Linköpings universitet
Linköping University | The Department of Physics, Chemistry and Biology
Master thesis, 30 ECTS | Applied Physics
2019 | LITH-IFM-A-EX–19/3746–SE
Transients and Coil Displacement
in Accelerator Magnets
Marcus Wallin
Supervisor : Ferenc Tasnadi Examiner : Peter Münger
Upphovsrätt
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Abstract
For a long time voltage spikes has been seen in measurement data from accelerator magnets during current ramps. These has been believed to be caused by movements, but has never before been studied in depth. The purpose of this thesis is therefore to prove, or disprove, that these events are caused by movements and to analyse what kind of displace-ments that actually occur. Measurement data from coil voltage, magnetic pick-up coils and current during transients has been acquired and analysed for the Nb3Sn-dipole magnets FRESCA2 and 11T models—named MBHSP107 and MBHSP109. The measurement data is compared to movement simulations that was done with the ROXIE-program, which is used to calculate mutual inductance change for a number of different movement types. The study strongly suggests that the transients are caused by movements, and also indicates that the maximal length of a single slip-stick motion can be up to around 10 µm, mostly in the direction of the magnet’s internal forces. The study has proven that transients in mea-surement data occur due to coil movements, and that these can be quantified—a discovery that can possibly affect future construction and design of accelerator magnets.
Acknowledgments
First of all I would like to thank my supervisor at CERN, Gerard Willering, for having guided me through this project and always being helpful—while also pushing me when necessary. I would also like to give a thanks to my section leader Marta Bajko and the rest of the CERN-staff for giving me the possibility to work in such a great place and with such an interesting subject. I would also like to thank my examinator Peter Münger and supervisor Ferenc Tas-nadi at Linköping University for taking their time, reading and giving me feedback on all the many iterations of this work.
I have had the luck of having many friendly and helpful colleagues at SM18, among oth-ers: Daniel Turi, Efstathios Karentzos, Bernardo Castaldo, Ioannis Koukovinis, Sara Benitez Berrocal, Franco Mangiarotti, Michal Duda, Yacine Raqai, Vincent Desbiolles, Jerome Feu-vrier, Jean-Luc Guyon and others that become so many that I can’t mention all of you. Thank you for all the help I have gotten in my work, in my life, and all the good times we have had together.
I want to give a big thank you to my family and my partner Julia for always supporting me and being there for me when things are tough—you are my backbone and I would not have been able to be here without you. A great thank you also to all my friends I have made here at CERN—you know who you are—that has made my time here so memorable. Thank you for all the skiing, beers at R1, chit-chatting and all the other things we have done, and I hope we will stay in touch our entire lives.
Contents
Abstract iii
Acknowledgments iv
Contents v
List of Figures vii
List of Tables ix 1 Introduction 1 1.1 About CERN . . . 1 1.2 Accelerator Magnets . . . 3 1.3 Superconductivity . . . 7 1.4 Quench Antennas . . . 9
1.5 Movements and Forces . . . 9
1.6 About The Project . . . 10
2 Hypothesis 13 2.1 Transients in Measurements . . . 13
2.2 Possible Causes For the Transients . . . 14
2.3 Predictions For Displacements . . . 16
2.4 Method For Studying Movements . . . 18
3 Theory 20 3.1 Coil Displacement & Pre-loading . . . 20
3.2 Electromagnetism . . . 23
3.3 ROXIE . . . 25
4 Measurements 26 4.1 Voltage Measurements . . . 26
4.2 Transient Selection . . . 27
4.3 Measuring the Effects . . . 28
4.4 Measurement Setup . . . 32
4.5 Power Converter . . . 34
4.6 Linearity Criteria . . . 35
5 Simulations 36 5.1 ROXIE Input & Output . . . 36
5.2 Stationary Post-Processing . . . 37
5.3 Modes of Movement . . . 38
5.4 Dynamic Post-Processing . . . 39
6 Results 48 6.1 MBHSP107 . . . 48 6.2 MBHSP109 . . . 53 6.3 FRESCA2 . . . 56 7 Discussion 61 7.1 Measurements . . . 61 7.2 Simulations . . . 63 7.3 Results of Comparisons . . . 63 8 Conclusions 65 8.1 Research Questions . . . 65 8.2 Future Work . . . 66 A Measurement Data 68 Bibliography 71
List of Figures
1.1 Overview of the CERN experiments . . . 2
1.2 Positioning of the FCC . . . 3
1.3 View from the inside of the LHC tunnel . . . 4
1.4 Magnetic field strength of the strongest magnets . . . 4
1.5 Ideal current density . . . 5
1.6 Cross-section of the MBHSP-magnet . . . 5
1.7 Longitudinal view of MBHSP . . . 6
1.8 Cross-section of the FRESCA2-magnet . . . 6
1.9 Longitudinal view of a the FRESCA2-magnet . . . 7
1.10 Critical surface of NbTi and Nb3Sn . . . 8
1.11 Load line of a Nb3Sn cable . . . 8
1.12 Showing how quench antennas can be positioned in a magnet . . . 9
1.13 Example of voltage measurements during a movement . . . 10
1.14 Number of vibrations in the MBHSP106 and FRESCA2 magnets . . . 10
1.15 Precursor from 1998 . . . 11
2.1 Differential voltage during a ramp . . . 13
2.2 Example of flux jump and transient . . . 14
2.3 Example of flux jump . . . 15
2.4 Direct voltages during a transient . . . 16
2.5 Example of a moving coil and how the mutual inductances would be affected . . . 17
2.6 Example of how a movement would cause a reduction of field inside the quench antenna . . . 18
2.7 Expected effects from coil movement . . . 18
3.1 Internal forces for FRESCA2 . . . 20
3.2 Simulated magnetic field and force in the MBHSP-magnet . . . 21
3.3 Nb3Sn rutherford cable . . . 21
3.4 Training of MBHSP105 . . . 22
3.5 Induction explanation . . . 23
4.1 Coil names and voltage measurements . . . 26
4.2 Difference between double peak and single peak transients . . . 27
4.3 All measured effects during a transient . . . 29
4.4 Voltages over each coil during a transient with start and end time . . . 30
4.5 Direct quench antenna voltages for a transient in MBHSP107 . . . 31
4.6 Showing how to separate the global and local effect in the quench antennas . . . . 31
4.7 All direct quench antenna signals for MBHSP107 . . . 32
4.8 Me and the FRESCA2 magnet inside the magnetic test facility SM18 . . . 33
4.9 Quench antenna placement for FRESCA2 and the MBHSP-magnets . . . 34
5.2 Illustration of how the coil is calculated to move . . . 38
5.3 Example of a movement mode . . . 39
5.4 Full cross-section view of MBHSP and FRESCA2. . . 40
5.5 The analysed modes of movement for the MHBSP-magnets . . . 40
5.6 The analysed modes of movement for FRESCA2 . . . 41
5.7 ROXIE output data for Ltotfor MBHSP . . . 44
5.8 ROXIE output data for Ltotfor the single coil modes of FRESCA2 . . . 44
5.9 ROXIE output data for Ltotfor the double coil modes of FRESCA2 . . . 44
5.10 B(I) for FRESCA2 and MBHSP . . . 45
5.11 Mode profiles for MBHSP . . . 47
5.12 Mode profiles for FRESCA2 . . . 47
6.1 Typical voltage measurement during a transient for MBHSP107 . . . 48
6.2 Normalized energy redistribution for MBHSP107 . . . 49
6.3 Histogram of the total energy transfer for MBHSP107 . . . 50
6.4 Total energy redistribution for all the analysed transients . . . 50
6.5 Current change as a function of energy transfer for MBHSP107 . . . 50
6.6 Location and size of each transient in the data set for MBHSP107 . . . 51
6.7 Quench antenna values for MBHSP107 . . . 51
6.8 Measurement data for MBHSP107 in the profile format . . . 52
6.9 Measurement data for MBHSP107 compared with the simulated profile modes . . 52
6.10 Typical voltage measurement during a transient for MBHSP109 . . . 53
6.11 Normalized energy redistribution for MBHSP109 . . . 53
6.12 Histogram of the total energy transfer for MBHSP109 . . . 54
6.13 Location and size of each transient in the data set for MBHSP109 . . . 54
6.14 Quench antenna values for MBHSP109 . . . 55
6.15 Current change as a function of energy transfer for FRESCA2 . . . 55
6.16 Measurement data for MBHSP109 in the profile format . . . 56
6.17 Measurement data for MBHSP109 compared with the simulated profile modes . . 56
6.18 Typical voltage measurement during a transient for FRESCA2 . . . 57
6.19 Normalized energy redistribution for FRESCA2 . . . 57
6.20 Histogram of the total energy transfer for FRESCA2 . . . 57
6.21 Total energy redistribution for all the analysed transients . . . 58
6.22 Current change as a function of energy transfer for FRESCA2 . . . 58
6.23 Location and size of each transient in the data set for FRESCA2 . . . 59
6.24 Measurement data for FRESCA2 in the profile format . . . 59
6.25 Measurement data compared with all simulated profile modes . . . 60
7.1 Showing two transients following each other and the measured voltages. . . 62
List of Tables
5.1 Result of simulations for MBHSP. . . 45 5.2 Result of simulations for the single coil modes for FRESCA. . . 46 5.3 Result of simulations for the double coil modes for FRESCA. . . 46 A.1 Measurement data for FRESCA2. Blank spaces means no data was available. . . . 69 A.2 Measurement data for MBHSP107. Blank spaces means no data was available. . . . 69 A.3 Measurement data for MBHSP109. Blank spaces means no data was available. . . . 70
1
Introduction
This project has been done at the science institution CERN in Geneva, with the collaboration of Linköping University. The research revolves around transients in voltage data from super-conducting Nb3Sn magnets, and is to a large extent based on the fields of electromagnetism and data analysis.
This introductory chapter will start by describing CERN and some important concepts for this thesis: how accelerator magnets work, superconductivity, quench antennas and move-ments and forces in magnets. After this, the project will be explained and motivated, and the goal and research questions will be formulated.
1.1
About CERN
This section describes the current state of the accelerator complex and outlines some possible upgrades and future projects.
1.1.1
Overview of CERN
CERN is a research insitution positioned in Geneva, Switzerland. It is an organisation with the goal of making new discoveries in particle physics, while at the same time training and uniting people and nations. CERN is in modern times most famous for the discovery of the Higgs boson in 2012, with the help of the LHC-accelerator [1]. There are many experiments at CERN, which require a wide variety of equipment. In fig. 1.1 an overview of all the experiments and accelerators at CERN can be seen.
The main idea of CERN is to accelerate particles to velocities very close to light speed, and then make them collide and observe the results. To achieve this the particles are accelerated in separate phases, starting with the Booster, followed by the Proton Synchrotron (PS), then the Super Proton Synchrotron (SPS), and then they reach the maximum velocity in the Large Hadron Collider (LHC), which spans over 27 km in circumference.
The particles travel in vacuum filled tubes, and are accelerated by injection into radiofre-quency cavities, where they receive electrical impulses that accelerates them. The steering and controlling of the particles is handled by magnets [2]. The biggest experiments at CERN are ATLAS and CMS, which use general-purpose detectors to be able to investigate as wide range of physics as possible. Two other large experiments positioned along the LHC is AL-ICE and LHCb, which are specialized for detecting more specific phenomena [1]. Recently, LHCb made a discovery of a new pentaquark particle called Pc(4312)+, which was described in a paper from 1964 but was not proved experimentally until now, more than 50 years later [3].
Figure 1.1: An overview of all the CERN experiments and accelerators. Image by CERN at: https://cds.cern.ch/
1.1.2
Future Developments
To be able to provide more discoveries in particle physics, CERN is always working on up-grades or future developments to the accelerator complex. Currently a lot of research is going into High-Luminosity LHC (HL-LHC), where the plan is to make upgrades to the LHC to in-crease the luminosity—a quantity proportional to the number of collisions—by a factor of 10 [1]. This upgrade consists for example of creating more powerful focusing (quadrupole) and bending (dipole) magnets of around 11 T, and inserting "crab" cavities in the collision points at ATLAS and CMS. The HL-LHC upgrade is scheduled to be operational by 2025, and will allow more detailed studies of many phenomenas, such as the Higgs boson [1].
Looking further into the future, the amount of discoveries that can be made with the current collision energies will eventually decrease. Therefore, researchers are looking into a number of new projects that could be completed around 2035-2050. There seems to be three main options available:
• Future Circular Collider (FCC) • High-Energy LHC
• Compact Linear Collider (CLIC)
The most ambitious alternative is the Future Circular Collider, which would just like the LHC be a circular collider with particles travelling in opposite directions and colliding at a number of collision points. The FCC is planned to be around 100 km in diameter, and be posi-tioned as can be seen in Fig. 1.2. Currently researchers are looking into three different options on which particles should be used in the FCC-accelerator. There could be proton-proton colli-sions, like in the LHC, which would create collision energies of 100 TeV (compared to 14 TeV for the LHC) [4]. Other alternatives are electron-positron or electron-proton collisions [1]. If this accelerator is built the aim is to have it operational around 2050 [4].
Another option is to further upgrade the LHC with stronger (16 Tesla) magnets and im-proved detectors, which would allow for collision energies of 27 TeV. Since the infrastructure
Figure 1.2: Left: Schematic of the underground structures for the FCC. Right: Proposed posi-tioning of the FCC. Image from the conceptual design report [4].
is already in place this improvement would be quicker than the FCC and could be operational by mid 2040 [5].
A third option would be the Compact Linear Collider, which unlike the circular colliders use a single straight section for particle acceleration and a single collision point. The acceler-ator is proposed in three lengths, 11.4 km, 29 km and 50.1 km [6], with 380 GeV, 1.5 TeV and 3.0 TeV of collision energy respectively. According to the design document this accelerator could be operational by 2035.
All these accelerators require large technological improvements and are very costly. The FCC is the most expensive to build and is expected to cost around 28.6 Billion CHF to con-struct.
1.2
Accelerator Magnets
Accelerator magnets are used to steer and control the momentum of the particles in the accel-erator. A view from inside the LHC tunnel can be seen in Fig. 1.3, where the curvature of the beam can be seen. There are dipole, quadropole, sextupole magnets, and so on. Looking at the entire accelerator complex there are hundreds of different types of magnets in use, both normal-conducting and superconducting. The normal-conducting magnets are also called iron-dominated, since the majority of their field comes from iron magnetization [7].
A more economical way of creating stronger fields is by the use of superconducting mag-nets, also called coil-dominated magnets. This requires much less material, and the magnets can be made smaller, but can be quite hard to manufacture and are expensive to research. In the LHC the superconducting cables are made of NbTi, which at this point is a well known technology but has its practical limitation of peak field at a bit above 8.3 T, which is what is used in the LHC [2]. For this reason, to construct the larger and more powerful accelerators of the future, NbTi is not possible to use. Intense research is currently being done on alternative materials that can be able to provide the required 16 T. Currently the most effort is put into Nb3Sn magnets, a material that has much better capacity for providing stronger field than NbTi.
With Nb3Sn, the expectation of being able to construct 16T magnets is high, but currently the technology is not there. The material is very brittle and therefore requires exceptionally careful handling, which makes the manufacturing process very difficult. For the HL-LHC upgrade described in section 1.1.2, there are currently 11-12 T dipoles and quadrupoles under
Figure 1.3: View from the inside the LHC tunnel with a 3D cut of a dipole magnet. Image from https://cds.cern.ch
Figure 1.4: Graph showing magnetic field strength of the strongest dipole magnets and what year they were produced. Image from [8]
construction that will be inserted into the LHC and could be operational by 2025 [9]. In this thesis the focus has been on these dipole magnets, aimed to be used for future upgrades of the LHC or the FCC-accelerator.
The two main magnet types that has been studied is the cosine-theta type magnets and the block-coil magnets, both part of future developments of CERN [10]. In Fig. 1.4 the devel-opment curve of dipole magnets over the last 40 years can be seen.
1.2.1
Field Quality
For the main dipoles in any of the accelerators used at CERN it is very important that the magnetic field inside the bore of the magnet is very uniform, since variations would cause problems in steering of the particles. The perfectly homogeneous dipole field can be achieved in theory by having a current density as in figure 1.5 [7].
The field homogeneity is normally called field quality, and for the LHC the requirements are very high. For example, the magnets used for the LHC has a specification on the main dipoles that the standard deviation of the field needs to be smaller than 8 104 T, for the nominal field of 8.3T [11]. To achieve this, the main dipoles in LHC have the cosine-theta design type which is trying to approach the ideal current density seen in fig. 1.5.
1.2.2
Cosine-Theta Magnets
I
I
B
Figure 1.5: Illustration of the cur-rent density required to create a perfectly homogeneous field in the aperture.
In fig. 1.6 the cross-section of model Nb3Sn magnets called MBHSP can be seen, which has the cosine-theta design and is designed to reach 11 T [12]. In the the-sis two of these magnets will be studied: MBHSP107 and MBHSP109, which are nearly identical apart from slightly different assembly [13].
As can be seen in the image, the magnet is cen-tered around the beam pipe, with superconducting coils wound around it, to create a coil. This mag-net is a model magmag-net and only has one beam pipe, while the main LHC dipoles has two. Surrounding the coils there are non-magnetic collars made of stainless steel, which contain the massive outward electromag-netic forces that is generated during operation. The big blue part is an iron yoke, which due to its ferromag-netic properties redirects and enhances the magferromag-netic field in the aperture, as well as creating rigidity to the structure [14].
To the left in Fig. 1.6 a more detailed view of the structure surrounding the coils can be seen. The MBHSP-magnet consists of two coils, one upper and one lower. In fig. 1.7 the longitudinal view of one coil can be seen where the wiring is done longitudinally along the beam pipe, to create a vertical field. Each coil consists of two layers, the inner and the outer, which in turn contain a number of blocks of wires separated by copper wedges. The two layers, including the copper wedges, are impregnated together with EPOXY-resin, which
Figure 1.6: Cross-section of a Nb3Sn cosine-theta magnet named MBHSP. 1. Beam Pipe
2. Superconducting Wires 3. Stainless Steel Collars
4. Iron Yoke 5. Titanium Pole 6. Loading Plate
7. Copper Wedge 8. Outer Coil Layer 9. Inner Coil Layer
Figure 1.7: Longitudinal view of a coil in the2m long MBHSP-magnet.
makes them into a solid block [12]. The titanium pole is not impregnated and can therefore move freely.
1.2.3
Block-Coil Magnets
Block-coil magnets are another type of magnet designs that are being researched at CERN, where the coils are arranged in alligned blocks. Currently this type of magnet has reached much higher fields than the cosine-theta magnets, such as the current world record holder for large apertures—FRESCA2—with a field of 14.6 T [15]. This magnet will be delivered to the FRESCA test facility at CERN, where tests of superconducting cables are being done [16]. Because its purpose is not to be placed in an accelerator, it did not have the same requirements on field quality as the 11 T cosine-theta magnets.
An image of the structure of a block-coil magnet can be seen in Fig. 1.8, in this case showing the cross-section of the FRESCA2 magnet.
Figure 1.8: Cross-section of the block-coil magnet FRESCA2. Image from [16]. 1. Iron Yoke
2. Aluminum Shell 3. Aperture
4. Stainless Steel Pad 5. Iron Pad
6. Coil
7. Mid Plane Insulation 8. Titanium Post 9. Iron Post
The magnet is made out of 4 coils with flared ends, with two layers of cables each in what is called a double pancake structure [16]. The assembly of the coils are first done separately for the upper and lower two coils, which are later conjoined in the supporting structure [17]. Surrounding the coils are a number of pads, made in iron and stainless steel. These are
designed for transferring the forces from the coils to the iron yoke. Just like for the cosine-theta magnets, the iron yoke is meant to retain the forces as well as to enhance the magnetic flux lines and shield the exterior. The outer shell of the magnet is made of aluminium and is also meant to retain the forces coming from the interior [16].
Below in Fig. 1.9 the longitudinal view of the FRESCA2-magnet can be seen. The ends of the magnet are flared to give room for the aperture.
Figure 1.9: Longitudinal view of a the FRESCA2-magnet. Image from [16].
1.3
Superconductivity
Superconductivity is a macroscopic phenomena that was discovered by Kammerlingh Onnes in 1911 [18], whereby certain materials become perfect conductors at very low temperatures. The resistivity of most materials will decrease gradually when being cooled, but the super-conducting state will appear abruptly at a certain temperature, where the resistivity will become essentially zero. This phenomena has been described by the so called BCS theory, named after Bardeen, Cooper and Schrieffer who created it in 1957 [18].
1.3.1
Critical Surface
It turns out that the superconducting state is not only dependent on temperature, but also two other factors: current density and applied field. Together these three elements creates a critical surface, which represents the maximum value before the material exits the supercon-ducting state. This is shown in Fig. 1.10, where the critical surface of NbTi and Nb3Sn can be seen.
When the conductor is situated within these limits, the material will be superconducting. As can be seen, it is beneficial to be as close to 0 K as possible, since this will allow for highest field and current density. Superconductors are also affected by the stress they are subject to. High stress will reduce the critical surface, for NbTi this effect is starting to appear when the superconductor is pressured at around 500 MN/m2[18].
1.3.2
Quenching
The event when a superconducting magnet is passing the critical surface and goes from su-perconducting and into the resistive state is usually called a quench [18]. Since the supercon-ducting cable has no resistance, a very high current can be held without any heat loss when
25 Temperature (K)
Magnetic Field (T) Current Density (kA/mm2)
5 10 15 20 5 10 15 20 5 10 15 Nb3Sn NbTi
Figure 1.10: Critical surface of NbTi and Nb3Sn. Data from [18].
superconducting. However, if the superconductor quenches and gets resistive, this massive amount of current will create heat according to Joule’s law, P=RI2. If all this energy is con-centrated into a small area, this will heat up the cable so much that the conductor can melt and get destroyed [18]. Therefore, protection against quenches is very important, and possi-bly the most important safety measure is to have the magnet operating with a good margin to the quench limit. This limit is usually called the short sample limit, and is the theoretical limit of the magnet before it quenches.
When powering a magnet there is a relation between the current in the magnet and the field it is subjected to. For a superconducting (coil dominated) magnet the relation is essen-tially linear due to the diminished effect of ferromagnetization. This relation, B(J), is called the load line, and is usually plotted as the black line in Fig. 1.11.
short sample limit
utimate nominal
Figure 1.11: The black line is the load line of a Nb3Sn cable at 1.9 K. The blue line represents the critical surface of the superconductor.
In the image two currents except for the short sample limit are marked: nominal and ulti-mate current. The nominal current is the current the magnet is designed to operate at, which keeps a good margin to the short sample limit, such as in the LHC where the nominal cur-rent is at 86% of the short sample limit [19]. The ultimate curcur-rent is usually defined to be 8% higher than nominal, and is used as a reference for a current that is favourable to be able to reach without quenching.
For the 11 T Nb3Sn magnets, it is known that the energy dissipation required at nominal current to reach the short sample limit is around 20 mJ/cm3[20].
1.4
Quench Antennas
Quench antennas are coils of wires that are being used to measure magnetic flux inside a magnet. They are placed inside the aperture of the magnet and will due to Faraday’s law (see Section 3.2) detect any kind of change in magnetic flux passing through the enclosed area of the wire loop.
The quench antennas can be placed in different directions and can be used differently depending on the experiment, but for this thesis they are always placed perpendicular to the field of the magnet, and there are always three layers of coils. A simplified image of how the quench antennas are placed inside a magnet can be seen in image 1.12.
Magnet A C E 1 2 3 Quench Antennas
Figure 1.12: Showing how quench antennas can be positioned in a magnet.
In this image there are three segments of pick-up coils named 1, 2 and 3. Normally there are 5 to 7 segments like this in a magnet, but for certain tests there can be many more as well. Each segment consists of three layers of coils named A, C and E, which are placed on top of each other with a distance of around 2 cm to each other. The quench antennas can, which will be explained later in Section 4.1, be measured with direct and differential voltage. For this thesis only direct voltages has been analysed, and the notation to describe the signal from coil A in segment 2 is written as 2A for example.
The quench antennas can be used for analysing a number of different properties or events of a magnet, they are for example the main tool for localising quench origin and are effective at investigating quench propagation. In this thesis they are used for analysing coil movement, which will be explained in Chapter 2.
1.5
Movements and Forces
When an accelerator magnet is powered it will experience strong electromagnetic forces, which is equal to:
F=
»
I(dl B) (1.1)
Since the magnetic field B is proportional to the current through Biot-Savarts law [21], this means that the force scales with the squared current, F9I2. In an accelerator magnet the operational current is very high, around 12000 Amperes, meaning the forces are very strong. These forces are contained through careful design of the magnet and by the use of pre-loading (see Section 3.1), but it is known that movements occur anyway, mostly at high currents. One way of observing movements is through vibrations, which can be seen both in the quench antennas and voltage measurements on the coils, such as in Fig. 1.13, where the transient can be seen as a damped oscillation.
Figure 1.13: Example of a voltage measurements during a movement, where the signal can be seen as a damped oscillation.
Investigations in these vibrations has been done at CERN by Håvard Kjellmo Arnestad [22], where vibra-tions where counted to get an understanding of what parts of the magnet is moving the most. Some of the results of the study can be seen in Fig. 1.14, where the number of vibrations at each current can be seen for a cosine-theta magnet called MBHSP106 and the block-coil magnet FRESCA2. The plots are showing number of events at certain current levels—the x-axis— and where longitudinally these events occurred—the y-axis. Red and yellow means many events, and blue means few movements. As can be seen, at high cur-rents the two magnet types behave very differently, where MBHSP106 is vibrating mostly at the ends of the coils and FRESCA2 in the middle of the magnet.
(a) Vibrations in MBHSP106. (b) Vibrations in FRESCA2.
Figure 1.14: Number of vibrations in the MBHSP106 and FRESCA2 magnets. X-axis is the current squared, y-axis is which location the vibrations occurred in and the color represents the number of events. Images from [22].
1.6
About The Project
This project is continuing the work done by Håvard Kjellmo Arnestad and Gerard Willer-ing in [22], but instead of analysWiller-ing the vibrations, the movements will be attempted to be quantified and explained.
1.6.1
Motivation
Researchers at CERN are now looking at upgrades for the existing particle accelerators, and the possibility of building bigger ones to be able to make more discoveries in particle physics. To do this would require higher energy particle collisions, which in turn would need big engineering feats—including a big increase in the magnetic field strength of the accelerator magnets. The main dipole magnets used for the Large Hadron Collider (LHC), use magnets made of NbTi that operates at 8.3 Tesla [2]—but for future projects the plan is to build much stronger magnets of up to as much as 16 Tesla [4], which would require a completely different
magnet technology. Currently the best possibility of achieving this is through the use of Nb3Sn magnets, where a lot of research is going on at the moment.
The superconducting Nb3Sn magnets are very difficult to produce: They are for example very brittle and require delicate handling to not break during the production—and if they do not get damaged before that then the electromagnetic forces during operation are incredibly strong and can easily impair the magnets. Another issue is that even though the magnets are large, some more than 5 meters, they need to be produced with a precision of less than 100 µm, and can only move a tiny bit during powering. Because of these reasons, it is of highest importance to understand every aspect of the Nb3Sn magnets, from the large scale mechanical aspects to the smallest details.
One of the most important factors of magnet development is to understand why a magnet quenches—i.e., goes from a superconducting to a resistive state. This can be caused by a number of reasons, and one of them is through frictional energy release coming from coil movement. Movements can not only cause quenches, but it can also sabotage the magnet’s properties by distorting the magnetic field quality beyond what is acceptable for operation.
The motivation behind this project is to investigate data coming from the magnetic test facility SM18 at CERN, and relate this to the movements of Nb3Sn magnets. This will bring more understanding to the behaviour of these magnets, which in turn can lead to improve-ments in magnet design. This can in turn get us closer to the goal of the 16 Tesla magnets required for future accelerators and make it possible to make more discoveries in particle physics.
1.6.2
Aim
During the testing of new Nb3Sn models and prototypes there can be seen voltage spikes, called transients or precursors, when ramping up the cur-rent in the magnet. These events has for a long time been believed to oc-cur due to some kind of short burst of movement, called slip-stick motions.
Figure 1.15: Precursor from a model LHC-magnet from 1997. Image from [23] An old example of one of these events can be
seen in Fig. 1.15, where voltage data coming from a model magnet from the LHC from 1997 can be seen [23]. When referencing the the Fig-ure, the author writes: "A spike, thought to be movement of the conductor, is followed by a resis-tance which grows, starts to recover and then grows again. Duration of the spike is ½msec.". The slip-stick movements has therefore been known, or assumed, to occur for a long time, but the phys-ical explanation of the spikes, such as if they are coming from ohmic resistance or inductive volt-age, has not been studied. Neither has it been studied what kind of movements actually occur and where in the magnet they happen.
With the help of more and better data ac-quired, and through the use of so called quench
antennas, the idea of studying these events more in depth has come up. The aim of the project is to prove or disprove that voltage transients occur due to coil movement, and if so, try to explain the measurements and quantify the motion as well as possible.
1.6.3
Research questions
To be able to know whether or not the goal of the project is achieved, it is advantageous to for-mulate research questions that can be answered. For this thesis the following two questions are used:
1. Can transients in voltage data be explained by coil displacement? 2. If so, can the displacement be quantified and localized?
2
Hypothesis
As was explained in Chapter 1, the goal of this project is to prove or disprove that the voltage transients seen during magnet tests are coming from movements—and if so, get an under-standing of what parts are actually moving and how.
The first section in this chapter will show examples of the transients as they are seen in the measurements, without interpreting them. After that, all the possible explanations for the spikes will be listed, followed in Section 2.3 where predictions for coil movement will be made, and the expected effects related to this will be described. Lastly, the general methodology of the project will be explained.
2.1
Transients in Measurements
Figure 2.1: Green plot is showing increasing current, and the red plot is the differential volt-age Vdi f for MBHSP109. Segment #1 is believed to be flux jumps and #2 is slip-stick motions.
In Fig. 2.1 a current ramp at 10 A/s can be seen for the MBHSP109 magnet, where the green graph shows the increasing current and the red curve shows the differential voltage— Vdi f, for the magnet (see Section 4.1). The time 0 in the tests is defined as when the magnet quenches, and usually marks the end of the test.
As can be seen there are quite a lot of disturbances especially in two phases of the ramp for the Vdi f-values. At around -1000 seconds at roughly 2.5 kA current, an initial time period of disturbances occur marked as #1 in Fig. 2.1. This is followed by a period of relatively low noise until it picks up again at around 8 kA, marked as segment #2, where the transients are increasing in size until the magnet quenches at time 0, sometimes due to a transient.
Looking closer at the events in these two segments reveals that there are some quite appar-ent differences between the spikes in the two sections, which can be seen in the two examples In Fig. 2.2. In this image the differential voltage between the coils, Vdi f, is displayed, as well as the differential voltage for the two coils, see Section 4.1 for reference. The largest
differ-(a) Transient in segment 1 (b) Transient in segment 2
Figure 2.2: Typical examples of transients in segment 1 and 2 from Fig. 2.1.
ences between the two types of transients is that they have different time scales and that the right transient is followed by oscillations. The spikes in segment 1 typically has transients that last for 20 ms, while in segment 2 the length is around 1 ms.
2.2
Possible Causes For the Transients
The transients in segment #1 in Fig. 2.1 are believed to be flux jumps, and the spikes in segment #2 are proposed to be movements, but for the sake of argumentation, expectations are here left aside and all possible explanations need to be investigated. After consideration, the spikes could possibly occur from 2 different causes:
• Flux jumps • Movements
2.2.1
Flux Jumps
Flux jumps are one of the biggest causes of disturbances when powering a superconducting magnet. Flux jumps has been studied thoroughly and every cable must be designed carefully to prevent them, since they can easily cause quenches [18]. For this thesis it is not necessary to know the exact details of how a flux jump occur—but the interested reader can learn more in Wilson’s book [18].
Flux jumps essentially occur when the electromagnetic forces increase in the supercon-ductor, which can cause the flux lines inside the cable to move. This flux change will dissi-pate heat, which with a poorly designed cable with bad thermal conductivity could create an avalanche effect of increasing heat and resistance, which could cause a quench [18]. The typical look of the voltage during a flux jump can be seen in Fig. 2.3.
Figure 2.3: Voltage measurement of a flux jump. Image from [24].
The flux jumps are avoided by reducing the diameter of the superconducting filaments in the cables, which has been studied in depth and with the cables of today they rarely cause any problems. However, they still occur, but do not cause quenches since the cooling of the cables are effective at removing the avalanche effect. They can be seen in voltage measurements through U = RI, and only at low currents [25] and are coming from temporary resistance increase in the cable. The flux jumps has also been seen to propagate in the cables, at velocities around 800 m/s [25].
Important for this thesis is that the flux jumps will mainly be seen in the quench anten-nas, through the flux change. If the flux jump is very strong, it can be seen in the voltage measurements as well through resistance U=RI.
2.2.2
Movements
A movement in the magnet means that the cables will change position, which will cause an adjustment in mutual inductance in the magnet. This can change the flux in the quench antennas and also in the internal voltage. A movement might cause frictional heat, which can create a quench, but the perturbed inductance does not necessarily cause any energy loss, but instead an energy redistribution in the magnet.
Fig. 2.4 shows direct voltages for the four coils in FRESCA2 during a transient. As can be seen, in this scenario the summation of all the coil voltages is close to 0. This is a clear pattern for almost all spikes at a current above 7 kA, and is enough to conclude that it seems quite likely that a movement is the cause for the events since there is no heat loss through U=RI. Another strong argument that can be made is the oscillations that is often following the transients (see Fig. 2.2b), which fits well into the description of a movement, since motion can in many scenarios be followed by a vibration.
The full equation to describe voltage in a dynamic, moving magnet is the following (fur-ther explanation in Section 3.2):
U=RI+LdI dt +I
dL
dt (2.1)
In theory the RI-term could be contributing to the voltages, but only positively since both R and I will always be positive. This means that in Fig. 2.4, the reduction of coil 3 and 4 can not be due to this term. It is also most likely that this term is very small or negligible.
-0.0235 -0.023 -0.0225 -0.022 -0.0215 -0.021 -0.0205 Time [s] -0.5 0 0.5 1
V
oltag
e
[V]
V_1 V_2 V_3 V_4Figure 2.4: Direct voltages during a transient. The voltage are over each of the four coils of FRESCA2.
This is because there is a difference between frictional energy loss and resistive voltage when it comes to superconducting conductors, since there can be frictional loss without resistive voltage, but not vice versa. This comes from the fact that the magnet is superconducting, and that resistive voltage only can be observed if there is enough temperature increase for the conductor to reach the critical surface (see Section 1.3). Any frictional energy dissipation will not be seen in the voltage until this happens, which means that the majority of the frictional energy loss will not be observed in the voltages—and if it did—would most likely quench the magnet as transients sometimes do. It is known from theory that the energy required to quench a magnet is around 20 mJ/cm3[20].
2.3
Predictions For Displacements
If a part of the magnet is moving, several effects should be visible during a movement. These can be separated into the global effects which affect the entire magnet equally, and the local ones. These effects can be seen in the following list, and will be explained in the coming sections:
• Current change—Global
• Changed magnetic field from current change—Global • Energy redistribution between the coils—Local
• Changed magnetic field from geometry change—Local
2.3.1
Global Effects
Since the frictional energy loss has been observed to be negligible, this means that the total energy in the magnet should remain constant during a movement. If a movement would occur, this would mean that the total inductance in the magnet, Ltot, would change, but the voltage Utotneeds to remain constant for the total magnet to conserve the energy:
Utot =LtotdI dt +I dLtot dt =0ùñ Ltot dI dt =I dLtot dt (2.2)
Since L and I are both positive, this means that for an increasing inductance, dLtot
dt ¡ 0, the current in the magnet needs to drop to maintain energy conservation. This prediction could be considered part of a proof of the movements, and will be studied.
The expected current change will also impact the magnetic field inside the magnet, since magnetic flux is proportional to current, B9I, coming from the Biot-Savart law. This flux change should therefore be picked up by the quench antennas, causing a global effect that should be measured equally on all pick-up coils.
2.3.2
Local Effects
Apart from the predicted current change effect that is expected to be seen from coil motion, there are also some other effects that are expected, but on a local scale instead of for the full magnet. Using eq. (2.1) the equation governing the voltage for coil i can be formed:
Ui =Li dI dt +I
dLi
dt (2.3)
Important to note here is that since the current in all coils are equal, the dIdt-factor can be calculated on the global scale using Eq. (2.2), and will for an increasing total inductance be negative for all coils. The other term, IdLi
dt depends on the change of mutual inductance to itself and the other coils. What Eq. (2.3) means is that the voltage is creating a redistribution of energy in the magnet, through the relationship between voltage and energy in Eq. (2.4).
W=V Iùñ ∆Ei= »te
ts
UiIdt (2.4)
The reason for the energy redistribution is coming from the change of mutual inductances within the magnet when and after the coil has moved, which is exemplified in Fig. 2.5. Coil
1
2
3
4
M14 M24 M13 M12 M23 M34 changed constantFigure 2.5: Example of a moving coil and how the mutual inductances would be affected, causing an energy redistribution in the magnet.
number 1 is in this example moving outwards, causing the mutual inductances to itself and all the other coils to change, while the mutual inductances between the non-moving coils to stay constant. Li =
°4
j=1M1j, which means that the inductance for coil 1, dLdt1, will change more than the values for the other coils: dL2
dt to dL4
dt . This mutual inductance change is therefore what is expected to cause the voltage spikes seen in Fig. 2.4. Exactly how the mutual inductance is changing will be investigated in Chapter 5.
Another local effect that is expected is that a geometry change should change the field inside the magnet slightly. This is exemplified in Fig. 2.6, where coil 1 is moved, creating a movement of the magnetic field shown as green lines. In this case, the movement would in-crease the distance to the quench antenna, and since magnetic field is proportional to distance squared to the source, it would reduce the field inside the pick-up coil, causing the measured voltage to drop according to Faraday’s law, which will be explained in Section 3.2.2.
1
2
3
4
QAB
Figure 2.6: Example of how a movement would cause a reduction of field inside the quench antenna, abbreviated as QA.
2.4
Method For Studying Movements
As explained in the previous sections, there seem to be indications that the transients are caused through motion. The expected effects that can be observed are summarized in Fig. 2.7, where the color of the box indicate the measurement system. These effects will be measured for as many transients as possible.
Movement
Inductance Change
Voltage change Current Change
Changed field
Local Effects: Global Effects:
Changed field Quench Antennas Voltage Acquisition Current Acquisition
Figure 2.7: Expected effects from coil movement. The upper image is an example of how the coil could move.
The four effects listed previously in Section 2.3 can all be measured directly, but the crucial part of inductance change can only be indirectly measured via the other effects, and would in that case need many assumptions, causing the theory to lose credibility. This is why the decision was made to calculate inductance and the other effects using the simulation tool
ROXIE. This will not only make it possible to compare simulations to reality—creating a stronger case—but also to get estimations of exactly what part of the magnet has moved and how long.
A summation of the methodology is therefore: Analyze a number of transients by measur-ing the four quantities mentioned previously for a large number of transients. Then simulate different types of movement using ROXIE, and try to fit the output of the simulation to the measured data as well as possible. If the measured quantities are coherent with each other and the simulation, then it can be proved that movements are the cause of the transients, and the motion can possibly even be localized and quantified.
3
Theory
This chapter will describe the theory and related work behind most of what has been done for the project.
3.1
Coil Displacement & Pre-loading
When a magnet is powered it will generate forces inside the coils, and depending on the as-sembly, enough to make the coil move or become deformed. To prevent this from happening the magnets are designed with this in mind, and are subject to heavy pre-loading to minimize these effects.
3.1.1
Forces in Coils
When a current is passing through an external magnetic field, the force it is subject to is: F= » I(dl B) (3.1) Force per 2 str ands [ N] x y
Figure 3.1: Internal forces for FRESCA2. The force is therefore proportional to the
cur-rent and the magnetic field inside the cable. For magnets like FRESCA2 and MBHSP, which has very high fields and currents, this force will be very big. In Fig. 3.2 the forces and fields in-side a coil has been simulated at the nominal current of 11.85 kA, which would be the oper-ational current of the finished magnet [26]. Gen-erally, forces are pressing the coil in the x and negative y direction, defined as in Fig. 3.1, where the forces of FRESCA2 can be seen at operational current.
In the figure the forces are calculated per strand—and the cables for MBHSP has 40 strands [12]—which results in a force for the inner cable of around 120 kN/m. For the FRESCA2-magnet, the maximum horizontal
pressure on the coil was observed to be 150 MPa, and the average for the entire coil was between 85-125 MPa [16]. This can be compared to the material properties for an experimen-tal 16 T dipole magnet found in [27], which states that the maximum stress tolerance at 4.2 K
(a) Field in magnet (b) Force in magnet
Figure 3.2: Showing simulated magnetic field and force per meter at 11.85 kA in a quadrant of the MBHSP-magnet. The force is displayed per strand in the cable.
is 200 MPa for the Nb3Sn coils and 720 MPa for iron. The brittleness of iron is lower however, with a value of around 200 MPa [28].
To prevent unwanted movement, the coils are pre-loaded when being assembled. This means that they are compressed with a certain force when inserted into the magnet structure. The pre-stress can be done in different ways, for example as for the FRESCA2-magnet where bladders and keys are inserted between the coils and the iron yoke, and with a shrinking aluminum cylinder when being cooled [29]. Currently the standard is to pre-load the coils to be equal to the force at nominal current. However, it can be very hard to achieve homogenous pre-load over the entire magnet [29].
3.1.2
Cable Deformation & Coil Movement
Due to the high pressure coming from the electromagnetic forces, the cables can become deformed and the coils can move slightly. The coil movement can be prevented by heavy pre-loading and a carefully assembled magnet, but if the pre-load is too strong or too in-homogeneous, the cables can become deformed which can destroy the functionality of the magnet. Therefore it is a balance of applying the right amount of pre-stress to minimize coil movement, while at the same time preventing cable degradation.
Figure 3.3: Showing a Nb3Sn rutherford cable. Note that this is two-stacked (two cables), while the normal cable is single-stacked. Image from [30].
In a recent study [30], the stress tolerance of Nb3Sn Rutherford cables—used in most su-perconducting accelerator magnets—was investigated. The researchers found that the cables received irreversible damage at a stress level of about 175 MPa in room temperature. The compression of the cables was smaller than the resolution of the scanner—10 µm—and the deformation was mostly due to cracking of the impregnation.
Coil movement has been studied in depth in the context of pressure coming from pre-loading, but not so much in the context of the magnet’s internal electromagnetic forces. From [31] it is known that for the LHC-magnets the maximum allowed conductor displacement is 100 µm from the nominal design. If the deformation is larger than this the magnetic field quality does not meet the specifications and can not be used in the LHC. In this paper the authors are comparing simulations of the field of magnets with possible block displacements, to measurements of prototype LHC-magnets. They found that the data seems to fit random movements in the production of the magnets of about 25 µm.
In one study the impact of pre-stress on the magnetic field through varying shim sizes has been done [32]. In this study the researchers assembled the same magnet with different shim sizes to get different pre-stress, and looked at how this deformed the coil. Interesting for this project is that the pressure from a coil in the angular direction will impose a movement not only in the the angular, but also the radial direction, and also that a shim of a certain size will increase the vertical radius of the steel collar by around 10% of that size.
3.1.3
Magnet Training
When a new magnet has been constructed, an interesting phenomena can be observed when powering the magnet repetitively. What can be seen is that for every consecutive current ramp, the magnet tend to reach higher current before quenching.
Figure 3.4: Training of MBHSP105. Image from [26].
An example of magnet training can be seen in Fig. 3.4, in this case for MBHSP105, one of the Nb3Sn magnets explained in Sec. 1.2.2. For this tests the current in the magnet has been increased at a constant rate until a quench is reached, at which point the test is over. The current is then quickly extracted from the magnet and is then prepared for a new ramp. The y-axis displays the current at which the quench occurred and the x-axis is the quench number. As can be seen, the first quenches only reach around 8 kA, way below the nominal current, but the quench current is steadily increasing until it stabilizes around a certain value, in this case around 12 kA.
As described in Section 1.3.2, a quench occur when a superconductor reaches its critical surface. Usually this happens due to some release of energy within the magnet, which raises the temperature locally and pushes the conductor out of the critical surface [18]. The release of energy can be considered a disturbance, and as described by Wilson [18] the most problematic types of disturbances are the transient ones: flux jumps (see Section 2.2.1) and mechanical movement. These two disturbances are very likely to have an impact on magnet training [18], and nowadays it is considered common understanding that the majority of the training comes from movement [33]. Mechanical training is explained by the strong forces acting on the cables, causing some part of the magnet to move in what is called a slip-stick motion [34]. The part has then moved into a more permanent position, where the force will not cause a movement during the next time it is subject to the same force.
3.2
Electromagnetism
In this section the electromagnetic theory behind the work will be presented. Two impor-tant concepts: Inductance and Faraday’s law, will be explained, and an introduction to the electromagnetic simulation program ROXIE will be given.
3.2.1
Inductance
Suppose two loops of wire are placed in proximity to each other. If loop 1 is having the current I1, then some of the flux lines from loop 1 will pass through loop 2 as can be seen in Fig. 3.5 [21]. To calculate the field from loop 1—B1—the Biot-Savart law, Eq. (3.2), can be
Figure 3.5: Two loops of wire. Image from [21]. used. B1= µ0 4πI1 ¾ dI1 ˆr r2 (3.2)
Now let’s look at the flux from loop 1 going through loop 2, which is calledΦ2. This can be written as
Φ2= »
Φ2is therefore based on B1and the positioning relative to loop 1. B1can be seen from Eq. 3.2 to be proportional to I1, and also based on location of the requested point. This means thatΦ2can be simplified to be dependent only on two factors [21]: I1and M21, where M21is a factor that represents the geometrical relationship between the two loops.
Φ2= M21I1=LI1 (3.4)
M21is called the mutual inductance, which is a constant of proportionality entirely based on geometry. It can be shown that M21= M12[21]. Inductance is depending on the situation also written as L, which is a notation that will be used in the thesis. If n loops are in the proximity of loop 1, then the total inductance for loop 1, which can be called L1, can be acquired by a simple summation: L1= n ¸ i=1 M1i (3.5)
Observe here that loop 1 can have a mutual inductance to itself, provided that the wire is not infinitely thin and has a current density.
The inductance has essentially no physical meaning unless it is considered in a time vary-ing system, which is what the next section will explain.
3.2.2
Faraday’s Law
Faraday’s law can be written in different ways, but all of them are based on Maxwell’s third equation:
∇ E=BB
Bt (3.6)
The simplest and most common simplification of this formula—commonly mistaken for "be-ing" Faraday’s law [21]—is the following equation for electromotive force:
E =dΦ
dt (3.7)
The electromotive force has the unit of voltage, and will be denotedE = U from here on. Eq. (3.7) can be derived from Eq. 3.6 by assuming a static source and using Eq. 3.3:
∇ E=BB Bt ñ ¾ Edl=U= » BB Btda= d dt » Bda=dΦ dt (3.8)
This calculation is based on the presumption that the integral area is constant, which means that the differentiation on time can be moved outside the integral in the second last step. By inserting Eq. 3.4 into 3.8, the standard rule for voltage can be derived where the inductance L is constant: U=dΦ dt = d(LI) dt =L dI dt (3.9)
However, if the integrated area in Eq. 3.8 is changing in time, then due to some conditions such as that the system need to be nonhysteretic and causal [7]—then Eq. 3.9 can be rewritten with a time dependent inductance:
U=d(LI) dt =L dI dt I dL dt (3.10)
This means that for a geometrically changing coil, the derivative of the inductance will have an impact on the voltage in the coil, as well as current change. Note here that the minus signs of Eq. 3.10 is only a matter of defining the direction of the voltage. For the rest of the thesis the voltage will be defined in a way that inverts these minuses to plus signs, which to clarify means:
3.3
ROXIE
ROXIE is a program that was started in 1992 at CERN for the purpose of designing and per-forming calculations on accelerator magnets [35]. It was created to aid the design of the LHC-magnets, since other commercial products used for electromagnetic simulation was consid-ered impractical when used for this purpose [36]. It has been used to design essentially every magnet at CERN since it was created, and has a wide variety of use cases apart from magnetic flux calculations, such as quench simulation, conceptual design through genetic algorithms and simulation of persistent currents.
According to [36], most commercial software is requiring mesh-modelling of the coil where the current is flowing, where Finite Element techniques would be applied to calcu-late field around the wires. Since FEM-techniques are essentially numerical approximations for solving difficult differential equations [7], the inaccuracy of these solutions could be sub-optimal for accelerator magnet design where high precision is a must. For ROXIE, it was therefore developed a technique where the field calculations can be done separately for the iron-part and the coil-part, where the strands in the cables are approximated as line currents. This means that when there is no iron in the model, as is the case for most of this project, the field in the magnet is calculated by ROXIE by simply applying the Biot-Savart law [35].
4
Measurements
In this chapter the methodology for doing the measurements and analysing the data is pre-sented, with the goal of measuring the four effects listed in Section 2.4.
The general idea of the measurement methodology is to study as many transients as possi-ble until a clear pattern is found. For every transient analysed, the energy redistribution will be calculated (Section 4.3.2), the current drop will be measured (Section 4.3.1), and the field change for the quench antennas will be quantified (Section 4.3.3). The transient start location, found through the quench antennas, is also noted. There are three magnets that has been investigated: two nearly identical cosine-theta magnets named MBHSP107 and MBHSP109, and the block-coil magnet FRESCA2.
4.1
Voltage Measurements
1
2
3
4
V
1V
2V
3V
41
2
3
4
Figure 4.1: Cross-section view of the coils for FRESCA2 and MBHSP, and their indexes used in this thesis. Top drawing illustrates all four coils in an electrical scheme and their respective direct voltage measurements.
When measuring voltage two types of data representation are used regularly in SM18: direct and differential voltage. The direct voltage is the normal way of measuring voltage, done by sampling the voltage level with a certain frequency between two points. These two points can, depending on how the magnet is constructed, be the entire magnet, a coil of it or a short segment of a cable. The advantage of this type of measurement is that you see exactly
what is happening in the segment you are measuring, but the disadvantage is that noise and other disturbances will be more apparent. The direct voltages are used for two magnets in the thesis, where the coils are indexed and separated as in Fig. 4.1. Note that coil 1 and 2 (and also coil 3 and 4) for the MBHSP-magnets technically are defined as coil layers in the same coil, unlike for the FRESCA2-magnet, but for the sake of simplicity they will also be called coils.
The other type of measurement being used is differential voltage, which means that two direct voltages is subtracted from each other to create a differential. The advantage of this method is that global effects such as voltage coming from inductance will be subtracted away from the measurement, which makes local effects easier to analyse. The most used differential voltage is the upper magnet half minus the lower half, which will be called Vdi f from now on. If the coils are indexed as in Fig. 4.1, this defines Vdi f as:
Vdi f = (V1+V2)(V3+V4) (4.1) Differential voltage is also used to investigate differences between inner and outer layer in the coils.
4.2
Transient Selection
To do proper analysis a number of transients large enough to get good statistical evidence need to be selected and analysed. It is also important that these transients are selected prop-erly, since the statistics can become faulty otherwise. Also it is advantageous if data for all the four expected effects exists, which is not always the case.
After investigation, many of the transients are not "clean" single spikes, but sometimes contain two peaks. The two types of transients that occur can be seen in Fig. 4.2. As can be
(a) Double peak transient (b) Single peak
Figure 4.2: Difference between double peak and single peak transients.
seen in this example, the double peak is essentially a repeat of the pattern for the single peak. Based on the idea of coil movement, this phenomena can be described as a movement in one coil which causes the first peak, which is then followed by vibrations that disturbs the second coil and causes it as well to move. To simplify the project this is an assumption that is used, and when selecting transients the double peaks are ignored, since getting accurate integrated values of the voltages is not possible in that case.
To summarize the selection, the idea is to investigate as many single peak transients as possible, and prioritize events where data for all the four effects are available.
4.3
Measuring the Effects
The measurable effects coming from a movement is, as explained in Section 2.4: energy re-distribution in the coils, current change, and quench antenna field change. An example of all the measurements can be seen in Fig. 4.3, where the regulator voltage, differential voltage, quench antennas and current measurements can be seen, all of which will be explained in this chapter.
4.3.1
Current Measurements
For current measurements there are two separate data channels available: from the acquisi-tion system, and directly from the power converter.
The data from the acquisition system is available for the same time period as the voltage and quench antenna measurements. However, it has a lot of noise and can only be used on the scale of amperes, and not below that. This is the data that is used when calculating the energy redistribution.
The data from the power converter is much more exact with a precision of 102A, which is enough to be able to observe the current change for most transients. The data is only available for a few seconds before the quench of the magnet, a time frame which only contains a fraction of all the transients—making it harder to attain high statistical certainty for the current change. Many transients that has been analysed does for this reason not contain information about the current drop.
The expected current drop is explained in Section 2.3, and is coming from the change in total inductance of the magnet after the movement. The current drop—seen as the difference before and after the displacement—is explained by Eq. (2.2), which can be written as a dif-ferential as in Eq. (4.2). A more in depth derivation will be done for this equation in Section 5.4.1. »te ts LtotdI dtdt= »te ts IdLtot dt dtùñ ∆I= I Ltot∆Ltot (4.2)
To actually see the current change can be hard for the eye, and therefore a method for analysing them better was created. By subtracting the real measured values with a linear fit of the current, a residual signal is received where the current drop is read as the maximum divergence from zero. This method can be seen in Fig 4.3, where the current change is barely visible in the measurement—graph Nr. 4 in the figure—but as a residual it can easily be quantified to around -0.1 A.
4.3.2
Energy Redistribution & Voltages
The total energy change in a coil is described in Eq. (4.3) from Section 2.3, where tsis the start time of the transient, and teis the end. Note that the time scale in this picture and in Fig. 4.3 are different, and that a normal transient lasts around 1 ms.
W=V Iùñ ∆Ei= »te
ts
UiIdt (4.3)
By integrating over all coil voltages, the full energy redistribution in the magnet can be ac-quired. In Fig. 4.4 the voltages over a transient can be seen, and the start and end time of the integration is marked.
Energy is a good unit in this scenario since it can say how much energy was lost or gained (therefore it is called∆E) over a certain time period in the coil, and it is also suitable since the law of energy conservation can be used. If the net sum of all the energies in all coils are equal to 0, it can be said with certainty that the reason for the transients are in fact movements.
-3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 -5 -2.5 0 2.5 5 7.5 Voltage [V] QA_A6QA_A4 QA_A2 -3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 9.64 9.645 9.65 9.655 V ol ta ge [V ] Regulator Voltage -3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 0 0.2 0.4 0.6 Voltage [V] V_diff -3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 12645 12650 12655 12660 C ur rent [A] I I_linear -3.25 -3 -2.75 -2.5 -2.25 -2 -1.75 Time [s] -0.15 -0.1 -0.05 0 0.05 0.1 C urren t[A ] Residual
1
2
3
4
5
differenceFigure 4.3: All measured effects during a transient. 1. Power converter output voltage.
2. Differential voltage as defined in Eq. 4.1. 3. Quench antenna voltage in coil A2, A4 and A6. 4. Measured current and linear fit.
5. Residual of the current, meaning Iresidual=I Ilinear.
For FRESCA2 and MBHSP107, direct voltages are available that can be used for this anal-ysis. For MBHSP109 only differential voltages are available, but luckily they can be converted into direct voltages by assuming energy conservation. The energy redistribution of the dif-ferential voltages, where the coils are indexed 1-4, can be described as the following, where 119 is the name of the top coil and 123 is the name of the bottom:
-0.0235 -0.023 -0.0225 -0.022 -0.0215 -0.021 -0.0205 Time [s] -0.5 0 0.5 1
V
oltag
e
[V]
V_1 V_2 V_3 V_4t
st
eFigure 4.4: Voltages over each coil during a transient, and also the chosen start and end times of the event.
$ & %
∆E1+∆E2 ∆E3 ∆E4=∆Edi f ∆E1 ∆E2 =∆Edi f ,119
∆E3 ∆E4=∆Edi f ,123
Adding the law of energy conservation to this equation system,∆E1+∆E2+∆E3+∆E4=0 results in an equation that can convert the differential values into direct voltages. This is done in Eq. (4.4). 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 ∆E1 ∆E2 ∆E3 ∆E4 = 0 ∆Edi f ∆Edi f ,119 ∆Edi f ,123 ùñ AEdirect =Edi f ùñ Edirect =A1Edi f (4.4)
As can be seen, the measurements can be converted into direct voltage by multiplying it with the inverted A-matrix, which is:
A1= 1 4 1 1 2 0 1 1 2 0 1 1 0 2 1 1 0 2 (4.5)
4.3.3
Quench Antennas
An example of the measured voltage in the quench antennas can be seen in Fig. 4.7, where values from all segments in the A-coil can be seen. As can be observed, an initial spike is followed by large vibrations, which makes individual transient analysis hard for the quench antennas, and are therefore better to analyse in bigger numbers to avoid this uncertainty.
Just like for the voltage in Section 4.3.2, the easiest thing to analyse is the integrated volt-age that each quench antenna pick-up coil is experiencing, calledEQA,tot coming from Eq.
(3.7). » te ts EQA,totdt= »te ts dΦQA,tot dt dt=∆ΦQA,tot (4.6)
The notation∆ΦQA,tot means that when integrated pick-up coil voltage is measured, this is actually the same as the total flux change in the quench antenna. An explanation on why this notation is used will come in Section 5.4.2.
