Method and apparatus for homogenizing magnetostatic field generated from superconducting magnet
A method includes: calculating a first optimum quantity of ferromagnetic arranged at each position so that each error component of a magnetic field distribution in a specific space satisfies a first restriction condition (S 33 , S 34 ); discretizing, for each position, the first optimum quantity (S 35 ); calculating the error components that are obtained when ferromagnetic having a quantity of the first combination is arranged at each position (S 36 ); when the error component is less than the first lower limit, setting a condition including a lower limit greater than the first lower limit and an upper limit greater than the first upper limit as a second restriction condition, and when the error component is greater than the first upper limit, setting a condition including a lower limit less than the first lower limit and an upper limit less than the first upper limit as a second restriction condition (S 38 ).
1. A method of homogenizing, in a specific space, a magnetostatic field generated from a superconducting magnet by arranging a plurality of ferromagnetic bodies in the specific space, the specific space being subjected to the magnetostatic field, wherein a plurality of positions in the specific space at which the plurality of ferromagnetic bodies are arranged are predetermined, and each of the plurality of ferromagnetic bodies is selected from a plurality of specific ferromagnetic bodies each having a corresponding predetermined quantity of ferromagnetic material, the method comprising:
setting a first restriction condition including a corresponding first lower limit and a corresponding first upper limit for each of a plurality of error components of a magnetic field distribution in the specific space, and calculating a respective first optimum quantity of ferromagnetic material arranged at each position of the plurality of positions so that each error component, of the plurality of error components, satisfies the first restriction condition corresponding to the error component;
calculating, for each position of the plurality of positions, a first combination of at least one ferromagnetic body selected from the plurality of specific ferromagnetic bodies, the first combination having a first total corresponding ferromagnetic material amount closest to the first respective optimum quantity corresponding to the position among all possible combinations of the at least one ferromagnetic body;
calculating the plurality of error components that result when ferromagnetic material is arranged at each of the plurality of positions in quantities specified by the calculated first combination;
when, for each error component of the plurality of error components, the calculated error component is less than the first lower limit corresponding to the error component, setting a condition including a lower limit that is greater than the first lower limit and an upper limit that is greater than the first upper limit as a second restriction condition, and when the calculated error component is greater than the first upper limit corresponding to the error component, setting a condition including a lower limit that is less than the first lower limit and an upper limit that is less than the first upper limit as the second restriction condition, and calculating a respective second optimum quantity of ferromagnetic arranged at each position of the plurality of positions so that each error component, of the plurality of error components, satisfies the second restriction condition corresponding to the error component; and
calculating, for each position of the plurality of positions, a second combination of at least one ferromagnetic body selected from the plurality of specific ferromagnetic bodies, the second combination having a second total corresponding ferromagnetic material amount closest to the respective second optimum quantity corresponding to the position among all possible combinations of the at least one ferromagnetic body.
2. The method according to claim 1 , wherein
the calculating the respective first optimum quantity includes setting a third restriction condition including a second upper limit on a specific physical quantity of the ferromagnetic material arranged at the plurality of positions, and calculating the respective first optimum quantity so that each error component, of the plurality of error components, satisfies the first restriction condition corresponding to the error component and that the specific physical quantity satisfies the third restriction condition, and
the calculating the respective second optimum quantity further comprises, when the specific physical quantity of ferromagnetic specified by the first combination is greater than the second upper limit, setting a condition including an upper limit less than the second upper limit as a fourth restriction condition, and calculating the respective second optimum quantity of the ferromagnetic material arranged at each position of the plurality of positions so that each error component of the plurality of error components satisfies the second restriction condition corresponding to the error component and that the specific physical quantity satisfies the fourth restriction condition.
3. The method according to claim 2 , wherein the specific physical quantity includes a total weight of the ferromagnetic material arranged at the plurality of positions and an electromagnetic power generated at the ferromagnetic material arranged at each of the plurality of positions.
4. An apparatus for homogenizing, in a specific space, a magnetostatic field generated from a superconducting magnet by arranging a plurality of ferromagnetic bodies in the specific space, the specific space being subjected to the magnetostatic field, the apparatus comprising:
processing circuitry; and
a memory configured to store a specific program therein, wherein
a plurality of positions in the specific space at which the plurality of ferromagnetic bodies are arranged are predetermined,
each of the plurality of ferromagnetic bodies is selected from a plurality of specific ferromagnetic bodies each having a predetermined quantity, and
when executing the specific program, the processing circuitry is configured to perform:
setting a first restriction condition including a corresponding first lower limit and a corresponding first upper limit for each of a plurality of error components of a magnetic field distribution in the specific space, and calculating a respective first optimum quantity of ferromagnetic material arranged at each position of the plurality of positions so that each error component, of the plurality of error components, satisfies the first restriction condition corresponding to the error component;
calculating, for each position of the plurality of positions, a first combination of at least one ferromagnetic body selected from the plurality of specific ferromagnetic bodies, the first combination having a first total corresponding ferromagnetic material amount closest to the respective first optimum quantity corresponding to the position among all possible combinations of the at least one ferromagnetic body;
calculating the plurality of error components that result when ferromagnetic material is arranged at each of the plurality of positions in quantities specified by the calculated first combination;
when, for each error component of the plurality of error components, the calculated error component is less than the first lower limit corresponding to the error component, setting a condition including a lower limit that is greater than the first lower limit and an upper limit that is greater than the first upper limit as a second restriction condition, and when the calculated error component is greater than the first upper limit corresponding to the error component, setting a condition including a lower limit that is less than the first lower limit and an upper limit that is less than the first upper limit as the second restriction condition, and calculating a respective second optimum quantity of ferromagnetic arranged at each position of the plurality of positions so that each error component, of the plurality of error components, satisfies the second restriction condition corresponding to the error component; and
calculating, for each position of the plurality of positions, a second combination of at least one ferromagnetic body selected from the plurality of specific ferromagnetic bodies, the second combination having a second total corresponding ferromagnetic material amount closest to the respective second optimum quantity corresponding to the position among all possible combinations of the at least one ferromagnetic body.