A METHOD FOR CHARGING A SUPERCONDUCTOR BULK MAGNET BY FIELD-COOLING, WITH AT LEAST ONE NON-HOMOGENEOUS MAGNETIC FIELD COMPONENT OF THE APPLIED CHARGER MAGNETIC FIELD

Abstract

A method for charging a superconductor bulk magnet includes: step a) charging the magnet charger system so as to generate a first magnetic field in the sample volume, the superconductor bulk magnet having a temperature T>T.sub.c (300); step b) cooling the superconductor bulk magnet to a temperature T<T.sub.c (400); step c) discharging the magnet charger system, which inductively charges the superconductor bulk magnet, such that the superconductor bulk magnet traps a second magnetic field in the sample volume (500). In step a), the field adjustment unit is set such that the first magnetic field generated by the magnet charger system in the sample volume includes a homogeneous magnetic field component and at least one non-homogeneous magnetic field component (300). The non-homogeneous field component is chosen so that the second magnetic field of step c) has a higher homogeneity than the first magnetic field of step a) in the sample volume.

Claims

1. A method for charging a superconductor bulk magnet by field-cooling using a magnet charger system, wherein the magnet charger system comprises a background charger magnet and a field adjustment unit, wherein the superconductor bulk magnet comprises a bulk magnet bore, wherein the bulk magnet bore contains a sample volume, wherein the background charger magnet comprises a charger bore, wherein the superconductor bulk magnet is arranged within the charger bore, wherein the background charger magnet and the field adjustment unit are arranged radially outside the bulk magnet bore, and wherein the superconductor bulk magnet has a critical temperature T.sub.c; said method comprising: step a) charging the magnet charger system to thereafter generate a first magnetic field in the sample volume, wherein the superconductor bulk magnet has a temperature T, with T>T.sub.c; step b) cooling the superconductor bulk magnet to a temperature T<T.sub.c; step c) discharging the magnet charger system, which inductively charges the superconductor bulk magnet, such that the superconductor bulk magnet traps a second magnetic field in the sample volume; before said step a), determining a correlation between a magnetic field applied by the magnet charger system from outside the superconductor bulk magnet and a resulting magnetic field trapped by the superconductor bulk magnet at least approximately in the sample volume, in said step a), setting the field adjustment unit such that the first magnetic field generated by the magnet charger system in the sample volume comprises a homogeneous magnetic field component and at least one non-homogeneous magnetic field component, wherein the at least one non-homogeneous field component is chosen, using the correlation, such that the second magnetic field of said step c) has a higher homogeneity than the first magnetic field of said step a) in the sample volume, wherein the correlation is chosen with a linear function for each applied non-homogeneous magnetic field component comprised in the first magnetic field and to be adjusted by the field adjustment unit, wherein each linear function is defined by a slope and an offset, and correlates a component strength value of the magnetic field applied with a corresponding component strength value of the magnetic field trapped for the non-homogeneous magnetic field component, and wherein said determining of the correlation includes at least determining the offset for each linear function by calculation and/or by measurement.

2. Method according to claim 1, wherein, for a majority of the applied non-homogeneous magnetic field components comprised in the first magnetic field and adjusted by the field adjustment unit, preferably for each of the applied non-homogeneous magnetic field components comprised in the first magnetic field and adjusted by the field adjustment unit, a corresponding applied component strength value of the first magnetic field is larger in absolute value than is a corresponding trapped component strength value in the second magnetic field.

3. Method according to claim 1, wherein the at least one non-homogeneous magnetic field component of the first magnetic field is one or a plurality of gradient components of the first magnetic field, in particular wherein the gradient components are associated with first or higher order spherical harmonics.

4. Method according to claim 3, wherein the field adjustment unit comprises a plurality of field adjustment coils, allowing a direct adjustment of one or a plurality of individual gradient components, in particular wherein the field adjustment unit is chosen with a field adjustment coil or set of field adjustment coils for each gradient component.

5. Method according to claim 1, wherein, for at least approximately determining the correlation, before a cycle of said steps a), b) and c), at least one preparatory cycle of steps is applied, with each preparatory cycle of said steps comprising: step a′) charging the magnet charger system, such that said charging generates a first provisional magnetic field in the sample volume, wherein a magnetic field profile of the first provisional magnetic field is measured or calculated, in particular from electric currents applied to the magnet charger system, wherein the superconductor bulk magnet has a temperature T, with T>T.sub.c; step b′) cooling the superconductor bulk magnet to a temperature T<T.sub.c; step c′) discharging the magnet charger system, which inductively charges the superconductor bulk magnet, such that the superconductor bulk magnet traps a second provisional magnetic field in the sample volume, wherein a magnetic field profile of the second provisional magnetic field is measured.

6. Method according to claim 5, wherein: during said step a′), a respective applied component strength value for each of the at least one non-homogeneous magnetic field component to be adjusted by the field adjustment unit is determined from the measured or calculated magnetic field profile of the first provisional magnetic field, and during said step c′), a respective trapped component strength value for each of the at least one non-homogeneous magnetic field component to be adjusted by the field adjustment unit is determined from the measured magnetic field profile of the second provisional magnetic field.

7. Method according to claim 6, wherein: during a next cycle of said steps a), b), c) or during a next preparatory cycle of said steps a′), b′), c′), in a respective next step a) or next step a′), the field adjustment unit is set such that a respective non-homogeneous magnetic field component of the first magnetic field to be adjusted by the field adjustment unit is chosen with a next applied component strength value being the applied component strength value of said previous step a′) minus the trapped component strength value of the previous preparatory cycle of steps.

8. Method according to claim 5, wherein, in said step c), a magnetic field profile of the second magnetic field is measured, wherein, in each said step c′) and said step c), the homogeneity of the measured second provisional magnetic field or the second magnetic field in the sample volume is compared to a predefined homogeneity threshold, and when the homogeneity of the measured second provisional magnetic field is worse than the homogeneity threshold in said step c′), then another preparatory cycle of said steps a′), b′), c′) or another cycle of said steps a), b) and c) is performed, and when the homogeneity of the measured second magnetic field is equal to or better than the homogeneity threshold in said step c), then the second magnetic field in the sample volume is retained, and the method ends.

9. Method according to claim 1, wherein, for at least approximately determining the correlation, before a cycle of said steps a), b) and c), a magnetic field trapping behavior of the magnet charger system and the superconductor bulk magnet is calculated in advance, in particular numerically simulated in advance, taking into account at least a geometry of the magnet charger system or a magnetic field of the magnet charger system, and a geometry of the superconductor bulk magnet.

10. Method according to claim 9, wherein the calculation of the magnetic field trapping behavior includes, for each respective at least one non-homogeneous magnetic field component to be adjusted by the field adjustment unit, determining a target component strength value to be applied in the first magnetic field in order to obtain a desired, in particular zero, trapped component strength value in the second magnetic field, and in a following cycle of said steps a), b), c) or in a following preparatory cycle of said steps a′), b), c′), the field adjustment unit is set such that the first magnetic field generated by the magnet charger system in the sample volume comprises the respective non-homogeneous magnetic field component with an applied component strength value corresponding to the determined target component strength value.

11. Method according to claim 1, wherein for each of the linear functions, the slope is chosen as 1 or between 0.95 and 1, or the slope is determined by calculation and/or measurement, in particular wherein the slope is smaller than 1.

12. Method according to claim 1, wherein the field adjustment unit comprises a plurality of field adjustment coils, the field adjustment coils having a maximum axial extension L.sub.adjust which is larger than a maximum axial extension L.sub.bulk of the superconductor bulk magnet, preferably with L.sub.adjust>2*L.sub.bulk, and further a maximum radial extension R.sub.adjust which is larger than 1.5 times the maximum radial extension R.sub.bulk of the superconductor bulk magnet, preferably with R.sub.adjust>2*R.sub.bulk.

13. Method according to claim 1, wherein the magnet charger system is chosen with a superconducting background charger magnet, arranged in a charger cryostat.

14. Method according to claim 13, wherein the field adjustment unit is chosen with superconducting field adjustment coils, arranged inside the charger cryostat, in particular wherein the field adjustment coils are arranged radially outside the superconducting background charger magnet.

15. Method according to claim 1, wherein the superconductor bulk magnet is attached to a cooling stage contacting the superconductor bulk magnet at one axial end, and wherein the at least one non-homogeneous magnetic field component comprises a gradient component associated with the z spherical harmonic of the first magnetic field adjusted by the field adjustment unit.

16. Method according to claim 1, wherein the superconductor bulk magnet is chosen with a cylinder jacket shape having a constant wall thickness, and wherein the at least one non-homogeneous magnetic field component comprises a gradient component associated with the z.sup.2 spherical harmonic of the first magnetic field adjusted by the field adjustment unit.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The invention is shown in the drawing.

[0058] FIG. 1 shows a schematic cross-sectional view of an arrangement for charging a superconducting bulk magnet in accordance with the invention;

[0059] FIG. 2 shows a schematic flow diagram of an exemplary variant of the inventive method for charging a superconductor bulk magnet;

[0060] FIG. 3 shows a schematic diagram indicating an applied conventional homogeneous magnetic field and an applied non-homogeneous magnetic field in accordance with the invention and the respective resulting trapped magnetic field in the superconducting bulk magnet;

[0061] FIG. 4 shows a schematic diagram that explains how to determine a gradient component strength value of a non-homogeneous magnetic field component comprised in the first magnetic field;

[0062] FIG. 5 shows a schematic cross-section of different possible designs for a superconductor bulk magnet for the invention;

[0063] FIG. 6 illustrates in a schematic diagram the example of z.sup.1 shimming for design B of FIG. 5;

[0064] FIG. 7 shows a trapped field map in case the applied magnetic field was homogeneous for design A of FIG. 5;

[0065] FIG. 8 shows a trapped field map in case the applied magnetic field was non-homogeneous in accordance with the invention, for design A of FIG. 5.

DETAILED DESCRIPTION

[0066] FIG. 1 shows schematically an exemplary arrangement 1 for magnetizing (charging) a superconductor bulk magnet 90a by field-cooling, for use in an example of the inventive method.

[0067] The charging arrangement 1 comprises a magnet charger system 10 that comprises a background charger magnet 10a and a field adjustment unit 10b. The field adjustment unit 10b includes a plurality of field adjustment coils 10c. The background charger magnet 10a is chosen here as a superconducting background magnet and arranged inside a charger cryostat 2. In general, the background charger magnet 10a generates a basically homogeneous magnetic field component for a first magnetic field. The background charger magnet 10a is basically of cylindrical shape, here with a single solenoid type coil operated with a single electrical current (alternatively the background charger magnet 10a may comprise e.g. a plurality of radially stacked coaxial coils, operated with individual electrical currents). The background charger magnet 10a has a charger bore 3 inside of which the largest magnetic field strength of the first magnetic field may be achieved.

[0068] The field adjustment unit 10b with its field adjustment coils 10c is arranged radially outside of the background charger magnet 10a in the example shown. Alternatively, the field adjustment unit 10b may be arranged radially inside of the charger magnet 10a (but outside of the bulk magnet bore 4) (not shown). In such a variant, however, there is less space available in the charger bore 3. The field adjustment coils 10c are chosen here as superconducting field adjustment coils and located in the charger cryostat 2 of the magnet charger system 10. The field adjustment unit 10b generally basically generates at least one non-homogeneous magnetic field component of the first magnetic field. The field adjustment coils 10c are chosen such that a plurality of individual gradient components may be set directly, in particular a z.sup.1 and a z.sup.2 gradient component (sometimes also referred to H1 and H2).

[0069] Inside the charger bore 3 of the background charger magnet 10a, and inside the room temperature bore 2a of the charger cryostat 2, a magnetic field generator 90 with a superconductor bulk magnet 90a is arranged. In the example shown, the superconductor bulk magnet 90a is of basically cylinder jacket shape of constant wall thickness. The superconductor bulk magnet 90a allows circular currents to run through it. In a preferred variant, the superconductor bulk magnet 90a is made of a high temperature superconductor material; in a particularly preferred variant, the superconductor bulk magnet 90a is made of a ReBCO type superconductor material. The superconductor bulk magnet 90a has a bulk magnet bore 4, and the bulk magnet bore 4 contains a sample volume 5 at its center. The sample volume 5 may be accessed from at least one side. In the example chosen, the sample volume can be accessed from the top; in other embodiments, the bulk magnet bore 4 may have two sides open (not shown). The superconductor bulk magnet 90a is arranged in a cryostat 90c, which is independent of the charger cryostat 2 of the magnet charger system 10, and the sample volume 5 is arranged in a room temperature bore 90d of the cryostat 90c. It is also possible to add radiation shields (not shown) to reduce the heat input to the superconductor bulk magnet 90a. In the example shown, the superconductor bulk magnet 90a is attached at its lower end to a cooling stage 90b inside the cryostat 90c; note that alternatively it is possible to use two or more cooling stages to prevent the formation of a temperature gradient inside the superconductor bulk magnet 90a (not shown). The cooling stage 90b is preferentially cooled with a cryocooler, such as a pulse tube cooler (not shown); alternatively it may be cooled with cryogenic fluids (not shown).

[0070] The background charger magnet 10a has in axial direction (z direction) a length L.sub.charger that is larger than the length L.sub.bulk of the superconductor bulk magnet 90a (e. g. L.sub.charger>L.sub.bulk, preferably L.sub.charger>2*L.sub.bulk). The correction coils 10c that make up the field adjustment unit 10b have a combined length L.sub.adjust that is larger than the length L.sub.bulk of the superconductor bulk magnet 90a (e. g. L.sub.adjust>L.sub.bulk, preferably L.sub.adjust>2*L.sub.bulk). Furthermore, the correction coils 10c have a (maximum) radius R.sub.adjust that is larger than the (maximum) radius R.sub.charger of the background charger magnet 10a (e. g. R.sub.adjust>R.sub.charger). The correction coils 10c also have a (maximum) radius R.sub.adjust that is more than 1.5 times larger than the (maximum) radius R.sub.bulk of the superconductor bulk magnet 90a (e. g. R.sub.adjust>1.5*R.sub.bulk, preferably R.sub.adjust>2*R.sub.Bulk). These dimensions ensure that the inventive method may be performed in a simpler way (compare description of FIG. 4).

[0071] FIG. 2 illustrates an inventive method for magnetizing (charging) a superconductor bulk magnet in an exemplary variant. The method may be performed with an arrangement as shown in FIG. 1, for example.

[0072] In a first step 100 a correlation between a desired trapped magnetic field in the superconductor bulk magnet and an applied field to achieve the desired trapped magnetic field is determined for the arrangement based on its general design. This correlation may be calculated from the design of the arrangement used, knowing in particular the geometry of the magnet charger system and the geometry of the superconductor bulk magnet. The correlation may also be known by prior experience with similar field trapping setups, i. e. from other specimen of charger magnet system and superconductor bulk magnet of the same type. Note that step 100 is optional; if the correlation is not known or determined in advance, it is also possible to determine a correlation via a preparatory cycle which will be described later.

[0073] In the variant shown, in a step 200 the magnetic field generator (comprising the superconductor bulk magnet) is placed in the magnet charger system (comprising the charger magnet and the field adjustment unit) inside the bulk magnet bore. Note that in general, the magnet charger system is stationary, and for example located at the premises of the manufacturer of the superconductor bulk magnet. Further note that in general, the superconductor bulk magnet is held inside a cryostat the inner temperature of which may be controlled.

[0074] Then in a next step 300, the magnet charger system is charged, generating an applied magnetic field on the superconductor bulk magnet, and in particular a first magnetic field in the sample volume.

[0075] If a correlation has been determined in a step 100 or a step 550 (see below) before, the first magnetic field comprises a homogeneous magnetic field component and at least one non-homogeneous magnetic field component (“gradient component”), wherein the latter is/are chosen in accordance with the correlation such that the (imperfect) trapping behavior of the arrangement will lead to an optimal (highly homogeneous) trapped second magnetic field in the sample volume after step 500 (see below).

[0076] If a correlation has not been determined yet, the first magnetic field may be chosen provisionally in an arbitrary way; in general then a homogeneous provisional first magnetic field is preferably chosen.

[0077] The charger magnet generates in general predominantly the homogeneous magnetic field component, and the field adjustment unit generates in general above all the at least one non-homogeneous magnetic field component. The magnetic field components are superposed to add up to the first magnetic field. A magnetic field profile of the first (provisional or final) magnetic field is measured or calculated (the calculation is for example based on the electric currents applied to the magnet charger system). The generation of the magnetic fields is achieved by ramping up the electrical currents of the magnet charger system. During the generation of the first magnetic field the temperature T of the superconductor bulk magnet is larger than its critical temperature T.sub.c, so the superconductor bulk magnet is normally conducting during step 300. As a consequence, the magnetic field generated by the charger magnet system penetrates the superconductor bulk magnet basically unhindered and fills the bulk magnet bore.

[0078] In a next step 400, the superconductor bulk magnet is made superconducting by lowering the temperature inside the cryostat, such that T becomes lower than T.sub.c (i. e. T<T.sub.c). Note that T should be chosen significantly below T.sub.c such that enough current carrying capacity for next step 500 is ensured.

[0079] Then in step 500, the magnetic field of the magnet charger system is turned off. To achieve this the electrical currents operating the charger magnet system are ramped down. The superconductor bulk magnet conserves the magnetic flux in its bulk magnet bore, resulting in a trapped magnetic field. More specifically, a second magnetic field is trapped in the sample volume. To remain superconducting the superconductor bulk magnet is kept with T<T.sub.c. Note that the second magnetic field in general differs somewhat from the first magnetic field, indicating the imperfect trapping behavior of the arrangement.

[0080] In a preferred optional sub-step the superconductor bulk magnet 90a may be further cooled down to an operation temperature T.sub.op. T.sub.op is smaller than the temperature to trap the magnetic field T.sub.t (e. g T.sub.op<T.sub.t, preferably T.sub.op<(T.sub.t−2.5 K). This additional reduction in temperature of the superconductor bulk magnet reduces drift. In other variants it is also possible to perform this sub-step during or after step 600 or after step 700.

[0081] Now in step 600, the magnetic field profile of the second magnetic field is measured within the bulk magnet bore.

[0082] Next in step 700, the homogeneity of the measured second magnetic field profile is then compared to a predefined homogeneity threshold. There are two possible choices in step 700: [0083] When the homogeneity of the second magnetic field is equal to or better than the homogeneity threshold, the (then final) second magnetic field in the sample volume of the bulk magnet bore is accepted and kept. Previous steps 300, 400, 500 then constitute the final cycle of (field-cooling) steps. The method continues with step 800, where the magnetic field generator is removed from the magnet charger system and the method ends. [0084] When the homogeneity of the second magnetic field is worse than the homogeneity threshold, the (then provisional) second magnetic field in the sample volume of the bulk magnet bore is rejected. The method continues with step 550, where the superconductor bulk magnet is warmed-up above T.sub.c and in this way discharged so that it can be charged again. If no correlation of applied magnetic field and trapped magnetic field has been determined up to now, the correlation is now determined based on the applied (provisional) first magnetic field of step 300 and the measured (provisional) second magnetic field of step 600. If a correlation has been determined before, it can now be updated or refined using the (then provisional) first magnetic field of step 300 and the measured (provisional) second magnetic field of step 600. Previous steps 300, 400, 500 then constitute a preparatory cycle of (field-cooling) steps, and the method continues at step 300.

[0085] When after step 550 another cycle of steps is started at step 300, the information obtained from the determination of the magnetic field profile of the first provisional magnetic field and the magnetic field profile of the second provisional magnetic field can be used to set the field adjustment unit such that for a respective non-homogeneous magnetic field component the trapped component strength value of the previous preparatory cycle is subtracted from the applied component strength value of the previous preparatory cycle, resulting in the component strength value to be applied in the following cycle of steps.

[0086] FIG. 3 illustrates in a schematic diagram an applied conventional homogeneous magnetic field and an applied non-homogeneous magnetic field in accordance with the invention, and respective resulting trapped magnetic fields of the superconducting bulk magnet after field-cooling. In this example z.sup.2 shimming was done in accordance with the invention. The superconductor bulk magnet was built according to Design A of FIG. 5. FIG. 3 depicts on-axis field profiles with a center field of 4.7 T. The abscissa shows the z-direction in mm and the ordinate shows the field variation in μT. First the case of an applied homogeneous magnetic field is discussed (dotted line AH in FIG. 3), then the case of an applied non-homogeneous magnetic field is shown (dashed line AS in FIG. 3).

[0087] Applied Homogeneous Magnetic Field

[0088] In a first attempt, an applied magnetic field that is as homogeneous as possible is generated (see curve AH). In this example the on-axis field profile of the applied homogeneous magnetic field in the bulk magnet bore does not show any field variation within the shown area. The charging process by field-cooling corresponds to steps 300, 400 and 500 in FIG. 2. The superconductor bulk magnet is charged with the applied homogeneous magnetic field but the resulting trapped magnetic field (curve RH) exhibits a lower homogeneity than the applied magnetic field. The trapped magnetic field in this example already starts to vary at about 2 mm and decreases non-linearly for larger z (dotdashed line RH in FIG. 3).

[0089] This insufficient trapping of the applied magnetic field may be caused by the geometry of the superconductor bulk magnet, in particular its finite length or a non-optimal notch design due to space constraints, temperature gradients in the superconductor bulk magnet, the presence of (even slightly) magnetic components in the arrangement and production tolerances of the different components. So as shown for the example design, an applied magnetic field that is as homogeneous as possible does not lead to a homogeneous trapped field.

[0090] Applied Non-Homogeneous Magnetic Field

[0091] With the knowledge about the trapped magnetic field of the former case it is now possible to set the field adjustment unit such that the first magnetic field generated by the magnet charger system comprises at least one non-homogeneous magnetic field component next to the homogeneous magnetic field component. The at least one non-homogeneous magnetic field component is chosen as the inverse value of the trapped magnetic field component of the first attempt. In the illustrated example of FIG. 3, the z.sup.2 gradient component strength value was determined for the curve RH. Then a shimmed field AS was applied, having the opposite z.sup.2 gradient component strength value. The charging process by field-cooling corresponds to steps 300, 400, 500 in FIG. 2. The superconductor bulk magnet is charged with the applied non-homogeneous magnetic field. As a result, the trapped magnetic field in this example is highly homogeneous and does not start to vary until about 6 mm (solid line RS in FIG. 3). When comparing the resulting trapped magnetic fields (dashdotted line RH and solid line RS in FIG. 3) one can see that the homogeneity of the trapped field is higher when the applied magnetic field has been chosen non-homogeneous in accordance with the invention.

[0092] FIG. 4 shows a schematic diagram that explains how to determine the applied non-homogeneous magnetic field components or their respective component strength values comprised in the first magnetic field. The at least one non-homogeneous magnetic field component corresponds to one or a plurality of gradient components in the first magnetic field. They may be described as spherical harmonics of first or higher order or their coefficients, respectively.

[0093] First of all, for a perfect charging arrangement there would be no offset between the applied (first) and the trapped (second) magnetic field. In other words the superconductor bulk magnet would exactly trap the applied magnetic field of the magnet charger system. However, reality is different in that an offset between a trapped field gradient and an applied field gradient may be found. There are two offset components, namely: [0094] a design offset, caused by the charging arrangement as designed, originating for example from the presence of real materials (paramagnetism of superconductor bulk magnet, magnetic components, temperature gradients etc.) and finite sizes of the components; it can in principle be calculated a priori and is the same for a given design (type) and given operating conditions; [0095] a non-design offset, caused by differences of the actual charging arrangement as compared to the charging arrangement as designed, originating for example from manufacturing tolerances of the components, variation in material properties etc.

[0096] The design offset and the non-design offset result in an actual offset of a charging arrangement, which can be determined experimentally (i. e. measured). In practice, there is also scatter in the data that is caused by measurement errors and slight variations in the measurement procedure (e. g. time of measurement, slight differences in the cooling process, settling-in of the superconductor bulk magnet etc.).

[0097] There is a correlation between the first magnetic field and the second magnetic field. Furthermore, this correlation may be described with a linear function for each gradient component which is defined by a slope and an offset. In many setups, in particular when using a set-up as it has been described in FIG. 1, the slope of the linear function may be chosen as 1 or approximately 1. Then it is possible to determine the needed gradient components with only one measurement point. In divergent cases the slope may be determined by calculation and/or measurement. This is especially the case when the slope may be significantly smaller than 1. In this case at least two measurement points are needed instead of one.

[0098] FIG. 4 illustrates by way of example a design offset of a trapped field gradient and an actual offset of a trapped field gradient. Shown is an applied field gradient in arbitrary units on the abscissa, and the correspond resulting trapped field gradient in arbitrary units on the ordinate. An approach to determine the field gradient that has to be applied to get a desired trapped field gradient of close to zero may look like the following.

[0099] Based on the general design of a charger arrangement (type of magnet charger system, type of superconductor bulk magnet), a correlation between the applied and trapped magnetic field may be determined (calculated). The trapped field resulting from a zero applied field gradient according to the correlation based on the general design is called the design offset, and the related location in the diagram is called the initial design Point DI. The correlation based on the general design also includes a slope, indicating how efficient an applied field gradient value is transformed in a trapped field gradient value. In the example, this slope is 1 in good approximation, what can in many cases be assumed without calculation. A design line with this slope is laid through the initial design point DI. The design line intersects the abscissa and the so determined point is called the target design point DT. This target design point DT may be a convenient starting point for an actual field trapping attempt and can be used to set up the field adjustment unit for a charging cycle to achieve a second magnetic field with an ideally zero trapped component strength value. In the example shown, the design offset is at about +50 a. u., and the target design point is at about −50 a. u. of applied field gradient.

[0100] As described earlier the actual offset of the trapped field gradient might differ from the design offset due to for example manufacturing tolerances or process variations. To determine the actual offset a preparatory cycle of steps is for example performed to obtain the measured magnetic field profile of the second provisional magnetic field for a known magnetic field profile of the first magnetic field (see FIG. 2). Then the applied field gradient strength value and the trapped field gradient strength value are determined from these magnetic field profiles, and are denoted in the diagram as initial measurement (or initial measurement point) I. For this initial measurement I a measured line may be constructed, which intersects initial measurement point I and can be assumed to have slope 1 again (Note that if the actual slope is uncertain, at least two measurement points should be obtained, and the measured line can be obtained by linear fit). The point where the measured line intersects the ordinate shows the actual offset of the trapped field gradient, here at about +60 a. u. Furthermore, the measured line intersects the abscissa and the so determined point is called the final target T. This final target T should give the correct component strength value to be applied in the first magnetic field to obtain a trapped magnetic field without an offset of the trapped magnetic field components, which is here at about −60 a. u. of applied field gradient.

[0101] Note that the slope of the linear function represents the efficiency of the charging process. Herewith, the slope of the linear function may never be larger than 1, since this would mean that the efficiency of the charging process was above 100%, which is physically impossible.

[0102] FIG. 5 shows a schematic cross-section of a possible design for superconductor bulk magnet that can be used with the invention. The superconductor bulk magnet 90a may be described via a stack diameter SD, a stack height SH, a stack bore (diameter) SB, a notch height NH and a notch bore (diameter) NB. Two different designs are described.

[0103] Design A (also depicted in FIG. 5 top) has a SD of 60 mm, a SH of 140 mm, a SB of 33 mm, a NH of 100 mm and a NB of 40 mm. In this case the superconductor bulk magnet 90a comprises a notch. Notches may be used to increase the homogeneity of the trapped magnetic field. Note however, that it is not always possible to use an optimized notch design due to space constraints within the superconductor bulk magnet 90a.

[0104] Design B (not shown) has a SD of 60 mm, a SB of 40 mm and no notch, in other words the superconductor bulk magnet 90a has a constant wall thickness then. Sometimes it is not possible or not desired to implement notches due to for example space limitations within the experimental setup or to simplify the construction.

[0105] FIG. 6 illustrates in a schematic diagram an experiment of z.sup.1 shimming on design B of FIG. 5. The superconductor bulk magnet in this case has no notch. The abscissa shows the applied (z.sup.1) gradient in mT/m, and the ordinate shows the resulting trapped gradient in mT/m.

[0106] In a first simplified model where the temperature of the superconductor bulk magnet is assumed to be uniform, there should be no significant offset of the trapped (z.sup.1) gradient. The simplified design point D at the origin of the diagram depicts this case.

[0107] However in reality, when cooling of the superconductor bulk magnet is done from one axial end only, the cooling process of the superconductor bulk magnet results in an axial temperature gradient over the bulk magnet, what in turn affects the trapping behavior. An initial measurement I (here taken at zero applied gradient) shows that there is an (actual) offset of the trapped gradient, here of about +45 mT/m. The correlation between the applied and the trapped gradient contained in the initial measurement I may than be used. The correlation, or more specifically the sub-correlation with respect to the z.sup.1 gradient component, is assumed as a linear function with slope 1 (as described in FIG. 4). Using the crossing point of the measured line (having slope 1 and containing the initial measurement point I) with the abscissa, it is possible to find the corresponding gradient component which has to be applied to reach a zero trapped gradient, here with about −45 mT/m. In this example several different gradient component strength values were applied to improve the homogeneity and to assess the linearity of the correlation and to confirm the value 1 of the slope, and to assess the reproducibility of the measurement (points T1, T2, T3). All points T1, T2 T3 are close to the measured line, indicating that the assumption of the slope value was justified and the reproducibility is high, and showing that a high homogeneity of the trapped field can be achieved.

[0108] The z.sup.1 shimming may be used when the superconductor bulk magnet is attached to a cooling stage and has contact to the cooling stage on one axial end only. In this case the at least one non-homogeneous magnetic field component should comprise a gradient component which is associated with the z spherical harmonic of the first magnetic field that is adjusted by the field adjustment unit.

[0109] FIG. 7 and FIG. 8 show trapped field maps of an experiment of z.sup.2 shimming on design A of FIG. 5. The superconductor bulk magnet has a notch, but due to space constraints within the superconductor bulk magnet an optimized notch design was not possible.

[0110] In FIG. 7 the applied magnetic field was homogeneous. In this case the 10 ppm cylindrical sample volume 70 (e. g. the sample volume with a desired high homogeneity level of the trapped magnetic field) has a diameter of 28 mm and a height of 15.4 mm (see black dotted line).

[0111] To improve the 10 ppm cylindrical sample volume 70 in this example and to overcome the problems of the not optimized notch design, a non-homogeneous magnetic field was applied as described earlier with an z.sup.2 gradient component of about 75 mT/m.sup.2 (also compare FIG. 3). As it can be seen in FIG. 8, in this case the 10 ppm cylindrical sample volume 71 is much larger and has a diameter of 35 mm and a height of 19.8 mm (see black dotted line).

[0112] The z.sup.2 shimming may be used when the superconductor bulk magnet has a cylinder jacket shape with a constant wall thickness (as it is the case for Design B in FIG. 5) or with a notch only incompletely shaping the trapping behavior (as it is the case for Design A of FIG. 5). In these cases the at least one non-homogeneous magnetic field component should comprise a gradient component which is associated with the z.sup.2 spherical harmonic of the first magnetic field that is adjusted by the field adjustment unit.

LIST OF REFERENCE SIGNS

[0113] 1 (charger) arrangement [0114] 2 charger cryostat [0115] 2a room temperature bore (charger cryostat) [0116] 3 charger bore [0117] 4 bulk magnet bore [0118] 5 sample volume [0119] 10 magnet charger system [0120] 10a background charger magnet [0121] 10b field adjustment unit [0122] 10c field adjustment coils [0123] 70 10 ppm cylindrical sample volume [0124] 71 10 ppm cylindrical sample volume [0125] 90 magnetic field generator [0126] 90a superconductor bulk magnet [0127] 90b cooling stage [0128] 90c (bulk) cryostat [0129] 90d room temperature bore (bulk cryostat) [0130] 100 Determination of correlation (based on general design) [0131] 200 Setting up of the magnetic field generator [0132] 300 Generation of the first (provisional or final) magnetic field [0133] 400 Cooling down to T.sub.c [0134] 500 Inductive charging of the superconductor bulk magnet [0135] 550 Discharging and warming up of the superconductor bulk magnet and determination of correlation (by experiment) [0136] 600 Measurement of the second (provisional or final) magnetic field [0137] 700 Comparison with homogeneity threshold [0138] 800 Removing of the magnetic field generator [0139] AH Applied homogeneous field [0140] AS Applied shimmed field [0141] DI Initial design point [0142] DT Target design point [0143] I Initial point [0144] L.sub.adjust Length field adjustment coils [0145] L.sub.bulk Length superconductor bulk magnet [0146] L.sub.charger Length background charger magnet [0147] NB Notch bore (diameter) [0148] NH Notch height [0149] R.sub.adjust Radius field adjustment coils [0150] R.sub.bulk Radius superconductor bulk magnet [0151] R.sub.charger Radius background charger magnet [0152] SB Stack bore (diameter) [0153] SD Stack diameter [0154] SH Stack height [0155] RH Resulting trapped field [0156] RS Resulting trapped field [0157] T Target point [0158] T1, T2, T3 Target points

REFERENCES

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