 µT . This limits flux pump testing to below the indicated value and also the persistent current decay at higher currents couldn’t be analyzed. In order to improve the monitoring of the persistent secondary current testing a different sensor should be used like the earlier used hall effect sensor. This sensor was not used anymore because of its high parasitic heat load on the load coil which caused the load coil to go out of superconductivity. So for setup V3.0 the sensor was not connected, also because of a tight time schedule. For future improvements the position of the hall effect sensor should be attached to the bottom of the copper plate instead of the load coil itself, which should enable the load coil to remain superconducting. A fluxgate 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 we didn’t succeed in doing another persistent current test. A persistent current test of more than 24 hours and a magnetic field within the measuring range would provide a nice approach to determine the current decay in the load coil circuit and which can be translated to a value for the joint resistance in the secondary circuit.

The automatic flux pump function of the LabVIEW VI sometimes shows a problem with the current of 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 happen two or three times in a row.

Also the VI can be improved by including some kind of failsafe to prevent system overheating when superconductivity is broken by ways of feedback from the measured magnetic field strength. This will allow for automatic flux pumping without the need to constantly monitor the system and to manually prevent overheating. Thus enabling the possibility of testing the flux pump during 24 hour 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 pumping at higher frequencies could be performed and analyzed better. With the current program fast flux pumping (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 fluxpumps Part 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 high current 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 MRI magnets”. 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 Applied Superconductivity 16.3 (Sept. 2006). Ed. by IEEE, pp. 1918–1923. [10] Hyun Chul Jo et al. “Experimental Analysis of Flux Pump for Compensating Current Decay in the Persistent Current Mode Using HTS Magnet”. In: IEEE Transactions on Applied Superconductivity 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 concept and 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 on Magnetics 4.3 (Sept. 1968). Ed. by IEEE, pp. 482–485. [15] S. P. Bernard and David L. Atherton. “Performance analysis of transformer-rectifier flux pumps”. In: Review of Scientific Instruments 48.10 (Oct. 1977). Ed. by American Institute of Physics, pages. [16] Sangkwon Jeong nd Sehwan In and Seokho Kim. “Superconducting micro flux pump using a cryotron-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.

37 [18] Dwi Prananto. Figure from ’Superconductivity’. Ed. by Dwi Prananto. May 6, 2012. url: https : / / simpliphy . wordpress . com / 2012 / 05 / 06 / superconductivity/ (visited on 07/06/2016). [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 on 07/06/2016). [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-SAFARI Update. Entechna Engineering. Sept. 13, 2016. 66 pp.

38 Appendices

39 Chapter A Measurements of test coil parameters

In this appendix the parameters of the three self-made coils are described in more detail, some background 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 attached the 16089B Medium Kelvin Clip Lead fixture. Each time before taking a series of measurements the LCR-meter is reset to its default setting using the system reset button. Then the test signal frequency is set to one of the available values (100, 120, 1k, 10k, 20k or 100k Hz) and the test signal voltage is set to 100 mVrms unless stated otherwise. There is also an option to set the length of the connector cables (at 0, 1, 2 or 4 m), which cancels the phase shift error caused by the length of the cable. The used fixture has connector cables with a total length of about 1 m. The default setting after resetting is 0 m. During the first set of measurements this was forgotten a few times so 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). To measure the inductance of a coil the ideal frequency setting is the one where the measured θ (phase shift) value is closest to 90°. Meaning the coil has the strongest induction characteristics at this test frequency. For each coil this was roughly determined by measuring the phase shift at different frequencies beforehand. Most often this was found to be at 20 or 100 kHz. Subsequently at the chosen 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 section 3.4. Here they will be described in a bit more detail, especially its dimensions. The (segment-)length of the coils is roughly the same, namely (21,6 ± 0,1) mm which is a bit more than the primary coil segments. The primary wire is wrapped around a cylindrical core with a diameter (5,5 ± 0,5) mm and divided in eight layers of about 100 turns per layer. In this way the primary self-inductance of coil 1 and 2 is comparable to a primary coil segment. The secondary windings consists of 20 turns around 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 MnZn ferrite 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 are shown in table A.1.

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

Aluminum (air)core Vespel (air)core Primary Secondary Primary Secondary Z (Ω) 227,7 Z (Ω) 0,7634 Z (Ω) 692,4 Z (Ω) 1,033 θ (°) 73,52 θ (°) 80,19 θ (°) 87,4 θ (°) 84 Lp (µH) 347,5 Ls (µH) 1,1970 Lp (µH) 1101,0 Ls (µH) 1,635 Rd (Ω) 8,683 Rd (Ω) 0,03132 Rd (Ω) 10,018 Rd (Ω) 0,03598 Lsprim (µH) 295,1 Lssec (µH) 0,6995 Lsprim (µH) 754 Lssec (µH) 0,7381 Z (kΩ) 74,8 Z (kΩ) 86,5 Coupling capacity θ (°) -89,4 Coupling capacity θ (°) -88 Cww (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 with a 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)core Primary Secondary Primary Secondary Z (Ω) 228,90 Z (Ω) 0,7241 Z (Ω) 1261,1 Z (Ω) 1,4107 θ (°) 73,72 θ (°) 80,2 θ (°) 66,03 θ (°) 74,03 Lp (µH) 349,7 Ls (µH) 1,135 Lp (µH) 1768,8 Ls (µH) 2,158 Rd (Ω) 8,7404 Rd (Ω) 0,03120 Rd (Ω) 10,084 Rd (Ω) 0,03599 Lsprim (µH) 264,6 Lssec (µH) 0,6344 Lsprim (µH) 976,4 Lssec (µH) 0,8277 Z (kΩ) 69,5 Z (kΩ) 76 Coupling capacity θ (°) -89,7 Coupling capacity θ (°) -89,7 Cww (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 bottom results 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 upper part and 20 and 10 kHz for the lower part.

Aluminum (air)core Vespel (air)core Primary Secondary Primary Secondary Z (Ω) 169,8 Z (Ω) 0,5908 Z (Ω) 628,6 Z (Ω) 0,9260 θ (°) 60,2 θ (°) 70,56 θ (°) 83,57 θ (°) 78,93 Lp (µH) 234,65 Ls (µH) 0,8880 Lp (µH) 995,4 Ls (µH) 1,447 Rd (Ω) 1,1785 Rd (Ω) 0,00655 Rd (Ω) 1,3743 Rd (Ω) 0,00895 R (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) 0,2100 θ (°) 71,33 θ (°) 78,30 θ (°) 87,7 θ (°) 83,34 Lp (µH) 356,18 Ls (µH) 1,15 Lp (µH) 1064,9 Ls (µH) 1,660 Rd (Ω) 1,18 Rd (Ω) 0,00659 Rd (Ω) 1,3796 Rd (Ω) 0,00904 R (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 high permeability core. The test signal frequency is set to f=100 kHz for coil 3 containing the MnZn ferrite core and to f=20 kHz for coil 3 without this core. The differences really show the impact on the 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 Secondary Z (Ω) 4536 Z (Ω) 571,52 Z (Ω) 78,085 Z (Ω) 8,888 θ (°) 89,86 θ (°) 89,83 θ (°) 87,83 θ (°) 86,97 Lp (µH) 36520 Ls (µH) 4170 Lp (µH) 124,18 Ls (µH) 14,129 Rd (Ω) 0,9750 Rd (Ω) 0,3041 Rd (Ω) 0,97902 Rd (Ω) 0,30474 Lsprim (µH) 392 Lssec (µH) 43 Lsprim (µH) 107,05 Lssec (µH) 12,027 Z (kΩ) 764 Z (kΩ) 260 Coupling capacity θ (°) -89,8 Coupling capacity θ (°) -89 Cww (pF) 10,4 Cww (pF) 6,1

42 Chapter B Results lock-in amplifier and simulation with LTspice IV With 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 intention to 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 is useful information in all of it, but due to irrelevancy of a large amount of data (a lot of data comes down to the same thing) and time constraints during the writing of this report, only a few graphs will be shown here. It is very time consuming to study everything thoroughly. In the end the new setup (V3.0) was shown to work anyway, so this also made these results a bit less relevant. Still some results will be discussed here in short. The following electrical diagrams (in figure B.1 and B.2) shows the circuits used in the measuring setup with a Stanford Research System 830 lock-in amplifier. This device was controlled by a self-made LabVIEW program that could perform frequency sweeps with an adjustable number of log 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 a capacitor 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. The induced emf is measured over a resistor in series with the secondary coil.

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

4K measurement Primary coil series capacitor and series resistor 1-100kHz (50 steps) 1kHz 10kHz 100kHz 0 100

80 -10

60 -20 40

-30 20

-40 0

-20

-50 Phase(theta)shift

Amplitude (R indB)(RAmplitude Amplitude (R) prim 100nF 100 ohm Amplitude (R) prim 10nF 100 ohm -40 Amplitude (R) prim 1nF 100 ohm -60 Phase (Theta) prim 100nF 100 ohm -60 Phase (Theta) prim 10nF 100 ohm Phase (Theta) prim 1nF 100 ohm -70 -80 Frequency (f, log scale)

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

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

In the case of figure B.5, however, strange things are happening. One could also say things are not 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) capacitor value is changed in a LCR circuit the self resonance frequency√ (SRF) should also change (a higher capacitor, 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 parasitic property of the setup.

4K measurement Coupling Primary-Secundary coils - parallel capacitor in primary circuit 10-100 kHz (25 steps) 10kHz 100kHz 0 Amplitude (R) 1nF 200

-10 Amplitude (R) 10nF 150 Amplitude (R) 100nF -20 Amplitude (R) 1000nF 100 -30 Phase (Theta) 1nF Phase (Theta) 10nF 50 -40 Phase (Theta) 100nF

-50 Phase (Theta) 1000nF 0

-60 -50

-70

-100 (theta)Phaseshift Ampltitude (R in dB)inAmpltitude(R -80

-150 -90

-100 -200 Frequency (in Hz)

Figure B.5: Coupling measurement test of the primary and secondary coils in transformer V2.0. 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 this strange frequency response. It first seem to be mainly happening when an external capacitor is externally connected and not when a series capacitor was connected. A changing value of the series capacitor did actually show a change of the SRF most of the time. Later it was found that this does not has to be the case, but the real cause was never exactly found.

45 Chapter C LabVIEW control and instrument setup of the flux pump system This appendix shows a figure (C.1) with the instrument setup, used cable types and the devices that are controlled by LabVIEW for the flux pumping operation. The DAQ and amplifier control the primary current, one Power Supply controls the heater currents and the other Power Supply controls the Hall sensor in Setup V2.0 and in setup V3.0 it is only used for inserting an external current in the secondary circuit. All voltage leads and control currents (primary and heaters) are measured by the Data Logger. The breakout boxes are an intermediary between the DB25 connectors and the connection with the Data Logger. It splits up the connector cable in 25 individual pins to be connected 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 the FTS This appendix includes two figures showing possible applications of the magnetic bearing in the FTS for the SAFARInstrument. Design and development of the setups shown in figures are done by Entechna Engineering [25, 26].

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

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

47 Chapter E Primary coils V1.0, V2.0 and V3.0 In 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 room temperature resistance of the primary coil is 11,33 kΩ and superconducting self-inductance of 1,098 mH (measured with an LCR-meter at f=100 kHz and phase shift θ = 68,16°. In the figure primary coil V2.0 is still placed on the copper ground plate with the secondary windings attached and 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 V3.0 has a room temperature of 17,45 kΩ and a superconducting self-inductance of 4,45 mH (measured with 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 and in the top right corner primary coil V3.0

48 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 - 101 Cernox cx1010 Ω-4w V+ - 12 24 - V- - 24 25 - Extra secondary V+ - 9 3 - 102 Voltage-2w copper coil leads V- - 21 4 -

10 2 Gr200 Ω-4w Not used in current setup (V3.0)

V+ - 3 5 - 103 Hall sensor Voltage-2w V- - 15 6 - V+ - 6 7 - 104 Load coil leads Voltage-2w V- - 18 8 - V+ - 7 9 - 105 Sec. coil 1 Voltage-2w V- - 19 10 - V+ - 8 11 - 106 Heater 2 Voltage-2w V- - 20 12 -

V+ 1/2 => Bar -13 - 107 Bartington Voltage-2w V- 14/15 => B ar -14 - V+ - 13 15 - 108 Primary coil leads Voltage-2w V- - 25 16 -

12 1 Hall sensor Current-2w Not used in current setup (V3.0)

I+ 3:13 - 48 (A meas with 49)* - 122 Primary Current Current-2w I- 16:25 - 49 (A meas with 48)* -

I+ - 4 => 4 7- b o x 3 - Pow. Sup. 2 (+25V) <= 46 (A meas wit h 47) 221 Heater 1 Current-2w I- - 16 => Pow. Sup. 2 com - 4 -b o x 1 <= 47 (A meas wit h 46)

I+ - 5 => 4 9 -b o x 3 - Pow. Sup. 2 (-25V) <= 48 (A meas wit h 49) 222 Heater 2 Current-2w I- - 17 => Pow. Sup. 2 com - 5-b o x 1 <= 49 (A meas wit h 48)

*48/49 naar coax con. / naar weerstanden

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

49