Prototype adjustable PM quadrupole and combined function magnets

I.FAST Innovation Fostering in Accelerator Science and Technolog y Horizon 2020 Research Infrastructures GA n° 101004730 DELIVERABLE REPORT Prototype adjustable PM quadrupole and combined function magnets DELIVERABLE: D11.3 Document identifier: IFAST-D11.3 Due date of deliverable: End of Month 28 (August 2023) Report release date: 15/09/2025 Work package: WP11: Sustainable concepts and technologies Lead beneficiary: UKRI Document status: Final ABSTRACT IFAST Task 11.3 has designed and built a prototype permanent magnet-based dipole-quadrupole magnet, referred to as the HEPTO magnet, as an energy saving alternative to an equivalent electromagnet. This report summarises the performance of the prototype with respect to the magnetic specification. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 2 / 28 I.FAST Consortium, 2025 For more information on IFAST, its partners and contributors please see https://ifast-project.eu/ This project has received funding from the European Union’s Horizon 2020 Research and Innovation programme under Grant Agreement No 101004730. IFAST began in May 2021 and will run for 4 years. Delivery Slip Name Partner Date Authored by Hinton UKRI 12/09/2025 Reviewed by M. Vretenar, L. Celona [on behalf of Steering Committee] CERN 15/09/2025 Approved by Steering Committee 15/09/2025 PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 3 / 28 TABLE OF CONTENTS 1 INTRODUCTION ......................................................................................................................................... 4 2 DESIGN OVERVIEW .................................................................................................................................. 5 2.1 DESIGN REQUIREMENTS..................................................................................................................................... 5 2.2 MAGNET DESIGN ................................................................................................................................................. 5 2.3 MECHANICAL DESIGN ......................................................................................................................................... 7 3 MAGNETIC MEASUREMENTS ............................................................................................................... 8 3.1 INITIAL MEASUREMENTS ................................................................................................................................... 8 3.1.1 Centre-plane Fields .................................................................................................................................. 9 3.1.2 Integrated Fields .................................................................................................................................... 12 3.2 MECHANICAL SHIMMING ................................................................................................................................. 16 3.3 TRIM COIL TUNING ........................................................................................................................................... 20 3.4 THERMAL STABILITY ....................................................................................................................................... 24 4 CONCLUSION ........................................................................................................................................... 26 5 REFERENCES ............................................................................................................................................ 27 6 ANNEX: GLOSSARY ................................................................................................................................ 28 PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 4 / 28 Executive summary The Hybrid Electromagnet-Permanent magnet Tuneable Optics (HEPTO) prototype has been designed and built in IFAST Work Package 11.3. The prototype is a permanent magnet device designed as a direct replacement for the electromagnet dipole-quadrupole combined function magnets designed for Diamond-II. Use of permanent magnets would facilitate a reduction in operating costs and carbon footprint. The magnet design has been completed in order to meet the same magnetic field requirements in the same space envelope as the electromagnet. Unique features include mechanical shimming mechanisms, trim coils for field tuning and thermal shunts for improved temperature stability. The target integrated gradient strength and field homogeneity were achieved using the mechanical shimming to adjust the field. The trim fields provide tuning of the field but are not as efficient as was originally predicted in the design. The relative change in field strength with temperature has been reduced through the use of thermal shunt material. Future work will focus on improving the trim coil and thermal shunt designs. Work on increasing the technology readiness level will facilitate applying tuneable permanent magnet technology to future accelerators. 1 Introduction The focus of IFAST Work Package 11 is the development of sustainable accelerator technologies to reduce the energy consumption and running costs of accelerator facilities. The Hybrid Electromagnet-Permanent magnet Tuneable Optics (HEPTO) prototype combined function dipole-quadrupole (DQ) magnet has been designed and built as the deliverable of IFAST Task 11.3. The design of the HEPTO magnet aims to replace resistive electromagnetic coils with permanent magnets as the main source of the field in the DQ magnets for the Diamond-II storage ring upgrade in order to reduce the energy consumption of these magnets from 2.3 kW per magnet to a peak power consumption of 25 W. These magnets require independent tuning of the dipole and gradient fields for commissioning purposes. Hence, the hybrid design includes air-cooled trim coils for the field tuning. The scope of this deliverable was to build the prototype magnet, and to demonstrate that it could meet the same magnetic field requirements as the equivalent electromagnet that has been designed for Diamond-II. Magnetic measurements of the built prototype have indicated that the specified integrated field strength and homogeneity have been achieved. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 5 / 28 2 Design Overview 2.1 DESIGN REQUIREMENTS The Diamond-II upgrade involves replacing the current double-bend achromat lattice with a multibend achromat in order to reduce the emittance of the electron beam and hence increase the brightness and coherence of the synchrotron radiation produced by the facility [1]. As part of this upgrade, the lattice requires 48 DQ magnets which act to simultaneously bend and focus the electron beam. A water-cooled electromagnet design has been completed as part of the Diamond-II technical design review. The nominal power dissipated by each of these magnets from electrical resistance alone is 2.3 kW. Water cooling circuits will increase the actual power consumption of the magnets. The aim of the HEPTO design is to achieve the same magnetic field parameters is the same physical space envelope, with a much reduced overall power consumption. This would reduce the running costs, and environmental impact of running the accelerator. The magnetic field requirements are summarised in Table 1. Parameter Value Unit Central dipole field -0.6951 T Central gradient 33.179 T/m Effective dipole magnetic length 870 mm Effective gradient magnetic length 850 mm Integrated dipole field -0.6047 T.m Integrated gradient 28.1857 T Bending radius 16.795 m Good field region (GFR) radius 7 mm Integrated field quality ΔB/B within GFR 5E-4 Integrated multipoles <1E-3 Dipole tuning range ±2.5 % Gradient tuning range ±2.5 % Temperature stability (3°C range) 0.01 % Table 1: Summary of magnetic field requirements. 2.2 MAGNET DESIGN The design of the HEPTO DQ prototype is based on a single sided electromagnet dipolequadrupole [2]. The design allows a combined function dipole-quadrupole field with high gradient to be achieved whilst being more efficient than an offset quadrupole design. Figure 1 shows an image of the Opera 3D [3] model of the design, with the key aspects labelled. The different colours represent PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 6 / 28 different materials and parts of the design. The permanent magnets (blue in Figure 1) are the primary sources of the magnetic field. By using permanent magnets instead of electromagnetic coils to generate the field, the power consumption of the magnet can be greatly reduced. The nominal power requirements of the equivalent electromagnet DQs designed for Diamond II is 2.3 kW per magnet [1]. The permanent magnet blocks are magnetised as shown by the thick black arrows in Figure 1 to create the required dipole-quadrupole field. The magnetic blocks used in the design were originally purchased for building the modulator undulators for the Compact Linear Accelerator for Research Applications (CLARA) at Daresbury Laboratory. These undulators are no longer set to be built in the near future, so the permanent magnet blocks were repurposed for building of the HEPTO prototype. The material of all the magnet blocks is neodymium iron boron (NdFeB) grade 45M6 with a remanent field of 1.3 T ±1%. The different magnet types (A, B, F) refer to blocks of different dimensions. Figure 1: Labelled image of the Opera 3D model of the HEPTO prototype. Thick black arrows represent the direction of magnetisation of the permanent magnet blocks. The yoke and poles (green in Figure 1) are made from Armco Iron soft magnetic steel so that the flux from the permanent magnets will flow through the yoke. The main and auxiliary poles are shaped so as to produce the desired dipole and quadrupole fields in the good field region whilst suppressing higher field harmonics. The pole tips are curved so that the dipole field on the beam axis is kept constant along the length of the magnet. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 7 / 28 Thermal shunts (purple in Figure 1) have been included in the design to improve the stability of the design with respect to changes in environment temperature. These shunts are made from a Fe-Ni alloy with a negative temperature coefficient [4]. At a given temperature, a portion of the flux at the surface of the permanent magnets is diverted through the shunt, rather than through the magnetic yoke to the poles and across the bore. As the temperature increases, the remanent field of the permanent magnet decreases, but the saturation polarisation of the shunt also decreases. Therefore, at higher temperatures, less flux is shunted by the Fe-Ni alloy. If the thickness of the shunt is chosen correctly, the temperature effects can be made to balance so that a small change in temperature does not affect the magnitude of the dipole or quadrupole fields in the good field region. A target temperature stability of the field of ±0.01% over a 3°C temperature range (around a nominal temperature of 20°C) has been set because this level of stability is comparable to what can be achieved within power supply fluctuations of typical electromagnets [5]. Spare shunt material available in 0.5 mm thick sheets has been purchased from Soleil for the building of the HEPTO prototype. The magnetic model predicts an achievable temperature stability using the available material of -0.056 %/°C. The cost of purchasing extra thermal shunt material to further improve the thermal stability was prohibitive for this prototype. Trim coils (red in Figure 1) have been included in the design so that the field under normal operation can be fine-tuned. This will allow the nominal fields to be reached from permanent magnet blocks of finite size and magnetisation error. The coils must also be capable of being used to sweep the dipole and quadrupole fields independently over a range ±2.5% of the nominal values for use during commissioning. The coils are designed to be air-cooled to reduce the infrastructure and power requirements of the design compared to water-cooled coils. 2.3 MECHANICAL DESIGN The mechanical design of the prototype has been completed by Kyma. Tuneability of permanent magnet devices is generally limited. Therefore, the strength and field quality of a built device is generally fixed. The mechanical design of HEPTO includes functionality to mechanically shim the positions of the main and auxiliary poles in order to adjust the field strength and homogeneity of the built magnet. This allows magnetisation and manufacturing tolerances to be loosened in the design, and accounted for in the built magnet. A photograph of the built magnet on the measurement bench at Daresbury Laboratory is shown in Figure 2. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 8 / 28 Figure 2: Photograph of the built HEPTO prototype magnet. 3 Magnetic Measurements 3.1 INITIAL MEASUREMENTS The first set of magnetic measurements focussed on measuring the field strength and homogeneity of the prototype magnet before any mechanical shimming was applied. Measurements were made using a Senis type H 3-axis Hall sensor and a 3MH3 Teslameter [6] to calculate the flux density vectors at a set of discrete points. The spatial resolution of the probe, as stated by the manufacturer, is 30 × 5 × 30 μm3 for the 𝐵𝑦 (vertical) field component and 150 × 10 × 150 μm3 for the 𝐵𝑥 (transverse) and 𝐵z (longitudinal) field components. The planar Hall effect is suppressed through the application of the spinning current technique. The 3MH3 Teslameter provides an accuracy of up to 0.05% and a precision of 0.1 mT. The sensor was translated using a precision 3-axis motion system. The probe was mounted in a custom-designed 3D-printed holder. This holder was bolted to an extruded aluminium arm, which was connected to the motion stages. This motion system achieves 2 μm precision in the transverse (x) and vertical (y) planes and 5 μm precision in the axial plane (z) through the use of stepper motors and absolute encoders. The achieved PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 9 / 28 precisions are defined by an allowable tolerance set in the motion control software between the set and measured absolute position of the stages. The software polls the read position of the stages after sending a movement command. If the read position is not within the given precision set by the tolerance within a set time, a time-out error is raised. The set precisions have been found to be practical limits which allow large 3D scans to be performed without time-out errors being regularly raised. A granite bench provided vibration isolation to the probe. The Hall sensor was connected to the Teslameter through a CaH cable. The fields measured by the Teslameter were recorded by the control PC through a USB connection. Every point measurement of the field was recorded as an average of 100 samples recorded at a sample rate of 300 Hz. The HEPTO magnet was mounted on a granite bench, independent of the probe bench. The magnet was aligned parallel to the Hall-probe bench using a laser tracker to an accuracy of ±0.075 mm over the full length of the magnet relative to all three axes of the Hall probe bench. 3.1.1 Centre-plane Fields The first set of measurements focused on the central field qualities. Figure 3 shows a plot of the vertical (By) field component against the transverse (x) coordinate inside the 7 mm radius GFR, with the centre of the GFR (x = 0 mm) being set at the point where the field was equal to the nominal dipole field of -0.6951 T. The gradient measured by a linear fit to repeat plots was 32.972 ± 0.004 T/m. The gradient predicted by the Opera model was 33.179 T/m. The measured gradient was therefore 0.62% lower than the target value. This discrepancy may be due to the material properties of the magnetic steel, permanent magnet blocks and thermal shunts being slightly different to the modelled properties, or to small machining and assembly tolerances. Figure 3: Plot of measured By field component vs transverse coordinate. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 16 / 28 Figure 10: Plot of integrated field homogeneity ΔB/B determined by reconstruction from integrated harmonic and BEM scans. Table 3 summarises the main integrated field components calculated by the harmonic analysis and BEM and compares them to the model. The measured integrated gradient is less than the target value, and the homogeneity exceeds the target. Therefore, the mechanical shimming is intended to increase the gradient and to improve the homogeneity. Model Integrated gradient / T Dipole effective length / m Gradient effective length / m Integrated ΔB/B Design 28.1857 0.870 0.850 < 5E-4 Harmonic analysis 28.070 ± 0.002 0.8726 ± 0.0001 0.8524 ± 0.0001 (8.2 ± 0.5)E-4 BEM 28.096 0.8726 0.8515 8.6E-4 Table 3: Summary of integrated field parameters of the pre-shimmed magnet. 3.2 MECHANICAL SHIMMING The mechanical design of the magnet accounts for expected material, machining and assembly tolerances by allowing small movement of the magnet poles to adjust the field. Given the measurements of the magnet, it is apparent that the integrated gradient was lower than the design value. The magnet can be mechanically shimmed to increase the gradient and to improve the homogeneity. The magnet was shimmed iteratively by adjusting the vertical positions of the top main and auxiliary poles relative to the bottom main pole and measuring the integrated gradient strength and PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 17 / 28 homogeneity. The goal of the shimming was to achieve an integrated gradient within 0.1% of the nominal value, and the integrated homogeneity within the specification of 5E-4. Figure 11 shows a plot of how the measured error in the integrated gradient relative to the target integrated gradient changed as a function of the mechanical shimming iteration. Before shimming, the measured gradient was 0.42% lower than the target value. By reducing the gap between the auxiliary poles in shimming iterations 1 to 3, the strength of the gradient was gradually increased, and the homogeneity at the low field end of the magnet improved. For shimming iterations 4 to 8 the gap between the main poles and the auxiliary poles was adjusted to maintain the homogeneity within the good field region, as well as minimising the error in the gradient. After 8 iterations, the measured integrated gradient was 28.196 ± 0.001 T, which is within 0.03% of the target integrated gradient. Therefore, the integrated gradient was brought within the target by the mechanical shimming. Figure 11: Plot of integrated gradient error as a function of shimming iteration. The shaded region highlights the target difference from the nominal integrated gradient of ±0.1%. The maximum absolute integrated field homogeneity as a function of the shimming iteration is shown in Figure 12. Before shimming the maximum homogeneity was 8.2E-4. After 8 iterations, the homogeneity was reduced to 2.7E-4, which is within the target value of 5E-4. Figure 13 shows a plot of the integrated homogeneity through the magnet as measured by integrating the harmonics along the reference trajectory before and after mechanical shimming. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 18 / 28 Figure 12: Plot of maximum absolute integrated field homogeneity as a function of shimming iteration. The dashed line represents the target homogeneity of 5E-4. Figure 13: Integrated field homogeneity ΔB/B before and after mechanical shimming. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 19 / 28 Figure 14 and Figure 15 show the multipole errors in the integrated real and skew field components respectively, compared to the design field components, for the magnet before and after shimming. The main differences between the pre-and and post-shimmed magnet harmonics are in the real and skew sextupole (n=3) and octupole (n=4). The shimming has resulted in a change in the normalised real skew from (0.021 ± 0.001)% to -0.018%. This is within the target value of 0.1% after shimming. Figure 14: Absolute errors in integrated real field components for different shimming iterations. Figure 15: Absolute errors in integrated skew field components for different shimming iterations. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 20 / 28 After the shimming iterations, the measured integrated real dipole and quadrupole were -0.6066 T.m and 28.196 T respectively. Through shimming, the measured integrated gradient was within 0.1% of the target, and the measured homogeneity was within the specification of 5E-4. Therefore, the mechanical shimming mechanism was extremely effective in adjusting the magnet to meet the specification. Table 4 summarises the main integrated field components before and after mechanical shimming. Dipole / T Gradient / T/m Integrated dipole / T.m Integrated Gradient / T Maximum ΔInt.B/Int.B Design -0.6951 33.1791 -0.6947 28.1857 <5E-4 Preshimming -0.69517 ± 0.00007 32.901 ± 0.005 0.6067 ± 0.003 28.070 ± 0.002 (8.2 ± 0.5)E-4 Postshimming -0.6951 ± 0.0001 33.083 ± 0.008 0.6066 ± 0.0001 28.196 ± 0.001 (2.9 ± 0.1)E-4 Table 4: Summary of main field components before and after mechanical shimming. 3.3 TRIM COIL TUNING The magnet also contains air-cooled trim coils which are required to allow independent tuning of both the dipole and quadrupole fields in the range ±2.5% in-situ for beam emittance measurements. The coils had been designed with a maximum current of 5 A to allow for air-cooling of these coils. Aircooled coils provide a significant reduction in required infrastructure and operating costs compared to water cooled coils. The coils were powered to different combinations of current in the range ±5 A, and a harmonic scan about the magnetic centre in the central plane used to find the changes in the real dipole, quadrupole and sextupole fields. Figure 16 and Figure 17 show the percentage change in the dipole and quadrupole field components respectively with different combinations of currents in the trim coils. Figure 18 shows the absolute changes in the sextupole field harmonic with different trim coil currents. It is of note that the sextupole field component is nearly independent of the main coil current. Therefore, the auxiliary coil current can be used to adjust the integrated sextupole component of the magnet. The main coil can then be used to adjust either the dipole or quadrupole strength. This may be useful in the operation of the machine to dynamically adjust the integrated sextupole field. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 21 / 28 Figure 16: Contour plot showing percentage change in central dipole field with trim coil currents. Figure 17: Contour plot showing percentage change in quadrupole field with trim coil currents. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 22 / 28 Figure 18: Contour plot showing sextupole field component measured in mT on the 7 mm GFR with trim coil currents. A linear fit was used to predict the trim coil currents required to achieve a given combination of percentage changes in the dipole and quadrupole field. Table 5 summarises the currents required in each of the corrector coils to achieve the nominal fields in the two-dimensional plane and to achieve the desired tuning range for emittance measurements. It can be seen from the table that the predicted currents in the auxiliary coil exceed the current limit of 5 A required for air-cooling. The initial magnetic design had predicted that currents lower than 5 A would be required in both the main and auxiliary coils to achieve the tuning range. However, when the magnetic models were re-investigated to identify discrepancies, an error in the magnetic models was discovered. When this error was corrected, the predicted currents required to achieve the tuning range were in good agreement with those measured, as shown in Table 5. The corrected Opera model predicted that the main coils would be able to achieve the desired tuning range within the 5 A limit, but the auxiliary coils would require a current exceeding 5 A. For future work, the auxiliary coils would require more turns in order to provide a larger tuning range within the current limit. There is sufficient space in the current design to accommodate larger coils. Change in dipole from nominal / % Change in quadrupole from nominal / % Required main coil current measured (predicted) / A Required auxiliary coil current measured (predicted) / A -2.5 0 -2.55 (-2.46) -11.42 (-15.41) +2.5 0 2.55 (2.46) 11.42 (15.41) 0 -2.5 -3.91 (-4.45) 11.44 (15.12) 0 +2.5 3.91 (4.45) -11.44 (-15.12) Table 5: Summary of coil currents required to achieve desired tuning range. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 23 / 28 The maximum independent tuning ranges of the dipole and quadrupole fields with the current coil design can be determined by plotting the required coil currents against the tuning range, as shown for the dipole and quadrupole in Figure 19 and Figure 20 respectively. For independent tuning of the dipole field, a maximum tuning range of ±1.1% is achievable with the current coil design. For independent tuning of the quadrupole field, a tuning range of ±1.1% is also achievable. Therefore, the current design could still be used to vary the dipole and quadrupole fields independently, allowing for some emittance measurements to be performed. Figure 19: Required trim coil currents as function of dipole tuning range for fixed quadrupole. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 24 / 28 Figure 20: Required trim coil currents as function of quadrupole tuning range for fixed dipole. The measurements of the tuning range using the coils highlight that the tuning of the field using coils is inefficient because the permanent magnet blocks effectively act as air gaps in the magnetic circuit. Therefore, the achievable field tuning range will always be limited. For the current design, the required tuning range of 2.5% is unachievable. 3.4 THERMAL STABILITY The design of the magnet includes Fe-Ni thermal shunts to minimise the change in the field strength in the bore of the magnet with ambient temperature fluctuations. To measure the thermal stability of the magnet, the Senis type H probe was replaced by a type C probe and 3MH6 Teslameter [9]. The type C probe is capable of also recording the measured temperature of the probe, unlike the type H. The type H was used for the majority of measurements due to its smaller physical size, allowing measurements of the fields at all points within the magnet GFR. The type C probe was mounted in the magnetic centre of the magnet. The dipole field and probe temperature were measured whilst the laboratory climate control system was used to vary the ambient temperature between 19°C and 21°C. Figure 21 shows the relative change in the measured field relative to the field measured at 20°C as a function of temperature and is compared to the expected change from the Opera model. By plotting a linear fit to all the measured points, the temperature stability was determined to be (0.173 ± 0.001) %/°C. From the Opera mode, the temperature stability was predicted to be -0.056%/°C. The absolute change in field strength with temperature is larger for the measured magnet than was predicted. With no thermal shunts, the temperature stability was predicted to be -0.209%/°C. Therefore, the presence of the thermal shunts does reduce the change in field strength with temperature, compared to the magnet with no thermal shunts. PROTOTYPE ADJUSTABLE PM QUADRUPOLE AND COMBINED FUNCTION MAGNETS Deliverable: D11.3 Date: 15/09/2025 Grant Agreement 101004730 PUBLIC 25 / 28 Figure 21: Measured relative change in dipole field with ambient room temperature relative to the field measured at 20°C. The sign of the measured temperature stability is positive. This shows that the field strength increases with increasing temperature. This suggests that the thickness of the thermal shunt sections is larger than the optimum value for minimising the change in field with temperature. If fewer layers of thermal shunt material were used, the gradient in field change would be reduced, and the measured field strength would be increased. The most likely cause for the discrepancy between the measured and predicted temperature stability is in the material behaviour of the thermal shunts. The exact BH material data of the thermal shunt material were not available. Instead, known data from a similar batch of material were used in the models. This result highlights the need to perform measurements of the BH data for the exact material to be used in building magnets and over the expected operational temperature range. This data is crucial for the accurate modelling of the magnets. Another potential cause of discrepancy is in the temperature measurement. The recorded temperature was measured by the Hall probe electronics. This was assumed to be the ambient air temperature of the measurement environment. However, as the HEPTO magnet structure is a large volume of material, the actual temperature of the permanent magnet blocks and thermal shunt materials may change at a slower rate than the ambient air temperature. Therefore, measurements of the air temperature may not be fully indicative of the actual magnet temperature.