Magnetic structure with improved cohesion, inverter and associated method

Description

Domaine technique

[0001] The present invention relates to a magnet structure. It also relates to an inverter comprising such a structure, as well as to an associated method.

[0002] Such a device allows a user to generate a magnetic field. The field of the invention is more particularly but not limited to that of particle accelerators. Etat de la technique antérieure

[0003] US 5,383,049 describes an elliptically polarized adjustable phase insertion device.

[0004] The article by Sasaki et al. (Nuclear Instruments & methods in Physics research A 331 (1993) July 1) describes the design of a new type of planar undulator to generate variable polarized radiation.

[0005] The article by Liang et al. (Nuclear Instruments & methods in Physics research A 987 (2021)) describes an analysis of the first magnetic results from the PSI APPLE X undulators in elliptical polarization.

[0006] An undulator is a device that generates a spatially periodic magnetic field. When charged particles (electrons in general) pass through this device, they are subjected to a force that gives them an oscillating movement and generates an electromagnetic wave. The emitted radiation called synchrotron radiation is, due to its spectral and optical qualities, used as a tool to probe matter in many scientific fields (biology, chemistry, etc.). Undulators are characterized by their spatial period and their magnetic field, the main parameters that impact the spectral extent of the emitted radiation. Apple and related undulators (APPLE I, II, III, X, Delta, etc.) produce a vertical and / or horizontal periodic magnetic field to generate linear polarization (pure or inclined) or circular polarization.They consist of rows of permanent magnets, the movement of two of which diagonally opposite ones allows the phase between the field components to be changed, as well as their intensity, and thus the helicity of the polarization to vary. On each row, the permanent magnets are assembled following a Halbach structure. This consists of alternating permanent magnets whose magnetization vector rotates 90° in the beam direction around the horizontal axis of the undulator, each magnet being magnetized in at most 1 direction. These permanent magnets are generally difficult to maintain in position because they repel each other or are in unstable equilibrium.

[0007] For long-period undulators, each magnet is usually held alone using a mechanical clamp. For short-period undulators, this single clamp is no longer sufficient due to the insufficient thickness of the magnet. The permanent magnets are then glued together in pairs, or even welded.

[0008] In a classical Halbach structure, over a magnetic period λ u , the magnetization vector rotates from one magnet to another by 90° around the horizontal axis if four magnets are used to constitute the period.

[0009] APPLE undulators consist of 4 beams that move longitudinally to vary the phase between the field components and therefore the polarization of the electrons, or vertically (bottom vs. top) to modify the strength of the magnetic field and therefore the resonance energy of the undulator. The two lower rows have the same magnet sequence, while on the upper beams, the longitudinally magnetized magnets are in the opposite direction to the lower beams.

[0010] The advantage of APPLE inverters is that they can vary the polarization linearly or circularly. However, in this type of magnetic structure, the horizontal and vertical field components are not equal, the resonance energy is then limited by the value of the lowest magnetic field component. To overcome the fact that the field components are not equivalent, it is possible to tilt the magnetization vector of the vertically magnetized magnets at 45°, which makes it possible to obtain equality of the horizontal and vertical components and thus no longer be limited in energy by one or the other, this is the case of APPLE I or APPLE X type inverters.

[0011] In the case of APPLE I or II or III or X inverters, the longitudinal dimension of each magnet is equal to the period divided by the number of magnets constituting the period. Thus, for an inverter with a magnetic period of 40 mm, the permanent magnets are 10 mm thick. It is not easy to mechanically hold a 10 mm wide element on which magnetic forces are exerted in 3 directions. To remedy this, some use glue, others even implement processes for welding the magnets together.

[0012] The aim of the present invention is to propose a magnet structure or an inverter making it possible to generate a magnetic field (preferably significant) while facilitating the assembly of the magnets together, and preferably being able to do without or limit the use of glue or solder or flange to assemble these magnets, preferably for an elliptical polarization, of short spatial period and efficient. Exposé de l'invention

[0013] This objective is achieved with a magnet structure comprising a number N of series of permanent magnets installed periodically along a direction S with a spatial period λ u (preferably including a first, second, third and fourth series), N being greater than or equal to four: each series comprising: a magnet of a first beam a magnet of a second beam a magnet of a third beam a magnet of a fourth beam the magnets of each beam succeeding one another along the direction S, the first beam and the second beam succeeding one another along a direction Z perpendicular to the direction S, the fourth beam and the third beam succeeding one another along the direction Z, the third beam and the second beam succeeding one another along a direction X perpendicular to the directions S and Z, the fourth beam and the first beam succeeding one another along the direction X, characterized in that, for at least four successive (but not necessarily neighboring) series of magnets of a spatial period λ u , the magnetization vector of each magnet (of these at least 4 series) of each beam has a non-zero component along each of the directions X, S and Z. N is a positive integer. N is preferably an even number.N is preferably greater than or equal to four. N is preferably less than or equal to ten. N is preferably less than or equal to eight. N may for example be equal to four, six, or eight.

[0014] The magnet structure according to the invention may further be characterized in that the series comprise a first, second, third and fourth successive series in this order, and in that: the magnetization vector of each magnet of the second beam and of the third beam has, in a projection in a plane comprising the directions Z and S, a direction which forms, with the direction Z: ∘ an angle of -θ x for the first series, and / or ∘ an angle of +θ x for the second series, and / or ∘ an angle of -θ x -180° for the third series, and / or ∘ an angle of θ x -180° for the fourth series.

[0015] The magnet structure according to the invention can further be characterized in that: the magnetization vector of each magnet of the first beam and of the fourth beam has, in a projection in a plane comprising the directions Z and S, a direction which forms, with the direction Z: ∘ an angle of θ x for the first series, and / or ∘ an angle of -θ x for the second series, and / or ∘ an angle of θ x -180° for the third series, and / or ∘ an angle of -θ x -180° for the fourth series.

[0016] The magnet structure according to the invention can further be characterized in that: the magnetization vector of each magnet of the first series and of the second series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction: ∘ an angle of -θs for the first beam, and / or ∘ an angle of θs for the second beam, and / or ∘ an angle of -θs for the third beam, and / or ∘ an angle of θs for the fourth beam.

[0017] The magnet structure according to the invention can further be characterized in that: the magnetization vector of each magnet of the third series and of the fourth series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction: ∘ an angle of -θs-180° for the first beam, and / or ∘ an angle of θs-180° for the second beam, and / or ∘ an angle of -θs-180° for the third beam, and / or an angle of θs-180° for the fourth beam.

[0018] θ x can be different from 0°, 90°, 180° or 270°, preferably ± 1°, or even preferably ± 5°.

[0019] θ x may be included in the interval ]5°; 80°], preferably in the interval [24°; 72°], preferably in the interval [24°; 54°] for N=4 and / or in the interval [28°; 72°] for N=6.

[0020] θs can be different from 0°, 90°, 180° or 270°, preferably ± 1°, or even preferably ± 5°.

[0021] θs can be different from 45°, 135°, 225° or 315°, preferably within ± 1°, or even preferably within ± 2°.

[0022] θ S may be in the interval ]5°; 43°[, preferably in the interval [30°; 42°], preferably in the interval [30°; 42°] for N=4 and / or in the interval [34°; 42°] for N=6.

[0023] The number N of series is equal to 4 or 6.

[0024] In the case where N=6, the series may also include: A fifth series between the first and second series A sixth series between the third and fourth series such that the series comprising the first, fifth, second, third, sixth and fourth successive series in that order. In this case, preferably: the magnetization vector of each magnet of the second beam and of the third beam has, in a projection in a plane comprising the Z and S directions, a direction which forms, with the Z direction: ∘ an angle of 0° for the fifth series, and / or ∘ an angle of 180° for the sixth series, and / or the magnetization vector of each magnet of the first beam and of the fourth beam has, in a projection in a plane comprising the Z and S directions, a direction which forms, with the Z direction: ∘ an angle of 0° for the fifth series, and / or ∘ an angle of 180° for the sixth series, and / or the magnetization vector of each magnet of the fifth series has,in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction: ∘ an angle of -θ S for the first beam, and / or ∘ an angle of θ S for the second beam, and / or ∘ an angle of -θ S for the third beam, and / or ∘ an angle of θ S for the fourth beam, and / or the magnetization vector of each magnet of the sixth series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction: ∘ an angle of -θs-180° for the first beam, and / or ∘ an angle of θs-180° for the second beam, and / or ∘ an angle of -θs-180° for the third beam, and / or ∘ an angle of θs-180° for the fourth beam. ,

[0025] λ u can be included in the interval [15 mm; 200 mm], preferably in the interval [20 mm; 70 mm].

[0026] The magnet structure according to the invention can further be characterized in that: the first beam and the second beam are separated by a distance G z along the Z direction, and / or the fourth beam and the third beam are separated by the distance G z along the Z direction, and / or the third beam and the second beam are separated by a distance G x along the X direction, and / or the fourth beam and the first beam are separated by the distance G x along the X direction.

[0027] G x may be in the range [1 mm; 250 mm], preferably in the range [1 mm; 50 mm], and / or G z is in the range [1 mm; 250 mm], preferably in the range [1 mm; 50 mm].

[0028] G x can be equal (or substantially equal to within ±500 µm, preferably within ±200 µm) to G z , subsequently denoted G.

[0029] θ x can be equal to, preferably if N = 4: with: Offset1 =33.634 ± 0.17 AGap1 =29.434 ± 0.109 BGap1 =-0.041763 ± 0.000374 APeriode1 =-39.534 ± 0.104 BPeriode1 =-0.027176 ± 0.000263

[0030] θ S can be equal to, preferably if N = 4: Offset2 =35.233 ± 0.147 AGap2 =-10.382 ± 0.0218 BGap2 =-0.066698 ± 0.000476 APeriode2 =13.866 ± 0.0918 BPeriode2 =-0.015736 ± 0.000349

[0031] θ x can be equal to, preferably if N = 6: with: Off4 =49.848 ± 0.3 AGap4 =41.206 ± 0.0801 BGap4 =-0.038149 ± 0.000217 APeriode4 =-54.559 ± 0.148 BPeriode4 =-0.018134 ± 0.000223

[0032] θ S can be equal to, preferably if N = 6: with: Off3 =37.222 ± 0.201 AGap3 =-9.6508 ± 0.0384 BGap3 =-0.038257 ± 0.000448 APeriode3 =12.099 ± 0.13 BPeriode3 =-0.01507 ± 0.000503

[0033] The magnet structure according to the invention may further be arranged to generate a magnetic field with its component along the Z direction equal, or substantially equal to ±5%, preferably ±1%, to its component along the X direction.

[0034] According to yet another aspect of the invention, there is provided an inverter comprising: a magnet structure according to the invention, preferably a vacuum chamber arranged o around the magnet structure so that the magnets of the magnet structure are located inside the vacuum, or ∘ inside the magnet structure, between the four beams preferably a cryogenic cooling system (preferably nitrogen or helium) arranged to cool the magnets of the magnet structure (preferably when the vacuum chamber is arranged around the magnet structure).

[0035] According to yet another aspect of the invention, there is provided a method of generating a magnetic field, characterized in that it is generated by means of a magnet structure according to the invention or an inverter according to the invention.

[0036] The magnetic field may be generated with its component along the Z direction equal, or substantially equal to ±5% preferably ±1%, to its component along the X direction. Description des figures et modes de réalisation

[0037] Other advantages and particularities of the invention will appear on reading the detailed description of implementations and embodiments which are in no way limiting, and the following appended drawings: [ Fig. 1 ] there figure 1 is a side view of four series 1, 2, 3, 4 of magnets (each series 1, 2, 3, 4 comprising a magnet of one of the beams 10, 20, 30, 40) of a first embodiment of a magnet structure 100 according to the invention (N=4) which is the preferred embodiment of the invention; in this figure, each magnet is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of the figure 1 including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet, [ Fig. 2 ] there figure 2 is a front view of the four beams 10, 20, 30, 40 carrying the magnets for the series of magnets 1 and 2 of the first embodiment of structure 100 of magnets according to the invention; in this figure, each magnet is represented by a square with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of the figure 2 including the X and Z directions, illustrated by an arrow inside the square of this magnet, [ Fig. 3 ] there figure 3 is a front view of the same four beams 10, 20, 30, 40 of the figure 2 , carrying the magnets for the series of magnets 3 and 4 of the first embodiment of structure 100 of magnets according to the invention; in this figure, each magnet is represented by a square with rounded corners and has a direction of its permanent magnetization vector, projected into the plane of the figure 3 including the X and Z directions, illustrated by an arrow inside the square of this magnet, [ Fig. 4 ] there figure 4 illustrates: In its upper part, the angle θ S as a function of the angle θ x for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100: B z =B x In its lower part, the value of B z =B x as a function of θ x . [ Fig. 5 ] there figure 5 illustrates: In its upper part, the value of B x and B z as a function of θ x according to two hypotheses: ∘ A first curve 11 for which a remanent field B r of each magnet of 1 Tesla is considered ∘ A second curve 12 for which a remanent field B r of each magnet of 2 Tesla is considered. In its lower part, two curves 110, 120 almost superimposed of the angle θ S as a function of the angle θ x corresponding to the cases of the two curves 11 and 12. [ Fig. 6 ] there figure 6 , obtained on the same principle as the upper part of the figure 4 or the lower part of the figure 5 , illustrates the angle θ S as a function of the angle θ x for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100, with different curves corresponding to different values of the distance G. [ Fig. 7 ] there figure 7 illustrates the angle θ S as a function of the angle θ x for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100 and is maximum, for different values of the distance G (in this case G=G x =G z ) which is the distance between the edges of the beams 10, 20, 30, 40 facing each other. [ Fig. 8 ] there figure 8 illustrates: A curve 210 of θ x as a function of G, and A curve 220 of θ S as a function of G, for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100 and maximum [ Fig. 9 ] there figure 9 illustrates the angle θ S as a function of the angle θ x for different values of spatial period λu, and for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100 and maximum [ Fig. 10 ] there figure 10 illustrates on the vertical axis values of angle θ corresponding to θ x or θ S: Points of a curve 310 of θ x as a function of the spatial period λ u , and Points of a curve 320 of θ S as a function of the spatial period λ u , for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100 and maximum [ Fig. 11 ] there figure 11 illustrates the values of the magnetic fields B x and B z generated by the structure 100 as a function of the longitudinal position S at the center of the four magnets of each series 1, 2, 3 or 4, outside of a vacuum or at the center of a vacuum chamber of the undulator 1000 comprising the structure 100, [ Fig. 12 ] there figure 12 is a generalization to N=6 series of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of this figure including the directions S and Z, illustrated by an arrow inside the rectangle of this magnet, [ Fig. 13 ] there figure 13 is a generalization to N=8 series of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of this figure including the directions S and Z, illustrated by an arrow inside the rectangle of this magnet, [ Fig. 14 ] there figure 14 is a generalization to N=10 sets of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected into the plane of this figure including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet [ Fig. 15 ] there figure 15 is a side view of six series 1, 5, 2, 3, 6, and 4 of magnets (each series comprising a magnet of one of the beams 10, 20, 30, 40) of a second embodiment of a magnet structure 200 according to the invention; in this figure, each magnet is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of the figure 15 including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet, [ Fig. 16 ] there figure 16 illustrates the angle θ S as a function of the angle θ x for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 200 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 200 and is maximum, for different values of the distance G (in this case G=G x =G z ) which is the distance between the edges of the beams 10, 20, 30, 40 facing each other. [ Fig. 17 ] there figure 17 illustrates: A curve 210 of θ x as a function of G, and A curve 220 of θ S as a function of G, for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 200 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 200 and maximum [ Fig. 18 ] there figure 18 illustrates the angle θ S as a function of the angle θ x for different values of spatial period λu, and for which the component B z along the Z direction of the magnetic field generated by the magnet structure 200 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 200 and maximum [ Fig. 19 ] there figure 19 illustrates on the vertical axis values of angle θ corresponding to θ x or θ S: Points of a curve 310 of θ x as a function of the spatial period λ u , and Points of a curve 320 of θ S as a function of the spatial period λ u , for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 200 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 200 and maximum.

[0038] In reference to the figure 11 , throughout the present description, it will be said that the component B z in the Z direction of the magnetic field generated by the magnet structure 100 or 200 is equal to the component B x in the X direction of the magnetic field generated by the magnet structure 100 or 200 (B z =B x ), when: The amplitude of B z , at the center of the four beams 10, 20, 30, 40 (the component B z according to the Z direction of the magnetic field generated by the magnet structure 100 or 200 having a value which varies according to the position according to S), is equal to: The amplitude of B x , at the center of the four beams 10, 20, 30, 40 (the component B x according to the X direction of the magnetic field generated by the magnet structure 100 or 200 having a value which varies according to the position according to S).

[0039] In other words, the peak fields of B z and B x are equal, and the fields B z and B x may be out of phase.

[0040] Since these embodiments are in no way limiting, it is possible in particular to consider variants of the invention comprising only a selection of characteristics described or illustrated subsequently isolated from the other characteristics described or illustrated (even if this selection is isolated within a sentence comprising these other characteristics), if this selection of characteristics is sufficient to confer a technical advantage or to differentiate the invention compared to the state of the prior art. This selection comprises at least one preferably functional characteristic without structural details, and / or with only a part of the structural details if this part alone is sufficient to confer a technical advantage or to differentiate the invention compared to the state of the prior art.

[0041] We will first describe, with reference to the figures 1 à 11 , a first preferred embodiment of structure 100 of magnets according to the invention.

[0042] This new magnetic structure 100 is derived from a Halbach structure and has a particular orientation of the magnetization vector for optimal magnet holding, and is preferably applied to the construction of undulators generating elliptical polarization.

[0043] In this embodiment, the magnet structure 100 comprises four successive series (first series referenced 1 in the figures then second series referenced 2 in the figures then third series referenced 3 in the figures then fourth series referenced 4 in the figures, in this order along the direction S) of permanent magnets installed periodically along a direction S (also noted Y) with a spatial period λ u , including a first, second, third and fourth series. These four series 1, 2, 3, 4 are represented only once on the figure 1 , but are actually repeated periodically along the S direction typically a few tens or hundreds of times.

[0044] Each series 1, 2, 3, 4 includes (preferably only as a magnet): a magnet of a first beam referenced 10 in the figures, this beam extending in the direction S, a magnet of a second beam referenced 20 in the figures, this beam extending in the direction S, a magnet of a third beam referenced 30 in the figures, this beam extending in the direction S, a magnet of a fourth beam referenced 40 in the figures, this beam extending in the direction S.

[0045] The magnets of each beam 10, 20, 20, 40 follow one another along the direction S.

[0046] The first beam 10 and the second beam 20 are parallel and follow one another along a direction Z perpendicular to the direction S.

[0047] The fourth beam 40 and the third beam 30 are parallel and follow one another along the Z direction.

[0048] The third beam 30 and the second beam 20 follow one another along a direction X perpendicular to the directions S and Z.

[0049] The fourth beam 40 and the first beam 10 follow one another along the direction X.

[0050] So, in a section view including the X and Z directions: Beam 10 is located at the bottom right of the center of these four beams Beam 20 is located at the top right of the center of these four beams Beam 30 is located at the top left of the center of these four beams Beam 40 is located at the bottom left of the center of these four beams

[0051] The magnetization vector (which leads to permanent magnetization, but not to temporary magnetization of an electromagnet), of each magnet of each beam 10, 20, 30, 40 has a non-zero component along each of the directions X, S and Z.

[0052] In reference to the figures 1 , 2 et 3 , we note that: the magnetization vector of each magnet of the second beam 20 and of the third beam 30 has, in a projection in a plane comprising the directions Z and S, a direction which forms, with the direction Z: ∘ an angle (around the X axis) of -θ x for the first series 1 ∘ an angle (around the X axis) of +θ x for the second series 2 ∘ an angle (around the X axis) of -θ x -180° for the third series 3 ∘ an angle (around the X axis) of θ x -180° for the fourth series 4 the magnetization vector of each magnet of the first beam 10 and of the fourth beam 40 has, in a projection in a plane comprising the directions Z and S, a direction which forms,with the Z direction: ∘ an angle (around the X axis) of θ x for the first series 1 ∘ an angle (around the X axis) of -θ x for the second series 2 ∘ an angle (around the X axis) of θ x -180° for the third series 3 ∘ an angle (around the X axis) of -θ x -180° for the fourth series 4 the magnetization vector of each magnet of the first series 1 and of the second 2 series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction: ∘ an angle (around the S axis) of -θ S for the first beam 10 ∘ an angle (around the S axis) of θ S for the second beam 20 ∘ an angle (around the S axis) of -θ S for the third beam 30 ∘ an angle (around the axis S) of θ S for the fourth beam 40 the magnetization vector of each magnet of the third series 3 and of the fourth 4 series has, in a projection in a plane comprising the directions Z and X, a direction which forms,with the Z direction: ∘ an angle (around the S axis) of -θs-180° for the first beam 10 ∘ an angle (around the S axis) of θ S -180° for the second beam 20 ∘ an angle (around the S axis) of -θs-180° for the third beam 30 ∘ an angle (around the S axis) of θs-180° for the fourth beam 40. θ x is different from 0°, 90°, 180° or 270°, preferably ± 1°, or even preferably ± 5°. θ S is different from 0°, 90°, 180° or 270°, preferably ± 1°, or even preferably ± 5°. θ S is different from 45°, 135°, 225° or 315°, preferably within ± 1°, or even preferably within ± 2°.

[0053] There figure 4 illustrates: In its upper part, the angle θ S as a function of the angle θ x for values of θ S and θ x for which the component B z along the Z direction of the magnetic field generated by the magnet structure 100 is equal to the component B x along the X direction of the magnetic field generated by the magnet structure 100: B z =B x In its lower part, the value of B z =B x as a function of θ x .

[0054] This figure 4 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm = 10 mm along the S axis λ u = 40 mm G z = G x = 1 mm Remanent field B r of 1.67T

[0055] In reference to the figure 4 , we note that there exists a pair θ S and θ x for which the value of B z =B x is maximum.

[0056] There figure 5 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = 1 mm Remanent field B r of 1 or 2 T.

[0057] In reference to the figure 5 , we note that the values of θ S and θ x for which the value of B z =B x is maximum do not depend on the remanent field B r of each magnet.

[0058] In reference to the figures 1 , 2 et 3 , we note that: the first beam 10 and the second beam 20 are separated by a distance (also called an air gap) G z along the Z direction, the fourth beam 40 and the third beam 30 are separated by the distance G z along the Z direction, the third beam 30 and the second beam 20 are separated by a distance (also called an air gap) G x along the X direction, the fourth beam 40 and the first beam 10 are separated by the distance G x along the X direction.

[0059] G x is typically in the range [1mm; 250mm], preferably in the range [1mm; 50mm], and / or G z is typically in the range [1mm; 250mm], preferably in the range [1mm; 50mm].

[0060] These values of G x or G z lead to a circular opening (for a passage of a beam in the center of beams 10, 20, 30, 40) whose diameter is greater than G x and G z and depends on G x , G z and the chamfers at the corners of the magnets.

[0061] The chamfer value is calculated as follows: ChanfreinZ = DiamGapCirculaire / racine 2 − Gz ChanfreinX = DiamGapCirculaire / racine 2 − Gx

[0062] With ChamferZ, CircularGapDiam and ChamferX as defined in figure 3 .

[0063] G x is equal, or substantially equal to within ± 500 µm, preferably within ± 200 µm, to G z , and is noted in this case in the present description as distance (also called air gap) G.

[0064] There figure 6 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G of variable value between 1 mm and 51 mm Remanent field B r of 1.67 T.

[0065] There figure 7 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G of variable value between 1 mm and 51 mm Remanent field B r of 1.67 T.

[0066] There figure 8 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G of variable value between 1 mm and 51 mm Remanent field B r of 1.67 T.

[0067] An interpolation gives: S =42.4-10.8.exp(-0.059.G) θ x =18.4+34.4.exp(-0.035.G) With θ S and O x expressed in degrees (°) and G expressed in mm.

[0068] In reference to the figures 6, 7 And 8 , we note that the ideal values of θ S and θ x for which the value of B z =B x is maximum depend on G. Examples of these ideal values as a function of G are noted in the table below with the hypotheses of figures 6 à 8 : [Table1] G (mm) θx (°) (valeurs optimales + / -0.5°) θs (°) (valeurs optimales + / -0.5°) 1 52 32 4 48 34 7 45 35 10 42 37 16 38 38 21 35 39 26 32 40 36 28 41 50 24 42

[0069] Furthermore, we note that an optimal pair (B x =B z and maximum) of values of θ S and θ x at an air gap G leads to B z = B x (but not necessarily maximum) for all other air gaps G tested.

[0070] There figure 9 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u variable from 20 to 70 mm G z = G x = G = 1 mm Remanent field B r of 1.67 T.

[0071] There figure 10 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u variable from 20 to 70 mm G z = G x = G = 1 mm Remanent field B r of 1.67 T.

[0072] An interpolation gives: θ S = 27 + 13 . exp − 0 , 024 . λ u θ x = 56 − 24 , 7 . exp − 0 , 036 . λ u

[0073] With θ S and θ x expressed in degrees (°) and λ u expressed in mm.

[0074] So, with reference to the figures 9 And 10 , we note that the ideal values of θ S and θ x for which the value of B z =B x is maximum depend on λ u . Examples of these ideal values as a function of λ u are noted in the table below with the hypotheses of figures 9 And 10 : [Table 2] Période λ u (mm) θx (°) (valeurs optimales + / -0.5°) θs (°) (valeurs optimales + / -0.5°) 20 44 36 25 46 35 30 48 34 35 49 33 40 50 33 45 51 32 50 52 32 55 53 31 60 53 31 65 53 31 70 54 30

[0075] Thus, based on the experiments and simulations carried out within the framework of the present invention, we note that: θ x is typically in the range ]5°; 80°], preferably in the range [24°; 54°]. θ S is typically in the range ]5°; 43°[, preferably in the range [30°; 42°]. λ u is typically in the range [15 mm; 200 mm], preferably in the range [20 mm; 70 mm].

[0076] Empirically, it has been determined by interpolation that the optimal value of θ x expressed in ° (for which B x =B z and is maximum) is equal to: with: Offset1 =33.634 ± 0.17 AGap1 =29.434 ± 0.109 BGap1 =-0.041763 ± 0.000374 APeriode1 =-39.534 ± 0.104 BPeriode1 =-0.027176 ± 0.000263

[0077] In this formula, G is expressed in mm and λ u is expressed in mm.

[0078] Empirically, it has been determined by interpolation that the optimal value of θ S expressed in ° (for which B x =B z and is maximum) is equal to: Offset2 =35.233 ± 0.147 AGap2 =-10.382 ± 0.0218 BGap2 =-0.066698 ± 0.000476 APeriode2 =13.866 ± 0.0918 BPeriod2 =-0.015736 ± 0.000349

[0079] In this formula, G is expressed in mm and λ u is expressed in mm.

[0080] Thus, the structure 100 is preferably arranged to generate a magnetic field with its component B z along the Z direction equal, or substantially equal to ±5%, preferably ±1% at minimum air gap, to its component B x along the X direction.

[0081] From the structure 100 or 200, an embodiment of inverter 1000 (not illustrated) according to the invention is constructed comprising: the magnet structure 100 or 200, a vacuum chamber arranged: ∘ inside the magnet structure, between the (preferably in the center of) the four beams 10, 20, 30, 40, or ∘ around the magnet structure so that the magnets of the magnet structure are located inside the vacuum, preferably a cryogenic cooling system (preferably nitrogen or helium) arranged to cool the magnets of the magnet structure (preferably when the vacuum chamber is arranged around the magnet structure).

[0082] In one embodiment of the method according to the invention, a magnetic field is generated by means of the magnet structure 100 or 200 or the inverter 1000. The magnetic field is generated with its component B z along the Z direction equal, or substantially equal to ±5%, preferably ±1% at minimum air gap, to its component B x along the X direction.

[0083] In addition, the distance G x and / or G z and / or G can be adjusted.

[0084] There figure 11 , which illustrates the fields B x and B z obtained by the structure 100, is obtained by numerical simulation using magnetic field calculation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G = 1 mm Remanent field B r of 1.67 T.

[0085] Thus, according to the invention, the new proposed structure 100 or 200 produces a magnetic field (with elliptical polarization) as strong as the Halbach structure and makes it possible to address the problem of holding the magnets. Indeed, all the magnets are magnetized in 3 directions (vertical, horizontal and longitudinal). Inclining the magnetization vector in the longitudinal direction makes it possible to hold two magnets together naturally. It is thus easier to hold a block of two magnets together naturally than a single, thinner magnet subjected to opposing forces or two magnets held together by other unnatural means (welding, glue, screws, etc.).

[0086] The new structure 100 or 200 proposed makes it possible to respond to this problem, while retaining the fact that the field components B z , B x in the two planes are always equivalent.

[0087] To do this, all magnets have a magnetization vector oriented in 3 directions (horizontal, vertical and longitudinal). The inclination of the magnetization vector in the longitudinal plane will allow certain magnets to stick naturally two by two, thus forming a block of two solid magnets. Thus, there is no need to weld / glue the magnets together.

[0088] Furthermore, it should be noted that it is not straightforward to magnetize a block of permanent magnet in three directions because the block must be compacted in the direction of its magnetization vector.

[0089] Thus, in a manufacturing method according to the invention of a structure 100 or 200 according to the invention, permanent magnets larger than the desired final size are compacted in a compaction direction parallel to the magnetization vector of these magnets, then each magnet is machined (“at an angle”) to give it its shape with the desired direction of its magnetization vector (relative to the orientation of some of its final flat faces).

[0090] Finally, it will be noted that, instead of four series 1, 2, 3, 4, all the embodiments of the invention previously described can be generalized to a number N of series of permanent magnets installed periodically along the direction S with the spatial period λ u .

[0091] N is a positive integer.

[0092] N is preferably an even number.

[0093] N is preferably greater than or equal to four.

[0094] N is preferably less than or equal to eight or ten.

[0095] N can for example be equal to four, six, or eight.

[0096] For example, in embodiments with N series of permanent magnets installed periodically along the direction S with the spatial period λ u and always with four beams 10, 20, 30, 40: there figure 12is a generalization to N=6 series of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of this figure including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet; thus, the structure for N=6 includes the series of magnets referenced 1, 2, 3, 4 of the N=4 case, plus two additional series of magnets referenced 5 and 6; Thus each spatial period λ u includes the series 1, 5, 2, 3, 6, 4 in this order along the S direction; the figure 13is a generalization to N=8 series of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of this figure including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet; thus, the structure for N=8 includes the series of magnets referenced 1, 2, 3, 4 of the N=4 case, plus four additional series of magnets referenced 7, 8, 9 and 13; Thus each spatial period λ u includes the series 1, 7, 8, 2, 3, 9, 13, 4 in this order along the S direction; the figure 14is a generalization to N=10 sets of magnets; each magnet (corresponding to a single bottom beam 10 or 40) is represented by a rectangle with rounded corners and has a direction of its permanent magnetization vector, projected in the plane of this figure including the S and Z directions, illustrated by an arrow inside the rectangle of this magnet; thus, the structure for N=10 includes the sets of magnets referenced 1, 2, 3, 4 of the N=4 case, plus two additional sets of magnets referenced 5 and 6 of the N=6 case, plus four additional sets of magnets referenced 7, 8, 9 and 13 of the N=8 case; Thus each spatial period λ u includes the sets 1, 7, 5, 8, 2, 3, 9, 6, 13, 4 in this order along the S direction.

[0097] We will now describe, with reference to the figures 12 And 15 à 19, the second embodiment of magnet structure 200 according to the invention, which will only be described for its differences compared to the first structure 100.

[0098] THE figures 12 And 15 which illustrate a generalization to N=6 series of magnets of the structure 100.

[0099] This structure 200 always includes the four beams 10, 20, 30, 40.

[0100] The number N of series is equal to 6.

[0101] Compared to structure 100, the series of magnets of structure 200 further comprise: A fifth series 5 between the first series 1 and the second series 2 A sixth series 6 between the third series 3 and the fourth series 4 so that the series comprising the first, fifth, second, third, sixth and fourth successive series in that order along the direction S.

[0102] The magnetization vector of each magnet of the second beam and of the third beam has, in a projection in a plane comprising the Z and S directions, a direction which forms, with the Z direction: o an angle of 0° for the fifth series o an angle of 180° for the sixth series

[0103] The magnetization vector of each magnet of the first beam and the fourth beam has, in a projection in a plane comprising the Z and S directions, a direction which forms, with the Z direction: ∘ an angle of 0° for the fifth series ∘ an angle of 180° for the sixth series

[0104] The magnetization vector of each magnet of the fifth series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction (as for the figure 2 ): ∘ an angle of -θ S for the first beam ∘ an angle of θ S for the second beam ∘ an angle of -θ S for the third beam ∘ an angle of θ S for the fourth beam

[0105] The magnetization vector of each magnet of the sixth series has, in a projection in a plane comprising the Z and X directions, a direction which forms, with the Z direction (as for the figure 3 ) : ∘ an angle of -θs-180° for the first beam ∘ an angle of θs-180° for the second beam ∘ an angle of -θs-180° for the third beam ∘ an angle of θs-180° for the fourth beam.

[0106] The directions of the magnetization vectors of the magnets of series 1, 23, 3 and 4 do not change compared to structure 100.

[0107] Thus, for at least four successive series of magnets of spatial period λ u , the magnetization vector of each magnet of each beam has a non-zero component along each of the directions X, S and Z

[0108] Figures 16, 17, 18 and 19 respectively for N=6 of the structure 200 are the equivalent figures of figures 7, 8, 9 and 10 respectively for N=4 of the structure 100.

[0109] Tables 2 and 3 for N=6 of structure 200 are the equivalent tables of tables 1 and 2 respectively for N=4 of structure 100.

[0110] There figure 16 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G of variable value between 1 mm and 51 mm Remanent field B r of 1.67 T.

[0111] There figure 17 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u = 40 mm G z = G x = G of variable value between 1 mm and 51 mm Remanent field B r of 1.67 T.

[0112] In reference to the figures 16 And 17, we note that the ideal values of θ S and θ x for which the value of B z =B x is maximum depend on G. Examples of these ideal values as a function of G are noted in the table below with the hypotheses of figures 16 And 17 : [Table 3] G (mm) θx (°) (optimal values at +, 0.5°) θs (°) (optimal values at + 0.5°) 1 64 34 4 62 34 7 56 36 10 54 36 16 46 38 21 42 40 26 38 40 36 34 42 50 28 42

[0113] We note that θ s for N=6 is almost similar to the 4-magnet structure for N=4.

[0114] There figure 18 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u variable from 20 to 70 mm G z = G x = G = 1 mm Remanent field B r of 1.67 T.

[0115] There figure 19 is obtained by numerical simulation using magnetic field simulation software (RADIA) which calculates the magnetic field generated by a permanent magnet or a sequence of permanent magnets with the following assumptions: magnets with transverse dimensions 35 mm x 35 mm along the X and Z axes and with dimensions λ u / N mm along the S axis λ u variable from 20 to 70 mm G z = G x = G = 1 mm Remanent field B r of 1.67 T.

[0116] So, with reference to the figures 18 And 19 , we note that the ideal values of θ x for which the value of B z =B x is maximum depend on λ u . Examples of these ideal values as a function of λ u are noted in the table below with the hypotheses of figures 18And 19 : [Table 4] Period λ u (mm) θx (°) (optimal values at + 0.5°) θs (°) (optimal values at + 0.5°) 20 54 34 25 60 34 30 62 34 35 64 34 40 64 34 45 66 34 50 68 34 55 68 34 60 70 34 65 72 34 70 72 34

[0117] For N=6, we note that θ s is constant whatever the value of the period λ u in the explored interval.

[0118] θ x is typically in the range ]5°; 80°], preferably in the range [28°; 72°].

[0119] θ S is typically in the range ]5°; 43°[, preferably in the range [34°; 42°].

[0120] Empirically, it has been determined by interpolation that the optimal value of θ S expressed in ° (for which B x =B z and is maximum) is equal to: with: Off3 =37.222 ± 0.201 AGap3 =-9.6508 ± 0.0384 BGap3 =-0.038257 ± 0.000448 APeriode3 =12.099 ± 0.13 BPeriod3 =-0.01507 ± 0.000503

[0121] In this formula, G is expressed in mm and λ u is expressed in mm.

[0122] Empirically, it has been determined by interpolation that the optimal value of θ x expressed in ° (for which B x =B z and is maximum) is equal to: with: Off4 =49.848 ± 0.3 AGap4 =41.206 ± 0.0801 BGap4 =-0.038149 ± 0.000217 APeriode4 =-54.559 ± 0.148 BPeriod4 =-0.018134 ± 0.000223

[0123] In this formula, G is expressed in mm and λ u is expressed in mm.

[0124] Of course, the invention is not limited to the examples which have just been described and numerous adjustments can be made to these examples without departing from the scope of the invention defined by the following claims.

[0125] Of course, the various features, forms, variants and embodiments of the invention may be combined with each other in various combinations provided that they are not incompatible or mutually exclusive. In particular, all the variants and embodiments described above may be combined with each other.

Claims

1. A magnet structure comprising a number N of sets (1, 2, 3, 4, 5, 6, 7, 8, 9, 13) of permanent magnets installed periodically along a direction S with a spatial period λu wherein N is greater than or equal to four, each set comprising: - a magnet of a first beam (10) - a magnet of a second beam (20) - a magnet of a third beam (30) - a magnet of a fourth beam (40) the magnets of each beam being arranged in succession in the direction S, the first beam and the second beam being arranged in succession in a direction Z perpendicular to the direction S, the fourth beam and the third beam being arranged in succession in the direction Z, the third beam and the second beam being arranged in succession in a direction X perpendicular to the directions S and Z, the fourth beam and the first beam being arranged in succession in the direction X, characterized in that, for at least four successive sets (1, 2, 3, 4) of magnets of a spatial period λu, the magnetization vector of each magnet of each beam has a non-zero component along each of the directions X, S and Z.

2. The magnet structure according to claim 1, characterized in that the sets comprise a first, second, third and fourth successive sets in this order, and in that: - the magnetization vector of each magnet of the second beam and of the third beam has, in a projection in a plane comprising the directions Z and S, a direction that forms, with the direction Z: ∘ an angle of -θx for the first set ∘ an angle of +θx for the second set ∘ an angle of -θx-180° for the third set ∘ an angle of θx-180° for the fourth set - the magnetization vector of each magnet of the first beam and the fourth beam has, in a projection in a plane comprising the directions Z and S, a direction that forms, with the direction Z: ∘ an angle of θx for the first set ∘ an angle of -θx for the second set ∘ an angle of θx-180° for the third set ∘ an angle of -θx-180° for the fourth set - the magnetization vector of each magnet of the first set and the second set has, in a projection in a plane comprising the directions Z and X, a direction that forms, with the direction Z: ∘ an angle of -θS for the first beam ∘ an angle of θS for the second beam ∘ an angle of -θS for the third beam ∘ an angle of θS for the fourth beam - the magnetization vector of each magnet of the third set and the fourth set has, in a projection in a plane comprising the directions Z and X, a direction that forms, with the direction Z: ∘ an angle of -θS-180° for the first beam ∘ an angle of θS-180° for the second beam ∘ an angle of -θS-180° for the third beam ∘ an angle of θS-180° for the fourth beam.

3. The magnet structure according to claim 2, characterized in that θx is different from 0°, 90°, 180° or 270°, preferably to ±1°, even preferably to ±5°.

4. The magnet structure according to either of claims 2 to 3, characterized in that θx is comprised in the interval ]5°; 80°], preferably in the interval [24°; 72°].

5. The magnet structure according to any one of claims 2 to 4, characterized in that θS is different from 0°, 90°, 180° or 270°, preferably to ±1°, even preferably to ±5°.

6. The magnet structure according to any one of claims 2 to 5, characterized in that θS is different from 45°, 135°, 225° or 315°, preferably to ±1°, even preferably to ±2°.

7. The magnet structure according to any one of claims 2 to 6, characterized in that θS is comprised in the interval ]5°; 43°[, preferably in the interval [30°; 42°].

8. The magnet structure according to any one of claims 2 to 7, characterized in that the number N of sets is equal to 4.

9. The magnet structure according to any one of claims 2 to 7, characterized in that the number N of sets is equal to 6, and in that the sets further comprise: - A fifth set between the first and the second set - A sixth set between the third and fourth sets so that the sets comprise the first, fifth, second, third, sixth and fourth successive sets in this order, and in that: - the magnetization vector of each magnet of the second beam and of the third beam has, in a projection in a plane comprising the directions Z and S, a direction that forms, with the direction Z: ∘ an angle of 0° for the fifth set ∘ an angle of 180° for the sixth set - the magnetization vector of each magnet of the first beam and the fourth beam has, in a projection in a plane comprising the directions Z and S, a direction that forms, with the direction Z: ∘ an angle of 0° for the fifth set ∘ an angle of 180° for the sixth set - the magnetization vector of each magnet of the fifth set has, in a projection in a plane comprising the directions Z and X, a direction that forms, with the direction Z: ∘ an angle of -θS for the first beam ∘ an angle of θS for the second beam ∘ an angle of -θS for the third beam ∘ an angle of θS for the fourth beam - the magnetization vector of each magnet of the sixth set has, in a projection in a plane comprising the directions Z and X, a direction that forms, with the direction Z: ∘ an angle of -θS-180° for the first beam ∘ an angle of θS-180° for the second beam ∘ an angle of -θS-180° for the third beam ∘ an angle of θS-180° for the fourth beam.

10. The magnet structure according to any one of the preceding claims, characterized in that λu is comprised in the interval [15 mm; 200 mm], preferably in the interval [20 mm; 70 mm].

11. The magnet structure according to any one of the preceding claims, characterized in that: - the first beam and the second beam are separated by a distance Gz along the Z direction, - the fourth beam and the third beam are separated by the distance Gz along the Z direction, - the third beam and the second beam are separated by a distance Gx along the X direction, - the fourth beam and the first beam are separated by the distance Gx along the X direction.

12. The magnet structure according to claim 11, characterized in that Gx is comprised in the interval [1 mm; 250 mm], preferably in the interval [1 mm; 50 mm], and / or Gz is comprised in the interval [1 mm; 250 mm], preferably in the interval [1 mm; 50 mm].

13. The magnet structure according to claim 11 or 12, characterized in that Gx is equal, or substantially equal, to ±500 µm, preferably to within ±200 µm, to Gz, subsequently denoted G.

14. The magnet structure according to claim 13 considered as dependent on claim 8, characterized in that θx is equal to: where: Offset 1 = 33.634 ± 0.17 AGap 1 = 29.434 ± 0.109 BGap 1 = − 0.041763 ± 0.000374 APeriode 1 = − 39.534 ± 0.104 BPeriode 1 = − 0.027176 ± 0.00026315. The magnet structure according to claim 13 or 14, considered as dependent on claim 8, characterized in that θS is equal to: Offset 2 = 35.233 ± 0.147 AGap 2 = − 10.382 ± 0.0218 BGap 2 = − 0.066698 ± 0.000476 APeriod 2 = 13.866 ± 0.0918 BPeriod 2 = − 0.015736 ± 0.00034916. The magnet structure according to claim 13 considered as dependent on claim 9, characterized in that θx is equal to: where: Off 4 = 49.848 ± 0.3 AGap 4 = 41.206 ± 0.0801 BGap 4 = − 0.038149 ± 0.000217 APeriod 4 = − 54.559 ± 0.148 BPeriod 4 = − 0.018134 ± 0.00022317. The magnet structure according to claim 13 or 14, considered as dependent on claim 9, characterized in that θS is equal to: where: Off 3 = 37.222 ± 0.201 AGap 3 = − 9.6508 ± 0.0384 BGap 3 = − 0.038257 ± 0.000448 Aperiod 3 = 12.099 ± 0.13 BPeriod 3 = − 0.01507 ± 0.00050318. The magnet structure according to any one of the preceding claims, characterized in that it is arranged to generate a magnetic field with its component along the direction Z equal, or substantially equal, to ±5%, preferably to ±1%, to its component along the direction X.

19. An undulator comprising: - a magnet structure according to any one of the preceding claims, - a vacuum chamber arranged around or inside the magnet structure among the four beams.

20. A method for generating a magnetic field, characterized in that it is generated by means of a magnet structure according to any one of claims 1 to 18 or an undulator according to claim 19.

21. The method according to claim 20, characterized in that the magnetic field is generated with its component along the direction Z equal, or substantially equal, to ±5%, preferably to ±1%, to its component along the direction X.