Design Aspects of High-Field Block-Coil Superconducting Dipole Magnets E. I. Sfakianakis August 31, 2006 Abstract Even before the construction of the Large Hadron Collider at CERN is finished, ideas about the next step in high energy physics experiments are being examined. The two main directions that are considered worth following are linear lepton colliders and even bigger hadron storage rings. The latter would require advances in dipole magnet technology in order to be considered a feasible solution for the future of high energy physics. This study concentrates on design issues of the steady-state and transient operation of block-coil dipole magnets in order to optimize and evaluate their performance. School of Electrical and Computer Engineering, National Technical University of Athens 1
1 Introduction and Objectives The purpose of this project is the study of an alternative approach to the LHC-design of superconducting dipole magnets, called block-coil configuration. The study is done for a high-field magnet such as the ones that will be required in a future high energy hadron ring accelerator, for example an upgraded version of the LHC. Topics such as field strength and quality in the steady state operation of the magnet will be considered. In addition to that, the transient behaviour of the magnet will be studied. The results obtained will be compared to the ones arising from a cos(θ) design with similar parameters. At the end we will be able to state the extent to which the block-coil approach can serve as a replacement for the current cos(θ) design philosophy in future high-field dipoles for particle accelerators. The simulation and optimization of the dipoles has been carried out using the ROXIE software package, developed by Stephan Russenschuck et al. at the AT-MEL-EM Section at CERN (for a full documentation see [2]). 2 Specifications In order to prepare the next generation of high-field superconducting dipole magnets, an EU-funded program referred to as NED (Next European Dipole) has been launched (see for example [3]). Inside this program salient specifications are stated. The superconducting material that is considered the best solution at this time is Nb 3 Sn. Although it is more brittle and more strain sensitive than the material used at present ( Nb-Ti), it has a higher current carrying capability and it can be used to produce the field required, while Nb-Ti cannot operate in the 10 T-15 T region. The cable used in this work is a Rutherford-Type cable without keystoning. The height and width of the cable are 15.6 mm and 2.175 mm respectively and it consists of 30 strands. A similar type of cable was used in a study to optimize the performane of large aperture cos(θ) dipole magnets within the NED Program [1]. The main differences between the two cables are the height and the number of strands of the cable used in [1], which were 26 mm and 40 respectively. In addition to that the cos(θ) design uses slightly keystoned cables (with a keystoning angle of about 0.22 degrees) so as to make the radial alignment of the blocks easier to achieve. Using similar cables facilitates comparison of the two approaches without having to put a lot of effort to estimate the effect of the shape of the cable itself to our results. 3 Outline At first the coil cross section for different apertures will be studied and optimized. Then the different effects of the nonlinearity of the yoke as well as the superconducting cable magnetization will be taken into account. Finally the two configurations, block-coil and cos(θ), will be presented in parallel and compared. 2
0 21.43 42.86 64.29 85.71 107.14 128.57 150 ROXIE 9.0 Figure 1: Coil cross section for a 40mm bore magnet 4 Steady-State Operation Design 4.1 Small Aperture Magnet At first the principles were studied for a 40mm bore magnet by using 4 independent blocks distributed at two different y-positions above the midplane. By optimizing the coil geometry, without taking the yoke into account, it was possible to keep all relative multipole field errors below 0.05, except b 7 and b 9. The radius of harmonic analysis was set to 10 mm. The coil geometry is shown in Figure 1 and the field data from the two-dimensional simulation are listed in Tables 1 and 2. Table 1: Field data for a 40mm bore magnet Excitation current 18000 A Main field B 1 13.634 T Peak field on conductor 14.272 T Peak field / Main field 1.047 Percentage on the load line 10.5 Excitation current at 0% margin on the load line 20250 A Peak field at 0% margin on the load line 16.056 T By introducing the iron yoke and further optimizing the design of the coil, a peak field of over 14.5 T was achieved. The total cross-section of the coil and yoke can be seen in 3
Figure 2 and the accompanying field data can be found in Tables 3 and 4. In the next step another design for a small aperture magnet was studied which resulted in a 52 mm bore. The idea was to use the intersecting ellipses scheme to create a field of better homogeneity, which indeed was achieved. In this design only two independent blocks were used. The field data are shown in Tables 5 and 6 and the design of the coil in Figure 3. The radius of harmonic analysis was set to 15 mm. By inserting the iron yoke and optimizing the coil geometry the peak field exceeded Table 2: Relative multipole field errors for a 40mm bore magnet b 3 b 5 b 7 b 9 b 11 b 13 b 15-0.00126-0.00016-2.54015-0.034937-0.04136-0.00675-0.00072 Table 3: Field data for a 40mm bore magnet with the insertion of the iron yoke Excitation current 15660 A Main field B 1 13.918 T Peak field on conductor 14.549 Peak field / Main field 1.045 Percentage on the load line 10.3 Excitation current at 0% margin on the load line 18000 A Peak field at 0% margin on the load line 16.471 T Table 4: Relative Multipole field errors for a 40mm bore magnet with the insertion of the iron yoke b 3 b 5 b 7 b 9 b 11 b 13 b 15-0.11907 0.31166-2.25847-0.28734-0.03461-0.00504-0.00047 Table 5: Field data for a 52mm bore magnet Excitation current 19520 A Main field B 1 13.395 T Peak field on conductor 14.158 T Peak field / Main field 1.057 Percentage on the load line 10.3 Excitation current at 0% margin on the load line 21920 A Peak field at 0% margin on the load line 15.899 T 4
B flux density (T) 7.261-7.664 6.857-7.261 6.454-6.857 6.051-6.454 5.647-6.051 5.244-5.647 4.840-5.244 4.437-4.840 4.034-4.437 3.630-4.034 3.227-3.630 2.824-3.227 2.420-2.824 2.017-2.420 1.613-2.017 1.210-1.613 0.807-1.210 0.403-0.807 0. - 0.403 0 21.43 42.86 64.29 85.71 107.14 128.57 150 0 50 100 150 200 250 300 350 400 450 500 550 600 BEMFEM ROXIE 9.0 * BEMFEM ROXIE 9.0 * 06/08/30 18:34 Figure 2: Coil cross section for a 40mm bore magnet with the insertion of the iron yoke 0 21.67 43.33 65 86.67 108.33 130 ROXIE 9.0 Figure 3: Coil cross section for a 52mm bore magnet Table 6: Field data for a 52mm bore magnet b 3 b 5 b 7 b 9 b 11 b 13 b 15-0.00134 0.01457-0.71914-1.43880-0.10109-0.01141-0.00576 5
14.5 T while the field quality remained in the desired level. The geometry of the coil and yoke is depicted in Figure 4 and the field data are given in Tables 7 and 8. Table 7: Field data for a 52mm bore magnet with the insertion of the iron yoke Excitation current 15200 A Main field B 1 14.014 T Peak field on conductor 14.559 T Peak field / Main field 1.039 Percentage on the load line 10.5 Excitation current at 0% margin on the load line 17120 A Peak field at 0% margin on the load line 16.169 T Table 8: Relative Multipole Field Errors for a 52mm bore magnet with the insertion of the iron yoke b 3 b 5 b 7 b 9 b 11 b 13 b 15 0.00131 0.08440 0.13017-1.60859-11746 -00993-0.01085 4.2 Large Aperture Magnet One of the characteristics of the block-coil model is its scalability. After having studied the basic characteristics of the small aperture block coil magnets an attempt was made to design a large aperture magnet (132 mm bore) in a fast and efficient way, simply by scaling up both the dimension of the aperture and the number of the blocks. By following the intersecting ellipses scheme and optimizing the coil cross-section two different designs were produced, one having 5 and one having 6 independent blocks. Their main differences are the peak field and of course the amount of superconducting material used. A characteristic that remained unchanged during the design and optimization phase of both magnets was the fact that the vertical distance between the blocks as well as between the lower block and the midplane was intentionally not zero. In fact it was set to 20 mm and was allowed to variate by a limited amount ( 2 mm) around this value during the optimization phase. This was done assuming that there is a supporting structure around each coil to guarantee mechanical stability and stress management, as demonstrated in [5]. However, on the one side a somewhat acceptable field quality was obtained, so there was no serious need for altering the vertical coordinates of the blocks dramatically and on the other side the interest was more on the advantages and drawbacks of the block-coil approach in general, rather than on producing an accurate design.this also justifies the fact that the magnetic iron yoke was 6
B flux density (T) 8.168-8.622 7.715-8.168 7.261-7.715 6.807-7.261 6.354-6.807 5.900-6.354 5.446-5.900 4.993-5.446 4.539-4.993 4.085-4.539 3.632-4.085 3.178-3.632 2.724-3.178 2.270-2.724 1.817-2.270 1.363-1.817 0.909-1.363 0.456-0.909 0.002-0.456 0 21.43 42.86 64.29 85.71 107.14 128.57 150 0 50 100 150 200 250 300 350 400 450 500 550 600 BEMFEM ROXIE 9.0 * BEMFEM ROXIE 9.0 * Figure 4: Coil cross section for a 52mm bore magnet with the insertion of the iron yoke not taken into account, thus only the coil itself was examined. However, as far as the field strength and quality of the configuration and the comparison between them, are concerned, the effects of the yoke can be neglected. The coil cross-section for the 5 block design is given in Figure 5 along with the data about the produced field (Tables 9 and 10). Table 9: Field data for a 132 mm bore magnet using 5 independent blocks Excitation current 14400 A Main field B 1 13.642 Peak field on conductor 14.624 T Peak field / Main field 1.072 Percentage on the load line 10.6 Excitation current at 0% margin on the load line 16200 A Peak field at 0% margin on the load line 16.452 T As one can see the field at a margin on the load line of roughly 10% is close to 15 T and all relative multipole field errors (with the exception of b9) are kept under 0.2. On the other hand by adding a sixth block on top of the previous 5 ones, it is possible to increase the peak field of the coil and one would expect the multipole errors to be manipulated in a more efficient way, whish is indeed proved to be true by the simulation. The cross-section of the coil and the field data are shown in Figure 6 and Tables 11 and 12 respectively. 7
0 21.43 42.86 64.29 85.71 107.14 128.57 150 ROXIE 9.0 Figure 5: Coil cross section for a 132 mm bore magnet using 5 independent blocks Table 10: Relative multipole field errors for a 132 mm bore magnet using 5 independent blocks b 3 b 5 b 7 b 9 b 11 b 13 b 15-0.00010-0.00019-0.00001-4.66079-0.35117-0.30851-0.21595 Table 11: Field data for a 132 mm bore magnet using 6 independent blocks Excitation current 12900 A Main field B 1 16.077 T Peak field on conductor 14.997 T Peak field / Main field 1.072 Percentage on the load line 9.4 Excitation current at 0% margin on the load line 14250 A Peak field at 0% margin on the load line 16566 T Table 12: Relative multipole field errors for a 132mm bore magnet using 6 independent blocks b 3 b 5 b 7 b 9 b 11 b 13 b 15 0.00001-0.00080 0.17097-0.157934 0.72681 0.02720-0.22920 8
0 20 40 60 80 100 120 140 160 ROXIE 9.0 Figure 6: Coil cross section for a 132 mm bore magnet using 6 independent blocks 5 Multipole Field Error Variation 5.1 Theoretical Baseline Until now we have been interested in the nominal and maximum field of the magnet and in the corresponding relative multipole errors. This analysis has been done for the so-called steady state operation of the dipole. However in a real accelerator the particles end up in a high energy circular collider after a (usually long) sequence of linear accelerators (linacs), smaller storage rings and boosters. In each of these steps the particles are accelerated to the nominal energy of each machine before being extracted and injected into the next one. From that it is clear that a high energy accelerator will operate at an energy far below its nominal energy during the first rounds after injection. For circular colliders this means that the bending dipoles will have to produce a magnetic field far lower than their nominal one. Otherwise the particles will be bent beyond the curvature of the ring and hence hit the beam pipe and be lost while at the same time damaging the beam pipe itself. After injection the particles will be accelerated until they reach the nominal energy of the ring, where the collisions and experiments will have to be carried out. During this procedure of accelerating the particles the field of the dipoles will have to be constantly increased to bend the particles of increasing energy to the same angle. It is therefore essential to have a highly homogeneous field not only for the nominal field strength, but also for operation below this point. If this is not the case the multipole errors can cause a degradation of the beam quality during the time after injection and before the nominal energy is reached which could even lead to a loss of a part of the injected particles. Two phases of a magnet s transient response are distinguished: the one 9
where the excitation current and accordingly the magnetic field are increased, which is referred to as up-ramp and the opposite one where the excitation current is decreased, which is referred to as down-ramp. It is obvious that the most important of the two phases is the up-ramp phase. That is because the up-ramp phase takes place after the injection where it is crucial that the beam quality is kept at a good level. The fact that different values of relative multipole errors appear for different values of the excitation current points to some source of nonlinearity in the response of the magnet. Here the two main sources of nonlinearities -the iron yoke and the superconducting magnetization- are defined and studied. It is known that the magnetic iron exhibits a nonlinear response and is fully saturated at a field strength of about 2 T and above. This indicates a highly nonlinear behaviour which results unavoidably in a variation of both the rise of the main field and the multipole errors depending on the excitation current. For the relative multipole errors this variation can be significant and can produce degradation of the beam quality if it is injected into the storage ring at a low energy. Another source of nonlinearity and hence multipole error variation are the so-called persistent currents that are produced on the superconducting cables and form another source of magnetic field that alters the field profile in the aperture. For hard superconductors like the ones used for building the coils of superconducting magnets, the persistent currents also show a hysteresis, which means that the response is different between up-and down ramp. The relation between these two errors and certain yoke geometries has been studied in order to identify possible compensation techniques. 5.2 Proposed Approach and Computer Simulation It has been proposed (in [4]) that inserting a magnetically permeable blade (which will be referred to as flux-blade ) between the two sets of blocks parallel to the horizontal axis would suppress the persistent-current-induced field errors and hence provide a method for persistent current compensation. We will try to examine the effect of such a structure and evaluate its performance. 5.2.1 Total Transient Response Analysis In the following analysis only the first coil geometry of the 40mm bore magnet has been examined (see Figure 1), because the interest lies only in the origin of these errors and the proposed compensation technique and not in the field quality itself. The geometry of the iron yoke chosen for this study is shown in Figures 7 and 8. We should note that the yoke is placed very close to the coil. This has to be done if one wishes to achieve the maximum field with a given number of cables. It is not an important result in this case to evaluate the steady-state value of the relative multipole error, since that can change by rearranging the blocks in the coil. However that would mainly shift the whole curve up or down. What is more important is the variation of the curve -from the minimum to the maximum value during the up-rampas well as the width of the hysteresis loop. One can see from Figure 9 that the lower 10
Figure 7: Iron yoke used for simulating the uncompensated magnet Figure 8: Iron yoke after the inclusion of the flux-blade 11
Figure 9: Transient response for the two yoke geometries (The upper curve represents the compensated yoke geometry) Figure 10: Width of the hysteresis curves for the two yoke geometries (The upper curve represents the compensated yoke geometry) curve (which corresponds to the uncompensated yoke geometry) shows a bigger spread of values during the up-ramp than the upper curve. From this point of view one could say that the flux-blade seems to improve the transient response of the magnet. By comparing the width of the two hysteresis curves, that is the difference of the values for the same excitation current during up- and down-ramp, one ends up with Figure 10. From these two figures one can see that the flux-blade in this geometry suppresses the variation of the relative sextupole error during the up-ramp, thus making injection at lower energies less damaging for the quality of the beam. However the width of the hysteresis curve is increased by the insertion of the flux-blade by more than 100% for low excitation current. 5.2.2 Persistent-Current-Induced Field Errors In the above analysis the total field error was considered. This means that one could not study the effect of the persistent-current-induced field errors and the field errors that are due to the non-linearities of the iron yoke separately. An easy way to do so is 12
Figure 11: Comparison between purely geometric and total errors for the two yoke geometries (The two upper curves represent the compensated yoke geometry) to calculate the variation of the field errors with respect to the excitation current, but without taking one of the two sources of non-linear errors into account. Using ROXIE, one can calculate the transient response of the magnet ignoring the persistent currents. This means that one uses an idealized model of the superconducting cables, where there is no superconductor magnetization while at the same time all the other properties are unchanged. The outcome of this calculation (ignoring the superconducting magnetization) is plotted in Figure 11, along with the total field errors (the ones calculated by taking the persistent currents as well as the non-linear behaviour of the yoke into account). One can see that after a certain value of the excitation current the two curves (purely geometric and total field error) tend to converge. This means that the relative persistentcurrent-induced field errors decrease with inceasing excitation current (and thus with increasing overall magnetic field) and that they play an important role only at low excitation current (i.e. low magnetic field). To study the different behaviour of the two geometries with respect to each one of the two sources of non-linear relative multipole field errors we plotted the difference between the geometric and the total sextupole error with respect to excitation current for both cases and ended up with Figure 12. As one can see, the difference between geometric and total sextupole error is twice as large for the compensated geometry, until of course the persistent currents become too small in both cases. After seeing their results on the field quality it can be useful to have an overview of the nature and the effects of the persistent currents by looking at the magnetization in the region of the coil. In Figures 13 to 16 we have plotted the magnetization of the coil for low and high excitation current and for both geometries. It is obvious that the magnetization profile changes with excitation current. However this change doesn t apply only to the magnetization strength, but also to its distribution on the coil. This proves the claim that superconductor magnetization in magnet coils is indeed a nonlinear effect. Therefore it has to be studied and taken into account if the magnets have to be used with a varying excitation current, for example during the up-ramp phase after 13
Figure 12: Difference between the purely geometrical and the total sextupole errors for the two yoke geometries (The upper curve represents the compensated yoke geometry) 06/08/30 20:27 Time (s) : 1. M (A/m) (*10 4 ) 32.60-34.67 30.53-32.60 28.46-30.53 26.39-28.46 24.32-26.39 22.25-24.32 20.18-22.25 18.11-20.18 16.04-18.11 13.97-16.04 11.9-13.97 9.829-11.9 7.759-9.829 5.688-7.759 3.618-5.688 1.547-3.618-0.52-1.547-2.59 - -0.52-4.66 - -2.59 0 21.43 42.86 64.29 85.71 107.14 128.57 150 BEMFEM ROXIE 9.0 * Figure 13: Magnetization in the coil for the uncompensated geometry at low excitation current 14
Time (s) : 1. M (A/m) (*10 4 ) -2.67 - -1.22-4.12 - -2.67-5.57 - -4.12-7.01 - -5.57-8.46 - -7.01-9.91 - -8.46-11.3 - -9.91-12.8 - -11.3-14.2 - -12.8-15.7 - -14.2-17.1 - -15.7-18.6 - -17.1-20.0 - -18.6-21.5 - -20.0-22.9 - -21.5-24.3 - -22.9-25.8 - -24.3-27.2 - -25.8-28.7 - -27.2 0 21.43 42.86 64.29 85.71 107.14 128.57 150 BEMFEM ROXIE 9.0 * Figure 14: Magnetization in the coil for the uncompensated geometry at high excitation current 06/08/30 13:25 Time (s) : 1. M (A/m) (*10 4 ) 30.53-33.49 27.57-30.53 24.61-27.57 21.65-24.61 18.69-21.65 15.73-18.69 12.77-15.73 9.812-12.77 6.852-9.812 3.892-6.852 0.933-3.892-2.02-0.933-4.98 - -2.02-7.94 - -4.98-10.9 - -7.94-13.8 - -10.9-16.8 - -13.8-19.7 - -16.8-22.7 - -19.7 0 21.43 42.86 64.29 85.71 107.14 128.57 150 BEMFEM ROXIE 9.0 * Figure 15: Magnetization in the coil for the compensated geometry at low excitation current 15
Time (s) : 1. M (A/m) (*10 4 ) -4.05 - -2.68-5.42 - -4.05-6.79 - -5.42-8.16 - -6.79-9.52 - -8.16-10.8 - -9.52-12.2 - -10.8-13.6 - -12.2-15. - -13.6-16.3 - -15. -17.7 - -16.3-19.1 - -17.7-20.4 - -19.1-21.8 - -20.4-23.2 - -21.8-24.5 - -23.2-25.9 - -24.5-27.3 - -25.9-28.6 - -27.3 0 21.43 42.86 64.29 85.71 107.14 128.57 150 BEMFEM ROXIE 9.0 * Figure 16: Magnetization in the coil for the compensated geometry at high excitation current injection. 6 Conclusions The conclusions that can be derived from the present work can be divided in two main categories. On the one hand a comparison can be done between the different kinds of block-coil design geometries which were tested. At the same time the overall capabilities and potentials of the block-coil approach to magnet design can be evaluated and compared to some extend with similar results derived for cos(θ) dipole magnets. In order to be fair to both designs, a fully optimized final design of a block-coil magnet should be produced before the comparison between the two philosophies can lead to a final decision. On the other hand the proposed flux-blade compensation scheme has been analyzed and can be further evaluated. 6.1 Steady-State Operation Four different coil geometries have been chosen and optimized in order to produce two small- and two large-aperture dipole magnets. The two small-aperture magnets have shown a relatively high field of over 14 T, which is further increased when the iron yoke is included. The scaling of the design to larger apertures was done in a fast way without the need of many time-consuming optimization rounds. However the final design of the 5-block magnet showed a good behaviour as far as the relative multipole errors are considered with the exception of b 9. By adding the sixth block all errors were kept at 16
a low level. The only exception is b 11 with a value of about 0.7. However one should not forget that the NED design proposed a cos(θ) magnet with a b 11 of more than 1. In addition to that the value of the lower order multipole (in this case the sextupole) is extremely low. The peak field of the coil approaches 15 T at the operation point and exceeds 16.5 T when the load-line-margin vanishes. This field strength has not yet been achieved using cos(θ) magnets. A point that would require further investigation is the excitation current. In this design the excitation current used is small relative to other designs. This results unavoidably to a larger amount of cables in order to produce the desired field. However the spread of the current over a larger area lowers the Lorentz force per area which can be crucial for the mechanical robustness of the magnet in highfield operation. Summarizing the above one can say that the block-coil configuration has the potential to provide the field strength and quality needed for future storage rings. However in order to be able to come to a decision a final design has to be carried out including both an optimized core geometry, as well as taking into account issues of cost and stored magnetic energy arising from the low excitation current and high number of windings. 6.2 Transient Response From calculating the relative sextupole error variation for the uncompensated and compensated yoke geometry it is seen that the flux-blade suppresses the variation, thus forcing the curve to become more flat. However this seems not to be because of persistent-current compensation. When subtracting the overall error from the purely geometric one (due to the non-linear iron yoke) one can isolate the contribution of the persistent currents. By doing that we found out that the persistent-current-induced field errors increase with the insertion of the blade. This means that although the flux-blade scheme suppresses much of the variation of the sextupole error this suppression does not come from a persistent-current compansation, but seems to be a purely geometrical effect. Acknowledgement This work was carried out during the 2006 CERN Official Summer Student Program, within the AT Department, MEL Group, EM Section. References [1] J. N. Schwerg, Electromagnetic Design Study for a 15 T Large Bore Superconducting Dipole Magnet, Berlin, November 2005 [2] S. Russenschuck, Electromagnetic Design and Mathematical Optimization Methods in Magnet Technology, Version 3.3, April 2006 17
[3] F. Toral, Progress in Comparison of Different High Field Magnet Designs for NED, CIEMAT, Madrid, Spain [4] R. Blackburn, T. Elliott, W. Henchel, L. McInturff, P. McIntyre, and A. Sattarov, Construction of Block-Coil High-Field Model Dipoles for Future Hadron Colliders, IEEE Transactions on Applied Superconductivity, Vol. 13, No. 2, June 2003 [5] P. Noyes, R. Blackburn, N. Diaczenko, T. Elliott, W. Henchel, A. Jaisle, A. McInturff, P. McIntyre, and A. Sattarov, Construction of a Mirror-Configuration Stress- Managed Nb 3 Sn Block-Coil Dipole, IEEE Transactions on Applied Superconductivity, Vol. 16, No. 2, June 2006 18