HILUMILHC-Del-Dx-x-Template-v1.0
Date: 30/11/2014
Grant Agreement No: 284404
HILUMI LHC
FP7 High Luminosity Large Hadron Collider Design Study
Seventh Framework Programme, Capacities Specific Programme, Research Infrastructures, Collaborative Project, Design Study
MILESTONE report
STUDY OF FINE-TUNING FIELD QUALITY IN MQXF QUADRUPOLE
Milestone: MS36
Document identifier: / HILUMILHC-Del-Dx-x-Template-v1.0Due date of deliverable: / End of Month 18 (October 2014)
Report release date: / 30/11/2014
Work package: / WP3: Magnets
Lead beneficiary: / [Short name of participant e.g. OEAW]
Document status: / Draft
Abstract:
In this report we present the results from studying fine-tuning of field quality in the MQXF quadrupole by applying shimming techniques. The study is based upon the current 2D magnet model of MQXF using ROXIE to compute the field in aperture and iron yoke. The study takes place well before the first prototype is built. Therefore the results must be validated by future field measurements of prototypes.
Copyright notice:
Copyright © HiLumi LHC Consortium, 2013.
For more information on HiLumi LHC, its partners and contributors please see www.cern.ch/HiLumiLHC
The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404. HiLumi LHC began in November 2011 and will run for 4 years.
The information herein only reflects the views of its authors and not those of the European Commission and no warranty expressed or implied is made with regard to such information or its use.
Delivery Slip
Name / Partner / DateAuthored by / P. Hagen / [CERN] / 4/10/2013
Edited by
Reviewed by / E. Todesco [WP leader]
L. Rossi [Project coordinator] / [CERN] / 15/10/2014
Approved by / Steering Committee / dd/mm/yy
TABLE OF CONTENTS
1. Introduction 4
2. MQXF CROSS-SECTION AND POSSIBLE SHIMMING 4
3. RODS 5
4. SHIMS IN THE BLADDER SLOTS 7
4.1. SHIM as function of size 8
4.2. SHIM CORRECTION AS FUNCTION OF COIL CURRENT 9
4.3. SHIM CORRECTION AS FUNCTION OF COMBINATIONS 9
5. RESULTS FROM SHIMMING IN MQXC 11
6. Conclusions and FUTURE plans 11
Annex: Glossary 13
Executive summary
In this report we present the results from studying fine-tuning of field quality in the MQXF quadrupole by applying shimming techniques.
1. Introduction
The field quality requirements for the 150 mm wide aperture MQXF magnet are described in [1]. One of the main concern is the control of the low order, not allowed multipole (mainly b3, a3, b4, a4) stemming from assembly or component asymmetries. The shimming technique is a passive technique to reduce undesired field harmonics. Rods or iron pieces are inserted in the collars or iron yoke to create geometric asymmetry in the effective permeability of the material around the coils. This asymmetry will excite different configurations of field harmonics and compensate the geometric component.
The study of shimming in MQXF is inspired by equivalent work carried out for the MQXC models [2]. The shimming technique is described several places in literature. See for example [3] and [4].
2. MQXF CROSS-SECTION AND POSSIBLE SHIMMING
Fig. 1 Cross section of the MQXF magnet (150 mm aperture)
The ROXIE magnetic model for MQXF is shown in Fig. 1. This model has only the essential features which affect the field; the coils, iron yoke, rods and shims. The collars are not visible in this model as the austenitic steel is magnetic transparent (μr = 1). Some small details in the iron yoke are omitted. This will not change the results as the impact of the rods and shims are expressed using finite difference (i.e. the case with shim minus the case without shim).
We considered two configurations of magnetic shims: circular rods in the collars and rectangular shims in the bladder slots.
3. RODS
The effect of one rod at 25 degrees from the midplane was studied (see Fig. 2). The diameter of the circular rod is 10 mm, so the radial position is practically fixed (rrod = 123 mm). This is the same size as used in the MQXC. We use the same BH-curve for the rod as for the iron (ROXIE BHiron1).
Fig. 2 Study of effect of one rod by changing rod radius (rrod) and rod angle (rodang)
The ramp of the magnet was simulated in ROXIE. The field computation has been done with currents ranging from 500 A to 17500 A in steps of 500 A. We assume the minimum current for operation will be around 500 A and that the injection current is around 1000 A. Simulation of persistent currents due to strand magnetisation was enabled, but since we compute the difference effect of “rod minus no rod”, it does not show up in our results.
The result of the study is shown in Fig. 3. We interpret the results is that magnetic rods have large effect at low current. As the current increases the effect on all multipoles goes asymptotically towards zero. This is the opposite situation we need for the final focus optics in an accelerator, where the field quality is critical at collision energy (around nominal gradient, 17.5 kA). The conclusion being that the usage of rods would correct little at nominal current and add extra field errors at low current. Therefore this option is discarded.
Fig. 3 Correction effect of one rod as function of current (hamonics @ Rref = 50 mm)
We investigated the reason why the rods in MQXF are so much less effective than for the MQXC. In MQXC we also have a drop of efficiency as the current increases, but less pronounced, with a factor of 2 (see section 5). The initial assumption being that the saturation and impact on permeability would be the driving source. This turned out to be correct. Fig. 4 and 5 show the iron field and relative permeability for currents 1 kA and 17.5 kA, respectively. At low current the rod can absorb a lot of flux, but at high current it becomes so saturated that it is practically transparent. In MQXC the saturation is lower and the rod has still some impact.
Fig. 4 Simulation of iron field and relative permeability at 1 kA
Fig. 5 Simulation of iron field and relative permeability at 17.5 kA
4. SHIMS IN THE BLADDER SLOTS
The effect of one shim was first studied as function of the shim size. We learnt from the rod study that we must not use shims too close to the coil for this magnet. Bladders slots are an ideal place to insert magnetic shims, without adding other holes in the iron yoke (see Fig. 1). The shims are rectangular and located symmetrically around the four poles. Also in this case eight angular positions are available. We use the same BH-curve for the shim as for the iron (ROXIE BHiron1). After the size study, we investigate the dependence on the current. Harmonics are as usual evaluated at reference radius of 50 mm.
4.1. SHIM as function of size
The shim width and height was varied (see Fig. 6 for a visual definition). The simulation was carried out with nominal gradient (140 T/m). A slightly simplified version of the iron yoke was used for this particular parametric study, and checked against the nominal shim size (width 10 mm and height 60 mm) to have almost identical effect (less than 0.1 unit of difference for any multipole). Table 1 contains the essential results. Multipoles with essential no correction are omitted (like a6). The overall conclusion is that the correction of multipoles roughly scales linearly with shim size, and that filling the whole slot one gets a reasonable change of low order multipole (in the range of a few units).
Fig. 6 Definition of shim size and its location
Table 1 Multipole correction as function of size (17.5 kA, @ Rref = 50 mm)
4.2. SHIM CORRECTION AS FUNCTION OF COIL CURRENT
We use a shim size of width 10 mm and height 60 mm to study the multipole correction as function of current. This particular size is deemed reasonable from mechanical and assembly considerations. Table 1 can be consulted if the size should not turn out to be adequate in the future.
We do the same ramp of the magnet as described in 3. That is, we vary the coil current from 500 A to 17500 A in steps of 500 A. Fig. 7 shows the results. The result is more promising than the equivalent study of the rods (Fig. 3). At low current, the shim is magnetically transparent (like air) because there is sufficient area of iron with high permeability closer to the coils, and the iron acts like a mirror, so the coil does not see the shim. When the current increases and saturation starts in the innermost iron area, the shim plays a more important role. The correction amplitude has a global maximum around 7 kA where the shim starts to be transparent and the role of the outermost iron area starts to dominate. Fortunately, at nominal current we still have most of the correction capability at disposition. We can correct units of the multipoles b3 and b4 but only fractions of units for other multipoles. We have to bear in mind this is the effect of one shim. We must investigate combinations of shims as well.
Fig. 7 Correction effect of one shim as function of current (hamonics @ Rref = 50 mm)
4.3. SHIM CORRECTION AS FUNCTION OF COMBINATIONS
If we consider the correction capability of one shim as a small perturbation of the iron (small size compared to the iron yoke, and small change in permeability), we can treat combinations of shims as a system of linear equations. That is, the effect of two shims is the sum of the two.
Table 2 shows effect of the 8 shims expressed by using symbolic coefficients rather than numeric values, i.e. in order to establish the general concept. There is a pattern of sign change as function of even and odd multipoles. For odd multipoles there is also an interchange of coefficients for normal and skew. The general rule is given in Table 2, where shim numbering is given in Fig. 1. So in general one shim excites all multipoles.
Table 2 Multipole correction as function of shim, expressed using unsigned coefficients
The actual values estimated with ROXIE for the coefficients of shim 1 in Table 2 are shown in Table 3. The correction capacity for b6 and a6 is modest. This is a good feature since we want to correct the low orders with no impact on the high order. We have therefore omitted these from the final results.
Table 3 Multipole correction for shim 1, coefficients replaced with numeric values
Next, we want to find the combinations which correct a single multipole, or at most two. The result of the search is that only combinations with four shims will change one or two multipoles. Table 4 summaries the interesting combinations. They represent 12 out of 70 possible 4-shim combinations. The symbols and values within parenthesis denote small (insignificant) quantities. We have omitted undesired side-effect, normal and skew dipole multipole for a few of these combinations. The worst case is a b1 and a1 of 23 units. These can presumably be corrected with associated conventional orbit correctors.
There are two ways of correcting a b3, (S 1,2,3,8) and (S 1,2,4,7), both giving about 3-5 units and a small b5 (0.2-0.6 units). A similar result holds for a3, which can be tuned in two ways in the range of 3-5 units. The normal octupole b4 can be corrected up to 2.8 units. On the other hand, little can be done on a4 (only 0.8 units maximum).
We also checked that the assumption of using linear combinations is valid. The result is shown in Table 5 for b3. We checked all 12 and the agreement is excellent. Table 5 also reveals the undesired normal dipole component. This was the very last step in our investigation.
Table 4 Shim combinations which correct 1 or 2 multipoles
Table 5 Cross-check for b3 shim correction; linear combinations of single effect versus ROXIE simulation with the full combination of shims
5. RESULTS FROM SHIMMING IN MQXC
We briefly present the result from similar shim studies of MQXC. Prototypes of this magnet has already been built and measured. The cross-section is shown in Fig. 8. The load line with one shim is shown in Fig. 9. The correction coefficients for MQXC shims, simulation versus measurement is shown in Table 6 (same notation and meaning as for MQXF in Table 2 and 3). There is a good agreement.
Fig. 8 Cross section of the MQXC magnet (120 mm aperture)
Fig. 9 Correction effect of one rod in MQXC as function of current (hamonics @ Rref = 27 mm)
Table 6 Harmonics correction coefficients in MQXC shims evaluated at room temperature and Rref = 27 mm. ROXIE model versus measurements.
6. Conclusions and FUTURE plans
The shim studies of MQXF described in this report have been carried out well before any working prototype magnet has been built. This work must therefore be followed-up by applying shims to the first model(s) and by actual measurements. The study shows that shims in the collars are not useful since in that place the iron is totally saturate at nominal current. Shims in the slots of the bladders are a good option, allowing to change up to 5 units of sextupole (normal or skew), 3 units of normal octupole. On the other hand, a4 can be changed of 0.8 units at max.