EP1182462B1 - Dimensionnement d'un agencement d'aimants avec un système supplémentaire de bobines parcourues par un courant - Google Patents

Dimensionnement d'un agencement d'aimants avec un système supplémentaire de bobines parcourues par un courant Download PDF

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EP1182462B1
EP1182462B1 EP01115747A EP01115747A EP1182462B1 EP 1182462 B1 EP1182462 B1 EP 1182462B1 EP 01115747 A EP01115747 A EP 01115747A EP 01115747 A EP01115747 A EP 01115747A EP 1182462 B1 EP1182462 B1 EP 1182462B1
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coil system
field
magnet
current
volume
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EP1182462A3 (fr
EP1182462A2 (fr
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Robert Schauwecker
Pierre-Alain Bovier
Andreas Amann
Werner Tschopp
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Bruker Biospin SAS
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F6/00—Superconducting magnets; Superconducting coils

Definitions

  • the field of application of superconducting magnets comprises various fields of application, in particular various magnetic resonance methods.
  • the magnet assembly requires that the field strength in the working volume can be modulated during an experiment.
  • this field modulation is generated by a variation of the current in the main coil system.
  • the main coil system has a high self-inductance and therefore allows only slow current and field changes.
  • the cooling of the superconducting magnet coil system if, during operation, power supply lines are connected from the room temperature range to the cooled superconducting magnet. If the range over which the magnetic field strength is to be modulated is not too large (in particular less than 0.1 Tesla), the field modulation can be generated by varying the current in a coil system that supplements the main coil system.
  • the focus of the invention is in the field of dimensioning of magnet assemblies with an additional current-carrying coil system, which can be powered by an external power source and the working volume of a substantially different magnetic field of zero, especially in the field of dimensioning such magnet assemblies with a superconducting magnet with active stray field compensation and other superconducting current paths.
  • a requirement of an additional field-generating coil system in a magnet arrangement is to generate as much field as possible and to occupy as little space as possible within the magnet arrangement.
  • an additional field-producing coil system often has to be mounted close to the working volume of the magnet assembly, which is associated with undesirable "swelling" and increased cost of the superconducting main coil system.
  • Object of the present invention is in contrast to modify a magnet assembly of the type mentioned with the simplest possible means so that an additional field-generating coil system can be integrated into the magnet assembly so that it inflates the main coil system less strong with the same effect.
  • this object is achieved in that in the case of a field of the further current-carrying coil system (D), which does not exceed the order of magnitude of 0.1 Tesla in the working volume,
  • the efficiency of the additional field-generating coil system is improved by the fact that interactions between the additional field-generating coil system and the rest of the magnet arrangement for Field generation can be used.
  • a diamagnetic behavior of the superconductor material in the superconducting magnet coil system is used in an inventive arrangement, which is characterized in that field changes less than 0.1 Tesla, as for example when loading an additional field-generating coil system occur, are displaced from the superconducting volume fraction of the magnetic coil system.
  • G D eff Field contribution per ampere current of the additional field-generating coil system in the working volume taking into account the field contributions of the additional field-generating coil system itself as well as the field change due to currents which in the superconducting magnet coil system and in other superconducting closed current paths are induced during charging of the additional field-generating coil system, taking into account a diamagnetic displacement of small field changes from the volume of the magnet coil system, G D eff .
  • g Pj field per ampere of the current path Pj in the working volume without the field contributions of the current paths Pi reacting inductively on flux changes for i ⁇ j and of the magnet coil system
  • g M field per amp of the magnet coil system in the working volume without the field contributions of additional inductively reacting to flux changes current paths
  • g D field per ampere of the additional field-generating coil system in the working volume without the field contributions of additional inductively reacting to flux changes current paths and the magnetic coil system
  • L cl Matrix of the inductive couplings between the magnet coil system and the additional inductive responsive to changes in flow stream paths as well as between the additional inductively responsive to changes in flow current paths with each other
  • L cor Correction to the inductance matrix L cl , which would result from the volume of the magnet coil system in the event of complete diamagnetic displacement of disturbing fields
  • L ⁇ D cl Vector of the inductive couplings of the additional field-generating coil system with the magnet coil
  • the magnet arrangement according to the invention is preferably part of an apparatus for magnetic resonance spectroscopy, for example in the field of EPR and NMR.
  • the magnetic field in the working volume must be able to be modulated frequently in order to start the resonance line with a so-called field sweep.
  • this is achieved with an additional coil system which supplements the magnet coil system and which can be dimensioned particularly efficiently in an arrangement according to the invention.
  • one or more additional superconducting closed current paths are provided, wherein the magnetic fields generated by the additional current paths ( P1 , ..., Pn ) in the operating state due to induced currents in the z- direction and the field of the current-carrying coil system ( D ) the amount of 0.1 Tesla in the working volume amount not exceed and that the additional current paths ( P1 , ..., Pn ) are arranged coaxially with the magnetic coil system (M).
  • the superconducting magnet coil system comprises a radially inner and a radially outer, electrically connected in series, coaxial coil system, these two coil systems each generate a magnetic field in the working volume in the opposite direction along the z-axis.
  • the magnetic shielding behavior of the superconductor in the magnetic coil system typically affects particularly strong on the effective field strength in the working volume G D eff certain additional field-generating coil systems.
  • the radially inner coil system and the radially outer coil system have approximately the same opposite magnitude dipole moments. This is the condition for optimal suppression of the stray field of the magnetic coil system. Due to the great technical importance of actively shielded magnets, it is a great advantage that even in such magnets, the effective field strength in the working volume G D eff additional field-generating coil systems can be reinforced according to the invention by the diamagnetic shielding behavior of the superconductor in the magnet coil system.
  • the magnetic coil system forms a first in the operating state superconductingly short-circuited current path, and that a galvanically not connected to the magnetic coil system Störkompensationsspule is arranged coaxially to the magnetic coil system and forms another in the operating state superconductingly short-circuited current path.
  • the presence of a spurious compensating coil improves the temporal stability of the magnetic field in the working volume under the influence of external field fluctuations.
  • the influence of an interference compensation coil on the effective field strength in the working volume G D eff an additional field-generating coil system.
  • a development which is characterized in that a bridged with a superconducting switch part of the magnetic coil system forms another in the operating state superconductingly shorted current path.
  • the temporal stability of the magnetic field in the working volume is improved under the influence of external field fluctuations.
  • a system for compensating for the drift of the magnet coil system forms a further current path which is superconductingly short-circuited in the operating state.
  • the temporal stability of the magnetic field in the working volume is improved.
  • the influence of the drift compensation on the effective field strength in the working volume G D eff an additional field-generating coil system.
  • a shim device forms another current path which is superconductively short-circuited in the operating state.
  • field inhomogeneities can be compensated.
  • a particularly preferred embodiment of the magnet arrangement according to the invention is characterized in that a device with a radially inner and radially outer part coil forms another in the operating state superconductingly shorted current path, wherein the partial coils are connected in series, the radially outer part coil per ampere current in the amount has much larger dipole moment than the radially inner, and wherein the radially inner coil part per ampere current in the working volume builds up in a much larger magnetic field than the radially outer.
  • the effective field strength in the working volume G D eff an additional field-generating coil system, if the additional field-generating coil system is located outside the radially outer part coil of said device.
  • the additional field-generating coil system is normally conducting.
  • the advantage of this arrangement is that the additional field-generating coil system can be mounted in the room temperature range and therefore the cooling of the superconducting part of the magnet arrangement is not impaired.
  • Another advantageous development of a magnet arrangement according to the invention is characterized in that the additional field-generating coil system is superconducting.
  • the advantage of this arrangement is that the additional field generating coil system can carry more current than if the coils were made of a resistive material.
  • the additional field-generating coil system is part of a device for the modulation of the magnetic field strength in the working volume.
  • such a coil system can be dimensioned particularly efficiently.
  • the additional field-generating coil system is part of a so-called Z 0 -Shims, which generates a substantially homogeneous magnetic field in the working volume.
  • the advantage of this method for dimensioning a magnet arrangement with an additional field-generating coil system is that the magnetic shielding behavior of the superconductor is taken into account in the magnet coil system.
  • the method is based on calculating correction terms for the inductive couplings and for all self-inductances, which are reflected by a weighting factor ⁇ on the corresponding quantities.
  • ⁇ weighting factor
  • the parameter ⁇ corresponds to the volume fraction of the superconductor material on the volume of the magnet coil system. This method of determining the parameter ⁇ is based on the assumption that in the superconductor the susceptibility to small field changes (-1) amounts to (ideal diamagnetism).
  • ⁇ exp G H exp G H .
  • G H exp measured field change in the working volume of the magnet arrangement per ampere current in the interference coil
  • ⁇ cl 1 - G M ⁇ ( L M ⁇ H cl L M cl ⁇ G H ) .
  • g M field per ampere of the magnet coil system in the working volume
  • g H field per ampere of the interference coil in the working volume without the field contributions of the magnet coil system
  • L M cl Inductance of the magnet coil system
  • L M ⁇ H cl inductive coupling of the interference coil with the magnet coil system
  • L M cor Correction to the magnetic inductance L M cl .
  • L M ⁇ H cor Correction for inductive coupling L M ⁇ H cl the interference coil with the magnetic coil system, which would result in complete diamagnetic displacement of interference fields from the volume of the magnetic coil system.
  • both the superconducting magnet coil system M and the additional field-generating coil system D and the further superconductingly closed current path P1 can be constructed from a plurality of partial coils, which can be distributed over different radii.
  • the small coil cross section of the additional field-generating coil system D and the further superconductingly closed current path P1 in FIG. 1 shows that the additional field-generating coil system D and the further superconductingly closed current path P1 generate only weak magnetic fields, but the main field originates from the magnet coil system M.
  • FIGS. 2 to 4 show the functions g eff, cl and g eff for a single partial coil of a field-generating coil system as a function of the radius of the partial coil.
  • both the field contributions of the coil system itself and the field changes due to currents induced in the superconducting magnet coil system M and in further superconductingly closed current paths during charging of the coil system D be taken into account.
  • the superconductor of the magnetic coil system is modeled as a material without electrical resistance.
  • additional magnetic properties of the superconductor are taken into account.
  • additional coil systems D have an effect on the effective field strength of additional coil systems D, above all in actively shielded magnet coil systems.
  • the measured effective field strength of the additional coil system D does not correspond to that calculated with the classical model.
  • the diamagnetic displacement of small field changes can be used to achieve very large effective field strengths of additional coil systems.
  • Such coil systems can be Z 0 shims or field modulation coils, for example.
  • the field of the superconducting magnet coil system is orders of magnitude stronger than the field of additional coil systems (eg, a Z 0 shim or a field modulation coil)
  • the z component the component parallel to the field of the magnet coil system (referred to herein as the z component) of the field is effective of the additional coil systems in the total field amount. Therefore, we consider hereinafter only B z fields.
  • the current ⁇ I M cl - ⁇ I D ⁇ L M ⁇ D cl L M cl induced, wherein L M cl the (classic) self-inductance of the magnetic coil system and L M ⁇ D cl mean the (classical) inductive coupling between magnetic coil system and field-generating coil system.
  • the classical inductive couplings and the self-inductances are extended by an additional contribution. Therefore, the currents induced in the magnet coil system M and in the additional current paths P1, ..., Pn will generally assume different values than the classically calculated ones. In the following, these corrections are calculated based on a model of the magnetic behavior of the superconductor in the magnetic coil system.
  • type I superconductors completely displace magnetic flux from their interior (Meissner effect). For type II superconductors, this is no longer the case above the lower critical field H c 1 .
  • the bean model CP Bean, Phys. Rev. Lett., 8, 250 (1962), CP Bean, Rev. Mod., Phys., 36, 31 (1964)
  • the magnetic flux lines adhere to the so-called "pinning centers”.
  • Small flux changes are captured by the "pinning centers” on the surface of the superconductor and do not reach the inside of the superconductor. This results in a partial displacement of interference fields from the superconductor volume.
  • a type II superconductor reacts diamagnetically to small field changes, while larger field changes largely penetrate into the superconductor material.
  • the principle of calculating the correction terms is the same in all cases, namely to determine how much the magnetic flux through one coil due to a small current change in another (or in itself) by the presence of the diamagnetically reacting superconducting material in the main coil of the magnetic coil system is reduced. Accordingly, the coupling of the first with the second coil (or the self-inductance) is reduced.
  • the size of the correction term depends on how large the proportion of the volume filled with superconductor material of the main coil within the inductively reacting coil is on the entire volume enclosed by the coil.
  • the relative position of the coils to one another has an influence on the correction term for their mutual inductive coupling.
  • a useful tool for calculating correction terms has been the introduction of "reduced coils".
  • the coil X reduced to the radius R we mean that hypothetical coil which would result if all the turns of the coil X were wound on the radius R.
  • the notation uses the index " X, red, R ". Thanks to the reduced coils, when a flux changes through a coil, the contributions of the flux change through partial areas of this coil can be calculated from the total flux change.
  • the correction term for coupling a field generating coil system D to the main coil C1 of the magnetic coil system is calculated.
  • the interference field .DELTA.B z, D is an average of the contribution ⁇ ⁇ .DELTA.B z, D reduced, where 0 ⁇ ⁇ 1 is an a priori still unknown parameter.
  • the disturbance flux through the main coil C1 and thus the inductive coupling L 1 ⁇ D of the main coil and additional field generating Coil system by a factor ( 1 - ⁇ ) compared to the classic value L 1 ⁇ D cl weakened if the interference field in the inner bore of the main coil is also treated as reduced by the factor ( 1 - ⁇ ).
  • the flow of the additional field-generating coil system is not displaced from the inner bore of the magnet.
  • L 1 ⁇ D ( 1 - ⁇ ) ⁇ L 1 ⁇ D cl + ⁇ L ( 1 . red . R i 1 ) ⁇ D cl
  • R a 1 ) ⁇ D cl - L ( 2 . red . R i 1 ) ⁇ D cl ) L ( 2 . red . R a 1 ) ⁇ D cl refers to the classic coupling of the additional field-generating coil system with the "reduced" to the radius Ra 1 shield (analogous to Ri 1 ).
  • L M ⁇ D L M ⁇ D cl - ⁇ L M ⁇ D cor
  • L M ⁇ D cor L 1 ⁇ D cl - L ( 1 . red . R i 1 ) ⁇ D cl + R a 1 R 2 ( L ( 2 . red . R a 1 ) ⁇ D cl - L ( 2 . red . R i 1 ) ⁇ D cl )
  • L 2 ⁇ 2 L 2 ⁇ 2 cl - ⁇ R a 1 R 2 ( L ( 2 . red . R a 1 ) ⁇ 2 cl - L ( 2 . red . R i 1 ) ⁇ 2 cl )
  • L 2 ⁇ 1 L 2 ⁇ 1 cl - ⁇ R a 1 R 2 ( L ( 2 . red . R a 1 ) ⁇ 1 cl - L ( 2 . red . R i 1 ) ⁇ 1 cl )
  • L M L M cl - ⁇ L M cor
  • L M cor L 1 ⁇ 1 cl - L ( 1 . red . R i 1 ) ⁇ 1 cl + L 1 ⁇ 2 cl - L ( 1 . red, R i 1 ) ⁇ 2 cl + R a 1 R 2 ( L ( 2 . red . R a 1 ) ⁇ 2 cl - L ( 2 . red . R i 1 ) ⁇ 2 cl + L ( 2 . red . R a 1 ) ⁇ 1 cl - L ( 2 . red . R i 1 ) ⁇ 1 cl )
  • L Pj ⁇ M L P j ⁇ M cl - ⁇ L P j ⁇ M cor
  • L P j ⁇ M cor f P j ( L ( P j . red . R a 1 ) ⁇ M cl - L ( P j . red . R i 1 ) ⁇ M cl )
  • the constant f Pj is calculated from the integration of (4) over the region r > R Pj .
  • R P j > R a 1 1 .
  • L Pj ⁇ D L P j ⁇ D cl - ⁇ L P j ⁇ D cor
  • L P j ⁇ D cor f P j ( L ( P j . red . R a 1 ) ⁇ D cl - L ( P j . red . R a 1 ) ⁇ D cl )
  • g Pj field per ampere of the current path Pj in the working volume without the field contributions of the current paths Pi for i ⁇ j and of the magnet coil system M and without the field contributions of the coil system D
  • g M field per ampere of the magnet coil system M in the working volume without the field contributions of the current paths P1,..., Pn and without the field contributions of the coil system D
  • g D field per ampere of the coil system D in the working volume without the field contributions of the current paths P1,..., Pn and the magnet coil system M
  • L cl Matrix of the inductive couplings between the magnet coil system M and the current paths P1, ..., Pn as well as between the current paths P1, ..., Pn with each other
  • L cor correction to the inductance matrix L cl , which would result from the volume of the magnet coil system M in the case of complete diamagne
  • a current path Pj comprises partial coils at different radii
  • the matrix elements in the correction terms L cor and L ⁇ D cor . which belong to Pj are calculated so that first each sub-coil is treated as a single current path and then the correction terms of all sub-coils are added up. This sum is the matrix element of the current path Pj .
  • the coil systems D that interest us are, above all, Z 0 shims or field modulation coils.
  • the field efficiency G D eff Such a coil system should typically be as large as possible.
  • the additional field-generating coil system and the remainder of the magnet arrangement can be optimized such that this field efficiency becomes maximum.
  • a magnet arrangement in which the magnetic shielding behavior of the superconducting material in the magnet coil system clearly contrasts with the field efficiency in comparison to small field changes G D eff of the additional field-effecting coil system comprises an actively shielded magnet coil system comprising a main coil C1 and a shielding coil C2 .
  • partial coils of a field-generating coil system behave in a classical way as long as they are in the region of the main coil C1 of the actively shielded magnet coil system, whereas their effective field efficiency is enhanced by the magnetic shielding behavior of the superconductor material in the magnet coil system when they are radial lie further outside. This effect can be used to provide an efficient additional large radius field-creating coil system, thereby gaining space for the small radius magnet coil system.

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Claims (11)

  1. Agencement magnétique supraconducteur (M, D, P1, ... Pn) pour générer un champ magnétique en direction d'un axe z dans un volume de travail situé autour de z = 0, comprenant un système de bobines magnétiques (M) avec au moins une bobine magnétique supraconductrice parcourue par du courant, un autre système de bobines (D) parcouru par du courant qui peut être alimenté par une source de courant externe et qui crée dans le volume de travail un champ magnétique substantiellement différent de zéro, sachant que le système de bobines magnétiques (M) et l'autre système de bobines (D) parcouru par du courant sont coaxiaux et entourent le volume de travail, et qu'au moins des parties de l'autre système de bobines (D) parcouru par du courant sont disposées radialement à l'extérieur de parties du système de bobines magnétiques (M),
    caractérisé par le fait
    qu'avec un champ de l'autre système de bobines (D) parcouru par du courant qui ne dépasse pas l'ordre de grandeur de 0,1 tesla en valeur absolue dans le volume de travail, | g D eff | > 1 , 2 ⋅ | g D eff , cl | ,
    Figure imgb0164
     où g S eff = g D − g T ⋅ ( L cl − α L cor ) − 1 ⋅ ( L ← D cl − α L ← D cor ) ,
    Figure imgb0165
     g D eff , cl = g D − g T ⋅ ( L cl ) − 1 ⋅ L ← D cl
    Figure imgb0166
    avec :
    g D eff :
    Figure imgb0167
     contribution au champ par ampère de courant du système de bobines (D) dans le volume de travail compte tenu des contributions au champ du système de bobines (D) lui-même ainsi que de la variation de champ résultant de courants qui sont induits lors de la charge du système de bobines (D) dans le système de bobines magnétiques (M) et dans d'éventuels autres trajets de courant (P1,...,Pn) fermés de manière supraconductrice, en tenant compte d'un refoulement diamagnétique des champs perturbateurs du volume du système de bobines magnétiques (M),
    g D eff , cl :
    Figure imgb0168
     contribution au champ par ampère de courant du système de bobines (D) dans le volume de travail compte tenu des contributions au champ du système de bobines (D) lui-même ainsi que de la variation de champ résultant de courants qui sont induits lors de la charge du système de bobines (D) dans le système de bobines magnétiques (M) et dans d'éventuels autres trajets de courant (P1, ..., Pn) fermés de manière supraconductrice, en négligeant le refoulement diamagnétique des champs perturbateurs du volume du système de bobines magnétiques (M),
    -α: susceptibilité magnétique moyenne dans le volume du système de bobines magnétiques (M) par rapport à des fluctuations de champ qui ne dépassent pas l'ordre de grandeur de 0,1 T en valeur absolue ; 0 < α ≤ 1, g T = ( g M , g P 1 , … , g P j , … g P n )
    Figure imgb0169
    g Pj : champ par ampère d'un trajet de courant Pj éventuellement présent dans le volume de travail sans les contributions au champ d'éventuels autres trajets de courant Pi pour i ≠ j et du système de bobines magnétiques (M),
    g M : champ par ampère du système de bobines magnétiques (M) dans le volume de travail sans les contributions au champ de trajets de courant (P1, ..., Pn) éventuellement présents,
    g D : champ par ampère du système de bobines (D) dans le volume de travail sans les contributions au champ de trajets de courant (P1, ..., Pn) éventuellement présents et du système de bobines magnétiques (M),
    L cl : matrice des couplages inductifs entre le système de bobines magnétiques (M) et des trajets de courant (P1, ..., Pn) éventuellement présents ainsi qu'entre les trajets de courant (P1, ..., Pn) éventuellement présents entre eux,
    L cor : correction à la matrice d'inductances L cl que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M),
    L ← D cl :
    Figure imgb0170
     vecteur des couplages inductifs du système de bobines (D) avec le système de bobines magnétiques (M) et les trajets de courant (P1,..., Pn) éventuellement présents,
    L ← D cor :
    Figure imgb0171
     correction au vecteur de couplage L ← D cl
    Figure imgb0172
     que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M).
  2. Agencement magnétique selon la revendication 1, caractérisé par le fait qu'il est prévu un ou plusieurs trajets de courant (P1, ..., Pn) fermés de manière supraconductrice supplémentaires, sachant que les champs magnétiques générés en fonctionnement en direction z par les trajets de courant (P1,..., Pn) supplémentaires par suite des courants induits et le champ du système de bobines (D) parcouru par du courant ne dépassent pas l'ordre de grandeur de 0,1 T en valeur absolue dans le volume de travail et que les trajets de courant (P1,..., Pn) supplémentaires sont disposés coaxialement au système de bobines magnétiques (M).
  3. Agencement magnétique selon l'une des revendications précédentes, caractérisé par le fait que le système de bobines magnétiques (M) comprend deux systèmes de bobines coaxiaux (C1, C2), l'un radialement intérieur et l'autre radialement extérieur, interconnectés électriquement en série, ces deux systèmes de bobines générant dans le volume de travail des champs magnétiques de sens opposés le long de l'axe z.
  4. Agencement magnétique selon l'une des revendications 2 à 3, caractérisé par le fait que le système de bobines magnétiques (M) forme un premier trajet de courant court-circuité de manière supraconductrice en fonctionnement et qu'une bobine compensatrice de perturbation non reliée galvaniquement au système de bobines magnétiques (M) est disposée coaxialement au système de bobines magnétiques (M) et forme un autre trajet de courant (P1) court-circuité de manière supraconductrice en fonctionnement.
  5. Agencement magnétique selon l'une des revendications 2 à 4, caractérisé par le fait qu'au moins un des trajets de courant supplémentaires (P1, ..., Pn) fait partie d'un dispositif de shim supraconducteur.
  6. Agencement magnétique selon l'une des revendications 2 à 5, caractérisé par le fait qu'au moins un des trajets de courant supplémentaires (P1, ..., Pn) comprend une bobine partielle radialement intérieure et une bobine partielle radialement extérieure qui sont connectées en série, sachant que la bobine partielle radialement extérieure présente, par ampère de courant, un moment dipolaire beaucoup plus grand en valeur absolue que la bobine partielle radialement intérieure, et que la bobine partielle radialement intérieure crée dans le volume de travail, par ampère de courant, un champ magnétique beaucoup plus grand que la bobine partielle radialement extérieure.
  7. Agencement magnétique selon l'une des revendications précédentes, caractérisé par le fait que le système de bobines (D) supplémentaire fait partie d'un dispositif de modulation de l'intensité du champ magnétique dans le volume de travail.
  8. Agencement magnétique selon l'une des revendications 1 à 6, caractérisé par le fait que le système de bobines (D) supplémentaire fait partie d'un shim dit Z0 qui génère un champ magnétique essentiellement homogène dans le volume de travail.
  9. Procédé pour dimensionner un agencement magnétique (M, D, P1, ... Pn) selon l'une des revendications 2 à 8, caractérisé par le fait que la grandeur g D eff ,
    Figure imgb0173
     qui correspond à la variation de champ dans le volume de travail à z = 0 par ampère de courant dans le système de bobines (D) supplémentaire, est calculée, compte tenu des champs magnétiques créés par suite des courants induits dans le reste de l'agencement magnétique (M, P1, ..., Pn), par la formule : g D eff = g D − g T ⋅ ( L cl − α L cor ) − 1 ⋅ ( L ← D cl − α L ← D cor )
    Figure imgb0174
    avec :
    -α: susceptibilité magnétique moyenne dans le volume du système de bobines magnétiques (M) par rapport à des fluctuations de champ qui ne dépassent pas l'ordre de grandeur de 0,1 T en valeur absolue ; 0 < α ≤ 1, g T = ( g M , g P 1 , … , g P j , … g P n )
    Figure imgb0175
    g Pj : champ par ampère du trajet de courant Pj dans le volume de travail sans les contributions au champ des trajets de courant Pi pour i ≠ j et du système de bobines magnétiques (M),
    g M : champ par ampère du système de bobines magnétiques (M) dans le volume de travail sans les contributions au champ des trajets de courant (P1, ..., Pn),
    g D : champ par ampère du système de bobines (D) dans le volume de travail sans les contributions au champ des trajets de courant (P1, ..., Pn) et du système de bobines magnétiques (M),
    L cl : matrice des couplages inductifs entre le système de bobines magnétiques (M) et les trajets de courant (P1,..., Pn) ainsi qu'entre les trajets de courant (P1, ..., Pn) entre eux,
    L cor : correction à la matrice d'inductances L cl que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M),
    L ← D cl :
    Figure imgb0176
     vecteur des couplages inductifs du système de bobines (D) avec le système de bobines magnétiques (M) et les trajets de courant (P1,..., Pn),
    L ← D cor :
    Figure imgb0177
     correction au vecteur de couplage L ← D cl
    Figure imgb0178
     que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M).
  10. Procédé selon la revendication 9, caractérisé par le fait que le paramètre α correspond à la part du volume du matériau supraconducteur dans le volume total du système de bobines magnétiques (M).
  11. Procédé selon la revendication 9, caractérisé par le fait que le paramètre α est déterminé expérimentalement à partir de la mesure de la grandeur βexp du système de bobines magnétiques (M) sans les trajets de courant (P1, ..., Pn) et sans système de bobines (D) supplémentaire par rapport à une bobine perturbatrice (H) qui génère dans le volume du système de bobines magnétiques (M) un champ perturbateur essentiellement homogène et en introduisant la grandeur βexp dans l'équation : α = g H ( L M cl ) 2 ( β exp − β cl ) g H ( β exp − β cl ) L M cl L M cor − g M ( L M ← H cl L M cor − L M ← H cor L M cl )
    Figure imgb0179
    dans laquelle β exp = g H exp g H ,
    Figure imgb0180
    g H exp :
    Figure imgb0181
     variation de champ mesurée dans le volume de travail de l'agencement magnétique par ampère de courant dans la bobine perturbatrice (H), β cl = 1 − g M ⋅ ( L M ← H cl L M cl ⋅ g H ) ,
    Figure imgb0182
    g M : champ par ampère du système de bobines magnétiques (M) dans le volume de travail,
    g H : champ par ampère de la bobine perturbatrice (H) dans le volume de travail sans les contributions au champ du système de bobines magnétiques (M),
    L M cl :
    Figure imgb0183
     inductance du système de bobines magnétiques (M),
    L M ← H cl :
    Figure imgb0184
     couplage inductif de la bobine perturbatrice (H) avec le système de bobines magnétiques (M),
    L M cor :
    Figure imgb0185
     correction à l'inductance magnétique L M cl
    Figure imgb0186
     que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M),
    L M ← H cor :
    Figure imgb0187
     correction au couplage inductif L M ← H cl
    Figure imgb0188
     de la bobine perturbatrice (H) avec le système de bobines magnétiques (M) que l'on obtiendrait en cas de refoulement diamagnétique complet des champs perturbateurs du volume du système de bobines magnétiques (M).
EP01115747A 2000-08-24 2001-07-09 Dimensionnement d'un agencement d'aimants avec un système supplémentaire de bobines parcourues par un courant Expired - Lifetime EP1182462B1 (fr)

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US7098663B1 (en) * 2005-03-18 2006-08-29 Timothy James Hollis Systems, methods and apparatus of an actively shielded superconducting magnet drift compensation coil
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DE10041672C2 (de) 2002-07-11
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US6680662B2 (en) 2004-01-20
JP2002158108A (ja) 2002-05-31
EP1182462A2 (fr) 2002-02-27
DE50110010D1 (de) 2006-07-20

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