Method for determining an arrangement of at least one magnet and arrangement of at least one magnet

Abstract

A method for determining an arrangement (26) of at least one magnet (20) is provided, the method comprising providing at least one magnet position (21) within a magnetic field region (22), providing at least one desired magnetic field parameter for at least one fixed position (23) within the magnetic field region (22), calculating the magnetic field at the at least one fixed position (23) for the case that at one of the at least one magnet position (21) one magnet (20) is arranged, and numerically determining the orientation of the magnet (20) in order to approximate the at least one desired magnetic field parameter for the at least one fixed position (23). Furthermore, an arrangement (26) of at least one magnet (20), a computer program product and a data processing syste, (27) are provided.

Description

[0001] P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0002] 1

[0003] Description

[0004] Method for determining an arrangement of at least one magnet and arrangement of at least one magnet

[0005] A method for determining an arrangement of at least one magnet, an arrangement of at least one magnet, a computer program product and a data processing system are provided.

[0006] By arranging magnets in a particular way, a magnetic field with desired properties can be created. For many applications it is required to obtain a magnetic field with predefined parameters at fixed positions . This is for example the case for ion traps . The ions are arranged at fixed positions and at these positions it is desired to have a magnetic field with predefined properties as the amplitude, the derivative of the amplitude or the direction. Moreover, the space where magnets can be positioned to create the magnetic field can be limited. Thus, several conditions are desired to be fulfilled.

[0007] It is an obj ective to provide an efficient method for determining an arrangement of at least one magnet .

[0008] This obj ective is achieved with the independent claim.

[0009] Further embodiments are the subj ect of dependent claims .

[0010] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the method comprises providing at least one magnet position within a magnetic field region. The magnetic field region can be a two-dimensional area or a three-dimensional volume . Within the magnetic field region, a magnetic field can be present .P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0011] The magnet position can be a point within the magnetic field region. The magnet position can be arbitrarily arranged. The magnet position can be arranged at a predefined position. The magnet position can be a position where a magnet is to be arranged. The method can comprise providing a plurality of magnet positions . The at least one magnet position can be provided or chosen by a user .

[0012] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the method comprises providing at least one desired magnetic field parameter for at least one fixed position within the magnetic field region. The desired magnetic field parameter can be any parameter of a magnetic field at the at least one fixed position. The desired magnetic field parameter can be a parameter that is desired for a particular application. The at least one fixed position is arranged within the magnetic field region. It is also possible that more than one desired magnetic field parameter is provided for one fixed position. It is also possible that for several fixed positions, one or more than one desired magnetic field parameter is provided. The desired magnetic field parameter and the at least one fixed position can be provided or chosen by a user .

[0013] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the method comprises calculating the magnetic field at the at least one fixed position for the case that at one of the at least one magnet position one magnet is arranged. The magnetic field at the at least one fixed position can be calculated analytically. For calculating the magnetic field at the at least one fixed position it can be assumed that a magnet or an ideal magnetic dipole is arranged at the magnet position.P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0014] 3

[0015] The ideal magnetic dipole can be assumed to be point-like . If more than one magnet position is provided, in this step the magnetic field at the fixed position is calculated for the case that at one of the magnet positions one magnet or one ideal magnetic dipole is arranged. This can mean, that the magnetic field at the at least one fixed position is calculated for the case that only one magnet is arranged within the magnetic field region. In other words, for the calculation of the magnetic field at the at least one fixed position only one magnet is considered. This magnet can be assumed to be an ideal magnetic dipole . The magnetic field at the at least one fixed position can be calculated by an algorithm.

[0016] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the method comprises numerically determining the orientation of the magnet in order to approximate the at least one desired magnetic field parameter for the at least one fixed position. Numerically determining the orientation of the magnet can be carried out by an algorithm. For numerically determining the orientation of the magnet an optimizer algorithm can be employed. The optimizer algorithm can be a gradient descent algorithm. Determining the orientation of the magnet can comprise determining the direction along which the magnetic axis of the magnet is oriented. Numerically determining the orientation of the magnet can comprise calculating the magnetic field at the at least one fixed position for different orientations of the magnet being arranged at the magnet position. Numerically determining the orientation of the magnet can comprise rotating the magnet until the at least one desired magnetic field parameter is approximated for the at least one fixed position. Also for numericallyP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0017] determining the orientation of the magnet, it can be assumed that the magnet is an ideal magnetic dipole that can be point-like .

[0018] The orientation of the at least one magnet can be the only parameter of the at least one magnet that is determined in order to approximate the at least one desired magnetic field parameter for the at least one fixed position. If more than one magnet position is provided, the orientation of the magnets can be the only parameter of the magnets that is determined in order to approximate the at least one desired magnetic field parameter for the at least one fixed position.

[0019] The optimization can aim to approximate the at least one desired magnetic field parameter for the at least one fixed position. This can mean, that the optimization is carried out in such a way that the at least one desired magnetic field parameter is fulfilled for the at least one fixed position as good as possible . That the desired magnetic field parameter is fulfilled as good as possible can mean that the value of the magnetic field parameter at the at least one fixed position is as close to the desired magnetic field parameter as possible . As good as possible and as close as possible refer to the ability of the algorithm employed herein. Thus, approximating the at least one desired magnetic field parameter for the at least one fixed position can mean that the value of the magnetic field parameter at the at least one fixed position is as close to the desired magnetic field parameter as possible . This can be achieved by determining the orientation of the magnet . In other words, the magnetic field at the at least one fixed position can be calculated for different orientations of the magnet being arranged at the magnet position until the value of the magnetic fieldP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0020] parameter at the at least one fixed position is as close to the desired magnetic field parameter as possible .

[0021] The at least one magnet with an orientation as determined by the method described herein can create a magnetic field with the feature that the magnetic field has a magnetic field parameter at the at least one fixed position. The magnetic field parameter at the at least one fixed position is as close as possible to the desired magnetic field parameter . As close as possible in this context means as close as possible in the framework of the employed algorithm. This can mean, the algorithm can determine an optimum orientation of the at least one magnet for approximating the desired magnetic field parameter for the at least one fixed position. However, this orientation is not necessarily an overall optimum orientation. This can mean, that by other methods, other optimum orientations might be determined.

[0022] The method can further comprise providing the orientation of the magnet as determined by the method for determining an arrangement of at least one magnet . Thus, the algorithm that is configured to carry out the method for determining an arrangement of at least one magnet can be configured to provide an output that comprises the information which orientation of the magnet was determined. Determining an arrangement of at least one magnet can therefore mean, that the orientation of at least one magnet being arranged at the magnet position is determined. The orientation of the at least one magnet can be determined in such a way that the at least one desired magnetic field parameter is approximated for the at least one fixed position.P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0023] 6

[0024] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the method comprises providing at least one magnet position within a magnetic field region, providing at least one desired magnetic field parameter for at least one fixed position within the magnetic field region, calculating the magnetic field at the at least one fixed position for the case that at one of the at least one magnet position one magnet is arranged, and numerically determining the orientation of the magnet in order to approximate the at least one desired magnetic field parameter for the at least one fixed position.

[0025] The method for determining an arrangement of at least one magnet has the advantage that for different setups and for different desired magnetic field parameters an arrangement of at least one magnet can be determined that leads to a magnetic field with desired properties . It is thus possible to create a magnetic field that has desired properties at one or more than one fixed position.

[0026] For many applications it is desired to have particular magnetic field properties at specific positions . One example are ion traps . In ion traps, the ions are located at fixed positions and for these positions particular magnetic field properties are required. For example, a particular amplitude, derivative and / or direction of the magnetic field are required at the positions of the ions . Furthermore, geometric constraints might be present as the ion trap being for example a two-dimensional structure . It is also possible that other components within the ion trap lead to geometric constraints for the arrangement of magnets . Other applications requiring particular magnetic field propertiesP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0027] at specific positions are for example magnetic resonance imaging and magnetic bearings .

[0028] The method described herein enables to automatically design an arrangement of at least one magnet, where the at least one magnet creates a magnetic field with one or more than one desired magnetic field parameter for at least one fixed position. It is possible to predefine several different desired magnetic field parameters for several fixed positions . This means, a large number of constraints is to be considered by the algorithm providing the arrangement of the at least one magnet . Considering this large number of constraints is made possible by analytically calculating the magnetic field created by at least one ideal magnetic dipole arranged at the at least one magnet position and by numerically approximating an optimum orientation of the at least one ideal magnetic dipole . With this, it is not required to find an analytical optimum. This reduces the computational power required to carry out the method described herein. In this way, an arrangement of at least one magnet can be determined in an efficient way.

[0029] According to at least one embodiment of the method for determining an arrangement of at least one magnet, at the same time as determining the orientation of the magnet or after determining the orientation of the magnet, the orientation of at least one further magnet is determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position, wherein the further magnet is arranged at a further magnet position within the magnetic field region. All features that are disclosed for the magnet are also disclosed for the further magnet . All features that are disclosed for theP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0030] magnet position are also disclosed for the further magnet position. The orientation of the at least one further magnet can be determined numerically in the same way as described for the magnet . This means, at the same time as determining the orientation of the magnet or after determining the orientation of the magnet, the orientation of at least one further magnet is determined in the same way. The orientations of the magnet and the further magnet can thus be determined at the same time . This is advantageous for the case that the magnet and the further magnet have the same orientation. It is also possible that after determining the orientation of the magnet, the orientation of more than one or a plurality of further magnets is determined after one another . In this case, each further magnet is arranged at a further magnet position within the magnetic field region.

[0031] The method described herein can be carried out for each magnet position. The method described herein can further be carried out for each further magnet position. Thus, the method described herein can be carried out until for each position within the magnetic field region where a magnet is to be arranged, the orientation of the respective magnet is determined .

[0032] The at least one magnet with an orientation as determined by the method described herein and the at least one further magnet with an orientation as determined by the method described herein can together create a magnetic field with the feature that the magnetic field has a magnetic field parameter at the at least one fixed position, wherein the magnetic field parameter is approximately equal to the desired magnetic field parameter . This is also possible for several desired magnetic field parameters at several fixedP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0033] positions . In this way, the method described herein enables to design a magnetic field with several constraints .

[0034] Employing more than one magnet for creating a magnetic field at the fixed position has the advantage that in many cases a more accurate approximation of the desired magnetic field parameter is possible .

[0035] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the magnet and the further magnet form a pair of magnets . It is also possible that the orientation of more than one pair of magnets is determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position. Thus, several pairs of magnets can be employed to create a magnetic field at the at least one fixed position. Employing several pairs of magnets has the advantage that in many cases a more accurate approximation of the desired magnetic field parameter is possible . The orientations of the pairs of magnets can be determined after one another .

[0036] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the magnet and the further magnet have the same orientation. This means, the magnets forming a pair of magnets have the same orientation. It is possible that for each pair of magnets, the two magnets forming the pair of magnets have the same orientation. This simplifies the arrangement of the magnets .

[0037] According to at least one embodiment of the method for determining an arrangement of at least one magnet, after determining the orientation of the further magnet, the orientation of at least one further pair of magnets isP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0038] determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position, wherein each magnet of the further pair of magnets is arranged at one further magnet position within the magnetic field region, wherein at least three further magnet positions are located within the magnetic field region. All features that are disclosed for the pair of magnets are also disclosed for the further pair of magnets . The orientation of the further pair of magnets is determined in the same way as described for the magnet . Employing several pairs of magnets has the advantage that in many cases a more accurate approximation of the desired magnetic field parameter is possible .

[0039] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the magnetic field at the at least one fixed position is calculated for the case that the magnet is an ideal magnetic dipole . This can mean, that for the calculation of the magnetic field at the at least one fixed position it is assumed that an ideal magnetic dipole is arranged at the magnet position. The ideal magnetic dipole can be a point like ideal magnetic dipole . By assuming that an ideal magnetic dipole is arranged at the magnet position, the magnetic field at the fixed position can be calculated analytically .

[0040] According to at least one embodiment of the method for determining an arrangement of at least one magnet, an optimizer algorithm is employed to determine the orientation of the magnet in order to approximate the at least one desired magnetic field parameter for the at least one fixed position. The optimizer algorithm can be a gradient descentP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0041] 11

[0042] algorithm. In this way, the optimization can be carried out in an efficient way.

[0043] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the magnetic field parameter is one of : an amplitude of a magnetic field, a derivative of the amplitude of a magnetic field, a direction of a magnetic field, a derivative of the direction of a magnetic field, a component of a magnetic field, any function of a component of a magnetic field. This can mean, that any parameter of a magnetic field at the at least one fixed position can be a desired magnetic field parameter . This enables to automatically design magnetic fields with desired properties at fixed positions which is required for a wide range of applications .

[0044] According to at least one embodiment of the method for determining an arrangement of at least one magnet, the magnetic field region is a two-dimensional area or a three-dimensional volume . This means, it is possible to determine two-dimensional and three-dimensional arrangements of magnets .

[0045] Furthermore, an arrangement of at least one magnet is provided. The arrangement comprises the magnet, wherein the magnet is arranged at a magnet position within a magnetic field region and has an orientation as determined by the method for determining an arrangement of at least one magnet described herein. Thus, all features that are disclosed for the method for determining an arrangement of at least one magnet are also disclosed for the arrangement of at least one magnet . In other words, the magnet is oriented in such a way that the at least one desired magnetic field parameter isP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0046] 12

[0047] approximated for the at least one fixed position as determined by the method for determining an arrangement of at least one magnet described herein. The magnet can be a permanent magnet or an electromagnet . If the magnet is an electromagnet, the electromagnet can comprise a coil .

[0048] It is also possible that the arrangement comprises at least two magnets, wherein the magnets are each arranged at one magnet position within the magnetic field region and have an orientation as determined by the method for determining an arrangement of at least one magnet described herein. It is also possible that the arrangement comprises at least one pair of magnets, wherein the magnets are each arranged at one magnet position within the magnetic field region and have an orientation as determined by the method for determining an arrangement of at least one magnet described herein. The magnets of the pair of magnets can have the same orientation. It is also possible that the arrangement comprises a plurality of pairs of magnets, wherein for each pair the magnets are each arranged at one magnet position within the magnetic field region and have an orientation as determined by the method for determining an arrangement of at least one magnet described herein. For each pair of magnets, the two magnets can have the same orientation.

[0049] Furthermore, a computer program product is provided. The computer program product comprises instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method for determining an arrangement of at least one magnet described herein. Thus, all features disclosed for the method for determining an arrangement of at least one magnet are also disclosed for the computer program product .P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0050] Furthermore, a data processing system is provided. The data processing system is configured to carry out the steps of the method for determining an arrangement of at least one magnet described herein. Thus, all features disclosed for the method for determining an arrangement of at least one magnet are also disclosed for the data processing system.

[0051] The following description of figures may further illustrate and explain exemplary embodiments . Components that are functionally identical or have an identical effect are denoted by identical references . Identical or effectively identical components might be described only with respect to the figures where they occur first . Their description is not necessarily repeated in successive figures .

[0052] With figure 1 an exemplary embodiment of the method for determining an arrangement of at least one magnet is described .

[0053] With figures 2, 3 and 4 another exemplary embodiment of the method for determining an arrangement of at least one magnet is described.

[0054] Figure 5 shows an exemplary embodiment of the arrangement of at least one magnet .

[0055] Figure 6 shows an exemplary embodiment of the data processing system.

[0056] With figure 1 an exemplary embodiment of the method for determining an arrangement 26 of at least one magnet 20 is described. In a first step SI of the method at least oneP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0057] 14

[0058] magnet position 21 within a magnetic field region 22 is provided. In a second step S2 of the method at least one desired magnetic field parameter is provided for at least one fixed position 23 within the magnetic field region 22. In a third step S3 of the method the magnetic field is calculated at the at least one fixed position 23 for the case that at one of the at least one magnet position 21 one magnet 20 is arranged. The magnetic field at the at least one fixed position 23 can be calculated for the case that the magnet 20 is an ideal magnetic dipole . In a fourth step S4 of the method the orientation of the magnet 20 is determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position 23. An optimizer algorithm can be employed to determine the orientation of the magnet 20 in order to approximate the at least one desired magnetic field parameter for the at least one fixed position 23.

[0059] The magnetic field parameter can be one of : an amplitude of a magnetic field, a derivative of the amplitude of a magnetic field, a direction of a magnetic field, a derivative of the direction of a magnetic field, a component of a magnetic field, any function of a component of a magnetic field. The magnetic field region 22 can be a two-dimensional area or a three-dimensional volume .

[0060] With figures 2, 3 and 4 another exemplary embodiment of the method for determining an arrangement 26 of at least one magnet 20 is described. Figure 2 shows a magnetic field region 22 with four fixed positions 23 as an example .

[0061] Furthermore, one magnet position 21 and three further magnet positions 25 are arranged within the magnetic field regionP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0062] 15

[0063] 22. For at least one of the fixed positions 23 at least one desired magnetic field parameter is provided.

[0064] Figure 3 shows that in a next step of the method the orientation of a magnet 20 being arranged at the magnet position 21 is numerically determined in order to approximate the at least one desired magnetic field parameter for the at least one fixed position 23. This is achieved by calculating the magnetic field at the at least one fixed position 23 for the case that the magnet 20 is arranged at the magnet position 21 as shown in figure 3. The magnetic field is calculated for different orientations of the magnet 20. In figure 3, as an example one orientation of the magnet 20 is shown .

[0065] Figure 4 shows that the orientation of a further magnet 24 being arranged at a further magnet position 25 is numerically determined in order to approximate the at least one desired magnetic field parameter for the at least one fixed position 23. The orientation of the further magnet 24 is determined in the same way as for the magnet 20. The orientation of the further magnet 24 can be determined at the same time as the orientation of the magnet 20 or after determining the orientation of the magnet 20. Figure 4 shows the example that the magnet 20 and the further magnet 24 form a pair of magnets that have the same orientation. In this case the orientation of the magnet 20 and the further magnet 24 is determined at the same time . It is however also possible that the magnet 20 and the further magnet 24 have different orientations .

[0066] Figure 5 shows an exemplary embodiment of the arrangement 26 of at least one magnet 20. Moreover, another exemplaryP2025, 0133 WO N / E2025, 0127 February 24, 2026

[0067] embodiment of the method for determining an arrangement 26 of at least one magnet 20 is described. After determining the orientation of the magnet 20 and the further magnet 24, the orientation of a further pair of magnets is determined in the same way as described for the magnet 20. The further pair of magnets comprises a magnet 20 arranged at a further magnet position 25 and a further magnet 24 arranged at a further magnet position 25. For the further pair of magnets, the magnet 20 and the further magnet 24 have the same orientation. The arrangement 26 of at least one magnet 20 thus comprises two magnets 20 and two further magnets 24. The magnets 20 and the further magnets 24 each have an orientation as determined by the method for determining an arrangement 26 of at least one magnet 20 described herein.

[0068] Figure 6 shows an exemplary embodiment of the data processing system 27. The data processing system 27 is configured to carry out the steps of the method for determining an arrangement 26 of at least one magnet 20 described herein.

[0069] This patent application claims priority from German patent application 10 2025 108 959.0, the disclosure content of which is hereby included by reference .P2025, 0133 WO N / E2025, 0127 February 24, 2026

[0070] - 17 -

[0071] Reference numerals

[0072] 20 magnet

[0073] 21 magnet position

[0074] 22 magnetic field region 23 fixed position

[0075] 24 further magnet

[0076] 25 further magnet position 26 arrangement

[0077] 27 data processing system S1-S4 steps

Claims

P2025, 0133 WO N / E2025, 0127 February 24, 2026Claims1. Method for determining an arrangement (26) of at least one magnet (20) , the method comprising:- providing at least one magnet position (21 ) within a magnetic field region (22 ) ,- providing at least one desired magnetic field parameter for at least one fixed position (23) within the magnetic field region ( 22 ) ,- calculating the magnetic field at the at least one fixed position (23) for the case that at one of the at least one magnet position (21 ) one magnet (20) is arranged, and- numerically determining the orientation of the magnet (20) in order to approximate the at least one desired magnetic field parameter for the at least one fixed position (23) .

2. Method for determining an arrangement (26) of at least one magnet (20) according to the preceding claim, wherein at the same time as determining the orientation of the magnet (20) or after determining the orientation of the magnet (20) , the orientation of at least one further magnet (24 ) is determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position (23) , wherein the further magnet (24 ) is arranged at a further magnet position (25) (21 ) within the magnetic field region ( 22 ) .

3. Method for determining an arrangement (26) of at least one magnet (20) according to the preceding claim, wherein the magnet (20) and the further magnet (24 ) form a pair of magnets .P2025, 0133 WO N / E2025, 0127 February 24, 2026- 19 -4. Method for determining an arrangement (26) of at least one magnet (20) according to one of claims 2 to 3, wherein the magnet (20) and the further magnet (24 ) have the same orientation .

5. Method for determining an arrangement (26) of at least one magnet (20) according to one of claims 2 to 4, wherein after determining the orientation of the further magnet (24 ) , the orientation of at least one further pair of magnets is determined numerically in order to approximate the at least one desired magnetic field parameter for the at least one fixed position (23) , wherein each magnet of the further pair of magnets is arranged at one further magnet position (25) within the magnetic field region (22 ) , wherein at least three further magnet positions (25) are located within the magnetic field region (22 ) .

6. Method for determining an arrangement (26) of at least one magnet (20) according to one of the preceding claims, wherein the magnetic field at the at least one fixed position (23) is calculated for the case that the magnet (20) is an ideal magnetic dipole .

7. Method for determining an arrangement (26) of at least one magnet (20) according to one of the preceding claims, wherein an optimizer algorithm is employed to determine the orientation of the magnet (20) in order to approximate the at least one desired magnetic field parameter for the at least one fixed position (23) .

8. Method for determining an arrangement (26) of at least one magnet (20) according to one of the preceding claims, wherein the magnetic field parameter is one of : an amplitude of aP2025, 0133 WO N / E2025, 0127 February 24, 2026- 20 -magnetic field, a derivative of the amplitude of a magnetic field, a direction of a magnetic field, a derivative of the direction of a magnetic field, a component of a magnetic field, any function of a component of a magnetic field.

9. Method for determining an arrangement (26) of at least one magnet (20) according to one of the preceding claims, wherein the magnetic field region (22 ) is a two-dimensional area or a three-dimensional volume .

10. Arrangement (26) of at least one magnet (20) , the arrangement (26) comprising the magnet (20) , wherein the magnet (20) is arranged at a magnet position (21 ) within a magnetic field region (22 ) and has an orientation as determined by the method for determining an arrangement (26) of at least one magnet (20) according to one of the preceding claims .

11. Computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method for determining an arrangement (26) of at least one magnet (20) according to one of claims 1 to 9 .

12. Data processing system (27 ) that is configured to carry out the steps of the method for determining an arrangement (26) of at least one magnet (20) according to one of claims 1 to 9 .

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