10．g-2/EDM 超伝導電磁石開発とMRI への精密磁場技術

高エネルギー加速器研究機構
阿

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g-2/EDM 超伝導電磁石開発とMRIへの精密磁場技術
１

はじめに ………………………………………………………………………………………………… 10−１

１．１

既開発の磁場設計技術 …………………………………………………………………………… 10−１

１．２

磁場設計と正則化 ………………………………………………………………………………… 10−２

１．３

本資料の内容 ……………………………………………………………………………………… 10−２２

最小二乗法と正則化…………………………………………………………………………………… 10−３

２．１

正則化による最小二乗解 ………………………………………………………………………… 10−３２．２

固有モード強度に注目したTSVD 正則化 ……………………………………………………… 10−４

２．３

目標磁場について ………………………………………………………………………………… 10−６

３

TSVD 正則化を用いる例題 …………………………………………………………………………… 10−７

３．１

例題の計算体系 …………………………………………………………………………………… 10−７３．２

電流-磁場の応答行列と特異値分解３．３

磁場・電流分布の再構成

３．４

目標磁場とMaxwell 方程式 ……………………………………………………………………… 10−13

３．５

3 章のまとめ ……………………………………………………………………………………… 10−16４…………………………………………………………… 10−９………………………………………………………………………… 10−11

MRI 用磁石の一様磁場設計 …………………………………………………………………………… 10−18………………………………………………………………… 10−19

４．１

MRI 磁石磁場設計の磁場成分

４．２

概念検討(Step-1) ………………………………………………………………………………… 10−19４．３起磁力配置の離散化(Step-2) …………………………………………………………………… 10−23

４．４

巻き線数の離散化(Step-3) ……………………………………………………………………… 10−25

４．５

鉄芯型MRI 磁石の場合 …………………………………………………………………………… 10−26

４．６

磁場シミング ……………………………………………………………………………………… 10−28

４．７

MRI 磁石静磁場設計のまとめ …………………………………………………………………… 10−33

５g-2/EDM磁石の磁場設計 ……………………………………………………………………………… 10−35

５．１

主磁場 ……………………………………………………………………………………………… 10−35

５．２調整装置 …………………………………………………………………………………………… 10−41

５．３

Muon 入射&蓄積関係の磁場発生機器 …………………………………………………………… 10−46

５．４

g-2/EDM 磁石磁場設計のまとめ ……………………………………………………………… 10−52

６

まとめ …………………………………………………………………………………………………… 10−53

参考文献 ……………………………………………………………………………………………………… 10−55

3.0cm, ㍈ ᪉ ྥ 㧗 ࡉ 10.0cm ࡢ 㡿 ᇦ ࡛ ࠊ3.0T±

g-2/EDM ㉸ ఏ ᑟ 㟁 ☢ ▼ 㛤 Ⓨ ࡜
MRI ࡬ࡢ⢭ᐦ☢ሙᢏ⾡

0.30 T(0.1ppm)ࡀ┠ᶆ࡛࠶ࡿ[6-7]ࠋඹ࡟ࠊᘧ(1-1)࡛ࡣᆒ୍ᗘࡢ┠ᶆࡣ 0.2ppm ࡛࠶ࡿࠋࡇࡢࡼ࠺࡞ᴟࡵ࡚Ⰻ࠸ᆒ୍࡞☢ሙࢆᚓࡿ࡟

1. ࡣࡌࡵ࡟ࡣࠊタ⨨᫬ࠊ౑⏝㛤ጞ๓࡟ࠊ☢ሙㄪᩚ(ࢩ࣑ࣥࢢ)J-PARC ࡛ࡣ࣑࣮ࣗ࢜ࣥ࡟ࡘ࠸࡚≀⌮ⓗᛶ㉁ࢆ

ࢆ⾜࠺ࡇ࡜ࡣᙜ↛࡛࠶ࡿࡀࠊࡑࡢ☢ሙㄪᩚࢆྍ

ࡍࡿ 2 ࡘࡢᐇ㦂ࡀ‽ഛࡉࢀ࡚࠸ࡿࠋඹ

⬟࡜ࡍࡿ࡟ࡣࠊ౑⏝ࡍࡿ☢▼࡟ࠊࡑࡢ⬟ຊࡀഛ࡟ࠊᴟࡵ୍࡚ᵝᛶࡢⰋ࠸㧗☢ሙࢆᚲせ࡜ࡋ࡚࠸ࢃࡗ࡚࠸ࡿࡇ࡜ࡀᚲせ࡛࠶ࡿࠋᮏ㈨ᩱ୰࡛⤂௓ࡿ ࠋ ୍ ᵝ ᛶ ࡢ Ⰻ ࠸ ☢ ሙ ࡣ ᪤ ࡟ MRI(Magneticࡍࡿࡀࠊᴫᛕⓗ࡟ࡣḟࡢࡼ࠺࡛࠶ࡿࠋᴟࡵ࡚Ⰻ

Resonance Imaging)࡛ᐇ⌧ࡉࢀࠊ฼⏝ࡉࢀ࡚࠸ࡿ

࠸ᆒ୍ᗘ࡟ㄪᩚࡍࡿ࡟ࡣࠊ✵㛫ⓗ࡟⣽࠿࠸☢ሙ

[1,2]ࡀࠊJ-PARC ࡛ࡢᐇ㦂࡟ᚲせ࡞☢ሙࡢ୍ᵝᛶศᕸࡲ࡛ㄪᩚࡍࡿᚲせࡀ࠶ࡾࠊ⣽࠿࠸✵㛫ศᕸࡣࠊMRI ࡟ẚ࡭ࡿ࡜ࠊࡉࡽ࡟ᴟࡵ࡚Ⰻዲ࡞☢ሙࡢㄪᩚ࡟ࡣࢩ࣒∦(ᙉ☢ሙ୰࡛☢໬ࡋࡓ㕲∦ࢩ࣒࡛࠶ࡿࠋࡇࢀࡽࡣࠊ࣑࣮ࣗ࢜ࢽ࣒࢘ࡢ㉸ᚤ⣽ᵓࢆ౑࠺ࡇ࡜ࡀከ࠸)ࢆ኱㔞࡟౑⏝ࡍࡿࠋ㐺ษ࡟☢

ᐃ ࡢ 㧗 ☢ ሙ MuSEUM (Muoniumሙタィࡀ࡞ࡉࢀ࡚࠸ࡿ࡜ࠊ〇స࣭⤌ࡳ❧࡚࣭タ

Spectroscopy Experiment Using Microwave)ᐇ 㦂⨨᫬࡟Ⓨ⏕ࡋࡓㄗᕪ☢ሙᡂศࡢࡳࡢ⿵ṇ࡟࡜࡝

[3,4]ࠊ࠾ࡼࡧࠊ࣑࣮ࣗ࢜ࣥ␗ᖖ☢Ẽ⬟⋡/㟁Ẽ⬟ࡲࡾࠊᑡ࡞࠸ࢩ࣒㔞࡛ᆒ୍☢ሙࡢᐇ⌧ࡀྍ⬟࡛⋡(g-2/EDM)㧗⢭ᗘᐃᐇ㦂࡛࠶ࡿ[5-7]ࠋࡇࢀࡽ

࠶ࡿࠋࡋ࠿ࡋࠊ㐺ษ࡟タィࡉࢀ࡚↓࠸ሙྜࠊᮏࡢ ᐇ 㦂 ෆ ᐜࡢ ㄝ ᫂ ࡣ ௚ᩥ ⊩ ࢆ ཧ ⪃࡟ ࡋ ࡚ 㡬 ࡃ᮶タィ᫬࡟ຍ࠼࡚࠾ࡃ࡭ࡁ✵㛫ⓗ࡟⣽࠿࠸☢ሙࡀࠊඹ࡟⢭ᗘⰋ࠸୍ᵝ☢ሙࢆᚲせ࡜ࡍࡿᐇ㦂࡛ᡂศࡲ࡛ࠊ⿵ṇࡍࡿࡇ࡜࡟࡞ࡾࠊ኱㔞ࡢࢩ࣒∦

࠶ࡿⅬ࡟ඹ㏻Ⅼࡀ࠶ࡿࠋࡑࢀࡒࢀࠊ1.7T ࠾ࡼࡧ

ࡀᚲせ࡜࡞ࡿࠋᐇ㝿ⓗ࡟ࡣ┠ᶆᆒ୍ᗘࡢᐇ⌧ࡀ

3.0T ࢆỌஂ㟁ὶ(Persistent current)㏻㟁ࡢ㉸㟁ᑟ☢

୙ྍ⬟࡜࡞ࡿࠋ☢ሙタィ࡛ィ⏬ࡋࡓᆒ୍ᗘ௨ୖ

▼ࢆ⏝࠸ࠊ☢ሙศᕸࢆ⿵ṇࡍࡿཷືⓗ(୺࡟☢໬࡟Ⰻ࠸ᆒ୍ᗘࢆᚓࡿࡇ࡜ࡣ஦ᐇୖࠊ୙ྍ⬟࡛࠶㕲∦฼⏝)ࢩ࣑ࣥࢢ࡟ࡼࡾࠊ〇స࣭⤌ࡳ❧࡚࣭タࡾࠊ☢ሙタィ࡛ࡣࠊ☢▼࡟Ⰻዲ࡞ᆒ୍ᗘࢆⓎ⏕⨨᫬࡟ΰධࡋࡓㄗᕪ☢ሙࢆ⿵ṇࡋ࡚ࠊᚲせ࡞✵࡛ࡁࡿ⬟ຊࢆ୚࠼ࡿタィࡀ㔜せ࡛࠶ࡿࠋ

ṇ☜࡟ィ

㐀⢭ᐦ

㛫ⓗ࡞ᆒ୍ᗘࢆᐇ⌧ࡍࡿࠋᮏ㈨ᩱࡢㄝ࡛᫂ࠊࠕᆒ

ࡇࡇ࡛ࠊ༢ㄒࠕ☢ሙタィࠖࢆᐃ⩏ࡋ࡚࠾ࡃࠋ

୍ᗘࠖ࡜ゝ࠺ゝⴥࡀ㢖⦾࡟ฟ࡚ࡃࡿࡀࠊࡇࡢᐃ

ࡇࡇ࡛ࡣࠊ☢Ẽᛂ⏝ᶵჾ࡛ᚲせ࡞☢ሙศᕸࡀ୚

⩏ࡣୗグ࡛࠶ࡿࠋ࠶ࡿ᳨ウ㡿ᇦ(VOI: Volume of࠼ࡽࢀࠊࡑࡢ☢ሙࢆⓎ⏕ࡍࡿ㉳☢ຊ㓄⨨ࢆタィInterest ࡜ゝ࠺ࡇ࡜ࡶ࠶ࡿ)ࡢ☢ሙᆒ୍ᗘ࡜ࡣࠊ

ࡍࡿࠊ࡜ゝ࠺ព࿡࡛࠶ࡿࠋᐇ㝿ⓗ࡟ᐇ⌧࡛ࡁࡿ࡜ゝ࠺ព࿡࡛ࠊࢥ࢖ࣝࡢ㟁ὶᐦᗘࠊ㉸㟁ᑟᑟయ☢ሙศᕸࡢ᭱኱᭱ᑠ್ࡢᕪ

ᆒ୍ᗘ㸻

ᖹᆒ☢ሙ

x106 [ppm]ࡢ⤒㦂☢ሙࠊࢩ࣑ࣥࢢྍྰࡶ⪃៖ࡍࡿᚲせࡀ࠶(1-1)ࡿࠋࡉࡽ࡟ࠊ㉳☢ຊࡀᑠࡉࡃࡋ࡚ࠊపࢥࢫࢺ࡛

࡛࠶ࡾࠊ㏻ᖖࠊppm ༢఩࡛⾲ࡍࠋ〇స࡛ࡁࡿタィࡀᮃࡲࡋ࠸ࠋࡇࡢࡼ࠺࡞᳨ウࢆ

MRI ᧜ീ࡟ࡣࠊ୍ᵝ࡞☢ሙ(୍⯡ⓗ࡞ MRI ⿦⨨ྵࢇ࡛☢ሙタィࢆ⾜࠺ࠋ

࡛ࡣ 0.3㹼3.0T)ࢆᚲせ࡜ࡍࡿࡀࠊ㏻ᖖࡢ MRI ☢▼1.1. ᪤㛤Ⓨࡢ☢ሙタィᢏ⾡࡛ࡣ 10ppm ⛬ᗘࡢᆒ୍ᗘ (┤ᚄ 50cm ⌫ෆ) ࡛࠶ࡿ[1,2]ࠋ

ࡇࡢࡼ࠺࡞ࠊ㉸⢭ᐦ☢ሙᢏ⾡࡟ࡘ࠸࡚ࠊMRI

୍᪉ࠊMuSEUM ᐇ㦂࡛ࡣ⊃࠸㡿ᇦ(20cm ┤ᚄ☢▼⏝࡟㛤Ⓨࡋࡓᢏ⾡ࡀ฼⏝࡛ࡁࡿ࡜⪃࠼࡚࠸

30cm 㛗 ᅇ ㌿ ᴃ ෇ య)࡛ ࡣ ࠶ ࡿ ࡀ ࠊ1.7Tࡿࠋᐇ㝿࡟ࠊⰋዲ࡞ᆒ୍ᗘᐇ⌧ࡢࡓࡵࠊMRI ☢

±0.17 T(0.1ppm)௨ෆࡢ㉸Ⰻዲ࡞୍ᵝ☢ሙࡀᚲせ▼ᢏ⾡ࢆᛂ⏝࣭฼⏝ࡋ࡚࠸ࡿࠋ୍⯡࡟ࠊMRI ⿦࡛࠶ࡿࠋࡑࡋ࡚ࠊ᪤࡟ࡇࡢࡼ࠺࡞㉸Ⰻዲᆒ୍ᗘ

⨨࡛ࡣࠊ᪤࡟ࠊJ-PARC ᐇ㦂ࡼࡾᩘ 10 ಸࡢᝏ࠸(኱ࢆᐇ⌧࡛ࡁࡿࡇ࡜ࡣ♧ࡉࢀ࡚࠸ࡿ[8]ࠋg-2/EDMࡁ࡞)ᆒ୍ᗘ࡛࠶ࡿࡀࠊࡼࡾᗈ࠸✵㛫࡛ᆒ୍☢ሙ⢭ᐦィᐇ㦂࡛ࡣࠊ༙ᚄ 0.333mࠊ༙ᚄ᪉ྥᖜ

1

10㸫 1

ࡉࢀࡓㄗᕪ☢ሙࡢ⿵ṇ☢ሙࢆ⏕ᡂࡍࡿ MMࢆᐇ⌧ࡋ࡚࠸ࡿࠋ➹⪅ࡣࠊMRI ⿦⨨࡛ࡢᆒ୍☢

࡟ィሙᐇ⌧ࡢࡓࡵ࡟ࠊ☢ሙタィᢏ⾡࡜タ⨨ᚋࡢ☢ሙ㓄⨨ࢆồࡵࡿ㏫ၥ㢟(ࢩ࣑ࣥࢢィ⟬)ࡶ࠶ࡿࠋ

ㄪᩚᢏ⾡ࢆ㛤Ⓨࡋࡓ[9-15]ࠋࡇࡢ☢ሙタィ࡟ࡣ㉳ࡲࡓࠊᐇ㦂࡟࠾࠸࡚ࡶࠊࡇࡢࡼ࠺࡞㏫ၥ㢟ࡀ☢ຊศᕸ࡜☢ሙศᕸࡢ㛫ࡢᛂ⟅⾜ิ࡟ᑐࡋ࡚ࠊ

Ꮡᅾࡍࡿࠋඛ࡯࡝㏙࡭ࡓࡼ࠺࡟ࠊ᰾⼥ྜศ㔝࡛᭱ ᑡ ஧ ஌ ἲ ࢆ ᡴ ࡕ ษ ࡾ ≉ ␗ ್ ศ ゎ(TSVD:ࡣࣉࣛࢬ࣐఩⨨ᙧ≧ࡸ⾲㠃఩⨨ࢆᐇ᫬㛫࡛ไᚚ

Truncated Singular Value Decomposition)ࢆ⏝࠸࡚ゎࡍࡿ㈇ᖐ㑏(FB: Feedback)ไᚚ₇⟬ࡶ㏫ၥ㢟࡛࠶ࡃᡭἲ[16-20]ࢆ฼⏝ࡋ࡚࠸ࡿࠋ⡆༢࡟ࠊTSVD ṇࡿ[21-23]ࠋ㝈ࡽࢀࡓⅬᩘࡢ☢ሙ࣭㟁ὶィ๎໬(regularization)࡜࠸࠺ࡇ࡜ࡶከ࠸ࠋ

ࢱࢆ⏝࠸࡚ࠊࣉࣛࢬ࣐௜㏆ࡢ࣏ࣟ࢖ࢲࣝ☢ሙศࡇࡢᡭἲࡣࠊᙜึࠊࢺ࣐࢝ࢡ⿦⨨ࡢࣉࣛࢬ࣐

ᕸࢆ✵㛫㐃⥆ⓗ࡟ᢕᥱ(෌ᵓᡂ)ࡍࡿ☢ሙィᏳᐃ໬ࡢࡓࡵ฼⏝ࡋ࡚࠸ࡓ☢ሙศᕸ࣭㟁ὶศ㓄

[24-26] ࡶ௦⾲ⓗ࡞㏫ၥ㢟࡜ࡋ࡚Ꮡᅾࡍࡿࠋ

ࢹ࣮ᡭἲࢆ≉␗್ศゎ(SVD: Singular Value Decomposition)ࡇࡢࡼ࠺࡞☢ሙ㛵㐃࡛㏫ၥ㢟ࢆゎࡃ᪉ἲ࡜ࡋ

ᅛ᭷࣮ࣔࢻ࡟ศゎࡋ࡚ไᚚ࣭ㄪᩚࡋࡓ᪉ἲ࡛࠶

࡚ࠊ᭱ᑠ஧஌ἲࢆ TSVD ࡟ࡼࡾゎࡃᡭἲࢆࠊ➹⪅ࡗࡓ[21-23]ࠋࡇࢀࢆࠊMRI ☢▼ࡢタィ࡜ㄪᩚ࡟ࡣᥦ᱌ࡍࡿ[9-15]ࠋࡑࡢ᪉ἲࢆᮏ㈨ᩱ࡛ࡶᢅ࠺ࠋ

ᛂ⏝ࡋࡓࠋSVD ᅛ᭷࣮ࣔࢻࡢຍ⟬ᩘࢆቑຍ(ᡴࡕࡇࡢᡭἲࡣ㧗⢭ᗘ࡞☢ሙศᕸࢆᐇ⌧ࡍࡿୖ࡛᭷

ษࡾᅛ᭷࣮ࣔࢻ␒ྕࢆቑຍ)ࡉࡏࡿࡇ࡜࡛☢ሙ⢭฼࡞タィᡭἲ࡜⪃࠼ࡿࠋᗘࢆྥୖࡉࡏࡿࡇ࡜ࡀฟ᮶ࡿࠋࡇࡢ฼Ⅼࢆ฼⏝ࡋ࡚☢ሙタィ࡟ᛂ⏝ࡋ࡚࠸ࡿࠋ୍᪉ࠊᅛ᭷࣮ࣔ

1.3. ᮏ㈨ᩱࡢෆᐜ

ࢻᩘࡀከࡍࡂࡿ࡜ࠊ☢ሙ⢭ᗘࡣⰋ࠸ࡀࠊᐇ⌧ࡀ

ᮏ㈨ᩱࡢෆᐜࡣࠊ

㞴ࡋ࠸(㧗ࢥࢫࢺ)ࡢ㉳☢ຊ※㓄⨨ࡢタィ࡜࡞ࡿሙ(i)ྜࡶ࠶ࡿࠋᐇ౛ࢆ㏻ࡋ࡚ TSVD ฼⏝ࡢ☢ሙタィࢆ(ii) TSVD ṇ๎໬฼⏝ࡢ⡆༢࡞ලయ౛

⤂௓ࡋࠊࡑࡢୖ࡛ࠊg-2/EDM ࡢヲ⣽ィ(iii) MRI ☢▼ࡢᆒ୍☢ሙタィᐇ㦂࡛᭱ᑠ஧஌ἲ࡜ TSVD ṇ๎໬

Muon ࢆ⵳✚ࡍࡿ☢ሙ(௨ᚋ࡛ࡣ⡆༢࡟ Muon ⵳✚(iv) g-2/EDM ☢▼(Muon ⵳✚☢▼)ࡢ☢ሙタィ☢▼ࠊMSM: Muon Storage Magnetࠊ࡜ࡍࡿ)ࡢ☢

࡛࠶ࡿࡀࠊ(iii) (iv)࡛ࡣㄗᕪ☢ሙࡢ⿵ṇ࡟ᚲせ࡞Ẽタィ࡜タ⨨ᚋࡢ⢭ᐦ☢ሙㄪᩚ(☢ሙࢩ࣑ࣥࢢ)࡟

☢ሙࢩ࣑ࣥࢢᡭἲࢆ௦⾲࡜ࡍࡿࠊ☢ሙ࡟㛵㐃ࡋࡘ࠸࡚ㄝ᫂ࡍࡿࠋ

ࡓㄗᕪࢆ⿵ṇࡍࡿᶵᵓ࡟ࡘ࠸࡚ࡶㄝ᫂ࡍࡿࠋࡲ
ࡓࠊ(iv)࡛ࡣࠊMuon ධᑕ࡟ᚲせ࡞☢ሙࢆసࡿࢥ࢖

1.2. ☢ሙタィ࡜ṇ๎໬ࣝ ⩌ ࡟ ࡘ ࠸࡚ ࡶ ࠊ ⌧ ≧ࡢ タ ィ ࢆ ㄝ᫂ ࡍ ࡿ ࠋ ඲ᐇ㦂⿦⨨ࡢ☢ሙศᕸࢆồࡵࡿ࡟ࡣࠊBiot-Savart

࡚ࠊTSVD ฼⏝ࡋࡓ᭱ᑠ஧஌ἲࢆ฼⏝ࡋ࡚࠸ࡿࠋ

ࡢἲ๎ࡸ᭷㝈せ⣲ࢥ࣮ࢻࢆ⏝࠸࡚ࠊ୚࠼ࡽࢀࡓ

ࡇࢀࡽࡢᐇ౛ࡸタィ≧ἣࢆ㏻ࡋ࡚ࠊ☢ሙタィ㟁ὶࡸ☢Ẽ࣮࣓ࣔࣥࢺ(MM㸸Magnetic Moment㸧࡟࠾ࡅࡿ㏫ၥ㢟ࠊṇ๎໬ࡢᚲせᛶࠊ࠾ࡼࡧࠊ≉ศᕸ➼ࡢ㉳☢ຊ㓄⨨࠿ࡽ☢ሙศᕸࢆィ⟬ࡍࡿࠋ␗್ศゎࡢ฼⏝౯್ࢆᢕᥱࡋ࡚ࡶࡽ࠼ࡿ࡜ࠊ᭷

ࡋ࠿ࡋࠊ☢Ẽᛂ⏝ᶵჾࡢタィ࡛ࡣࠊ┠ᶆ࡜ࡍࡿព⩏࡛࠶ࡿ࡜⪃࠼ࡿࠋ☢ሙศᕸࡀ୚࠼ࡽࢀࠊࡑࢀࢆᐇ⌧࡛ࡁࡿࢥ࢖ࣝ

వㄯ࡛࠶ࡿࡀࠊཧ⪃ᩥ⊩[19]࡟ࡼࢀࡤࠊ≉␗್ศࡸᙉ☢ᛶయ➼ࡢ㉳☢ຊ㓄⨨ࢆồࡵࡿࠋ࠸ࢃࡺࡿ

ゎࡀ௵ពࡢ⾜ิ࡟㐺⏝࡛࠸ࡿࡇ࡜ࡣ 1939 ᖺ[27]࡟ึ

㏫ၥ㢟࡜࡞ࡿࠋ☢Ẽᛂ⏝ᶵჾࡢタィ࡛ࡣᚲࡎゎࡵ࡚♧ࡉࢀࡓࠋィ⟬ᶵࡢㄌ⏕࡜ྠࡌ᫬ᮇ࡛࠶ࡿࠋࡲࡃᚲせࡢ࠶ࡿၥ㢟࡛࠶ࡿ[20]ࠋ

ࡓࠊࡇࡢᩥ⊩[19]࡟ࡣࠊࠕࢩࢫࢸ࣒ไᚚࡢ᭷ຠ࡞ᡭ

➹⪅ࡣࠊ᰾⼥ྜ⿦⨨ࡢタィࡸ☢Ẽඹ㬆᧜ീ

ἲࡢ 1 ࡘ࡜ࡋ࡚ᐃ╔ࡋ࡚࠸ࡃ࡛࠶ࢁ࠺࡜ᛮࢃࢀࡿࠖ

(MRI: Magnetic Resonance Imaging)⿦⨨࡞࡝ࡢ㧗⢭࡜᭩࠿ࢀ࡚࠸ࡿࡀࠊ☢ሙタィࡢศ㔝࡛ࠊ✚ᴟⓗ࡟⏝ᗘ࡞☢ሙࢆᚲせ࡜ࡍࡿᶵჾ࡛ࠊ㏫ၥ㢟ࢆゎ࠸࡚࠸ࡓ౛ࡣぢ࡚࠸࡞࠸ࠋ

ࡁࡓࠋከࡃࡣ㉸ఏᑟ฼⏝࡛࠶ࡿࠋ㟁ὶࡸ☢ᛶయࡢ㓄⨨ࢆṇ☜࡟ồࡵࡿ㏫ၥ㢟࡟ຍ࠼ᶵჾタ⨨ᚋ

10㸫 2

2. ᭱ᑠ஧஌ἲ࡜ṇ๎໬ࡁ࡞ , ࡛Ⓨ⏕ࡍࡿゎࢆ⟬ฟࡋࠊ㐣኱࡞㉳☢ຊࢆせ࠶ࡿ☢ሙศᕸࢆᣢࡘ☢Ẽᛂ⏝ᶵჾࢆタィࡍࡿሙྜࠊࡑࡢ☢ሙࢆⓎ⏕ࡍࡿ㟁ὶศᕸ , ࢆồࡵ(☢ሙタィ)ࠊࡑࢀࢆಖᣢ࡛ࡁࡿᵓ㐀(⪏㟁☢ຊࠊ⪏㟁ᅽࠊ㟁ὶᐦᗘࠊ෭༷࡞࡝)ࢆタィࡋ࡚࠸ࡃࠋ☢ሙタィࡢ㒊ศ࡛㏫ၥ㢟ࢆゎࡃࠋ┠ᶆ☢ሙศᕸ࡜ࡋ
࡚ࠊከࡃࡢሙྜࠊ☢ሙ࣭☢᮰ᐦᗘ(Wb/m2)ศᕸ࡛
࠶ࡿࡀࠊ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝࡸ☢᮰(Wb)ศᕸ

ồࡍࡿゎࡀ⟬ฟࡉࢀࡿ஦ࡀከ࠸ࠋࡇࡢࡓࡵࠊᘧ
(2-4)ࡢゎ࡛ࡣࠊ☢ሙタィ࣭☢Ẽᛂ⏝ᶵჾࡢタィ࡟ࡣ౑࠼࡞࠸ࠋ
⌧ᐇⓗ࡞ゎࢆồࡵࡿࡓࡵ࡟ࠊṇ๎໬ἲࢆ౑࠺
[20]ࠋ௦⾲ⓗ࡞ṇ๎໬ᡭἲ࡜ࡋ࡚ࠊTihonov ṇ๎໬࡜ࡇࡇ࡛ྲྀࡾᢅ࠺ TSVD ṇ๎໬ࡀ࠶ࡿࠋᚋ⪅࡟ࡣḟࡢ฼Ⅼࡀ࠶ࡿ࡜⪃࠼ࡿࠋࢆ⪃࠼ࡿࡇ࡜ࡶ࠶ࡿࠋከᩘࡢ☢ሙホ౯Ⅼ(MFEP:(i) ༢఩㟁ὶ(㉳☢ຊ䠅䛒䛯䜚䛾☢ሙᙉᗘ(≉␗್)䛜

Magnetic Field Evaluation Point)ୖࡢ☢ሙศᕸ %(せ኱䛝䛺(పḟ)ᅛ᭷䝰䞊䝗䛛䜙㑅ᢥ䛩䜛䚹ᚑ䛳䛶䚸⣲ Bi ࡣ i ␒┠ MFEP ࡢ☢ሙ)࡜㟁ὶศᕸ ,(せ⣲ Ij ࡣ᭱ᑠ䛾㉳☢ຊ䛷ᚲせ䛺☢ሙ䜢Ⓨ⏕䛩䜛㟁ὶศj ␒┠ᅇ㊰ࡢ㟁ὶ್)ࡢ㛵ಀࡣࠊ⥺ᙧ᪉⛬ᘧ⣔ࠊᕸ䜢㑅ᢥ䛩䜛ᶵ⬟䜢 TSVD 䛜ᣢ䛳䛶䛔䜛䚹(ii) ᅛ᭷䝰䞊䝗ᩘ䛸☢ሙศᕸ䛾㏆ఝ⢭ᗘ䛻䛿᫂☜䛺

% = A,

(2-1)࡛⾲⌧࡛ࡁࡿࠋ㟁ὶ࠿ࡽ☢ሙ࡬ࡢᛂ⟅⾜ิ A ࡢ
せ⣲ Aij[T/A]ࡣ i ␒┠㟁ὶࡀ j ␒┠ MFEP ࡟సࡿ༢㛵ಀ䛜䛒䜚䚸ᚓ䜙䜜䜛⢭ᗘ䜢ᢕᥱ䛧䛺䛜䜙䚸పḟᡂศ䛷㉳☢ຊ㓄⨨䜢᳨ウ䛷䛝䜛䚹(iii) ྛ SVD ᅛ᭷䝰䞊䝗䛸┠ᶆ☢ሙศᕸ䜢ẚ㍑䛩䜛䛣

఩㟁ὶ࠶ࡓࡾࡢ☢ሙᙉᗘ࡛࠶ࡾࠊBiot-Savart ࡢἲ䛸䛷䚸౑⏝䛩䜛ᅛ᭷䝰䞊䝗䛛䜙ᐇᶵ䛷ᚲせ䛸䛩䜛๎➼࡛⟬ฟࡋࠊ(MFEP ᩘ)×(㟁ὶせ⣲ᩘ)ࡢḟඖࢆ㉳☢ຊ㓄⨨䜢ᢕᥱ䛷䛝䜛䚹ᣢࡘࠋ┠ᶆࡢ☢ሙศᕸ %TG ࢆ෌⌧ࡍࡿ㟁ὶ㓄ศࡣ(iv) ศᕸ㟁ὶ䛷⮬⏤ᗘ䛾ከ䛔㉳☢ຊ㓄⨨䛻䛴䛔䛶䜒䚸☢ሙ䛻ᑐ䛧䛶኱䛝䛺ᐤ୚䜢ᣢ䛴㉳☢ຊศᕸA ࡢ㏫⾜ิࢆ⏝࠸ࡿࡇ࡜࡛ᢕᥱ࡛ࡁࡿࠋࡋ࠿ࡋࠊ

䜢䛒䜙䛛䛨䜑ᢕᥱ䞉㑅ᢥ䛧䚸ᚲせ䛺⢭ᗘ䜢☜ಖ䛧୍⯡ⓗ࡟ࡣ A ࡣ㠀ṇ๎࡛࠶ࡾࠊ㏫ၥ㢟ࡢከࡃ౛
࡛ࠊᘧ(2-1)ࡣ୙Ⰻタᐃ(ill-posed)ၥ㢟࡜࡞ࡿࠋࡑ

䛺䛜䜙䚸⮬⏤ᗘ䜢ῶᑡ䛥䛫䛶䚸☢ሙタィ䛷䛝䜛䚹

ࡢࡓࡵࠊ%TG ࢆ㏆ఝⓗ࡟෌⌧ࡍࡿ㟁ὶศᕸ , ࢆࠊࡲ࡜ࡵࡿ࡜ࠊ᭱ᑡࡢ㉳☢ຊ(i)࡛ࠊồࡵࡿ☢ሙศ᭱ᑠ஧஌ἲ[17, 20, 28, 29]࡟ࡼࡾ⟬ฟࡍࡿࠋࡘࡲ

ᕸ(iii)࡜☢ሙ⢭ᗘ(ii)ࢆࠊ㑅ᢥ⠊ᅖࢆ⊃ࡵ࡚(iv)ࠊ

ࡾࠊ㆟ㄽࡋ࡚࠸ࡃࡇ࡜ࡀฟ᮶ࡿࠋࡇࢀࡽ฼Ⅼ࡟ࡘ࠸࡚ࡣࠊ౛㢟࡜ᐇᶵタィ౛࡛♧ࡋ࡚࠸ࡃࡀࠊୖグ||(%TG A,)||2 = (%TG A,)t(%TG A,) 䊻 ᭱ᑠ

(2-2)ࡢ㟁ὶศᕸ , ࡢ㏆ఝゎࢆồࡵࡿࠋࡇࡢゎࡣࠊ, ࡟㡯┠඲య࡟ඹ㏻ࡋ࡚࠸ࡿࡇ࡜ࡣࠊᅛ᭷࣮ࣔࢻࡢ
㑅ᢥࢆ㏻ࡌ࡚ᢕᥱ࡛ࡁࡿࡇ࡜࡛࠶ࡿࠋ
ṇ๎໬ࡣ⥺ᙧ᪉⛬ᘧ⣔ࡢ㏫ィ⟬ࢆᏳᐃ࡟⾜࠺ࡘ࠸࡚ᚤศࡋ࡚ࠊᴟ್ࢆᣢࡘ᮲௳࠿ࡽࠊ

ᡭἲ࡛࠶ࡿࡀࠊ௨ୗ࡛ࡣୖグ≉ᚩࢆᘬࡁฟࡍࡓ
(2-3)ࡵ࡟ࠊᅛ᭷࣮ࣔࢻ࡟ὀ┠ࡋ࡚ࠊࡑࡢຍ⟬࡛㏫ၥࢆゎࡃࡇ࡜࡛ᚓࡽࢀࡿࠋࡇࡇ࡛ୖῧ࠼Ꮠ t ࡣ㌿⨨㢟ࢆゎࡃࠋᚑࡗ࡚ࠊṇ๎໬࡜࠸࠺ࡼࡾࠊ᭷┈࡞(AtA),=At%TG,

⾜ ิ ࡛ ࠶ ࡿ ࡇ ࡜ ࢆ ♧ ࡍ ࠋ(AtA)ࡣ ṇ ᪉ ⾜ ิ ࡞ࡢ࡛ࠊከࡃࡢሙྜࠊ㏫⾜ิࢆ⟬ฟ࡛ࡁࠊᘧ(2-3)࠿
ࡽୗグࢆᚓࡿࠋ
,= (AtA)-1At%TG

ᅛ᭷࣮ࣔࢻࡢᢳฟ࡜ࡑࡢ฼⏝᪉ἲ࡟ࡘ࠸࡚ࡢ㆟
ㄽ࡜࡞ࡿࠋ2.1. ṇ๎໬࡟ࡼࡿ᭱ᑠ஧஌ゎᶵჾタィ࡟ᚲせ࡞ゎ , ࡣࠊጇᙜ࡞⢭ᗘ࡛ࠊᐇ⌧(2-4)

᭱ࡶࡼࡃ▱ࡽࢀࡓ㏫ၥ㢟ゎ࡛࠶ࡿࡀࠊࡇࡢゎ࡛⟬ฟࡍࡿ㟁ὶศᕸ࡟ᇶ࡙࠸ࡓ☢Ẽᛂ⏝ᶵჾࡢタィ࣭〇సࡣ㞴ࡋ࠸ࠋከࡃࡢሙྜࠊᚲせ௨ୖࡢ☢

ྍ⬟࡞㟁ὶศᕸࢆ୚࠼ࡿࡶࡢ࡛࠶ࡿࠋࡇࢀ࡟ᑐ
ࡋ࡚ࠊ☢ሙ⢭ᗘ࡜ , ࡢᐇ⌧ᛶࢆྲྀᘬࡍࡿᡭἲ࡜ࡋ
࡚ࡢṇ๎໬ἲࡀ࠶ࡾࠊ௦⾲ⓗ࡟ࡣࠊTihonov ἲ࡜ሙ⢭ᗘࢆ᣺ᖜ(せ⣲ I㹨ࡢ᭱኱࣭᭱ᑠ್ࡢᕪ␗)ࡢ኱

10㸫 3

TSVD ἲ ࡢ ṇ ๎ ໬ ࡀ ࠶ ࡿ [20] ࠋ ᮏ ㈨ ᩱ ࡛ ࡣ ࠊồࡵࡿࠋ⾜ิ(AtA +TSVD ἲࢆᛂ⏝ࡋࡓ㆟ㄽ࡜࡞ࡿࠋ

ࡵࡿ㟁ὶ㓄ศ(㏫ၥ㢟ゎ), ࡣࠊ

2LtL)ࡣṇ๎࡜࡞ࡿࡓࡵࠊồ⾜ิ A ࡟ SVD ࢆ㐺⏝ࡍࡿ࡜ࠊ, = (AtA + 2LtL)-1 At%TG
A=䃂Xk kYkt,

(2-5)

(2-9)

࡛ࠊゎࡣࠊSVD ᅛ᭷࣮ࣔࢻࢆ⏝࠸࡚♧ࡍ࡜ࠊ࡛࠶ࡾ[16-19]ࠊ☢ሙศᕸࢆ⾲ࡍᇶᗏ Xkࠊࡇࢀ࡜୍ᑐ୍࡟ᑐᛂࡋࡓ㟁ὶศᕸࡢᇶᗏ Ykࠊ࠾ࡼࡧࠊ

䡇

, =σ

Yk

(2-10)

䡇┦஫ࡢ᥮⟬ಀᩘ[T/A]࡜⪃࠼ࡿࡇ࡜ࡢ࡛ࡁࡿ≉␗್ k ࡢ⤌ࡳྜࢃࡏࢆࠊᅛ᭷࣮ࣔࢻ␒ྕ k ࡟ࡘ࠸࡚࡛࠶ࡿࠋࡓࡔࡋࠊᘧ(2-10)࡛ࡣ L ࢆ༢఩⾜ิ࡜ࡋຍ⟬ࡋࡓᘧ࡛⾲⌧࡛ࡁࡿࠋ㏻ᖖࠊ≉␗್ k ࡢ኱ࡓࠋ࿴ࡣࠊᅛ᭷࣮ࣔࢻ␒ྕ k ࡟ࡘ࠸࡚⾜࠺ࠋᘧ(2-ࡁࡉࡢ㡰࡟ᅛ᭷࣮ࣔࢻࡢ␒ྕ k ࢆ௜ࡅࡿࠋࡇࢀࢆ

7)࡜ᘧ(2-10)ࢆẚ㍑ࡍࡿ࡜ࠊTihonov ṇ๎໬࡛ࡣࠊ

⏝࠸࡚ A* = (AtA)-1At ࢆồࡵࡿ࡜ࠊk㸻࡜࡞ࡿᅛ᭷࣮ࣔࢻ␒ྕ௜㏆࡛ຍ⟬ࢆᡴࡕษࡾࠊ࠾࠾ࡼࡑ TSVD ࡜ྠᵝ࡞ゎࢆฟຊࡍࡿ࡜⌮ゎ
*A= (AtA)-1At = σ

/

,

(2-6)

࡛ࡁࡿࠋࡓࡔࡋࠊ㏻ᖖࠊTihonov ṇ๎໬࡛ࡣࠊ

࡛࠶ࡿࠋࡇࢀࡀ A ࡢ୍⯡㏫⾜ิ࡛࠶ࡿࡇ࡜ࡣࠊ(AtA +

ᘧ(2-5, 2-6)࠿ࡽࠊAA*A = A ࡀᡂࡾ❧ࡘ(ࡘࡲࡾࠊ࡜ࠊᅛ᭷࣮ࣔࢻࢆព㆑ࡍࡿࡇ࡜ࡣ࡞࠸ࠋ

2LtL)ࡢ㏫⾜ิࢆồࡵ࡚ィ⟬ࢆᐇ⾜ࡍࡿAA* ࡣ↓స⏝)ࡇ࡜࡛☜ㄆ࡛ࡁࡿࠋࡘࡲࡾࠊSVD

ᘧ(2-3)࡜ᘧ(2-8)ࡢព࿡ࢆ⪃࠼ࡿ࡜ࠊ☢ሙ %TG ࢆᅛ᭷࣮ࣔࢻࢆ⏝࠸ࡿ࡜ࠊᐜ᫆࡟୍⯡㏫⾜ิࢆồ෌⌧ࡍࡿ᫬࡟ᘧ(2-3)࡟|L,|ࢆᑠࡉࡃࡍࡿ᮲௳ࢆ

ࡵࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡇࡢ⤖ᯝࠊ, ࢆᘧ(2-4)࠿ࡽࠊ

㏣ຍࡋࡓࡇ࡜࡟࡞ࡿࠋL ࡜ࡋ࡚༢఩⾜ิࢆ⏝࠸ࢀࡤࠊᘧ(2-9)࡛㟁ὶࣀ࣒ࣝ|,|ࢆᑠࡉࡃࡍࡿ᮲௳ࢆ

, = σ䡇(Xkt%TG)Yk/ k(2-7)ຍ࠼ࡓࡇ࡜࡟࡞ࡿࡀࠊࡇࢀࡣ TSVD ṇ๎໬ࡶᣢ࡛ồࡵ࡚ࠊ㏫ၥ㢟ࢆゎࡃࠋຍ⟬ࡣࠊᅛ᭷࣮ࣔࢻ

ࡗ࡚࠸ࡿ≉ᚩ࡛࠶ࡿࠋ༢఩⾜ิ௨እࡢ L ࢆ౑࠺ࡇ␒ྕ k ࡟ࡘ࠸࡚⾜࠸ࠊᚲせ࡞☢ሙ⢭ᗘࡀ☜ಖ࡛ࡁ࡜ࡶྍ⬟࡛࠶ࡾࠊ㟁ὶ௨እࡢࣃ࣓࣮ࣛࢱࢆᑠࡉࡿ ᅛ ᭷ ࣔ ࣮ ࢻ ␒ ྕ MT ࡛ ຍ ⟬ ࢆ ᡴ ࡕ ษ ࡾ(Truncation)ࠊపḟ(኱ࡁ࡞ k)ࡢ SVD ᅛ᭷࣮ࣔࢻࡃ ࡍ ࡿ ᮲ ௳ࢆ ຍ ࠼ ࡿ ࡇ࡜ ࡶ ྍ ⬟ ࡛࠶ ࡿ ࠋ ࡋ ࠿ࡋࠊTihonov ṇ๎໬࡛ࡣࠊᡴࡕษࡾࡀ⦆ࡸ࠿࡟⾜ࡢࡳຍ⟬࡟ຍ࠼ࡿࠋ඲࡚ࡢᅛ᭷࣮ࣔࢻࢆຍ⟬ࡍࢃࢀࡿࡓࡵ࡟ࠊᮏ᮶ᚲせ࡛࡞࠸㧗ḟ(ᑠ≉␗್)ᡂ

ࡿ࡜㏻ᖖࡢ᭱ᑠ஧஌ゎ{ᘧ(2-4)}࡛࠶ࡿࠋࡇࡢሙ

ศࡀゎ࡟ධࡾ㎸ࡳࠊ㟁ὶࢆ኱ࡁࡃࡍࡿྍ⬟ᛶࡀྜࠊ㧗ḟ(ᑠࡉ࡞ i)ࡢᅛ᭷࣮ࣔࢻࢆྵࡵ࡚ຍ⟬ࡍ࠶ࡿḞⅬࡀᏑᅾࡍࡿࠋ➹⪅ࡢ☢ሙタィ࡛ࡣ TSVDࡿࡓࡵࠊศẕ࡟ᑠࡉ࡞ k ࢆᣢࡘ㡯ࡢຍ⟬࡛ࠊゎࡀṇ ๎ ໬ ࢆ ౑ࡗ ࡚ ࡁ ࡓ ⌮⏤ ࡢ ࡦ ࡜ ࡘࡀ ࡇ ࢀ ࡛ ࠶୙Ᏻᐃ࡜࡞ࡾࠊ㐣኱࡞㟁ὶࢆồࡵࡿࡇ࡜࡟ࡘ࡞

ࡿࠋ

ࡀࡿࠋTSVD ṇ๎໬ࡣࠊపḟࡢᅛ᭷࣮ࣔࢻࢆຍ⟬2.2. ᅛ᭷࣮ࣔࢻᙉᗘ࡟ὀ┠ࡋࡓ TSVD ṇ๎໬ࡋࠊⓎ⏕ࡍࡿ☢ሙࡣல⣽࡜ࡋ࡚㧗ḟᡂศࢆ↓どࡋ࡚ࠊጇᙜ࡞㟁ὶ࡛☢ሙࢆ㏆ఝⓗ࡟෌⌧ࡍࡿࠋ

TSVD ṇ๎໬࡛ࡣࠊ୍⯡ⓗ࡟ࠊᘧ(2-7)࡛ࠊ≉␗ຍ⟬ࡍࡿᅛ᭷࣮ࣔࢻࡢ㑅ᢥ࡟ࡘ࠸࡚ࡣࠊḟ⠇್࡛ࡢ኱ࡁ࡞ࡶࡢ㸦పḟ㸧࠿ࡽຍ⟬ࡋࠊᚲせ࡞⢭ᐇ౛ࢆᑐ㇟࡟ࡋ࡚ࠊ㆟ㄽࡍࡿࠋᗘࡀᚓࡽࢀࡿ MT ␒┠࡛ᡴࡕษࡿࡀࠊᘧ(2-7)ࢆཧ

୍᪉䚸Tihonov ṇ๎໬䜢౑䛖䛸䚸ᘧ(2-3)䛻ㄗᕪ 䜢ྵ䜎䛫䚸(AtA + 2LtL),= At%TG⪃࡟ࡍࡿ࡜ࠊᅛ᭷࣮ࣔࢻࡢᐤ୚ࡣ (Xkt%TG)/ k ࡛ゎ , ࡟཯ᫎࡉࢀࡿࡇ࡜ࡀゎࡿࠋゝ࠸᥮࠼ࡿ࡜ࠊillposed ࡣ(Xkt%TG)/ k ࡀⓎᩓࡋ࡚࠸ࡃࡼ࠺࡞⾜ิ A(2-8)

࡜ࡍࡿࠋL ࡣ⥺ᙧ࡞⾜ิ࡛࠶ࡾࠊ༢఩⾜ิ࡛࠶ࢀࡤࠊୖᘧࡣࠊ ࡟ᛂࡌ࡚㟁ὶ , ࢆᑠࡉࡃࡍࡿゎࢆࢆᣢࡘၥ㢟࡜⌮ゎ࡛ࡁࡿࠋࡇࡢព࿡࡛ࠊ k ࡀᑠࡉ࠸ࡓࡵࠊࢃࡎ࠿࡞☢ሙࡋ࠿Ⓨ⏕࡛ࡁ࡞ࡁ࡞࠸㧗ḟᅛ᭷࣮ࣔࢻࡣ୙ᚲせ࡛࠶ࡾࠊຍ⟬࠿ࡽ㝖እࡍ10㸫 4䛸䛺䜛 MT 䜢㑅䜆䚹ࡿࠋࡇࢀ࡟ࡼࡾᏳᐃ࡞ゎࢆ⋓ࡿࡇ࡜ࡀฟ᮶ࡿࠋ
ࡇࢀࢆࠊ☢Ẽᛂ⏝ᶵჾࡢ☢ሙタィ࡟ᛂ⏝ࡋ࡚ࡁ2) SVD ᅛ᭷䝰䞊䝗䛾☢ሙศᕸ䛸ᙉᗘ䛻ὀ┠䚸ࡓࡀࠊ➹⪅ࡢ TSVD ṇ๎໬࡛ࡣࠊຍ⟬࡟㑅ᢥࡍࡿᘧ(2-5)䛷ㄝ᫂䛧䛯䜘䛖䛻䚸☢ሙᇶᗏ Xk䚸㟁ὶᇶ᮲௳࡟ࠊᅛ᭷࣮ࣔࢻࡀ᭷ព࡞☢ሙศᕸࢆᣢࡕࠊ

ᗏ Yk 䛚䜘䜃≉␗್ k 䛷 k ␒┠䛾ᅛ᭷䝰䞊䝗䜢ᵓᙉᗘࢆᣢࡘ ࡇ࡜ࢆ᮲௳ ࡟ຍ࠼ࡓࠋ ࡘࡲࡾࠊill-ᡂ䛩䜛䚹ಶ䚻䛾☢ሙᇶᗏ Xk 䛜ᚲせ䛷䛒䜛䜒䛾䛛

posed ࡢၥ㢟࡟ࡼࡿⓎᩓࢆ㜵ࡂࠊ㏆ఝゎࢆồࡵࡿ䜢䚸(i)ࡓࡵ࡟ࠊྛᅛ᭷࣮ࣔࢻ࡛☢ሙ࡟ᑐࡋ࡚ୗグࡢࡼ

せ䛺ᅛ᭷䝰䞊䝗䛛䠛䛛䜙ุ᩿䛧䛯ୖ䛷䚸ຍ⟬䛩࠺࡟ࠊᐇ⌧࡛ࡁࡿ㟁ὶ࡛᭷ព࡞ᐤ୚ࢆᣢࡘᅛ᭷

䜛䚹Xk 䛿 MFEP 䛷䛾☢ሙ䜢♧䛧䛶䛔䜛䛾䜏䛷䛒䜛࣮ࣔࢻࡢࡳࢆ㑅ᢥ࣭ຍ⟬ࡋ࡚┠ᶆࡢ☢ሙࢆ㏆ఝ

䛜䚸Yk 䛷ィ⟬䛩䜛༢఩㟁ὶศᕸ䛒䛯䜚䛾☢ሙศⓗ࡟Ⓨ⏕࡛ࡁࡿ㉳☢ຊ㓄⨨ࢆồࡵࡿࠋᕸ E(Yk)䜢ᅛ᭷䝰䞊䝗䛾☢ሙศᕸ䛸䛩䜛䛸⌮ゎ䛧䜔䛩䛔䚹ᅛ᭷䝰䞊䝗䛾㑅ᢥ䛾䛯䜑䛻䚸ᘧ(2-7)䜢᭩䛝┤䛧䛶䚸/, =䃂YkXkt%TG/ k =σ

Yk PTGk / k,

(2-11)

3) ᚲせ㟁ὶᙉᗘ䛾ᐇ⌧ᛶ䚸ᘧ(2-11)䛷ྛ㟁ὶ Ij 䛜ᐇ⏝ⓗ䛻ᐇ⌧䛷䛝䜛⠊ᅖ䛷䛒䜛䚹䛸䛧䛶䚸ୗグ䛾ᅛ᭷䝰䞊䝗ᙉᗘ䚸
PTGk = Xkt%TG/np1/2

䛜᭷ព䛺኱䛝䛥䛛䠛 (ii)┠ᶆ☢ሙ䛻ᚲ

(2-12)

䛷䚸ᅛ᭷䝰䞊䝗䜢ຍ⟬䛩䜛䚹䛣䛣䛷䚸np 䛿 MFEP ᩘ䛷䚸௨ୖࡢ᮲௳࡛ᡴࡕษࡾḟᩘ MT ࡸຍ⟬ࡍࡿᅛ᭷࣮ࣔࢻࢆタᐃࡍࡿࡀࠋୖグࡢ 3 㡯┠ࢆྠ᫬࡟‶ࡓࡉ࡞࠸ሙྜࡶ࠶ࡿࠋࡓ࡜࠼ࡤ☢▼ࡢタィ࡛࠶ࢀ%TG 䜔 Yk 䛾ḟඖᩘ䛷䛒䜛䚹ᅛ᭷䝰䞊䝗ᙉᗘ䜢つ᱁໬ࡤࠊ㟁ὶ㓄⨨ࢆ⪃࠼࡚࠸ࡿ㡿ᇦࡀ୙㐺ษࠊࡶࡋ䛩䜛䛯䜑䛻 np1/2 䛷๭䛳䛶䛔䜛䚹෌⌧☢ሙ %REC 䛿䚸㟁ࡃࡣ㐣኱࡞┠ᶆ☢ሙ㡿ᇦࡢ኱ࡁࡉࡸ⢭ᗘ(ᆒ୍ᗘ)ὶ , 䛷䜒ィ⟬䛷䛝䜛䛜䚸MFEP Ⅼ䛷䛾☢ሙ䛿䚸➼ࡢཎᅉࡀ࠶ࡿࠋࡇࡢሙྜࠊ᳨ウࡋ࡚࠸ࡿᗄఱ

%REC = σ/PTGkXk(2-13)

Ꮫⓗయ⣔ࡸ☢ሙ௙ᵝࢆ෌᳨ウࡍࡿࡇ࡜࡟࡞ࡿࠋ
௨ୗ࡛ࡣࠊTSVD ṇ๎໬࡟ࡼࡿ㏫ၥ㢟ゎἲࢆᛂ䛷䛒䜛䚹TSVD ṇ๎໬䛻䜘䜛㏫ၥ㢟䛾ゎἲ䚸≉䛻ᘧ⏝ࡋࡓ☢Ẽᛂ⏝ᶵჾࡢ☢ሙタィ౛ࢆ♧ࡍࡀࠊ㟁

(2-11), (2-13)䛾ຍ⟬䜢ᶍᘧⓗ䛻 Fig. 21-1 䛻♧䛩䚹ὶ , ࡜☢᮰ᐦᗘ % ࡢ㛵ಀ{ᘧ(2-1)}࠿ࡽࡢ㆟ㄽࡔࡅSVD 䛷䚸☢ሙ䛸㟁ὶศᕸ䛾ᇶᗏ䛸≉␗್䜢ồ䜑䚸ᘧ࡛ ࡞ ࡃ ࠊ ௚ࡢ ⤌ ࡳ ྜ ࢃࡏ ࡢ ሙ ྜ ࡶ࠶ ࡿ ࠋ ౛ ࠼(2-12)䛾 PTGik 䜢ᅗྑഃ䛾ᵝ䛻ồ䜑䚸ᕥഃ䛾䜘䛖䛻䚸ࡤࠊ☢ሙ % ࡛ࡣ࡞ࡃࠊ☢᮰(࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕ

ᘧ(2-11)䛾ຍ⟬䜢ᐇ⾜䛩䜛䚹ຍ⟬䛩䜛ᅛ᭷䝰䞊䝗䜢ࣝ) ࡜ࡍࡿሙྜࠊ㉳☢ຊഃ࡛ࡣࠊ㟁ὶ , ࡛࡞ࡃ☢

ከ䛟䛩䜛䛸䚸ୖ㒊ᕥഃ䛾䜘䛖䛻⣽䛛䛟᣺ື䛩䜛୙ᏳᐃẼ࣮࣓ࣔࣥࢺศᕸ 0 ࡜ࡍࡿሙྜࠊࡶ࠶ࡿࠋ

䛺ゎ䛻䛺䜛䛣䛸䛜ከ䛔䛜䚸ᅛ᭷䝰䞊䝗ᩘ䜢పḟ䛰䛡䛷㐺ᩘ䛻䛩䜛䛸䚸ᐇ⏝ᛶ䛾䛒䜛ゎ䜢ᚓ䜛䚹TSVD 䛷ຍ⟬䛩䜛ᅛ᭷䝰䞊䝗䛾㑅ᢥ䛿䚸ୗグ䛾ᵝ䛻⪃䛘䜛䚹1) ṧᕪ☢ሙ %RE 䛜┠ᶆ್ r ௨ୗ䛸䛺䜛䜘䛖䛻ຍ⟬䚸%RE = %TG- %REC = %TG-䃂np1/2PTGkXk(2-14)

䛷䚸ຍ⟬䛩䜛ᅛ᭷䝰䞊䝗ᩘ MT 䜢ከ䛟䛩䜛䛸䚸ṧᕪ☢ሙ䛿ᑠ䛥䛟䛺䜛䚹ୗグ䛾᣺ᖜ(PP: peak-to-peak)䛜┠ᶆ್௨ୗ䛸䛺䜛䜎䛷ᅛ᭷䝰䞊䝗䜢ຍ⟬䛩䜛䚹䛴䜎䜚䚸
BREPP = BREMAX - BREMIN < r(2-15)

10㸫 5

Fig. 2-1. ᡴࡕษࡾ≉␗್ศゎṇ๎໬ࢆ⏝࠸ࡓ㏫ၥ㢟ゎἲࡢᶍᘧⓗㄝ᫂2.3. ┠ᶆ☢ሙ࡟ࡘ࠸࡚

ࢆồࡵࡿࡇ࡜ࡀฟ᮶ࡿⅬ࡟୰ࡶࡋ࡚ࠊ⡆༢࡟ࠊ┠ᶆ☢ሙ %TG 䛿୍⯡ⓗ䛻䛿௵ពᡂศ䛾☢ሙศᕸ

TSVD ṇ๎໬฼⏝࡜⾲⌧ࡍࡿࡇ࡜ࡶ࠶ࡿࠋ

䛜ྍ⬟䛷䛒䜚䚸ḟ❶䛷䛿䚸BR ᡂศ䜢ᢅ䛖ሙྜ䜒ㄝ᫂ࡑࢀ࠿ࡽࠊవㄯ࡛࠶ࡿࡀࠊ’90 ᖺ௦ጞࡵࡲ࡛

䛩䜛䚹䜎䛯䚸໙㓄䛾Ꮡᅾ䛩䜛☢ሙ䜢ᢅ䛖ሙྜ䜒䛒䜛䚹

ࡣࠊInternet ࡀ༑ศ࡟ࡣ฼⏝࡛ࡁࡎࠊ≉␗್ศ䛧䛛䛧䚸ᮏ㈨ᩱ䛷୺䛻ᢅ䛖ᆒ୍☢ሙ䛾ሙྜ䚸% 䛿ゎࡢࣉࣟࢢ࣒ࣛࡶ⮬సࡏࡊࡿࢆᚓ࡞࠿ࡗࡓࠋ➹MFEP 䛾☢ሙศᕸ䜢㍈᪉ྥᡂศ(BZi)䛷ᵓᡂ䛩䜛䚹⪅ࡶṇ᪉⾜ิࡢᅛ᭷್࣭ᅛ᭷࣋ࢡࢺࣝࢆồࡵࡿ

MRI 䛷䛿☢ሙ⤯ᑐ್ B 䛷ᆒ୍䛺☢ሙࡀᚲせ࡛࠶ࣉࣟࢢ࣒ࣛࢆඖ࡟⮬సࡋࡓࠋ⌧ᅾ࡛ࡣࡼࡾⰋ࠸

ࡿࡀࠊ㉳☢ຊ㓄⨨᳨ウࡣ㍈᪉ྥᡂศ BZ ࡛ᐃᘧ໬ࣉࣟࢢ࣒ࣛࡀ web ୖ࠿ࡽධᡭ࡛ࡁࡿࠋ౽฼࡞᫬

ࡍࡿࠋᚲせ࡞ᆒ୍☢ሙࡀᚓࡽࢀࡓẁ㝵࡛ࡣࠊ☢

௦ ࡛ ࠶ ࡿ ࠋ౑ ࡗ ࡚ ⾜ ࡃࡇ ࡜ ࡀ ฟ ᮶ࡿ ࡜ ⪃ ࠼ ࡲሙᙉᗘࡢኚືศࡣ㏻ᖖࠊ୺☢ሙࡀ 0.5T ࠿ࡽ 3.0Tࡍࠋ࡛࠶ࡗ࡚ࡶࠊ☢ሙ⤯ᑐ್䛾ኚື䛿 1 ࢞࢘ࢫ(3.0T࡟ᑐࡋ࡚ 33.3ppm peak to peak)௨ୗ࡛࠶ࡾࠊ☢▼㍈࡟ᆶ┤࡞☢ሙᡂศ(୺࡟༙ᚄ᪉ྥᡂศ BR)ࡶྠ⛬ᗘ௨ୗ࡛࠶ࡿࠋࡑࡢࡓࡵࠊBZ ࡜ B ࡢᕪ␗ࡣ0.02 T ௨ୗ࡜࡞ࡾࠊMRI ࡛ᚲせ࡞ᆒ୍ᗘࡢᩘ
ppm(ᚑࡗ࡚ 1 T㹼10 T ࡢ☢ሙ᣺ᖜ)࡟ᑐࡋ࡚༑ศ
ᑠࡉ࠸ࠋࡑࡇ࡛ࠊᆒ୍☢ሙࢆⓎ⏕ࡍࡿ☢▼ࡢ☢
ሙタィ࡛ࡣ BZ ࡛☢ሙタィࢆ㐍ࡵࡿࡇ࡜ࡀฟ᮶
ࡿࠋࡑࡢࡓࡵࠊᢅ࠺ᘧࡀ⥺ᙧ࡜࡞ࡾࠊࡇࢀࡲ࡛
ヰࡋࡓᘧࢆ౑ࡗ࡚タィࢆ㐍ࡵࡿࡇ࡜ࡀฟ᮶ࡿࠋ
ࡇࡢ⪃࠼ࡣࠊ4.6 ⠇࡛ㄝ᫂ࡍࡿࢩ࣑ࣥࢢィ⟬(ィ☢ሙ࠿ࡽ☢ሙࢆ⿵ṇࡋ࡚ᆒ୍☢ሙศᕸ࡟ㄪᩚࡍ
ࡿࡓࡵࡢ☢Ẽ࣮࣓ࣔࣥࢺ㓄⨨ 0 ࢆồࡵࡿィ⟬)࡛ࡶྠࡌ࡛࠶ࡾࠋ㍈᪉ྥᡂศ BZ ࡛ࢩ࣑ࣥࢢィ⟬(4.6⠇)ࡶᐃᘧ໬ࡍࡿࠋ
୍᪉ࠊᆒ୍☢ሙ࡛࡞࠸ሙྜࠊ౛࠼ࡤࠊBZ ᡂศ௨እࡶᢅ࠺ሙྜ࡜࠿ࠊ୍ᵝ࡛࡞࠸☢ሙࢆᢅ࠺ሙ
ྜ࡟ࡣὀពࡀᚲせ࡛ࠊ≉࡟ࠊMaxwell ᪉⛬ᘧ࡜▩┪ࡋ࡞࠸┠ᶆ☢ሙ࡜࡞ࡿࡼ࠺࡟ὀពࡍࡿᚲせࡀ࠶ࡿࠋ౛㢟ࢆ㏻ࡋ࡚ࠊḟ❶࡛ㄝ᫂ࡍࡿࠋ
2.3.1. ⿵㊊/ࢥ࣓ࣥࢺ௨ୗ࡛ࠊグྕ %**(ୖῧ࠼Ꮠ㸨㸨ࡣࠊMS(ィ☢

ሙ), TG(┠ᶆ☢ሙ), REC㸦෌ᵓᡂ☢ሙ㸧,RE㸦ṧᕪ☢ሙ㸧➼)ࡢせ⣲ࡣ i ␒┠☢ሙホ౯Ⅼ࡟ᑐࡋ࡚ ‫ככ‬࡛࠶ࡿࠋḟ❶࡛ࠊලయⓗ࡞౛㢟ࢆ㏻ࡋ࡚ࠊ⌮ゎࡢຓࡅ࡜࡞ࡿࡼ࠺ㄝ᫂ࡋ࡚࠸ࡃࠋࡲࡓࠊᮏタィᡭἲࡢ୰ᚰࡣࠊ᭱ᑠ஧஌ἲ࡜ TSVD ⤌ࡳྜࢃࡏ࡚᭱㐺࡞㉳☢ຊ㓄⨨ࢆồࡵࡿᡭἲ࡛࠶ࡿࠋࡋ࠿ࡋࠊ௨ୗ
࡛ࡣࠊᘧ(2-6)ࡢ SVD ᅛ᭷࣮ࣔࢻ฼⏝୍࡛⯡㏫⾜10㸫 6

3. TSVD ṇ๎໬ࢆ⏝࠸ࡿ౛㢟ሙࢆࠊࡇࡇ࡛ࡣࠊBZ ࡜ࡋ࡚࠸ࡿࡀࠊBR ➼ࡢ௚ᡂᮏ❶䛷䛿 TSVD ṇ๎໬䛻䜘䜚㉳☢ຊ㓄⨨䜢ồ䜑䜛౛㢟䜢ゎ䛝䚸g-2/EDM ☢▼䛾☢ሙタィ䛻౑䛳䛶䛔䜛䚸☢ሙタィᡭἲ䛾⌮ゎ䜢ຓ䛡䜛䚹෇⎔(䝖䞊䝷䝇)య⣔䛾ලయ౛䜢㏻䛧䛶䚸TSVD ṇ๎໬䛾᭷⏝ᛶ䜢⌮ゎ䛧䛶䜒䜙䛖䚹ศࡢሙྜࡸࠊ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝࡢሙྜࡶ࠶
ࡿࠋࡲࡓࠊFig. 3-1 ࡢࡼ࠺࡞෇⟄ᗙᶆࡢ 2D య⣔࡛ࡣࠊ࿘ᅇ᪉ྥࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝᡂศ ‫ࢆ ׎‬
ʌR ಸࡋ࡚ࠊ☢ሙホ౯Ⅼࢆ㏻㐣ࡍࡿ෇㠃ࢆ㏻㐣ࡍࡿ☢᮰(Wb)ࢆ☢ሙホ౯ࡢ≀⌮㔞࡜ࡍࡿሙྜࡶ࠶
ࡿࠋࡲࡓࠊ᰾⼥ྜ◊✲ࡢศ㔝࡛ࡣ R ‫☢ࢆ ׎‬᮰㛵ᩘ

3.1. ౛㢟ࡢィ⟬య⣔[Wb/radian]࡜࿧ࡪሙྜࡶ࠶ࡿࠋ

ࡇࡇ࡛ࡣࠊᡴࡕษࡾ≉␗್ศゎࢆ฼⏝ࡋ࡚᭱ᑠ஧஌ゎࢆồࡵࡿ TSVD ṇ๎໬ࢆ౑ࡗ࡚ࠊ┠ᶆࡢ☢ሙࢆ⏕ᡂ࡛ࡁࡿ㟁ὶศᕸࡢ☢ሙタィࢆࠊ⡆༢࡞య⣔࡛ヨࡳࡿࠋ෇⎔(ࢺ࣮ࣛࢫ)㠃ୖࡢ෇㟁ὶศᕸࢆ෇⎔ࡢෆ㒊࡟ୖ᪉ྥࡢ୍ᵝ☢ሙ(BZ=1.0T)ࢆ
సࡾ㟁ὶศᕸࢆ⟬ฟࡍࡿࠋ┤෇⟄ୖ࡛࡞ࡃࠊ෇
⎔ୖ࡞ࡢ࡛ࠊ୕ゅ㛵ᩘࡢࢥ࢖ࣝ(ࢧ࢖ࣥࢥ࢖ࣝ)ࡢ
㟁ὶศᕸ࡛ࡣ࡞࠸㟁ὶศᕸ࡛࠶ࡿࠋ

ࡇࡢ౛㢟࡛ࡣ㍈᪉ྥ(Z ᪉ྥ)ᡂศ BZ(T)ࢆホ౯☢
ሙᡂศ࡜ࡍࡿࠋᛂ⟅⾜ิࡢᡂศ Aij ࢆồࡵࡿ࡟ࡣࠊ⥺㍯㟁ὶࡀసࡿ☢ሙࢆṇ☜࡟ィ⟬ࡍࡿᚲせࡀ࠶ࡿࠋࡇࡇ࡛ࠊࠕṇ☜࡟ࠖ࡜ࡣࠊ0.1ppm ࡢ☢ሙศᕸࢆṇ☜࡟ィ⟬࡛ࡁࡿ⢭ᗘ࡛࠶ࡾࠊ0.01ppm ⛬ᗘ௨ୗࡢㄗᕪ࡛☢ሙィ⟬࡛ࡁࡿᚲせࡀ࠶ࡿࠋࡲ
ࡓࠊ☢ሙタィ࡟౑࠺௨ୖࠊ㧗㏿࡟ィ⟬ฟ᮶ࡿᚲせࡶ࠶ࡿࠋࡑࡢ᪉ἲࢆḟ࡟㏙࡭ࡿࠋィ⟬య⣔ࡣ Fig. 3-1 ࡛࠶ࡿࠋ෇⎔(ࢺ࣮ࣛࢫ)య

3.1.1. ෇㟁ὶ࡟ࡼࡿ☢ሙ⣔࡛࠶ࡾࠊ࣏ࣟ࢖ࢲ᩿ࣝ㠃(෇⎔ᙧ≧ࡢᆶ┤᩿㠃)࡛ ♧ ࡍ ࠋ እ ഃ ࡟ 㟁 ὶ 㠃(CCS: Current Carrying
Surface) ࡀ࠶ࡾࠊCCS ୖ࡟෇㟁ὶ(X ༳ࠊj㸻1㹼NF)ࡀከᩘ㓄⨨ࡉࢀࠊࡑࡢ㟁ὶ್࣭ศᕸࢆồࡵࡿࠋ
CCS ࡢෆ㒊࡟☢ሙホ౯Ⅼ(MFEPs, X ༳ࠊi=1㹼M)ࢆᣢࡘ☢ሙホ౯㠃ࡀ㓄⨨ࡉࢀ࡚࠸ࡿࠋᅗ୰ࡢ Aij౛㢟ࢆゎࡃࡓࡵ࡟ࡣࠊ⣽࠸෇㟁ὶ(⥺㍯㟁ὶ)ࡀసࡿ☢ሙࢆṇ☜࡟ィ⟬ࡍࡿᚲせࡀ࠶ࡿ(Fig. 3-2
ཧ↷)ࠋ☢ሙࡢィ⟬ᘧࡢᇶᮏࡣ Maxwell ᪉⛬ᘧ࡛࠶ࡿࡀࠊࡑࡢኚᙧ࡛࠶ࡿୗグࡢ Biot-Savart ᘧࢆ฼⏝ࡍࡿࠋࡣࠊj ␒┠ࡢ෇㟁ὶࡀࠊi ␒┠ࡢ☢ሙホ౯Ⅼ࡟సࡿ=☢ሙ࡛࠶ࡾࠊᛂ⟅⾜ิ A ࡢᡂศ࡛࠶ࡿࠋホ౯☢

4× ( െ Ԣ)| െ Ԣ|(3 െ 1)

ࡇࡇ࡛ࠊE ࡣ☢ሙ࣋ࢡࢺࣝ(bR, bZ)࡛ࠊU ࡜ U'ࡣࠊZࡑࢀࡒࢀࠊ☢ሙホ౯Ⅼ࡜㟁ὶ఩⨨ࡢ఩⨨࣋ࢡࢺ
ࣝࠊ 0 ࡣ┿✵୰ࡢ㏱☢⋡ࠊࡑࡋ࡚ࠊ✚ศࡣ㟁ὶ

Z=0.5mAij⤒㊰࡟ἢࡗ࡚㟁ὶ್ಸ࡛ᐇ⾜ࡉࢀࡿࠋ☢Ẽᛂ⏝ᶵჾ࡛ࡣ෇ᙧࢥ࢖ࣝࢆ⤌ࡳྜࢃࡏ࡚

ũ=EF/2
ũ=1+EF/2

ŝ=1+M/2

ŝ=2
ŝ=1
ŝ=D

ũ=2
ũ=1
ũ=EF

R

┠ᶆࡢ☢ሙࢆⓎ⏕ࡍࡿࡼ࠺࡟タィࡉࢀࡿࡇ࡜ࡀከ࠸ࠋ〇సࡢ㠃࠿ࡽࡣࠊ᭱ࡶసࡾࡸࡍ࠸ᙧ≧࡛

R=2.0mZԃ‫؂‬ుླྀ໚
(CCS: Current Carrying Surface)

Z=0

Fig. 3-1. ⦎⩦ၥ㢟ࡢィ⟬య⣔(࣏ࣟ࢖ࢲ᩿ࣝ㠃)ࠋ෇⎔(ࢺ࣮ࣛࢫ)㠃ୖ࡟࿘ᅇ᪉ྥ㟁ὶࢆከᩘ㓄⨨ࡋࠊࡑࡢෆഃ࡟ᑠ༙ᚄࡢᑠࡉ࠸෇⎔ୖ࡟☢ሙホ౯Ⅼ(MFEP)ࢆ㓄⨨ࡋࡓࠋ

Z=Zm

RC
Rm

ࣕ৖‫ܯ‬଎఼

Fig. 3-2. ⥺㍯(⣽࠸෇)㟁ὶ

10㸫 7

࠶ࡾࠊ༢఩⥺ᮦ㔞࠶ࡓࡾࡢ☢ሙ✵㛫ࡀ኱ࡁ࡞ᙧ

ཧ⪃ᩥ⊩[33] ࡟ࡣࠊ4 ḟࡢከ㡯ᘧ࡛ࡢ㏆ఝィ⟬≧࡛࠶ࡾࠊᛂຊⓗ࡟ࡣᖹᆒ໬ࡉࢀ࡚⪏ᙉ☢ሙ࡟࡛ࠊከ㡯ᘧࡢಀᩘࡀ♧ࡉࢀ࡚࠸ࡿࠋࡇࡢᩥ⊩࡟㒔ྜࡀⰋ࠸ࠊ࡜ゝ࠼ࡿࠋࡑࡇ࡛ࠊ෇㟁ὶ࡟ࡼࡿࡣ⢭ᗘࡀ 4 ḟࡢᒎ㛤ᘧࢆ౑࠺ሙྜ࡛ࠊ2.0E-8 (ィ☢ሙࢆ㧗㏿࡟ィ⟬࡛ࡁࡿࡇ࡜ࡣࠊ☢ሙタィୖࠊ⟬ㄗᕪ/☢ሙᙉᗘ) ⛬ᗘ࡜᭩࠿ࢀ࡚࠸ࡿࠋMRI ☢▼㔜せ࡞㡯┠࡛࠶ࡿࠋࡇࡇ࡛ࠊ⢭ᗘࡢⰋ࠸ࠊ㧗㏿ࡢ☢Ẽタィ࡟ࡣ฼⏝࡛ࡁࡿ⢭ᗘ࡛࠶ࡿࠋ
ཧ⪃ᩥ⊩[34]࡟ࡣ 10 ḟࡢከ㡯ᘧ࡟ࡘ࠸࡚ಀᩘࡀ

࡞ィ⟬ἲࢆ⤂௓ࡍࡿࠋ⥺㍯㟁ὶ(ኴࡉࡣ↓㝈ᑠ࡛ Z=0 㠃ୖࠊ༙ᚄ RC ࡢ♧ࡉࢀ࡚࠸ࡿࠋࡇࡢᩥ⊩࡟ࡣ⢭ᗘࡀ 1.0E-14 ௨ୗ⥺㟁ὶ I(A))ࡀࠊ༙ᚄ Rm, ㍈᪉ྥ఩⨨ Zm ࡟సࡿ☢

ࡀᚓࡽࢀࡿ࡜᭩࠸࡚࠸ࡿࠋࡑࡇ࡛ࠊᩥ⊩[34]ࡢಀ

ሙ(Fig. 3-2 ཧ↷)ࡣࠊ෇㟁ὶ࡟ἢࡗ࡚ Biot-Savart ᘧᩘ್ࢆ౑࠺ࡇ࡜࡟ࡍࡿࠋᩥ⊩[32]࡟ࡶ 10 ḟࡢィᩘࢆ✚ศࡋࠊ㟁☢ẼᏛࡢᩍ⛉᭩࡟᭩࠿ࢀ࡚࠸ࡿࡼ

್ࡀ♧ࡉࢀ࡚࠸ࡿࡀࠊᩘ್ࡀⱝᖸ␗࡞ࡿࠋヨࡋ࠺࡟ࠊୗᘧ࡛ィ⟬࡛ࡁࡿࠋィ⟬ࢆ⾜ࡗࡓ࡜ࡇࢁ[32]ࡢᩘ್࡛ࠊ10 ḟ࡛ࡣⰋ࠸⢭ᗘࡣᚓࡽࢀ࡞࠿ࡗࡓ(฼⏝ࡣ᥍࠼ࡓ᪉ࡀⰋ࠸)=ξ(( )+ ( ))(3-2)

ࡀࠊ9 ḟ࡛ࡣⰋ࠸⢭ᗘࡢィ⟬ࡀฟ᮶ࡿࡼ࠺ࡔࠋ
➹⪅ࡣࠊࡇࢀࡲ࡛ࠊࡇࢀࡣ᰾⼥ྜ⿦⨨ࡸ MRI

=

ξ
(

)

( ) െ ( ) (3-3)⏝☢▼ࡢタィࡢࡓࡵ࡟ࠊ4 ḟࡢከ㡯ᘧ㏆ఝࢆ౑
err

0࠸ࠊィ⟬ㄗᕪࢆ B /B ҩ2E-8 (0.02ppm)⛬ᗘ࡛࠶ࡿࡇࡇ࡛ࠊ ( ), ( )ࡣࡑࢀࡒࢀ➨ 2 ✀ࠊ➨ 1 ✀ࡢ᏶඲ᴃ෇✚ศ࡛࠶ࡾࠊࡑࢀࡒࢀࠊ

࡜⪃࠼࡚ࡁࡓࠋࡋ࠿ࡋࠊJ-PARC ࡛‽ഛࡀ㐍ࡵࡽ( ) = ‫ ׬‬ξ1 െ(3-4)

せ࡞ᆒ୍ᗘ 0.1ppm ⢭ᗘ(3T ࡟ᑐࡋ࡚±3E-7T ௨ෆ)( )= ‫׬‬

(3-5)

=(

)࡛ᚲ

࡛ࡢタィ࡟ࡣవ⿱ࡢ࡞࠸ィ⟬⢭ᗘ࡜࡞ࡗࡓࠋࡑ

ξ)ࢀ࡚࠸ࡿᐇ㦂(MuSEUM ཬࡧ g-2/EDM ィ(k=0㹼1.0)ࡇ࡛ࠊ⌧ᅾࡣࠊ⢭ᗘࡢᨵၿࡢࡓࡵ᏶඲ᴃ෇✚ศ

(3-6)࡛࠶ࡿࠋᘧ(3-6)ࡢ k ࡣே࡟ࡼࡗ࡚ࡣ k2 ࡜ᐃ⩏ࡍࡿሙྜࡶ࠶ࡿࡢ࡛ὀពࡍࡿᚲせࡀ࠶ࡿࠋࡇࡢ࡞࠿
ుླྀϩʖϕ
ుླྀ஍I

࡛ ࠊ 㛗 ࠸ ィ⟬ ᫬ 㛫 ࢆ せࡍ ࡿ ྍ ⬟ ᛶࡢ ࠶ ࡿ 㒊 ศࡣࠊ᏶඲ᴃ෇✚ E(k), K(k)ࡢィ⟬࡛࠶ࡿࡀࠊⰋ࠸
㏆ఝᘧࡀᥦ᱌ࡉࢀ࡚࠾ࡾࠊ฼⏝࡛ࡁࡿࠋࡲࡓࠊ

Fig. 3-3(a) ᭤⥺ࡢ⥺ศศ๭ᘧࡢᙧ࠿ࡽぢ࡚ࠊ☢ሙィ⟬ࡢ⢭ᗘࡣ᏶඲ᴃ෇✚1.0E+00ᙧ࠿ࡽぢ࡚ࠊE(k), K(k)ࡢ㏆ఝ⢭ᗘࡣࠊࡑࡢࡲࡲ
☢ሙィ⟬್ࡢ⢭ᗘ࡜࡞ࡿࠋ᏶඲ᴃ෇✚ศ್ࡢィ⟬࡟ࡣࠊᘧ(3-4, 3-5)ࢆᩘ್✚ศࡍࡿ᪉ἲࡶ࠶ࡿ
ࡀࠊࡇࡢሙྜࠊィ⟬᫬㛫ࡀ㛗ࡃ࡞ࡾࠊ☢Ẽタィ࡟ᑐࡋ࡚ࠊᐇ⏝ⓗ࡞㐺⏝ࡣ㞴ࡋ࠸ࠋ୍᪉ࠊኚᩘ(1-k)ࡢከ㡯ᘧ࡛㏆ఝࡍࡿ᪉ἲࡀᥦ
᱌ࡉࢀ࡚࠸ࡿ[30, 31]ࠋཧ⪃ᩥ⊩[32]࡟ࡣࠊᩥ⊩[30]ࢆཧ⪃࡟ Chebyshev ㏆ఝィ⟬ἲࡀゎㄝࡉࢀ࡚࠾ࡾࠊ2 ḟ࠿ࡽ 10 ḟࡲ࡛ࡢከ㡯ᘧ࡛ィ⟬ࡍࡿࡓࡵࡢಀᩘࡀグ㏙ࡉࢀ࡚࠸ࡿࠋ

10㸫 8|ત෾෾ׄ‫ࢋܯ‬-ଡߴࣞ‫( |ࣇۛࢋܯ‬T)ศࡢィ⟬⢭ᗘ࡟౫Ꮡࡍࡿࠋࡘࡲࡾࠊᘧ(3-2, 3-3)ࡢ

ుླྀʁz=0.15mɼൔ‫ܚ‬RC=0.52, 0.81 m
ࣕ৖‫఼ࢋܯ‬,Z=0.0m, Rm=0.25, 0.0, 0.333 m

1.0E-02
1.0E-04
1.0E-06

4࣏Zm=0.25m

1.0E-084࣏Zm=0.00m

1.0E-101.0E-12Zm=0.333m, ZC=0.81m, C=0.15m
1.0E-14
1.E+00

1.E+02

1.E+04

1.E+06

1.E+08ત෾෾਼ׄFig. 3-3(b) ☢ሙィ⟬⢭ᗘࡢ☜ㄆࠋ᏶඲ᴃ෇✚ศ࡟㏆ఝᘧࢆ౑ࡗࡓゎᯒᘧ࡟ࡼࡿ್࡜⥺ᩥศ๭࡟ࡼࡿィ⟬್ࡢẚ㍑ࠋ

ᘧ(3-2), (3-3)࡛ ࠊRm=Rmi ࡜ ࡋ ࠊ ᘧ ୰ ࡢ Zm ࢆࡢィ⟬⢭ᗘࢆࠊ(1-k)ࡢ 10 ḟࡲ࡛ࡢከ㡯ᘧࢆ⏝࠸

Zm=Zmi-ZCj, ࡑࡋ࡚ࠊ㟁ὶ I ࢆ 1.0A ࡢ༢఩㟁ὶ࡜࡚ࠊ༑ศ࡞⢭ᗘࡢ☢ሙタィࢆ⾜ࡗ࡚࠸ࡿࠋ
ᘧ(3-2㹼3-6)࡟ࡼࡿ☢ሙィ⟬⢭ᗘࢆ☜ㄆࡍࡿࡓࡍࢀࡤ,ࡵࠊᘧ(3-1)ࢆ࿘ᅇᩘ್✚ศࡋ࡚ồࡵࡓ್࡜ẚ㍑
ξ=ࡍࡿࠋᩥ⊩[34]࡟ࡼࢀࡤࠊ1.0E-14 ࡢ⢭ᗘࡀᮇᚅ( )+ ( )(3-8)࡛ࡁࡿࠋẚ㍑ࡣࠊᘧ(3-2),(3-3)࡛ィ⟬ࡋࡓ್࡜ࠊ
ᘧ(3-1)ࢆ౑࠸ࠊFig. 3-3(a)ࡢࡼ࠺࡞⥺ศࡢ㞟ྜ࡛ࡶࡋࡃࡣࠊ෇㟁ὶࢆ⾲⌧ࡋࡓሙྜ࡛ࠊ㍈᪉ྥ☢ሙ BZ ࢆẚ㍑
ᩘ ࠊ ⦪ ㍈ ࡣ㸰 ࡘ ࡢ ィ ⟬್ ࡢ ᕪ ␗ ࡢ⤯ ᑐ ್ ࡛ ࠶ࡿࠋศ๭ᩘࢆቑࡸࡍ࡜⥺ศศ๭ἲࡢ☢ሙィ⟬⢭ᗘࡀⰋࡃ࡞ࡾࠊᘧ(3-2)ࢆ 10 ḟࡢ㏆ఝᘧ࡟ࡼࡿィ⪅ࡢィ⟬್ࡀ୍⮴ࡋ࡞ࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࡢ཯ᫎ
࡛࠶ࡿࡀࠊ10 ḟᘧࡢሙྜࠊᑡ࡞ࡃ࡜ࡶࠊ1.0E-12ࡢィ⟬⢭ᗘࡣ☜ಖࡉࢀ࡚࠸ࡿ࡜ุ᩿࡛ࡁࡿࠋ
ࡋ࠿ࡋࠊࡇࡢศ๭ᩘ࡛ࡣࠊ୍ಶࡢ෇㟁ὶࡢసࡿ☢ሙࡢ୍Ⅼࡢィ⟬᫬㛫ࡀ 10 ⛊௨ୖ࡟࡞ࡾࠊᩘ
ⓒಶࡢ෇㟁ὶࡀᩘ༓Ⅼࡢ఩⨨࡛ࠊ☢ሙィ⟬ࡍࡿ☢ሙタィ࡛ࡣከ኱࡞ィ⟬᫬㛫ࢆせࡍࡿࠋᐇ㝿࡟(R)᪉ྥᡂศ࡛࠶ࡿࠋࡲࡓࠊ
Aij = cos(ȟ)+ sin(ȟ)(3-10)

࡜ࡋ࡚ࠊ☢ሙࡢࢺ࣮ࣛࢫᑠ༙ᚄ᪉ྥᡂศ Br ࢆホ౯ࡍࡿࡇ࡜ࡶྍ⬟࡛࠶ࡿࠋࡇࡇ࡛ࠊk ࡣᘧ(3-6)࡛
ィ⟬ࡍࡿࡀࠊj ␒┠㟁ὶ఩⨨࡜ i ␒┠☢ሙィ⟬఩⨨࡟ᑐᛂࡋ࡚ᐇ⾜ࡉࢀࡿࠋᘧ(3-8)ࡣ BZ ☢ሙ࡟ὀ┠ࡋࡓᛂ⟅⾜ิ࡟㛵ࡍࡿࡶࡢ࡛࠶ࡿࡀࠊBR{ᘧ(39)}ࠊࡲࡓࡣࠊ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ Aĭ ࡟ὀ┠ࡋ࡚ᵓᡂࡍࡿሙྜࡶ࠶ࡿࠋAĭ ࡢሙྜࡣࠊ

ࡣࠊ౑⏝࡛ࡁ࡞࠸ࠋࡇࡢィ⟬᫬㛫ࡢၥ㢟ࡣᘧ(3-=2), (3-3)ࢆ᏶඲ᴃ෇✚ศ E(k), K(k)ࡢ㏆ఝィ⟬ἲ࡜ేࡏ࡚౑࠺ࡇ࡜࡛ࠊ኱ࡁࡃ⦆࿴ࡉࢀࡿࠋ

=㟁ὶࡣ㟁ὶ᪉ྥ࡟ᖹ⾜࡞࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕ
ࣝࢆⓎ⏕ࡍࡿࡀࠊ෇㟁ὶࡢሙྜ࡟ࡣ࿘ᅇ᪉ྥࡢ( ) െ ( ) (3-9)ࡀᛂ⟅⾜ิࡢせ⣲࡛ࠊ༢఩㟁ὶᙜࡓࡾࡢ☢ሙࡢ Z⟬್࡜ࡼࡃ୍⮴ࡋ࡚ࡃࡿࠋࡋ࠿ࡋࠊ600 ୓ศ๭ࢆ㉸࠼ࡿ࡜ࠊ༢ㄪ࡞ῶᑡࡣ↓ࡃ࡞ࡿࠋࡇࢀࡣࠊ୧

ξ=ࡋࡓࠋ⤖ᯝࡣ Fig. 3-3(b) ࡛࠶ࡾࠊᶓ㍈ࡣ⥺ศศ๭1െ( )െ ( )(3-11)(k=0㹼1.0)(3-12)

࡛࠶ࡿࠋ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝᡂศ ‫ࡀࡳࡢ ׎‬Ꮡᅾࡋࠊ
‫= ׎‬

1െ

( )െ ( )(3-7)࡛࠶ࡿࠋࡇࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩ್ࣕࣝࡶ 1.0E-12௨ୗࡢㄗᕪ࡛ィ⟬࡛ࡁࡿࠋࡇࡢᘧࡣࠊR-Z ᗙᶆ࡛☢᮰➼㧗⥺ࢆ᭩ࡃሙྜ(☢᮰ࡣ ʌRm ‫෇ࠊ) ׎‬ᙧࢥ࢖ࣝࡢ࢖ࣥࢲࢡࢱࣥࢫࡢ⟬ฟ࡟฼⏝࡛ࡁࡿࠋ
3.2. 㟁ὶ-☢ሙࡢᛂ⟅⾜ิ࡜≉␗್ศゎ㟁ὶ࡜☢ሙホ౯ⅬࢆࠊFig. 3-4(a)࡟♧ࡋࡓࠋࡇࡢィ⟬య⣔࡟ࠊ㍈᪉ྥ☢ሙ BZ ࢆ⟬ฟࡍࡿᘧ(32)ࠊ࠾ࡼࡧࠊ༙ᚄ᪉ྥ☢ሙ BR ࢆ⟬ฟࡍࡿᘧ(33)ࠊࢆ౑ࡗ࡚ࠊᛂ⟅⾜ิ A ࢆồࡵࡿࠋࡑࡋ࡚ࠊ⾜ิ࡟≉␗್ศゎࢆ㐺⏝ࡋࠊᅛ᭷ศᕸࡀ࡝ࡢࡼ࠺
࡞ศᕸ࡛࠶ࡿ࠿ࢆᢕᥱࡍࡿࠋ

10㸫 9

Fig. 3-4(a) ᅛ᭷࣮ࣔࢻィ⟬య⣔ࡢ࣏ࣟ࢖ࢲࣝ
᩿㠃ࠋ᩿㠃୰ᚰࡢ୺༙ᚄࡣ 2.0m, ᑠ༙ᚄ
25cm ࡢ෇⎔ୖ࡟☢ሙホ౯Ⅼࢆ㓄⨨ࠊ▮༳(ᑠ༙ᚄ)᪉ྥ☢ሙࢆホ౯ࡍࡿࠋ‫ࡣۑ‬㟁ὶ఩⨨ࠋ

Fig. 3-4(b) ⥺㍯㟁ὶ-ᑠ༙ᚄ᪉ྥ☢ሙࡢ⾜ิ࡟ࡼࡿ SVD ᅛ᭷ศᕸࠋ୺༙ᚄ 2.0m ࢆ୰ᚰ࡜ࡋࡓ࣏ࣟ࢖
ࢲ᩿ࣝ㠃ୖ࡛♧ࡍࠋᕥୗ࡟ᅛ᭷࣮ࣔࢻ␒ྕࠊྑୗ࡟≉␗್ࢆ♧ࡍࠋᑠ༙ᚄ 0.5m ୖࡢ‫༙ࡣۑ‬ᚄ࡟ẚ౛ࡋࡓ㟁ὶ࡛࠶ࡾࠊٔࡣ㈇㟁ὶࢆ♧ࡍࠋᑠ༙ᚄ 0.25m ෇⎔㠃ୖࡢ▮༳ࡣ☢ሙࡢ᪉ྥࢆ♧ࡍࠋ➼㧗⥺ࡣ㟁ὶࡢ SVD ᅛ᭷ศᕸ Yk ࠿ࡽィ⟬ࡉࢀࡓ➼☢᮰⥺(☢ຊ⥺)࡛࠶ࡾࠊᡴⅬ㡿ᇦ࡛☢᮰ࡣ㈇࡛࠶ࡿࠋ
≉␗್ศゎࡣ A ࢆᘧ(2-5)ࡢࡼ࠺࡟ᒎ㛤ࡍࡿ

࡚࠾ࡃࠋFig.3-1 ࡢᗄఱᏛⓗయ⣔ࠊFig.3-4(a)ࡣィ࡜ࠊᅛ᭷☢ሙศᕸ Xk ࡜ᅛ᭷㟁ὶศᕸ Yk ࢆᚓࡿࠋ⟬ య ⣔ ࡛ ࠊồ ࡵ ࡓ ☢ ሙཬ ࡧ 㟁 ὶ ࡢᅛ ᭷ ศ ᕸ ࡀࡑࢀࡒࢀࠊ☢ሙศᕸ࡜㟁ὶศᕸࡢᇶᗏ࡛࠶ࡾࠊ

Fig.3-4(b)࡛࠶ࡿࠋFig.3-4(a)࡛ࠊ‫ࡢۑ‬୰ᚰ࡟෇㟁☢ሙศᕸ࣭㟁ὶศᕸࡣࠊࡑࢀࡽࡢᅛ᭷ศᕸࡢ⤌ὶࢆ᝿ᐃࡋࠊ▮༳ࡢጞⅬ࡟☢ሙホ౯Ⅼࢆ᝿ᐃࡋࡳྜࢃࡏ࡛⾲⌧࡛ࡁࡿࠋࡲࡎࠊࡇࡢᇶᗏࢆㄪ࡭

Fig. 3-5 ⥺㍯㟁ὶ-࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ࿘ᅇ᪉ྥᡂศࡢ⾜ิ࡟ࡼࡿ SVD ᅛ᭷ศᕸࠋ

10㸫 10࡚࠸ࡿࠋホ౯☢ሙࡣ(3-10)ࢆ⏝࠸࡚ࠊFig.3-4(a)ࡢ࠸ࡿࠋ┠ᶆ☢ሙࡣ༙ᚄ 25cm ࡢ෇᩿㠃ୖ(࣏ࣟ࢖ࢲ▮༳᪉ྥࡢ☢ሙࢆホ౯ࡍࡿࠋࡇࡢィ⟬య⣔࡛ồࡵࡓᅛ᭷ศᕸࢆ Fig.3-4(b)࡟పḟ࠿ࡽ 8 ಶ♧ࡋࡓࠋ୺༙ᚄ 2.0m ࢆ୰ᚰ࡟࣏ࣟ
࢖ࢲ᩿ࣝ㠃ୖ࡛♧ࡋ࡚࠸ࡿࠋ⥺㍯㟁ὶ-☢ሙ(ᑠ༙ᚄ᪉ྥᡂศ)࡟ࡘ࠸࡚ࡢᅛ᭷ศᕸ࡛࠶ࡿࠋ᩿ࣝ㠃)࡛ࠊ1.0T ࡢ㍈᪉ྥ(⣬㠃ୖ᪉ྥ)☢ሙ࡜ࡋ࡚࠸ࡿࠋຍ⟬ᩘ(MT)ࢆቑࡸࡍ࡜ṧᕪ☢ሙᑡࡋࠊ⢭ᗘⰋࡃ┠ᶆ☢ሙࢆ෌⌧ࡍࡿ㉳☢ຊ㓄⨨(㟁ὶศᕸ)ࡀồࡲࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋSingular value Ok [T/A], Eigenmode strength PTGk [T],[T]
Peak-to-peak residual㡰␒ࡣ≉␗್ࡢ኱ࡁࡉ㡰࡛࠶ࡿࠋゝ࠸᥮࠼ࡿ࡜ࠊᑡ࡞࠸㟁ὶ࡛኱ࡁ࡞☢ሙᙉᗘࢆฟࡏࡿ 8 ಶࡢ
ᅛ᭷ศᕸ{☢ሙ Xk(▮༳࠾ࡼࡧ➼㧗⥺)ࠊ࠾ࡼࡧࠊ
㟁ὶ Yk‫ۑ‬༳}ࢆ♧ࡋ࡚࠸ࡿࠋ஫࠸࡟┤஺ࡋࠊࡑࢀ
ࡒࢀࡢศᕸ࡟ᑐࡋ࡚ᇶᗏࢆసࡗ࡚࠸ࡿࠋồࡵࡿ☢ሙศᕸ࠾ࡼࡧࡑࡢ☢ሙศᕸࢆⓎ⏕࡛ࡁࡿ㟁ὶศᕸࡣࠊࡇࢀࡽࡢᅛ᭷ศᕸࡢຍ⟬࡛ᵓᡂ࡛ࡁࠊ
ຍ⟬ࡣᘧ(2-11~13)࡛⾜ࢃࢀࡿࠋ⥺㍯㟁ὶ-࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ࿘ᅇ᪉ྥᡂศ
‫{ิ ⾜ ࡢ ׎‬ᘧ(3-7)}ࢆ ≉ ␗ ್ ศ ゎ ࡍ ࡿ ሙ ྜ ࡶ ࠶ࡿ ࠋ ࡇ ࡢ ሙྜ ࠊFig.3-5 ࡟ ♧ ࡋ ࡓ ᅛ᭷ ศ ᕸ ࡛ ࠶ࡿࠋ࣏ࣟ࢖ࢲ᩿ࣝ㠃୰ᚰ(R=2.0m, Z=0.0m)࡛ࡣࠊ
1 ␒┠ࡢᅛ᭷࣮ࣔࢻࡣṇ࿡ࡢ࿘ᅇ᪉ྥ☢ሙᡂศ ‫׎‬

1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
1.0E-08
1.0E-09
1.0E-10
0

5

10

15

20

Eigen mode Number MD
Truncation Eigen mode Number MT

Fig. 3-6 ≉␗್ k ࠊᅛ᭷࣮ࣔࢻᙉᗘ 3TGk ࡜ṧᕪ☢ሙࢆࡑࢀࡒࢀࠊᅛ᭷࣮ࣔࢻ␒ྕ 0D ࡜ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ 0T ࡛♧ࡍࠋࢆᣢࡘࡀࠊ2 ␒┠௨㝆ࡢᅛ᭷࣮ࣔࢻ࡛ࡣ ‫( ׎‬2.0㸪0.0)=0 ࡛࠶ࡿࠋ☢ሙศᕸ࡟ᑐࡋ࡚᭷ព࡞ࡶࡢࡣࠊ
2 ␒┠௨㝆ࡢᅛ᭷࣮ࣔࢻ࡛࠶ࡿࡀࠊFig.3-4(b)࡜ఝ

㧗ḟ(ᑠ≉␗್ࠊ኱␒ྕ㸸␒ྕࡣ≉␗್ࡢ㝆㡰ࡓศᕸࡀ୪ࢇ࡛࠸ࡿࡇ࡜ࡀゎࡿࠋ2D ఩⨨(R, Z)࡛
‫=׎‬

ࡀῶ

‫( ׎‬R, Z)࡜ࡍࡿ

࡟␒ྕ௜ࡅ)࡛ࡣࠊ≉␗್ࡢῶᑡ௨ୖ࡟ᅛ᭷࣮ࣔ

࡜ࠊ2D య⣔࡛ࡣ(R, Z)఩⨨ࡢ෇㠃ࢆ㏻㐣ࡍࡿ㠃ࡢࢻᙉᗘࡀᑠࡉࡃ࡞ࡿࡇ࡜ࡀゎࡿࡀࠊࡇࡢሙྜࠊ

☢᮰ (R, Z)ࡣࠊᘧ(2-11)ࡢ ຍ ⟬ ࡛ ࠊ ᅛ ᭷ ࣔ ࣮ ࢻ ẖ ࡢ 㟁 ὶ ศ ᕸࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝࢆ

(R, Z) = 2 R ‫( ׎‬R, Z) [Wb](3-13)

࡛࠶ࡿࠋ1 ␒┠௨እࡢᅛ᭷࣮ࣔࢻࡣࠊ࣏ࣟ࢖ࢲࣝ
᩿㠃୰ᚰࡢ☢᮰ࡣ㞽࡛࠶ࡿࡀࠊ⥺㍯㟁ὶ̿☢ሙ࡛ồࡵࡓᅛ᭷࣮ࣔࢻࡢ㟁ὶ࣭☢ሙศᕸ࡜ࡼࡃఝ
ࡓศᕸ࡛࠶ࡿࠋࡇࡢࡓࡵࠊࡇࡕࡽࡢᅛ᭷࣮ࣔࢻ
ࢆ⏝࠸࡚ࡶ┠ᶆࡢ☢ሙศᕸࢆᵓᡂ࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿࠋ
3.3. ☢ሙ࣭㟁ὶศᕸࡢ෌ᵓᡂ
ࡇࡇ࡛ࡣࠊᘧ(2-11)~(2-13)࡜๓⠇(3.2 ⠇)ࡢ SVD⤖ᯝࢆ⏝࠸࡚┠ᶆ☢ሙࢆ෌⌧ࡍࡿ㟁ὶศᕸࢆ⟬ฟࡍࡿ౛ࢆ♧ࡋ࡚࠸ࡃࠋFig. 3-6 ࡟ࡣࠊᅛ᭷࣮ࣔ
ࢻ␒ྕࡢ㛵ᩘ࡛ࠊ≉␗್࡜ᅛ᭷࣮ࣔࢻᙉᗘ{ᘧ(212)}ࠊࡑࢀ࡟ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ MT ࡛,ṧᕪ☢ሙ{ᘧ(2-14)}ࡢ peak-to-peak ್ࢆ♧ࡋ࡚

np1/2Yk PTGk / k ࡀ㧗ḟ(኱ k ␒ྕ)࡛ࡣࠊῶ⾶ࡋ࡚࠸ࡿࠋ㟁ὶศᕸࡣ཰᮰ࡋ࡚࠸ࡃࡇ࡜ࢆ♧ࡋ࡚࠾
ࡾࠊᛶ㉁ࡢⰋ࠸ၥ㢟(well-posed problemࠊⰋタᐃၥ㢟)࡛࠶ࡿ࡜ゝ࠼ࡿࠋᗄఱᏛⓗ࡞య⣔࡟౫Ꮡࡋ࡚ࠊ㧗ḟ࣮ࣔࢻࡢ㟁ὶࡀቑຍࡋ࡚࠸ࡃၥ㢟ࡶ࠶ࡿࠋࡇࡢࡼ࠺࡞ᛶ㉁ࡢ ᝏ ࠸ ၥ 㢟(ill-posed problem, ୙ Ⰻ タ ᐃ ၥ 㢟)࡛
ࡣࠊᚲせ࡞☢ሙ⢭ᗘ࡟ᛂࡌ࡚ࠊMT ࢆᑠࡉࡵ࡛ຍ
⟬ࢆᡴࡕษࡾࠊᕤᏛⓗ࡟ᐇ⌧ྍ⬟࡞㟁ὶศᕸ࡜ࡍࡿ࠿ࠊࡶࡋࡃࡣࠊᗄఱᏛⓗయ⣔ࡸ┠ᶆ☢ሙࢆ෌⪃ࡍࡿࡇ࡜ࡀᚲせ࡛࠶ࡿࠋࡇࡢࡼ࠺࡞ၥ㢟ࡢ౛࡟ࡘ࠸࡚ࡣᮏ⠇ࡢᚋ༙࡛♧ࡍࠋ
Fig. 3-7 ࡣ௨ୖࡢ㆟ㄽࢆ⫼ᬒ࡟ࠊFig. 3-4(b)ࡢᅛ
᭷࣮ࣔࢻ࡜ᘧ(2-11)ࡢ㟁ὶศᕸィ⟬࡛ࠊ┠ᶆ☢ሙ
BZ=1.0 T ࢆ☢ሙホ౯Ⅼ(MFEPs)࡛ᐇ⌧ࡋࡼ࠺࡜ࡍ
ࡿ㟁ὶศᕸ࡜☢ሙᙉᗘศᕸࢆ♧ࡋ࡚࠸ࡿࠋ☢ሙ

10㸫 11

Fig. 3-7. ࣏ࣟ࢖ࢲ᩿ࣝ㠃ࡢ኱༙ᚄ 2.0m, ᑠ༙ᚄ 25cm ෇᩿㠃ࢆᣢࡘ෇⎔㠃ୖ୍࡛ᵝ☢ሙ 1.0T ࢆⓎ⏕ࡍࡿࡼ࠺࡟ᵓᡂࡋࡓ㟁ὶศᕸ(‫ٔࡧࡼ࠾ۑ‬:஫࠸࡟㟁ὶ᪉ྥࡀ㏫)࡜ࡑࡢ㟁ὶศᕸ࡟ࡼࡿ☢ሙศᕸࠋᨺ
ᑕ≧ᶍᵝࡢ➼㧗⥺ࡣṧᕪ☢ሙᙉᗘศᕸ࡛ࠊ୰ᚰ☢ሙ࠿ࡽ±1nT(1.0E-9)㹼 ±1mT(1.0E-3)ࡢ୍᱆ẖ࡟♧ࡍࠋ㟁ὶ࡛ᅖࡲࢀࡓ෇⎔ෆ࡛ୖୗࡢ➼㧗⥺ࡣ࿘ᅇ᪉ྥࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩ࡛ࣕࣝ 4.0E-3 Tm/⥺ࠋศᕸࡣ➼㧗⥺࡛᭩࠸࡚࠸ࡿࡀࠊ⦪᪉ྥ࡟㉮ࡗ࡚࡛࠶ࡿࡢ࡛ࠊBZ=1.0 T ࢆࡘࡃࡿ࡟ࡣࠊ

࠸ࡿ➼㧗⥺ࡣ࿘ᅇ᪉ྥ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ ‫׎‬‫= ׎‬

࡛ࠊ4.0E-3Tm ẖ࡟ࣉࣟࢵࢺࡋ࡚࠸ࡿࠋࡇࡢ➼㧗

/2.0 +/(3-15)ࣟ ࢵ ࢺ ࡋ ࡚ ࠸ ࡿ ࠋ ࡸ ࡸ ኴ ࠸ ➼ 㧗 ⥺ ࡣ 1.0E-6 Tࡀ┠ᶆศᕸ࡜࡞ࡿࠋConst ࡣ௵ពࡢᖖᩘ࡛࠶ࡾࠊ
࠸ࡃࡘ࡛࠶ࡗ࡚ࡶ☢ሙศᕸ࡟ᙳ㡪ࡀ↓࠸ࡀࠊᑠ
༙ᚄ୰ᚰ(ࡇ ࡇ࡛ࡣ R=2.0m)࡛ࡢᘧ(3-15)್ࡣࠊ
1.0+/2࡛࠶ࡾࠊ༙ᚄ 2m ࡢ෇㠃ࢆ㏻㐣ࡍࡿ☢᮰ࡀࠊ2p ‫࡛ ׎‬᭷ࡿࡇ࡜ࢆ⪃࠼ࡿ࡜ࠊ☢ሙศᕸ࡟ࡣᙳ㡪ࢆ୚࠼࡞࠸ࡀࠊ☢᮰ࡸ☢Ẽ࢚ࢿࣝࢠ࣮ࠊ
ࡲࡓࠊ⥺㍯㟁ὶ್࡟ࡣᙳ㡪ࢆ୚࠼ࡿ㔞࡛࠶ࡿ࡜ண᝿࡛ࡁࡿࠋ

(1.0ppm)࡟┦ᙜࡍࡿࠋ☢ሙホ౯Ⅼ௜㏆ࢆ㏻㐣ࡍࡿFig. 3-7 ࡢ R=2.0m ࡛ࡣࠊ ‫= ׎‬0.57167 Tm ࡛࠶ࡗ⥺ࡣ☢ຊ⥺࡛ࡶ࠶ࡿࠋୖୗ᪉ྥ࡟୍ᵝ࡟㉮ࡗ࡚࠾ࡾࠊ┠ᶆ㏻ࡾࠊ㍈᪉ྥ☢ሙ BZ ࡀⓎ⏕࡛ࡁ࡚࠸ࡿࡇ࡜ࡀゎࡿࠋ
ᨺᑕ≧࡟ᶍᵝࡢ࠶ࡿ➼㧗⥺ࡣࠊ☢ሙᙉᗘ࡜࣏
ࣟ࢖ࢲ᩿ࣝ㠃୰ᚰ(R=2.0m Z=0.0m)ࡢ☢ሙᙉᗘࡢ
ᕪ␗ࢆࠊ±1.0E-3 ࠿ࡽ±1.0E-9 T ࡛ࠊ୍᱆ẖ࡟ࣉࡓ ࡢ ࡛ ࠊ ࡇ ࢀ ࢆ ෌ ⌧ ࡍ ࡿ ࡼ ࠺ ࡟ ࠊConst =௦⾲ⓗᢞ✏⧄⥔ࡣᩘᏐࢆグධࡋࡓࠋ(a)ࠊ(b)ࠊ(c)࡛ࡣࠊࡑࢀࡒࢀࠊMT= 4, 8, 12 ࡛࠶

0.85666 ࡜ࡋࠊFig. 3-7(b)࡜ྠࡌ☢ሙ෌⌧⢭ᗘࢆࡿࠋᘧ(2-11)࡛ຍ⟬ࡍࡿᅛ᭷࣮ࣔࢻᩘࢆቑຍࡉࡏ

ồࡵ࡚ࠊMT=9 ࡜ࡋࡓሙྜࢆࠊFig. 3-8(a)࡟♧ࡋࡓࠋࡿࡇ࡜࡛ࠊᵓᡂࡉࢀࡓ☢ሙศᕸࡢ⢭ᗘࡀྥୖࡍ

୧⪅ࡣྠᵝࡢ☢ሙศᕸ࡜࡞ࡗ࡚࠸ࡿࡇ࡜ࡀゎࡿࠋࡿࡇ࡜ࡀゎࡿࠋࡇࢀࡣࠊFig. 3-6 ࡜▩┪ࡋ࡞࠸ࠋࡘࡲࡾࠊ ‫࡟ ׎‬ὀ┠ࡋࡓ┠ᶆ☢ሙࢆ฼⏝ࡍࡿࡇ࡜࣏ࣟ࢖ࢲ᩿ࣝ㠃୰ᚰ࠿ࡽ༙ᚄ 25cm ࡢ෇᩿㠃ෆ࡛ࡶྍ⬟࡛࠶ࡿࡇ࡜ࡀゎࡿࠋࡓࡔࡋࠊFig. 3-8(a)࡛

±0.1ppm ⛬ᗘ௨ෆ࡛ᆒ୍࡞☢ሙࢆⓎ⏕ࡋࡼ࠺࡜ࡣࠊ࣏ࣟ࢖ࢲ᩿ࣝ㠃࡛ࠊ ‫= ׎‬0.57167 Tm ࡜ࡋࡓࡀࠊ

ࡍࡿሙྜࠊMT=12 ࡜ࡍࢀࡤࠊᐇ㝿࡟ࠊFig. 3-7(c)ࡇࡢ್ࡣࠊᘧ(3-15)ࡢ Const ࢆኚ᭦ࡍࡿࡇ࡜࡛ࠊ

ࡢࡼ࠺࡟±0.1ppm (±1.0E-7 T ࡢ➼㧗⥺)௨ෆ࡟☢

௵ព࡟ኚ᭦ࡀྍ⬟࡛࠶ࡿࠋ
Fig. 3-8(b)࡜(c)࡟ࡣ ‫( ׎‬0)ࢆ±0.15Tm(Const ࡣ±ሙᙉᗘ᣺ᖜ࡟཰ࡲࡿ୍ᵝ☢ሙࡀᚓࡽࢀࡿࠋ
୍᪉ࠊFig. 3-5 ࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ࿘ᅇ᪉

0.3)ኚ᭦ࡋࡓሙྜࢆ♧ࡋࡓࠋ➼㧗⥺࡛♧ࡋࡓ☢ሙྥᡂศ ‫࡟ ׎‬㛵ࡍࡿᅛ᭷࣮ࣔࢻࢆ฼⏝ࡍࡿࡇ࡜ࡶ

ศᕸ࡟኱ࡁ࡞ኚ໬ࡣ࡞ࡃࠊྠࡌ☢ሙศᕸࢆࠊ␗

ྍ⬟࡛࠶ࡿࠋ☢ሙ BZ ࡣ࿘ᅇ᪉ྥ࣋ࢡࢺ࣏ࣝࢸࣥ࡞ࡗࡓ ‫( ׎‬0)್࡛ᐇ⌧࡛ࡁ࡚࠸ࡿࠋࡋ࠿ࡋࠊ ‫( ׎‬0)ࢩࣕࣝ ‫ࠊࡽ࠿ ׎‬್ࢆኚ᭦ࡍࡿࡓࡵ࡟㟁ὶ್ࡣࠊ≉࡟ࠊ㈇ഃ(኱༙ᚄࡢᑠഃ)ࡢ㟁ὶࠊኚ໬ࡋ࡚࠸ࡿࠋ, ࡢࣀ࣒ࣝࠊ
=(3-14)

10㸫 12

Fig. 3-8. ࿘ᅇ᪉ྥ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ࡟ࡼࡿ SVD ᅛ᭷࣮ࣔࢻ 9 ಶ࡜୰ᚰ ‫ࢆ ׎‬ㄪᩚࡋ࡚ồࡵࡓ☢
ሙศᕸࠋFig. 3-7 ࡛ 0T=8 ࡢሙྜ࡜ྠᵝࡢ☢ሙศᕸࠊ㟁ὶศᕸࡀᚓࡽࢀࡿࠋ
ᘧ(3-17)ࡣࠊ㛫㐪ࡗࡓၥ㢟タᐃ࡛࠶ࡿࠋdiv%=0 ࡛|,| = σ(3-16)

࠶ࡿࡓࡵࠊ෇⟄య⣔࡛ࡣࠊ

࡛ẚ㍑(ྛᯟୖ㒊ࡢ|,|)ࡍࡿ࡜ࠊ☢ሙ࡛ホ౯ࡋࡓሙྜ࡜ྠࡌ᮲௳ࡢ(a)࡛ࠊ|,|ࡀᑠࡉࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࡀゎࡿࠋ୍⯡࡟ࠊ≉␗್ศゎࡢᅛ᭷࣮ࣔࢻࡣࠊ≉␗್ kࡢ኱ࡁ࡞ࡶࡢ࠿ࡽ฼⏝ࡍࡿࠋ☢ሙタィ࡟ᛂ⏝ࡍࡿሙྜ࡟ࠊ≉␗್ k ࡣ༢఩㟁ὶ࠶ࡓࡾࡢ☢ሙᙉᗘ࡜⌮ゎ࡛ࡁࡿࠋTSVD ṇ๎໬࡛ࡣࠊ኱ࡁ࡞࣮ࣔ
ࢻ࠿ࡽᚲせᩘࡔࡅ㑅ᢥࠊᚲせᙉᗘࢆ⪃៖ࡋ࡚ࠊຍ⟬ࡍࡿࠋࡇࡢࡓࡵࠊᑡ࡞࠸㟁ὶ࡛ᚲせ࡞☢ሙࢆ⏕ᡂ࡛ࡁࡿࡼ࠺࡟㟁ὶ್ࢆỴࡵ࡚࠸ࡿ࡜⌮ゎ+࡛࠶ࡾࠊ᫂ࡽ࠿࡟ࠊᘧ(3-17)ࡣṇࡋࡃ࡞࠸ࠋࡇࡢ
ሙྜࡢṧᕪ☢ሙ࡜ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ

MT ࡢ㛵ಀࢆࠊ≉␗್ 㹩ࠊᅛ᭷࣮ࣔࢻᙉᗘ

࡜ඹ࡟♧ࡍࠋᙜ↛࡛᭷ࡿࡀࠊࡇࡢࡼ࠺࡞≀⌮ⓗ࡟ṇࡋࡃ࡞࠸(maxwell ᪉⛬ᘧ࡜▩┪)┠ᶆ☢ሙࢆ୚࠼ࡓሙྜࠊMT ࢆ኱ࡁࡃࡋ࡚ࡶࠊ

ࡣῶᑡࡋ࡞࠸㸦Fig. 3-9 ཧ↷㸧ࠋḟ࡟ࠊMaxwell ᪉⛬ᘧ࡜▩┪ࡋ࡞࠸┠ᶆ☢ሙࠊ࡛ࡁࡿࠋࡇࡢⅬ࡟ࡶࠊTSVD ṇ๎໬ࡢ฼Ⅼࡀ࠶ࡿࠋ

3.4.1. ┠ᶆ☢ሙࢆ BR ࡜ࡍࡿሙྜ
┠ᶆ☢ሙ࡟ࡣ௵ពࡢ %TG ศᕸࡀ᭷ࡾᚓࡿࡀࠊMaxwell ᪉⛬ᘧ࡜▩┪ࡍࡿ஦ࡀ↓࠸ࡼ࠺࡟ࡋ࡚࠾ࡃᚲせࡀ࠶ࡿࠋᴟ➃࡞౛࡛᭷ࡿࡀࠊFig. 3-4(a)ࡢయ⣔࡛ࠊ┠ᶆ☢ሙ࡜ࡋ࡚༙ᚄ᪉ྥࡢ୍ᵝ☢ሙࠊ
(3-17)

ࢆ⏕ᡂࡋࡼ࠺࡜ࡍࡿሙྜࢆヨࡳࡿࠋ୍ᵝ BR ࡜ࡋ
ࡓࡢ࡛ࠊBZ=`0.0 ࡛࠶ࡿࠋ๓㡯ࡲ࡛ࡢ౛㢟ࡣࠊ┠ᶆࡢ☢ሙศᕸࡀ☜ᐇ࡟Ⓨ⏕࡛ࡁࡿࠊࠕᛶ㉁ࡢⰋ࠸ࠖ
ၥ㢟࡛࠶ࡗࡓࡀࠊᐇ㝿ࡢ☢▼☢Ẽタィ࡛ࡣࠊᗄఱᏛⓗ࡞㓄⨨࠿ࡽࠕᛶ㉁ࡢᝏ࠸ࠖሙྜࡶከ࠸ࡀࠊ

10㸫 13= R/2.0 [T]Singular value Ok [T/A], Eigenmode strength PTGk [T],[T]
Peak-to-peak residual

3.4. ┠ᶆ☢ሙ࡜ Maxwell ᪉⛬ᘧ= 1.0 [T](3-18)=0(3-19)

1.0E+01
1.0E+00
1.0E-01࢔ࠫࣕ৖

1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
1.0E-08
1.0E-09
1.0E-10
0

5

10

15

20

Eigen mode Number MD
Truncation Eigen mode Number MT

Fig. 3-9. ┠ᶆ☢ሙ
= 1.0 ࡜ࡋ࡚ࠊ≉␗್TGࢆk ࠊᅛ᭷࣮ࣔࢻᙉᗘ 3 k ࡜ṧᕪ☢ሙᅛ᭷࣮ࣔࢻ␒ྕ 0D ࡜ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒
ྕ 0T ࡢ㛵ᩘ࡛♧ࡍࠋ

(3-20)࡜ඹ࡟ࠊFig. 3-10 ࡟♧ࡋࡓࠋࡇࡢ┠ᶆ☢ሙ࡛ࢆヨࡳࡿࠋࡇࡢ┠ᶆ☢ሙࡣ࢝ࣉࢫ☢ሙ࡛࠶ࡿࠋ
࣏ࣟ࢖ࢲ᩿ࣝ㠃୰ᚰ(R=2.0m, Z=0.0)࡛ BR=1.0T ࡜ࡋ࡚࠸ࡿࠋࡇࢀࡣࠊ

ࡣࠊṧᕪࡀࠊ౑⏝ࡍࡿᅛ᭷࣮ࣔࢻᩘࡢቑຍ(኱

=െ

[T]

Singular value Ok [T/A], Eigenmode strength PTGk [T],Peak-to-peak residual[T]‫ = ׎‬㺎RZ/2.0(3-21)MT)࡜ඹ࡟ࠊᑠࡉࡃ࡞ࡾࠊ☢ሙศᕸࡢ෌ᵓᡂࡀ⢭ᗘⰋࡃྍ⬟࡛᭷ࡿ࡜ゎࡿࠋ
Fig. 3-4(b)3-11 ࡟ ࡣ ෌ ᵓ ᡂ ࡋ ࡓ ☢ ሙ ศ ᕸ ࢆ ♧ ࡍ ࠋ

Fig.3-5 ࡢᅛ᭷࣮ࣔࢻ࡜ᘧ(2-11)ࡢ㟁ὶศᕸィ⟬࡛ࠊ┠ᶆ☢ሙࢆ☢ሙホ౯Ⅼ(MFEPs)࡛ࠊᘧ(3-19)

1.0E+01࡜ᘧ(3-20)ࢆ⧳ࡵ࡚ᘧ(3-10)ࡢ☢ሙࢆᐇ⌧ࡋࡼ࠺

1.0E+00
1.0E-01

࡜ࡋࡓ TSVD ィ⟬࡛ᚓࡽࢀࡓ㟁ὶศᕸ࡜☢ሙᙉᗘ

1.0E-02ศᕸࢆ♧ࡋ࡚࠸ࡿࠋ☢ሙศᕸࡣ➼㧗⥺࡛᭩࠸࡚

1.0E-03࠸ࡿࡀࠊᶓ᪉ྥ࡟㉮ࡗ࡚࠸ࡿ➼㧗⥺ࡣ࿘ᅇ᪉ྥ

1.0E-04࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ ‫ࠊ࡛ ׎‬0.01Tm ẖ࡟ࣉࣟࢵ

1.0E-05
1.0E-06
1.0E-07ࢺࡋ࡚࠸ࡿࠋࡇࡢ➼㧗⥺ࡣ☢ຊ⥺࡛ࡶ࠶ࡿࠋᨺ

1.0E-08ᑕ≧࡟ᶍᵝࡢ࠶ࡿ➼㧗⥺ࡣࠊṧᕪ☢ሙࢆ±1.0E-3

1.0E-09

㹼±1.0E-9 T ࡛ࠊ୍᱆ẖ࡟ࣉࣟࢵࢺࡋ࡚࠸ࡿࠋࡸ

1.0E-10
0

5

10

15

ࡸኴ࠸➼㧗⥺ࡣ 1.0E-6 T (1.0ppm)࡟┦ᙜࡍࡿࠋᡴ

20

Eigen mode Number MD
Truncation Eigen mode Number MTࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ MT ࡣ㺂(a)ࠊ(b)ࠊ(c)࡛ࠊࡑ
ࢀࡒࢀࠊ4, 8, 12 ࡛࠶ࡿࠋᘧ(2-11)࡛ຍ⟬ࡍࡿᅛ᭷

Fig. 3-10 ┠ᶆ☢ሙ %R=5/2.0, %Z=-= ࡜ࡋࠊ≉␗್ k ࠊᅛ᭷࣮ࣔࢻᙉᗘ 3TGk ࡜ṧᕪ☢ሙࢆࠊᅛ᭷࣮ࣔࢻ␒ྕ 0D ࡜ᡴࡕษࡾᅛ᭷࣮ࣔ
ࢻ␒ྕ 0T ࡢ㛵ᩘ࡛♧ࡍࠋ࣮ࣔࢻᩘࢆቑຍࡉࡏࡿࡇ࡜࡛ࠊᵓᡂࡉࢀࡓ☢ሙศᕸࡢ⢭ᗘࡀྥୖࡍࡿࡇ࡜ࡀゎࡿࠋࡇࢀࡣࠊFig.
3-10 ࡜▩┪ࡋ࡞࠸ࠋࡇࡢࡼ࠺࡞ࠊBR ࡟ὀ┠ࡋࡓ☢ሙࢆ෌ᵓᡂࡍࡿሙྜ࡛ࡶࠊ๓㡯ࡢ BZ ࡟ὀ┠ࡋ

࡜ࡋࠊBZ=(1/R)()࠾ࡼࡧ BR= 㺎࠿ࡓሙྜ࡜ྠᵝ࡟ࠊMT ࡢቑຍ࡜ඹ࡟ࠊ෌ᵓᡂ☢ሙࡽỴࡵ࡚࠸ࡿ࡜ࡶゝ࠼ࡿࠋࡇࡢ┠ᶆ☢ሙ࡛ࠊMTࢆ┠ᶆ☢ሙ࡟ࠊࡼࡾ㏆࡙ࡅࡿ㟁ὶศᕸࡀᚓࡽࢀ

࡜ṧᕪࡓࡇ࡜ࡀゎࡿࠋ

‫׎‬/

‫׎‬/

ࡢ㛵ಀࢆࠊ≉␗್ 㹩ࠊᅛ᭷࣮ࣔࢻᙉᗘ

Fig. 3-11. ┠ᶆ☢ሙࢆ %R=5/2.0, %Z=-= ࡜ࡋࡓሙྜࡢ☢ሙ෌ᵓᡂ⤖ᯝࠋ࣏ࣟ࢖ࢲ᩿ࣝ㠃ࡢ኱༙ᚄ
2.0m, ᑠ༙ᚄ 25cm ෇᩿㠃ࢆᣢࡘ෇⎔㠃ୖ࡛ࠊ┠ᶆ☢ሙࢆ %R=5/2.0, %Z=-= ࡜ࡋ࡚ᵓᡂࡋࡓ㟁ὶศᕸ(‫ٔࡧࡼ࠾ۑ‬:஫࠸࡟㟁ὶ᪉ྥࡀ㏫)࡜ࡑࡢ㟁ὶศᕸ࡟ࡼࡿ☢ሙศᕸࠋᨺᑕ≧ࡢᶍᵝࢆᣢࡘ➼㧗⥺ࡣṧᕪ☢ሙᙉᗘศᕸࢆ୰ᚰ☢ሙ࠿ࡽ±1nT(1.0E-9)㹼 ±1mT(1.0E-3)ࡢᕪ␗ࢆᣢࡘ఩⨨ࢆࠊ୍᱆ẖࡢᕪ␗࡛♧ࡋ࡚࠸ࡿࠋ1.0E-6 T ࡛ኴ⥺࡜ࡋࡓࠋ㟁ὶ࡛ᅖࡲࢀࡓ෇⎔ෆ࡛ᕥྑ࡟㉮ࡗ࡚࠸ࡿ➼㧗⥺ࡣ࿘ᅇ᪉ྥࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩ࡛ࣕࣝ 0.01 T ẖ࡟ࣉࣟࢵࢺࡋࠊ☢ຊ⥺ࡢ᪉ྥࢆ♧ࡋ࡚࠸ࡿࠋ

10㸫 14

Singular value Ok [T/A], Eigenmode strength PTGk [T],Peak-to-peak residual[T]

1.0E+01ṧᕪ

1.0E+00ࡿ㟁ὶศᕸࡀ⢭ᗘⰋࡃồࡲࡿࡇ࡜ࡀゎࡿࠋồࡵ

1.0E-01ࡓ㟁ὶศᕸ࡛ィ⟬ࡋࡓ☢ሙศᕸࢆࠊMT=9 ࡢሙྜ

1.0E-02ࡀᑠࡉࡃ࡞ࡾࠊᘧ(3-21)ࡢ☢ሙࢆ෌⌧ࡍ

1.0E-03࡟ࡘ࠸࡚ࠊFig. 3-12(b)࡟♧ࡍࠋࡇࢀࡣࠊFig. 3-

1.0E-04

11(b)࡜ ྠ ࡌ ᮲ ௳ ࡛ ࡢ ☢ ሙ ศ ᕸ ෌ ᵓ ᡂ ⤖ ᯝ ࡛ ᭷

1.0E-05
1.0E-06

ࡿࠋFig. 3-12(b)࡛ MT=9 ࡜ࡋࡓ⌮⏤ࡣࠊ࣋ࢡࢺࣝ

1.0E-07࣏ࢸࣥࢩࣕࣝ࡟ࡼࡿ SVD ᅛ᭷࣮ࣔࢻࡢሙྜࠊFig.

1.0E-08

3-5 ࡢᵝ࡟ࠊ1 ␒┠ᅛ᭷࣮ࣔࢻࡀ☢ሙศᕸ࡟ࡣᐤ

1.0E-09୚ࡋ࡞࠸ࡓࡵ࡛᭷ࡿࠋᐇ㝿࡟౑⏝ࡋࡓ SVD ᅛ᭷

1.0E-1005
10
15
Eigen mode Number MD
Truncation Eigen mode Number MT

20࣮ࣔࢻᩘࡣ 8 ಶ࡛࠶ࡾࠊᘧ(3-19), (3-20)࡛☢ሙ࡟ᑐࡋ࡚┠ᶆࢆ୚࠼ࡓሙྜ࡜ྠᵝ࡞㟁ὶ㓄⨨࡜☢
ሙศᕸࡢ෌ᵓᡂ⤖ᯝࡀᚓࡽࢀࡿࡇ࡜ࡀゎࡿࠋࡓ

Fig. 3-12(a). ┠ᶆ☢ሙࢆ ‫= ׎‬5=/2.0 ࡜ࡋࡓሙྜ
ࡢࠊ≉␗್ k ࠊᅛ᭷࣮ࣔࢻᙉᗘ 3TGk ࡜ṧᕪ☢
ሙࢆࠊᅛ᭷࣮ࣔࢻ␒ྕ 0D ࡜ᡴࡕษࡾᅛ
᭷࣮ࣔࢻ␒ྕ 0T ࡛♧ࡍࠋ

ࡔࡋࠊFig. 3-12(b)࡛ࡣ┠ᶆ☢ሙࡀ ‫ = ׎‬㺎 RZ/2.0࡛࠶ࡗࡓࡢ࡛ࠊᨺᑕ≧࡟ᥥ࠸࡚࠸ࡿṧᕪࡣࠊ ‫׎‬ࡢṧᕪ࡛࠶ࡾࠊศᕸᙧࡣఝ࡚࠸ࡿࡀࠊ್ࡣ␗࡞
ࡿࡇ࡜ࢆࢥ࣓ࣥࢺࡋ࡚࠾ࡃࠋ

3.4.2.

┠ᶆ☢ሙ࡟࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ฼⏝3.4.3.

๓㡯ྠᵝ࡟ BR ࡟ὀ┠ࡋࡓሙྜ࡛ࡶ࣋ࢡࢺ࣏ࣝ
ࢸࣥࢩ࡛ࣕࣝ㉳☢ຊ㓄⨨ࡀྠ⛬ᗘࡢ⢭ᗘ࡛ồࡲࡿࡇ࡜ࢆḟ࡟♧ࡋ࡚࠾ࡃࠋ┠ᶆ࡜ࡍࡿ࣋ࢡࢺࣝ
࣏ࢸࣥࢩࣕࣝࡣ࿘ᅇ᪉ྥᡂศ࡛ᘧ(3-21)࡛࠶ࡿࠋ

ḟ࡟ࠊBZ ศᕸ࡟໙㓄(ഴᩳ: MRI ศ㔝࡛ࡣഴᩳ☢
ሙ)ࢆᣢࡓࡏࡿሙྜࢆ⪃࠼ࡿࠋࡘࡲࡾࠊ㉥㐨㠃
(Z=0.0m)ୖࡢ R=2.0m ௜㏆࡛ࠊFig. 3-5 ࡢ SVD ᅛ᭷࣮ࣔࢻࢆ฼⏝ࡍࡿ࡜ࠊFig. 312(a)ࡀᚓࡽࢀࠊFig. 3-10 ࡜ྠᵝ࡟ࠊࡇࡢ┠ᶆ☢ሙ࡛౑⏝ࡍࡿᅛ᭷࣮ࣔࢻᩘࡢቑຍ(኱ MT)࡜ඹ࡟ࠊ

┠ᶆ☢ሙ࡟໙㓄ࡢ࠶ࡿ BZ ศᕸBZ(R) = 1.0 + Const(R – 2.0) [T]㺂(3-22)

ࡢࡼ࠺࡟ࠊ☢ሙ࡟໙㓄ࠊ
[T/m]

=

(3-23)

ࡀ࠶ࡿࠋࡇࡢሙྜࠊ㉥㐨㠃(Z=0)㠃௨እ࡛ࡣࠊBR
ᡂศࡀ࠶ࡾࠊrot%=0 ࠿ࡽࠊ

=

=

࡛࠶ࡾࠊ
(3 െ 24)

࡛ࠊZ ఩⨨࡟ẚ౛ࡍࡿ BR ᡂศࡀ࠶ࡿࠋࡲࡓࠊࡇ
ࡢ BR ࡜ඹ࡟ div%=0 ࡛࠶ࡿࡓࡵࠊ෇⟄ᗙᶆ࡛ࠊ+= 0࡛࠶ࡿ஦ࡀᚲせ࡛ࠊZ=0 㠃௨እ࡛ࡣࠊ
ο
Fig. 3-12(b) ┠ᶆ☢ሙࢆ ‫= ׎‬㺎 5=/2.0 ࡜ࡋࡓሙྜࡢ☢ሙ෌ᵓᡂ⤖ᯝࠋᕥྑ࡟㉮ࡿ⥺ࡣ☢ຊ⥺(➼ ‫ࠊ)⥺ ׎‬ᨺᑕࣃࢱ࣮ࣥࡢ➼㧗⥺ࡣࠊ ‫ࡢ ׎‬ṧᕪ࡛ࠊ෇⎔᩿㠃୰ᚰ࠿ࡽ±1.0E-07, ±1.0E-8,±1.0E-9(Tm)ࡢṧᕪ࡛ࣉࣟࢵࢺࠋ= െ‫׬‬= െ‫׬‬=(3-25)

ࢆ┠ᶆ☢ሙ࡟ຍ࠼ࡿ஦ࡀᚲせ࡛࠶ࡿࠋ༙ᚄ᪉ྥ࡟໙㓄ࢆᣢࡘ㍈᪉ྥ☢ሙ BZ(R)ࡣࠊ

10㸫 15

Fig. 3-13. ໙㓄☢ሙ࡟ᑐࡍࡿ෌ᵓᡂ☢ሙ࡜ṧᕪ☢ሙࠋ(a) ṇࡋࡃᘧ(3-28)ࢆ┠ᶆ☢ሙ࡜ࡋࡓሙྜࠋ (b)ᘧ(3-28)ࡢ =2 ࡟ẚ౛ࡍࡿ㡯ࢆຍ࠼ࡎ㛫㐪ࡗࡓ┠ᶆ☢ሙ࡜ࡋࡓሙྜࠋ☢ሙホ౯㠃࡛ࡢࡳ┠ᶆ☢ሙ࡟㏆࠸෌ᵓᡂ☢ሙ࡜࡞ࡗࡓࠋ(c) %Z ᡂศṧᕪ☢ሙ(=െ)ࠋ
Ⅼ(MFEP)ࡣ Z=+/-0.25m ࡢ఩⨨࡟Ꮡᅾࡍࡿࠋ㛫㐪
BZ(R) ‫ן‬,

(3-26)

ࡗࡓ┠ᶆ☢ሙ࡛ࡣ MFEP ఩⨨௨እ࡛ࡣṧᕪࡀ኱ࡁࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࡀゎࡿࠋࡘࡲࡾࠊMaxwell ᪉⛬ࡢࡼ࠺࡟༙ᚄࡢ n-index ஌࡛⾲⌧ࡉࢀࡿሙྜࠊ

ᘧ࡟▩┪ࡍࡿ☢ሙࢆ┠ᶆ☢ሙ࡜ࡋࡓሙྜࠊࡓ࡜
n-index = െ(3-27)

࡛࠶ࡾࠊ┠ᶆ☢ሙࡣ(R=2.0m, Z=0.0m)ࡢ㏆ഐ࡛ࠊ
=െ
=1.0 +(n-index)(3-28)) (R-2.0) +࡚࠸࡚ࡶࠊ฼⏝ࡍࡿ☢ሙ✵㛫඲య࡛ࡣ୍⮴ࡋ࡚࡞࠸ྍ⬟ᛶࡶ࠶ࡿࠋ⠊ᅖࢆᗈࡆ࡚☢ሙศᕸࢆ☜ㄆࡍࡿࡇ࡜ࢆ່ࡵࡿࠋ
3.5. 3 ❶ࡢࡲ࡜ࡵ(R-2.0)-=1.0 +(n-index){(-࠼ࠊ☢ሙホ౯(MFEP)Ⅼ࡛⢭ᗘⰋ࠸☢ሙࢆ෌⌧ࡋ

}(3-29)➨ 2 ❶࡛㏙࡭ࡓᡴࡕษࡾ≉␗್ศゎἲ(TSVD)࡜᭱ᑠ஧஌ἲࢆ౑ࡗ࡚┠ᶆ☢ሙࢆṇ☜࡟෌⌧ࡍ࡛࠶ࡿࠋࡇࡇ࡛ࠊR0 ࡜ BZ0 ࡣᇶ‽࡜࡞ࡿ༙ᚄ఩⨨ࡿ㉳☢ຊ㓄⨨ࢆồࡵࡿᡭἲ(TSVD ṇ๎໬)ࢆࠊᛶ

(ࡇࡇ࡛ࡣ R0=2.0m)࡜ࡑࡢ఩⨨࡛ࡢ㍈᪉ྥ☢ሙ BZ㉁ࡢⰋ࠸ၥ㢟(well-posedࠊⰋタᐃၥ㢟)࡟㐺⏝ࡋ

࡛࠶ࡿࠋ

ࡓࠋ

Fig. 3-13 ࡟ࠊ☢ሙศᕸࡢ෌ᵓᡂ⤖ᯝࢆ♧ࡍࠋ(a)‽ഛ࡜ࡋ࡚ࠊ⥺㍯෇㟁ὶࡢసࡿ☢ሙࢆṇ☜࡟ࡀṇࡋ࠸┠ᶆ☢ሙ{ᘧ(3-29)}ࡢሙྜ࡛ࠊ(b)ࡣᘧ(3-ồࡵࡿ㏆ఝィ⟬ἲࢆ☜ㄆࡋࡓࠋࡇࡢ㏆ఝィ⟬࡛22)ࡢࡳࢆ Z=0 㠃௨እ࡛ࡶ౑⏝ࡋ࡚ࠊᘧ(3-29)ࡢ Z2

ࡣࠊ᥮⟬ᴃ෇✚ศ್࡟ Chebyshev ㏆ఝィ⟬ࢆ౑࡟ẚ౛ࡍࡿ㡯ࢆ↓どࡋࡓㄗ┠ᶆ☢ሙࡢሙྜ࡛࠶

࠺ࠋࡇࡢ౑⏝࡛ࠊ☢ሙศᕸࡢ᭱㐺໬ィ⟬ࢆᐇ⏝ࡿࠋୖୗ࡟㉮ࡗ࡚࠸ࡿ ‫➼ࡢ ׎‬㧗⥺ࡣ୧⪅࡛ྠࡌⓗ࡞ィ⟬᫬㛫࡛⾜࠺ࡇ࡜ࡀฟ᮶ࡿࠋࡼ࠺࡟ぢ࠼ࡿࠋ☢ሙࡢᕪ␗ࢆ⣽࠿ࡃぢࡿࠋ➼㧗ࢺ࣮ࣛࢫ(෇⎔)㠃ୖ࡟࿘ᅇ᪉ྥ⥺㍯㟁ὶࢆከᩘ⥺(ᨺᑕ≧ࡢ➼㧗⥺)ࡣࠊṧᕪ⤯ᑐ್ࡀ 1nT㹼1mT㓄⨨ࡋࠊࢺ࣮ࣛࢫෆ㒊࡛┠ᶆ☢ሙࢆ୚࠼ࠊࡑࡢ

୍࡛᱆ẖࡢ➼㧗⥺࡛♧ࡋ࡚࠸ࡿࡀࠊࡑࡢᶍᵝࡣ☢ሙࢆ෌⌧ࡍࡿ౛㢟ࢆ TSVD ṇ๎໬࡛ゎࡁࠊ☢ሙ␗࡞ࡗ࡚࠸ࡿࠋ෌ ⌧ ⢭ ᗘ ࢆ☜ ㄆ ࡋ ࡓ ࠋ☢ ሙ ศ ᕸ ࢆ୚ ࠼ ࡿ ሙ ྜᇶ‽༙ᚄࡢ R=2.0m ୖ࡛ࠊୖୗ᪉ྥ Z=-0.35㹼࡜ࠊࡑࡢ☢ሙࢆⓎ⏕ࡍࡿ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ

+0.35m ࡛ࠊᘧ(3-29)ࡢ☢ሙ࡜෌ᵓᡂ☢ሙࡢᕪ␗ࢆ୚࠼ࡿሙྜࡢ 2 ✀㢮ࢆヨࡋࡓࡀࠊྠ➼ࡢ⢭ᗘ࡛)ࢆ(c)࡟ࣉࣟࢵࢺࡋ࡚࠸ࡿࠋ☢ሙホ౯☢ሙศᕸࢆ෌⌧࡛ࡁࡓࠋࡋ࠿ࡋࠊ☢ሙศᕸࢆ୚

(െ

10㸫 16

࠼ࡿሙྜ࡛ࡣࠊ㟁ὶࡢ 2 ஌ຍ⟬್ࡣ᭱ᑠ࡜࡞ࡗ࡚
࠸ࡿ࡜☜ㄆࡋࡓࠋ୍᪉ࠊ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ
ࢆ୚࠼ࡿሙྜࠊᐃᩘຍ⟬ࡢ⮬⏤ᗘࡀ࠶ࡾࠊ᭱ࡶ
ᑠࡉ࠸㟁ὶࡢ 2 ஌ຍ⟬್ࡢሙྜࡀ☢ሙࢆ┠ᶆ್࡜ࡋࡓሙྜ࡜୍⮴ࡋࡓࠋࡉࡽ࡟ࠊ┠ᶆ☢ሙ࡜ Maxwell ᪉⛬ᘧࡢᩚྜᛶ࡟
ࡘ࠸࡚㆟ㄽࡋࡓࠋ㛫㐪ࡗࡓ☢ሙศᕸ(Maxwell ᪉⛬ᘧ࡜▩┪ࡍࡿሙྜ)ࢆࠊ୚࠼ࡿ࡜☢ሙࡢ෌ᵓᡂ
ࡣ☢ሙホ౯Ⅼ࡛⢭ᗘࡀᝏࡃ࡞ࡿሙྜ࡜ࠊ☢ሙホ౯Ⅼ࡛ࡣ⢭ᗘࡀⰋ࠸ィ⟬⤖ᯝ࡛ࡶࠊ☢ሙホ౯Ⅼ௨እ࡛ࡣࠊᐇ㝿࡟ᚓࡓ࠸☢ሙ࡜ࡣ␗࡞ࡗࡓ☢ሙศᕸࢆฟຊࡍࡿሙྜࡀ࠶ࡿࡇ࡜ࡶゎࡗࡓࠋ
3.5.1.

⿵㊊/ࢥ࣓ࣥࢺ

ᮏᩥ୰(3.1.1 㡯)࡟࡛ࡶ㏙࡭ࡓࡀࠊᩥ⊩[32]ࡢከ
㡯ᘧࡢಀᩘ್࡟ࡘ࠸࡚㸸௚ࡢᩥ⊩[34]࡜␗࡞ࡿ್
ࡀ♧ࡉࢀ࡚࠸ࡿሙྜࡀ࠶ࡿࠋᑡ࡞ࡃ࡜ࡶ[32]ࡢ 10ḟࡢಀᩘ࡛ࡣⰋዲ࡞☢ሙィ⟬⢭ᗘࡣᚓࡽࢀ࡞࠿
ࡗࡓࠋ୍᪉ࠊ[32] ࡢᩘ್࡛ࡶ 9 ḟࡢಀᩘ࡛ࡣⰋ࠸
☢ሙィ⟬⢭ᗘࡀᚓࡽࢀࡓࠋࡑࡢࡓࡵࠊᩥ⊩[32]ࡢ
ಀᩘࡢ౑⏝ࡣせὀព࡛࠶ࡿࡇ࡜ࢆࢥ࣓ࣥࢺࡋ࡚
࠾ࡃࠋ➹⪅ࡣ[34]࡟グ㏙ࡉࢀ࡚࠸ࡿ 10 ḟࡢಀᩘࢆ౑ࡗ࡚࠸ࡿࠋ

10㸫 17

4. MRI ⏝☢▼ࡢ୍ᵝ☢ሙタィ⨨ゎࡣᏑᅾࡋ࡞࠸ࠋࡇࢀࡣࠊMRI ☢▼࡛ࡣ⿕᳨☢Ẽඹ㬆᧜ീ⿦⨨ MRI ࡛ࡣୗグࡢ 3 ✀㢮ࡢ㟁☢ሙࢆ฼⏝ࡍࡿࠋ

⪅ࡢࡓࡵࡢ✵㛫ࡀᚲせ࡛࠶ࡾࠊ㉳☢ຊࢆ㓄⨨ฟ᮶࡞࠸✵㛫ࡀᏑᅾࡍࡿࡓࡵ࡛࠶ࡿࠋࡘࡲࡾࠊᚲ
せ࡞☢ሙᙉᗘ࣭ᆒ୍ᗘࢆᚓࡿࡇ࡜ࡀฟ᮶ࠊྍ⬟1) ᙉ࠸㟼☢ሙ୍࡛ᵝ࡞☢ሙศᕸ{ࡓ࡜࠼ࡤࠊ40cm࡞㝈ࡾ⊃࠸⠊ᅖ࡛㉳☢ຊ㓄⨨ࢆ⾜࠺஦ࡀồࡵࡽ⌫యෆ࡛±1.5ppm ௨ෆࡢ☢ሙᙉᗘ᣺ᖜ}ࠋ

ࢀࡿࠋ㏻ᖖࡢ෇⟄ᆺ MRI ☢▼࡛ࡣࠊᗈ࠸࣎࢔࡛

2) ✵㛫ⓗ࡟ᙉᗘ໙㓄ࢆᣢࡘ☢ሙศᕸ࡛ࣃࣝࢫ☢

▷࠸㍈㛗ࡢ☢▼ࡀࠊᮃࡲࢀࡿࠋ

ሙ(ࡓ࡜࠼ࡤᙉᗘ໙㓄ࡣ᧜ീ✵㛫ෆ࡛ X, Y, Z ࡢ 3ࡇࡢ≧ἣ࡟ࡘ࠸࡚ࠊ➹⪅ࡀ㛤Ⓨࡋࡓ TSVD ṇ๎᪉ྥ࡟ 40mT/m)໬࡛ゎࡃ᪉ἲࢆࠊࡇࡢᡭἲࡢᛂ⏝࡟ࡼࡿタィ౛3) 㧗࿘Ἴ(1.5T ࡛ࡣ⣙ 63.866MHz ࡛☢ሙᙉᗘ࡟ẚࢆ♧ࡋ࡞ࡀࡽㄝ᫂ࡍࡿࠋ୍⯡ⓗ࡞ࢩࣜࣥࢲᙧ≧౛)ࠊ

ࡢỈᖹ☢ሙᆺ MRI ☢▼ࢆᑐ㇟࡟ࡋࠊヨタィࡢ௙࡛࠶ࡿࠋ1)࡛≉࡟ 0.7T ௨ୖࡢᙉ☢ሙ MRI ⿦⨨࡛ᵝࡣࠊཧ⪃ᩥ⊩[10]࡟ἢࡗ࡚ Table 4-1 ࡜ࡍࡿࠋࡣ㉸ఏᑟ☢▼ࢆ౑ࡗ࡚࠸ࡿࠋࡇࡇ࡛ࡣ 1)ࡢ☢Ẽࡇࡢ㉳☢ຊ(ࡇࡇ࡛ࡣࢥ࢖ࣝࣈࣟࢵࢡ CB: Coilタィ࡟ TSVD ฼⏝౛ࢆグ㏙ࡍࡿࠋ2)ࡣഴᩳ☢ሙࢥ

Block)㓄⨨ࡢタィᡭ㡰ࢆ Fig. 4-1[10]࡟ᶍᘧⓗ࡟♧࢖ࣝ࡜࿧ࡤࢀࠊࡇࡢࢥ࢖ࣝࡢタィ⏝࡟㛤Ⓨࡋࡓࡍࠋ୕ࡘࡢẁ㝵(Step)࡟ศࡅ࡚タィࡍࡿࠋ㉳☢ຊᡭἲ[14, 15]ࡣᮏ㈨ᩱ᭱ᚋ(5.3.3 㡯)ࡢ⬟ື☢Ẽࢩ࣮㓄⨨ࡣࠊ᧜ീ࡟ᚲせ࡞✵㛫(ࡇࡇ࡛ࡣ┤ᚄ 40cm ✵ࣝࢻࢫࢸ࢔ࣜࣥࢢ☢▼(ASSM)ࡢタィ࡟ᛂ⏝ࡋ࡚㛫ࠊ40cm-DSV: Diameter Spherical Volume)୍࡛ᵝ

࠸ࡿ(ᮏ㈨ᩱ᭱ᚋ)ࠋ

࡞☢ሙศᕸ(ᆒ୍☢ሙ)ࢆ㧗☢ሙ(ࡇࡇ࡛ࡣࠊ3.0T)

MRI ࡛ࡣᙉ☢ሙ୍࡛ᵝᙉᗘࡢ㟼☢ሙศᕸࢆᚲ

࡛Ⓨ⏕ࡍࡿ஦ࡀ௙ᵝ࡛࠶ࡿࠋせ࡜ࡍࡿࠋデ᩿⏝ࡢ඲㌟ MRI ⿦⨨(1.5, 3.0T ࡢ㉸୕ẁ㝵ࡢ࡞࠿࡛ࠊStep-1 ࡛ࡣࠊྠ㍈⥺㍯㟁ὶࡢ㟁ᑟ☢▼฼⏝)࡛ࡣࠊ┤ᚄ 40cm ⌫యෆ(40cm-DSV:㞟ྜ࡛ࠊồࡵࡿᆒ୍ᗘࡀ༑ศྍ⬟࡞ᗄఱᏛⓗ࡞Diameter Spherical Volume)࡛ ☢ ሙ ኚ ື ࡀ㓄 ⨨(☢ ▼ ࡢ 㛗 ࡉ ࡸ ࣎ ࢔ ᚄ ࡞ ࡝)ࢆ Ỵ ࡵ ࡿ[9]ࠋ

3ppm(peak-to-peak)௨ୗ⛬ᗘ࡛࠶ࡿ[1,2]ࠋࡇࡢࡼ

Step2 ࡛ࡣ㍈᪉ྥ࡟ᒣ㇂ࢆᣢࡗ࡚ศᕸࡋ࡚࠸ࡓ㟁࠺࡟ᆒ୍࡞☢ሙศᕸࢆᚓࡿ࡟ࡣࠊ☢▼タ⨨⌧ሙὶࢆࠊᆒ୍ᗘࢆಖࡕ࡞ࡀࡽᩘಶࡢ CB ࡟ࡲ࡜ࡵ࡛ࡢ☢ሙㄪᩚ(ࢩ࣑ࣥࢢ)[12, 13]ࡶᚲせ࡛࠶ࡿࡀࠊ

ࡿࠋࡇࡢẁ㝵࡛ࡣࠊCB ෆࡢ㟁ὶ್ࡣ㐃⥆್࡛࠶☢▼タィ᫬࡟ᆒ୍࡞☢ሙศᕸࢆᣢࡘ⬟ຊࢆ☢▼

ࡿࠋStep-3 ࡛ࡣࠊᆒ୍ᗘࡀಖ࡚ࡿࡼ࠺࡟ࠊᐇ㝿ࡢ࡟୚࠼࡚࠾ࡃᚲせࡀ࠶ࡿࠋ୍᪉ࠊᆒ୍࡞☢ሙࢆᑟయ㓄⨨(㍈᪉ྥ࡜༙ᚄ᪉ྥࡢᕳࡁᩘ)ࢆ⪃៖ࡋࠊⓎ⏕ࡍࡿ㉳☢ຊ㓄⨨ࢆồࡵࡿタィィ⟬ࡣ୙Ⰻタ⣲⥺㟁ὶࢆỴࡵࡿࠋ
MRI ⏝☢▼࡟ࡣࠊᙉ☢ሙࢆⓎ⏕ࡍࡿ୺ࢥ࢖ࣝ

ᐃၥ㢟(ill-posed problem)࡛࠶ࡾࠊṇ☜࡞㉳☢ຊ㓄ࣈࣟࢵࢡ(MC-CB: Main coil CB)࡜☢▼࿘ᅖ࡬ࡢ₃
Table 4-1 MRI ☢▼ࡢヨタィ௙ᵝ (ᩥ⊩[10],Table 1 ࡼࡾᘬ⏝)Parameter
Number of MC-CBs(NMC)
Magnetic field at center(B0)
Inner radius of coil blocks (RIN)Electrical length of MC (Le)
Homogeneity in 40 cm DSV (h40)
Volume of interest(VOI)
Radius of shield coil
(RSC)
Current density in end-MC-CBs (DCi)Current density in other CBs (DCi)Max. magnetic field conductor (Bex)
Current drive modeValue
6 (5 to 7)
3.00 T
0.500 m1.520 m< 1.00 ppm
0.400 m DSV
0.945 m
150 A/mm2
180 A/mm2<6.20 T
PersistentFig. 4-1 㟼☢ሙ☢▼ࡢ㉳☢ຊ㓄⨨タィᡭ㡰ࠋᩥ
⊩[10], Fig.1 ࡼࡾᘬ⏝10㸫 18ࢀ☢ሙࢆ㐽ⶸࡍࡿࢩ࣮ࣝࢻࢥ࢖ࣝ(SC-CB㸸Shieldࡇࡢࡓࡵࠊ% ࡢせ⣲ࡣ i ␒┠☢ሙホ౯Ⅼ࡟ᑐࡋ࡚

coil CB)ࡀ࠶ࡿࠋMC-CB 㓄⨨ࡣୖグ 3 ẁ㝵ࡢィ⟬BZi ࡛࠶ࡿࠋࡇࡢ⪃࠼ࡣࠊ4.6 ⠇࡛㆟ㄽࡍࡿࢩ࣑ࣥ

࡛ࠊᆒ୍࡞ᙉ☢ሙࢆⓎ⏕ࡍࡿࡼ࠺࡟ỴࡵࡿࠋSC-ࢢィ⟬(ィCB ࡢ༙ᚄ఩⨨࡜㟁ὶࡣ MC-CB ࡀᣢࡘ MM ࢆ࡯ᕸ࡟ㄪᩚࡍࡿࡓࡵࡢ☢Ẽ࣮࣓ࣔࣥࢺ㓄⨨ 0 ࢆồࡰᡴࡕᾘࡍࡼ࠺࡟ࠊ඲࡚ Step ࡛ㄪᩚࡍࡿࠋኚ᭦

ࡵࡿィ⟬)࡛ࡶྠࡌ࡛࠶ࡾࠊ㍈᪉ྥᡂศ BZ ࡛ࢩ࣑ࡉࢀࡓ SC-CB ࡢ☢ሙࢆ⪃៖ࡋ࡚ MC-CB 㓄⨨ࢆỴࣥࢢィ⟬ࡶᐃᘧ໬ࡍࡿࠋࡉࡽ࡟ࠊ5 ❶ࡢ࣑࣮ࣗ࢜

ࡵࠊ᪂ࡓ࡞ MC-CB 㓄⨨࡟ࡼࡿ MM ࢆᡴࡕᾘࡍ

ࣥ g-2/EDM ヲ⣽ィSC-CB 㓄⨨ࢆ෌ᗘỴࡵࡿࠋࡇࡢࡼ࠺࡟ࠊSC-CB࣑ࣥࢢ࡛ࡶྠᵝ࡛࠶ࡿࠋ☢ሙ࠿ࡽ☢ሙࢆ⿵ṇࡋ࡚ᆒ୍☢ሙศ⏝ࡢ☢▼(MSM)ࡢタィࡸࢩ࡜ MC-CB 㓄⨨ࡣ⧞ࡾ㏉ࡋィ⟬࡛Ỵࡵࡿࠋ௨ୗ࡛

ᐇ㝿࡟ BZ ᡂศ௨እࡀ↓ど࡛ࡁࡿ≧ែ࡞ࡢ࠿㸽ࡣࠊᆒ୍☢ሙࢆⓎ⏕ࡍࡿ MC-CB 㓄⨨タィᡭἲࢆ࡟ࡘ࠸࡚ࡣࠊὀពࡋ࡚☜ㄆࡋ࡚࠸ࡃᚲせࡀ࠶ࡿㄝ᫂ࡍࡿࠋࡇ࡜ࢆࢥ࣓ࣥࢺࡋ࡚࠾ࡃࠋ

4.1. MRI ☢▼☢ሙタィࡢ☢ሙᡂศ

4.2. ᴫᛕ᳨ウ(Step-1)

タィᡭἲࡢᮏㄽ࡟ධࡿ๓࡟タィ࡛ᢅ࠺☢ሙᡂ

Step-1 ࡛ࡣࠊ┠ᶆࡢ☢ሙᙉᗘ࡜ᆒ୍ᗘࢆᣢࡘࡼ

ศࢆㄝ᫂ࡋ࡚࠾ࡃࠋࡍ࡛࡟ 2.3 ⠇ࡢ┠ᶆ☢ሙ࡛ࡶ࠺࡟ࢯࣞࣀ࢖ࢻ≧࡟㐃⥆ⓗ࡟ྠ㍈㓄⨨ࡋࡓ⥺㍯㏙࡭ࡓࡀࠊMRI ☢ሙ(ᆒ୍☢ሙ)࡛ࡣࠊᘧ(2-1)ࡢ %㟁ὶ(ኴࡉ↓㝈ᑠࡢ෇㟁ὶ)ࡢ㟁ὶศᕸࢆࠊFig. 4-2

ࡣ MFEP ࡢ☢ሙศᕸࢆ㍈᪉ྥᡂศ(BZi)࡛ᵓᡂࡍ

ࡢィ⟬య⣔࡛⟬ฟࡍࡿࠋ⥺㍯㟁ὶࡣࠊMRI ☢▼ࡿࠋMRI ࡛ࡣ☢ሙ⤯ᑐ್ B ࡛ᆒ୍࡞☢ሙࡀᚲせ࡛࡛୺࡟☢ሙࢆసࡿ୺ࢥ࢖ࣝ఩⨨࡟෇⟄≧࡟㓄⨨࠶ࡿࡀࠊ㉳☢ຊ㓄⨨ࡣ BZ ᳨࡛ウࡍࡿࠋࡋࠊ୍᪉ࠊ኱༙ᚄ఩⨨࡟ࡣࠊእ㒊࡬ࡢ₃ࢀ☢ሙᚲせ࡞ᆒ୍☢ሙࡀᚓࡽࢀࡓẁ㝵࡛ࡣࠊ☢ሙᙉࢆ㞽࡟㏆࡙ࡅࡿࡓࡵࠊ඲య࡜ࡋ࡚ MM ࢆᡴࡕᾘᗘࡢኚືศࡣ㏻ᖖࠊ୺☢ሙࡀ 3.0T ࡛࠶ࡗ࡚ࡶࠊ1ࡍࢩ࣮ࣝࢻࢥ࢖ࣝࢆ⨨ࡃࠋ⥺㍯㟁ὶࡣィ⟬⤖ᯝ࢞࢘ࢫ(3.0T ࡟ᑐࡋ࡚ 33.3ppm peak to peak)௨ୗ࡛

࡟ᇶ࡙࠸࡚୺ࢥ࢖ࣝࢆᵓᡂࡍࡿ CB ࡟ࠊ௨ᚋࡢ

࠶ࡾࠊ༙ᚄ᪉ྥᡂศ BR ࡶྠ⛬ᗘ௨ୗ࡛࠶ࡿࠋࡇ

Step ࡛⨨ࡁ᥮࠼ࡿࠋࡇࡢ Step-1 ࡛ࡣࠊ⥺㍯㟁ὶ㓄

ࡢሙྜࠊBZ ࡜ B ࡢᕪ␗ࡣᑠࡉࡃ(1nT ௨ୗ)ࠊMRI⨨ࢆ⾲ࡍ࣋ࢡࢺࣝ , ࡟ᑐࡋ࡚ࠊ☢ሙホ౯Ⅼ(MFEP)࡛ᚲせ࡞ᆒ୍ᗘࡢᩘ ppm(ᚑࡗ࡚ 1 T㹼10 T ࡢ☢

ࡢ☢ሙศᕸ % ࡣࠊᘧ(2-1)ࡢࡼ࠺࡟ࠊ% = A, ࡜⾲ሙ᣺ᖜ)࡟ᑐࡋ࡚༑ศᑠࡉ࠸ࠋࡑࡇ࡛ࠊᆒ୍☢ሙࡉ ࢀ ࡿ ࠋMFEP ࡣ ࠊFOV(᧜ ീ 㡿 ᇦ: Field OfࢆⓎ⏕ࡍࡿ☢▼ࡢ☢ሙタィ࡛ࡣ BZ ࢆホ౯ࡍࡿࠋ

Viewࠊ┤ᚄ 40㹼50cm ⛬ᗘࡢ⌫య)⾲㠃࡟㓄⨨ࡉࢀࡿࠋᛂ⟅⾜ิ A ࡢせ⣲ Aij ࡣ j ␒┠⥺㍯㟁ὶ(༢఩㟁ὶ)ࡀ i ␒┠ MFEP ࡟సࡿ☢ሙ࡛࠶ࡿࠋ

Shield coil (SC)ཧ⪃ᩥ⊩[9,10]࡛ࡣࠊࢯࣞࣀ࢖ࢻ≧࡟㓄⨨ࡋࡓ෇⥺㍯㟁ὶ࠿ࡽᆒ୍☢ሙࢆணᐃࡍࡿ㡿ᇦࡢ☢ሙ

FOV࡬ࡢᛂ⟅⾜ิ A ࡢ SVD ᅛ᭷࣮ࣔࢻࢆ㔜ࡡྜࢃࡏ࡚ MRI ࡛ᚲせ࡜ࡍࡿ㟁ὶศᕸ{ᘧ(2-7)}ࢆ⟬ฟ⥺㍯㟁ὶࡋ ࠊ ࡑ ࡢ 㟁ὶ ศ ᕸ ࠿ ࡽヲ ⣽ ࡞ ☢ ሙศ ᕸ ࢆ ⟬ ฟ

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Y

⥺㍯㟁ὶ

Magnetic fieldz at L-th
positionFOVũ-th current=

40cm-DSV
Length

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Solenoid (Filament loop currents)

ࡋࠊᚲせ࡜ࡍࡿᆒ୍ᗘࢆᚓࡿ᮲௳ࢆ᳨ウࡋࡓࠋࡇࡢẁ㝵࡛ࡣ Fig. 4-1 ࡢ Step-1 ࡟♧ࡋࡓࡼ࠺࡟㐃⥆ⓗ࡟ศᕸࡍࡿ㟁ὶ࡛࠶ࡿࠋࡇࡢẁ㝵࡛ࠊᚲせ࡞☢▼㍈㛗ࡉࡸ୺ࢥ࢖ࣝࡢ CB ᩘࢆ᳨ウࡍࡿࠋ୙Ⰻタᐃၥ㢟(ill-posed problem)࡛࠶ࡿࡓࡵࠊࡇࡇ
࡛ࠊ༢⣧࡞ィ⟬ࣔࢹࣝࢆ౑࠸ࠊⰋ࠸ぢ㏻ࡋ(౑⏝Fig. 4-2 MRI ☢▼☢ሙタィ Step-1 ィ⟬ࣔࢹࣝᩥ⊩[9], Fig.1 & Fig.2 ࡼࡾᘬ⏝10㸫 19

Fig. 4-3 Step-1 ࡢᅛ᭷࣮ࣔࢻࠋྛᯟୖ㒊࡟㟁ὶศᕸࠊୗ୰ኸ࡟☢ሙศᕸࢆ▮༳࡛♧ࡍࠋ☢ሙࡢ᪉ྥࡣ㍈(⣬㠃ᶓ)᪉ྥ࡛࠶ࡿࡀࠊࡇࡇ
࡛ࡣ୰ᚰ࠿ࡽᨺᑕ≧࡟♧ࡋࡓࠋᑐ⛠ᛶࡢࡓࡵ࡟ወᩘ␒ྕࡢࡳ౑⏝ࠋᩥ⊩[10]㺂Fig.3 ᘬ⏝
Fig. 4-4 Step-1 ࡢィ⟬⤖ᯝ౛ࠋຍ⟬ᅛ᭷࣮ࣔࢻ
ᩘࡣୖ࠿ࡽࠊ5㸪6㸪7 ಶࠋᕥྑ࡟㉮ࡿ➼㧗⥺ࡣ➼☢᮰⥺࡛ࠊ୰ᚰ࠿ࡽᨺᑕ≧ࡢ⥺ࡣ 3.0T
±3.0ppm ࡢ☢ሙᙉᗘ⥺ࠋᅛ᭷࣮ࣔࢻᩘࡢቑຍ
࡛ࠊ3T±4.5ȝT (1.5ppm)ࡢ➼㧗⥺ࡀᅖࡴ㡿ᇦࡀᗈࡀࡿࠋᡴⅬ㡿ᇦ࡛ࡣタィ☢ሙࡼࡾ㧗☢ሙࠋྍ⬟࡞ࢫ࣮࣌ࢫ࡛ᚲせ࡞☢ሙᙉᗘ࣭ᆒ୍ᗘࢆ☜ಖ)ࢆࡘࡅࡿࡇ࡜ࡣ㔜せ࡛࠶ࡿࠋFig. 4-3 ࡣ༙ᚄ 0.525m, 1.50m 㛗ࡢ෇⟄㠃࡟ከᩘࡢ⥺㍯㟁ὶࢆ㓄⨨ࡋࠊMFEPs ࢆ㓄⨨ࡍࡿ☢ሙホ౯ 㠃 ࡟ 40cm ⌫ 㠃 (40cm-DSS, DSS: Diameter
Spherical Surface)ࢆ࡜ࡾࠊMFEPs ࡬ࡢᛂ⟅⾜ิ࡟≉␗್ศゎࡋ࡚ᚓࡽࢀࡓ SVD ᅛ᭷࣮ࣔࢻࢆࠊྛ
ࣇ࣮࣒ࣞୖ㒊ࡢ༙ᚄ 0.525m ┦ᙜ఩⨨࡟㟁ὶศᕸࢆ▮༳࡛ࠊ୰ኸୗ㒊ࡢ 40cm-DSS ࡟☢ሙศᕸࢆ▮༳{ᐇ㝿࡟ࡣ㍈᪉ྥ(ᕥྑ᪉ྥ)ࢆྥ࠸ࡓ☢ሙ࡛࠶ࡿࡀࠊࡇࡇ࡛ࡣ୰ᚰ࠿ࡽ༙ᚄእ࣭ෆ(ṇ࣭㈇)᪉ྥ
࡛♧ࡍ}࡛♧ࡋࡓࠋഅᩘ␒ࡢᅛ᭷࣮ࣔࢻࡣࠊ㍈᪉ྥ࡟཯ᑐ⛠࡛࠶ࡾࠊ฼⏝࡛ࡁ࡞࠸ࠋཧ⪃࡟ 2 ␒┠ࡢࡳ♧ࡋࡓࠋ

≉␗್(T/A)
6.056E-5
4.026E-6
3.199E-7
2.665E-8
2.258E-9
1.926E-10
1.549E-11

ᩘࡀከࡃ࡞ࡿࡇ࡜ࡀゎࡿࠋTable 4-2 ࡟ࡣ≉␗್ࠊᅛ᭷࣮ࣔࢻᙉᗘࠊࡑࢀ࡟㟁ὶ(ࣀ࣒ࣝ)ࢆ♧ࡋࡓࠋ᭷㝈㛗ࢯࣞࣀ࢖ࢻ࡛ࡣཝᐦ࡟ᆒ୍࡞☢ሙࡣᚓࡽࢀ࡞࠸ࡢ࡛ࠊࡑࡢព࿡࡛ ill-posed ࡛࠶ࡿࠋ㟁ὶ್ࡀ㧗ḟᡂศ࡛ࡣୖ᪼ࡍࡿࡇ࡜ࡶࠊࡑࡢ≧ἣࢆ♧ࡋ࡚࠸ࡿࠋࡋ࠿ࡋࠊ3.0T ୍ᵝ☢ሙࢆ⏕ᡂࡍࡿࡓࡵ࡟ᚲせ࡞ 13 ḟᡂศࡣࠊ1 T ௨ୗ࡛࠶ࡾࠊᑠࡉ
࠸ࠋࡑࡢࡓࡵࠊ11 ␒┠ࡲ࡛ࡢወᩘ␒ྕࡢᅛ᭷ࣔ

Table 4-2 ᅛ᭷࣮ࣔࢻᙉᗘ࡜㟁ὶᐤ୚(3.0T)
No.
1
3
5
7
9
11
13

㧗ḟ࣮ࣔࢻ࡛ࡣࠊ☢ሙࠊ㟁ὶศᕸඹ࡟ࣆ࣮ࢡ

ᙉᗘ(T)
2.998
0.10947.869E-3
7.018E-4
6.985E-5
7.425E-6
8.190E-7

㟁ὶ (MA)
2.638
1.448
1.312
1.403
1.649
2.054
2.646

࣮ࢻ 6 ಶࡢ⤌ࡳྜࢃࡏ࡛ࠊ᣺ᖜࡀ 1ppm ⛬ᗘ௨ෆࡢᆒ୍࡞☢ሙࢆⓎ⏕࡛ࡁࡿ࡜ゎࡿࠋᅛ᭷࣮ࣔࢻᩘࡣࠊMC-CB ᩘ࡜ᐦ᥋࡟㛵㐃ࡍࡿࡇ࡜ࡣḟ⠇(4.3)࡛㏙࡭ࡿࡀࠊStep-1 ࡛ࡢᵝᏊࢆ
Fig. 4-4 ࡟♧ࡋࡓࠋᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ MT ࢆ,ୖ࠿ࡽ 9, 11, 13 ࡜ࡋࡓሙྜ࡛ࠊᕥྑᑐ⛠࡞ᅛ᭷࣮ࣔࢻࢆࡑࢀࡒࢀࠊ5㸪6㸪7 ಶࢆຍ⟬{ᘧ(2-11)}ࡋ

10㸫 20࡚ࠊᆒ୍☢ሙࢆⓎ⏕ࡍࡿ㉳☢ຊ㓄⨨ࢆ෇⟄≧࡟ᅛ᭷࣮ࣔࢻ␒ྕ MT ࢆᐇᩘ࡜⪃࠼ࠊᑠᩘⅬ௨ୗࢆ⟬ฟࡋ࡚࠸ࡿࠋ౑⏝ࡍࡿᅛ᭷࣮ࣔࢻᩘ࡜ྠࡌᩘ

ษࡾᤞ࡚ࡓᩚᩘࢆ MTI ࡜ࡍࡿ࡜ࡁࠊMTI ࡲ࡛ࡣຍࡢࣆ࣮ࢡࡀ㟁ὶศᕸ࡟☜ㄆ࡛ࡁࡿ(Step-2 ࡛ࡣಶ⟬๭ྜࢆ PTGk ࡜ࡋࠊMTI +1(M1 ࡜グ㏙ࡍࡿ)␒┠ࡢࡢ఩⨨࡟ CB ࢆ㓄⨨ࡍࡿ)ࠋࡲࡓࠊᅛ᭷࣮ࣔࢻᩘࡀ

ᅛ᭷࣮ࣔࢻࡣࠊຍ⟬๭ྜࢆ(MT- MTI)

ቑຍࡍࡿ࡜ࠊ3.0T ±ȝ7 SSP ࡢ➼㧗⥺ࡀᅖຍ⟬ࢆ⾜࠺ࡇ࡜࡛ࠊ⪃៖ࡍࡿ᭱㧗ḟࡢᅛ᭷࣮ࣔ

ࡴ୰ᚰ㡿ᇦࡀᗈࡀࡗ࡚࠾ࡾࠊࡼࡾⰋዲ࡞ᆒ୍
☢ሙࢆⓎ⏕࡛ࡁ࡚࠸ࡿࡇ࡜ࡀゎࡿࠋࡲࡓࠊᡴ
Ⅼ㡿ᇦ࡛ࡣࠊ☢ሙࡀタィ┠ᶆ☢ሙ(ࡇࡇ࡛ࡣ
3.0T)ࡼࡾ㧗ࡃ࡞ࡗ࡚࠸ࡿࠋ
Fig. 4-5 ࡛ࡣ෇⟄≧࡟㓄⨨ࡍࡿ㉳☢ຊ㓄⨨ࡢ඲㛗ࡢ 2 ✀㢮ࢆẚ㍑ࡋ࡚࠸ࡿࠋ☢▼฼⏝⪅ࡣࢥࣥࣃࢡࢺ࡞☢▼ࢆᮃࡴ࡜⪃࠼ࡽࢀࡿࡀࠊୖഃ
ᅗࡢࡼ࠺࡟ࠊ㈇㟁ὶࢆὶࡍ㒊ศࡀⓎ⏕ࡋࠊྜィ㉳☢ຊࡣቑຍࡍࡿࠋࡲࡓࠊ☢ሙᙉᗘࡢ➼㧗⥺఩⨨ࡀ⊃ࡲࡗ࡚ࡁ࡚࠸ࡿ஦࠿ࡽࠊᆒ୍ᗘࡶ
ᝏ໬ࡍࡿࡇ࡜ࡀゎࡿࠋࢻࢆ㐃⥆ⓗ࡟ㄪᩚࡋ࡚ࠊ㉳☢ຊ㓄⨨ࢆỴࡵࡿࡇ࡜ࡍࡿ࡜ࢆྍ⬟࡜ࡍࡿࠋࡘࡲࡾࠊ, =σξ
+ (MT- MTI)ξ

/ 䡇
/

,

(4-1)

ࡢຍ⟬࡛࠶ࡿࠋࡇࡢຍ⟬ἲࡢᐇ౛ࢆ Fig. 4-6 ࡟♧ࡍࠋୖഃᅗ࡟ࡣࠊMT=10.7 ࡜ 12.3 ࡢሙྜ࡛ࠊ㟁ὶศᕸ࡜ 3.0T±4.5 T(1.5ppm)ࡢ➼㧗⥺ࢆ♧ࡋ࡚࠸ࡿࠋ㟁ὶࡢࣆ࣮ࢡᩘࡣྠࡌ࡛࠶ࡿࡀࠊࡑࡢศ
ᕸᙧࡣ␗࡞ࡗ࡚࠾ࡾࠊᆒ୍ᗘࡶ␗࡞ࡗ࡚࠸ࡿࠋ
ᕥ࡛ࡣࠊ10 ␒┠ࡲ࡛ᅛ᭷࣮ࣔࢻࢆᙉᗘ PTGk ࡛ࠊ
11 ␒┠ࢆ 0.7 PTG11 ࡢᙉᗘ࡛ຍ⟬ࡋ࡚࠸ࡿࠋ୍
᪉ࠊྑഃࡣࠊ12 ␒┠ࡲ࡛ࡢᅛ᭷࣮ࣔࢻࢆᙉᗘ
PTGk ࡛ࠊ13 ␒┠ࢆ 0.3 PTG13 ࡢᙉᗘ࡛ຍ⟬ࡋ࡚࠸ࡿࠋࣆ࣮ࢡᩘࡣྠࡌ࡛࠶ࡾ࡞ࡀࡽࠊᆒ୍ᗘࡀྥ
ୖࡋࡓࠋࡋ࠿ࡋࠊ㟁ὶࣆ࣮ࢡࡣ㧗ࡃࠊᐇ☢▼࡛ࡣᑟయࡢ⤒㦂☢ሙࡀᙉࡃ࡞ࡾࠊ⣲⥺㟁ὶࡀไ㝈ࡉࢀࡿྍ⬟ᛶࡶ࠶ࡿࡓࡵࠊὀពࢆせࡍࡿࠋ
Fig. 4-6 ୗ㒊ࡣࠊᆒ୍ᗘ࡜⤯ᑐ್ࡢྜィ㟁ὶ್ࢆᐇᩘ໬ࡋࡓ MT ࡢ㛵ᩘ࡛♧ࡋࡓࠋྜィ㟁ὶ್࡜

Fig. 4-5 ␗࡞ࡗࡓ඲㛗࡟ᑐࡍࡿ Step-1 ⤖ᯝࠊᅛ᭷࣮ࣔࢻ 6 ಶ౑⏝ࠊୖ㸸1.30mࠊୗ㸸1.55m
௨ୖࡢ㆟ㄽ ࡛ࡣᘧ(2-11)ࡢᅛ᭷࣮ࣔ ࢻࡢຍ⟬࡛ࠊ㟁ὶ್ࢆỴࡵ࡚࠸ࡿࡀࠊྛᅛ᭷࣮ࣔࢻࡢᐤ
୚ࡣࠊPTGk ࡛Ỵࡵࡓࠋࡇࡢຍ⟬ἲࡣࠊ฼⏝ᅛ᭷࣮ࣔࢻᩘࡀࠊᩚᩘ࡛㞳ᩓⓗ࡛࠶ࡿࠋࡋ࠿ࡋࠊᐇ㝿࡟ࡣࠊຍ⟬๭ྜࢆ

PTGk ࡛ࡣ࡞ࡃࠊ௵ពࡢ๭ྜ࡛

ຍ⟬ࡍࡿࡇ࡜ࡣྍ⬟࡛࠶ࡿࠋࡑࡇ࡛ࠊᡴࡕษࡾ

10㸫 21

Fig. 4-6 ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕࢆᐇᩘ࡜ࡋ
࡚ࠊ㉳☢ຊ㓄⨨ࢆồࡵࡓሙྜࡢ☢ሙศᕸࠊᆒ
୍ᗘࠊ࠾ࡼࡧࠊ⤯ᑐ್ྜィ㟁ὶ್ࠋᆒ୍ᗘࡣ MT ࡢ㛵ᩘ࡛㐃⥆ⓗ࡟ኚ໬ࡋ࡚࠾ࡾࠊ☢
▼タィ࡛ࡣồࡵࡿᆒ୍ᗘࡀᚓࡽࢀࠊタィྍ⬟࡞㉳☢ຊ㓄⨨࡛࠶ࡿ᮲௳(MT)ࢆỴࡵࡿࠋ
4.2.1. CB ᩿㠃ࡢ✚ศ࡟ࡘ࠸࡚
ᮏ㡯ࡣᮏㄽ࠿ࡽእࢀࡿࡀࠊḟ⠇࡛㉳☢ຊ㓄⨨ࡢ㞳ᩓ໬(Step-2)ࡢㄝ᫂࡟⛣ࡿ๓࡟ࠊCB ᩿㠃ࡢ✚ศ࡟ࡘ࠸࡚ㄝ᫂ࡋࠊ☢ሙィ⟬⢭ᗘ࡟ࡘ࠸࡚☜ㄆ
ࡍࡿࠋCB ᩿㠃ࡣ㛗᪉ᙧ࡛࠶ࡿࡀࠊࡇࡢ᩿㠃ෆ࡟ከᩘࡢ⥺㍯㟁ὶࢆ㓄⨨ࡋ࡚ࠊ᩿㠃✚ศࢆ⾜࠸ࠊṇ☜࡞☢ሙࢆồࡵࡿࠋᩘ್✚ศἲ࡟ࡣࠊ▴ᙧࠊ஧ḟᘧ㏆ఝࡢࢩࣥࣉࢯࣥἲࠊࡑࢀ࡟࢞࢘ࢫ✚ศ

Fig. 4-7 CB ᩿㠃ෆࡢ✚ศࣔࢹࣝࡢ㧗ḟ㏆ఝࡢ✚ศἲ➼ࡀ࠶ࡿࡀࠊ࢞࢘ࢫ✚ศࡀ㧗⢭ᗘ࡛࠶ࡾࠊィ⟬᫬㛫ࡣ▷᫬㛫࡛࠶ࡿࠋ➹⪅࢘ࢫศⅬ)ࢆୗഃ࡟♧ࡋࡓࢥ࢖᩿ࣝ㠃ࡢᅗ࡟♧ࡋࡣࠊ࢞࢘ࢫồ✚ἲࢆ౑ࡗ࡚࠾ࡾࠊࡇࡇ࡛ࠊ࢞࢘

ࡓࠋཧ⪃࡟ࠊ➼ศ๭ࡢሙྜࡢ✚ศⅬ(ᐇ㝿ࡼࡾᑡࢫồ✚ἲࢆ⤂௓ࡋ࡚࠾ࡃࠋ

࡞࠸ศⅬᩘ࡛࠶ࡿࡀ)ࡶ♧ࡋࡓࠋCB ୰ ᚰ ༙ ᚄ Rc ࢆ Rc=0.82mࠊ ༙ ᚄ ᪉ ྥ ᖜ᩿㠃ࡢ✚ศࡣࠊ

a=4.0cm,㍈᪉ྥ᩿㠃㛗ࡉ b=20.0cm ࡜ࡋࠊ☢ሙィ
( , )

ൎ

( ,

) (4 െ 2)ࡢࡼ࠺࡟ࠊ࢞࢘ࢫศⅬ఩⨨࡟㔜ࡳࢆ௜ࡅ࡚✚ศࢆࠊຍ⟬࡟⨨ࡁ᥮࠼࡚ࠊᐇ⾜ࡍࡿࠋ ,
ࢫศⅬ࡛ࠊ

,

ࡣ࢞࢘

࡟ධᡭ࡛ࡁࡿࠋ
༙ᚄ Rc ࡛㧗ࡉ Zc ఩⨨࡟࠶ࡿ⥺㍯㟁ὶࡀィ⟬Ⅼ
Rm, Zm ࡟సࡿ☢ሙ bZ ࡣᘧ(3-2)ࢆ౑ࡗ࡚ィ⟬࡛ࡁࡿࡀࠊࡇࡢ್ࢆ
bz = Ibz(Rc, Rm, Zmc)

(4-3)

࡜⪃࠼ࠊFig. 4-7 ࡢ CB ࡀసࡿ☢ሙࡣࠊ᩿㠃 a,b ࡟ࡘ ࠸ ࡚ ࠊ ୗグ ࡢ ࢞ ࢘ ࢫồ ✚ ἲ ࡛ ィ⟬ ࡍ ࡿ ࡇ ࡜࡛ࠊ⢭ᗘⰋࡃ☢ሙࢆ⟬ฟ࡛ࡁࡿ࡜ᮇᚅ࡛ࡁࡿࠋ

ࡣ༙ᚄ᪉ྥ࡜㍈᪉ྥ࡛ 4x7 ಶ࡛࠶ࡿࡀࠊ➼ศ๭ἲ
࡛ࡣ 1000x5000 Ⅼࡢศ๭Ⅼࢆྲྀࡗ࡚࠸ࡿࠋ
Table 4-3 ☢ሙ✚ศ್ࡢẚ㍑+ ,୧⪅ࡣ 9 ᱆࡛ᩘ್ࡀ୍⮴ࡋ࡚࠾ࡾࠊṇࡋࡃィ⟬࢘ࢫ✚ศἲ࡟ẚ࡭ࠊ⣙ 180 ಸከࡃ࡞ࡾࠊ㉳☢ຊ㓄െ ),☢ሙィ⟬Ⅼ ࢞࢘ࢫồ✚(4x7) ➼ศ๭(1000x5000)
BZ
BZ
Rm Zmc(m) (m)BR
BR0.694431840Ϯϭϳ
0.694431840ϯϬϱ
0.333 0.0
0.0
0.0
0.366090422ϮϭϬ
0.366090422ϮϬϴ
0.333 0.50
0.110401434ϳϲϭ
0.110401434ϳϳϴ
0.670767518Ϯϭϭ
0.670767518Ϯϴϵ
0.333 0.10
0.0574310032ϴϯϵ 0.0574310033Ϭϯϲ
0.688363919ϯϬϭ
0.688363919ϯϴϲ
0.333 0.05
0.0298539491Ϯϵϵ 0.0298539491ϰϬϰ࡛ࡁ࡚࠸ࡿ࡜⪃࠼ࡿࠋィ⟬㔞ࡣ➼ศ๭࡛ࡣࠊ࢞

/

(1.0,
/

☢ሙィ⟬್ࢆࠊTable 4-3 ࡛ẚ㍑ࡋࡓࠋ࢞࢘ࢫศⅬࡣ㔜ࡳ࡛࠶ࡿࠋࡇࢀࡽࡣࠊ

Gauss-Legendre ๎࡛Ỵࡵࡽࢀࡿࡀࠊweb ୖ࡛ᐜ᫆/⟬Ⅼࡢ༙ᚄ್ Rm=0.333m ࡜ࡋ࡚ࠊZcm Ⅼ࡟ࡘ࠸࡚⨨ࡢタィ࡛฼⏝ࡍࡿࡇ࡜ࡣ㞴ࡋ࠸࡜ゎࡿࠋ10 ᱆/┠࠿ࡽᕪ␗ࡀ࠶ࡿࡀࠊᕷ㈍ࡢィ⟬ࢥ࣮ࢻ࡜ẚ㍑
ൎ

1.0,

+2

,

,

െ2

ࡍࡿ࡜ࠊ⾲ࡢ࢞࢘ࢫ✚ศἲ࡜୍⮴ࡋ࡚࠾ࡾࠊ10(4-4)

ࡇࡇ࡛ࠊZmc ࡣ Zm-Zc ࡛ࠊィ Ⅼ࡜⥺㍯㟁ὶࡢ Z ఩᱆┠௨㝆࡛ࡣ࢞࢘ࢫ✚ศἲࡀࡼࡾṇࡋ࠸ィ⟬್࡛࠶ࡿ࡜⪃࠼࡚࠸ࡿࠋ࢞࢘ࢫ✚ศἲ࡛ࠊCB ࡀసࡿ☢ሙࡢ⟬ฟ࡟฼⏝ࡍࡿࡇ࡜ࢆ᥎ዡࡍࡿࠋ

⨨ࡢᕪ␗࡛࠶ࡿࠋࡇࡢ࢞࢘ࢫ✚ศ࡛ࠊィ⟬Ⅼ(࢞10㸫 22

4.3. ㉳☢ຊ㓄⨨ࡢ㞳ᩓ໬(Step-2)

ࡓࡵ࡟ rCB ࡜࿧ࡪࡇ࡜ࡶ࠶ࡿࠋCB ࡢ㓄⨨ࡸ఩⨨๓⠇ࡢ Step-1 ࡛ࡣ㐃⥆ⓗ࡞㟁ὶศᕸ࡛ᆒ୍☢ሙᙧ≧ࡣ CB 㓄⨨࡛ィ⟬࡛ࡁࡿ☢ሙศᕸ %CB ࡜ Step-ࢆ Ⓨ ⏕ ࡛ ࡁࡿ ㉳ ☢ ຊ ศᕸ ࢆ ồ ࡵ ࡓࡀ ࠊ ᮏ ⠇ ࡢ

1 ࡛ồࡵࡓ☢ሙࡢᇶᗏ࡛ࠊᅛ᭷࣮ࣔࢻᙉᗘ PCBi

Step-2 ࡛ࡣࣆ࣮ࢡ࡜࡞ࡗࡓ఩⨨࡟୺ࢥ࢖ࣝࡢࢥ࢖

ࡀࠊ┠ᶆ☢ሙࡢᅛ᭷࣮ࣔࢻᙉᗘ࡟➼ࡋࡃ࡞ࡿࡼ

ࣝࣈࣟࢵࢡ(MC-CB)ࢆ㓄⨨ࡍࡿࡇ࡜࡛ࠊ㉳☢ຊ㓄࠺࡟ㄪᩚࡍࡿࠋࡘࡲࡾࠊ

⨨ࢆ㞳ᩓ໬ࡍࡿࠋࡑࡢ⤖ᯝࠊ㟁ὶࣆ࣮ࢡᩘ࡜ᐇ
㝿࡟㓄⨨ࡍࡿ MC-CB ᩘࡀྠᩘ࡛࠶ࡾࠊᅛ᭷࣮ࣔ

PCBi = Xit%CB/np1/2 ĺPTGi(4-5)ࢻᩘ࡜ᐦ᥋࡞㛵ಀ࡟࠶ࡿ஦ࡀ⌮ゎ࡛ࡁࡿࠋࡘࡲ
ࡾࠊᮏ⠇ࡢ┠ᣦࡍ࡜ࡇࢁࡣࠊFig. 4-8 ࡛࠶ࡿࠋࡇ
ࡢᅗ࡛ࡣࠊୖഃ࡟ Step-1 ࡛ồࡵࡓ㟁ὶศᕸ(୺ࢥ࢖ࣝ㒊ࡣ㐃⥆ศᕸ)ࡀ♧ࡉࢀࠊୗഃࡣ Step-2 ࡛㞳ᩓ໬ࡋࡓ CB 㓄⨨࡛࠶ࡿࠋ3.0T±1.5ppm ࡢ☢ሙᙉᗘ➼㧗⥺ࡀ♧ࡍࡼ࠺࡟ࠊ☢ሙศᕸࡢ୍ᵝᛶ࡟኱ࡁ࡞ኚ໬ࡣ࡞࠸ࠋࡲࡓࠊྜィ㉳☢ຊ(㟁ὶࡢ⤯ᑐ್࿴)࡟ࡶ኱ࡁ࡞ኚ໬ࡣ࡞ࡃࠊStep-1 ࡛ồࡵࡓ☢
ሙࡀࠊStep-2 ࡛ࡶ෌⌧ࡉࢀࡿࡇ࡜ࢆ┠ᶆ࡟㉳☢ຊ㓄⨨ࡢ㞳ᩓ໬ࢆ㐍ࡵࡿࠋ
඲࡚ࡢ CB ࡣྠ㍈࣭㞳ᩓ㓄⨨࡛࠶ࡿࠋStep-2 ࡛ࡣྛ CB ࡢᕳࡁ⥺ᩘࡣᐇᩘ࡜ࡋࠊCB ඲యࡢ㟁ὶ(AT: Ampere-Turn)࡜᩿㠃ᙧ≧ࡣ㐃⥆ⓗ(ᐇᩘ࡜ࡋ࡚)࡟ኚ໬ࡉࡏ࡚ࠊCB 㓄⨨ࢆ᭱㐺໬ࡍࡿࠋStep-3
࡛ࡣ㟁ὶ್ࡀᐇᩘ࡛࠶ࡾࠊStep-3(ᕳࡁ⥺ᩘࡀ㞳ᩓ໬࡛ࠊCB ࡢ AT ್ࡶ㞳ᩓ໬)ࡢ CB ࡜༊ูࡍࡿ

Fig. 4-8 Step-2 ࡀ┠ᣦࡍ㐃⥆㟁ὶ㓄⨨࠿ࡽ㞳ᩓࢥ࢖ࣝࣈࣟࢵࢡ㓄⨨࡬ࡢኚ᥮౛

Fig. 4-9 ࢯࣞࣀ࢖ࢻ≧ࡢ㐃⥆㟁ὶศᕸࣔࢹࣝ࡟ࡼࡿᆒ୍☢ሙศᕸࡢィ⏬ࠋୖ㸸ࢥ࢖᩿ࣝ㠃ࡢㄪᩚ㒊ศ(▮༳)ࠊୗ㸸ࢥ࢖ࣝ㓄⨨ࡢㄪᩚ࡟⏝࠸ࡿᅛ᭷࣮ࣔࢻࠋᩥ⊩[10], Fig. 4, Fig. 5 ᘬ⏝

10㸫 23࡛࠶ࡿࠋࡇࡢㄪᩚࡣࠊFig. 4-9 ୖᅗ࡛ࠊ୧▮༳࡛ࢻ␒ྕ(MODE ␒ྕ)࡜ࠊ2 ࡘࡢ☢ሙศᕸࡢᇶᗏࡢ

᭩࠿ࢀࡓ᩿㠃∦఩⨨ࢆㄪᩚࡍࡿࠋ×༳ࡢ CB ෆᚄෆ✚(XCBitXFLi)ࢆ♧ࡋ࡚࠸ࡿࠋࡍ࡭࡚ࡢᯟ࡛ 0.99࡜඲㛗ࡣ㏻ᖖồࡵࡿ☢▼ࡢ௙ᵝ࡛Ỵࡲࡿࡓࡵࠊ

ࢆ㉸࠼࡚࠾ࡾࠊ2 ࡘࡢ☢ሙศᕸᇶᗏࡣ࡯ࡰྠࡌศ

タィ⪅ࡶࡋࡃࡣ☢▼౑⏝⪅ࡢタᐃ್࡛࠶ࡿࠋCBᕸࢆ♧ࡋ࡚࠸ࡿࠋᚑࡗ࡚ࠊStep-1 ࡛ᚓࡓ☢ሙศᕸ᩿㠃㛗᪉ᙧࡢ㎶࡛▮༳ࡢ㒊ศࢆ⛣ືࡉࡏ࡚ࡇࡢ

ࡣࠊ㎶ୖ࡟Ⓨ⏕ࡍࡿ㟁ὶ࠿ࡽ MFEP ୖࡢ☢ሙ࡬ࡢᛂ⟅ࡇ࡜ࡀྍ⬟࡛࠶ࡿࠋࡘࡲࡾࠊStep-1 ࡛ᐇ⌧ྍ⬟࡜⾜ิࢆసࡾࠊࡑࡢ≉␗್ศゎ࡛ᚓࡽࢀࡿ㟁ὶ࡜ุ᩿ࡉࢀࡓ☢ሙศᕸ㺃ᆒ୍ᗘࡣࠊ㞳ᩓ໬ࡋࡓ CB☢ሙࡢᅛ᭷࣮ࣔࢻࢆ฼⏝ࡍࡿࠋ౛࠼ࡤࠊCB ࡢ㟁࡛ࡶᐇ⌧࡛ࡁࡿ࡜⤖ㄽ࡛ࡁࡿࠋࡇࡢᛶ㉁ࢆ฼⏝2ὶᐦᗘࢆ CD(A/m )࡜ࡋࠊ㍈᪉ྥᖜࢆ ǻROT ኚ໬ࡉ㞳ᩓ㓄⨨ࡢ CB ⩌࡛ࡶྠࡌ☢ሙศᕸࢆᚓࡿ

ࡋ࡚ࠊᅛ᭷࣮ࣔࢻᙉᗘ PCBi{ᘧ(2-12)}ࢆࠊ

ࡏࡿ࡜ࡍࡿ࡜ࠊ༙ᚄ኱ഃࡢ᩿㠃㎶ୖ࡟㟁ὶ
PCBi ĺPTGi= PFLi
iOT = CD(ZTP ZBT)ǻROT

(4-6)

(4-7)

࡜᩿㠃㎶఩⨨(Fig. 4-9 ୖ)ࢆㄪᩚࡍࡿࠋ

ࡀ⌧ࢀࡿࠋ㍈᪉ྥ఩⨨ࡢ⛣ື࡟ࡘ࠸࡚ࡶྠᵝ࡟ྛᯟࡢྑഃ࡟ࡣࠊ3 ಶࡢᩘ್ࡀ᭩࠿ࢀ࡚࠸ࡿ

㍈᪉ྥࡢ୧➃㎶࡟ྠࡌ㟁ὶᐦᗘ CD ࡛㟁ὶࡀ⌧ࢀࡀࠊࡑࢀࡒࢀୖ࠿ࡽࠊ≉␗್(ࡇࡇ࡛ࡣ T/A)ࠊ2

ࡿ࡜⪃࠼ࡿࠋᅗࡢ୧▮༳ᩘ࡜ྠࡌ࡛ࠊ6 ಶࡢ CB஌ᖹᆒ☢ሙᙉᗘ(T)࠾ࡼࡧ☢ሙ᣺ᖜ(T)ࢆࠊ3.0T ୍ࡢሙྜࠊ16 ಶࡢᅛ᭷࣮ࣔࢻࡀ࠶ࡾࠊࡑࡢ࠺ࡕ 8 ಶᵝ☢ሙࢆ 40cm ┤ᚄ⌫ࡢ FOV ⾲㠃࡛ᐇ⌧ࡍࡿࡓࡵࡀ㍈᪉ྥ࡟ᑐ⛠࡞ࡶࡢ࡛࠶ࡿࠋࡇࡇ࡛ࡣࠊMFEP

࡟ᚲせ࡞್ࢆ᭩࠸࡚࠸ࡿࠋ␒ྕࡀ኱ࡁࡃ࡞ࡿ(㧗ࢆ⌫యࡢ FOV ⾲㠃ୖ࡟㓄⨨ࡋࠊࡑࡢ㛫ࡢᛂ⟅⾜ḟ࡛ᑠ≉␗್)࡯࡝ࠊ☢ሙᙉᗘࡀᑠࡉࡃ࡞ࡿࠋ

ิࢆసᡂࡍࡿࠋࡑࡢᚋࡣࠊ2 ❶ࡢ TSVD ṇ๎໬࡟

MODE13 ࡛ࡣ 1ppm(3 T)௨ୗࡢᐤ୚࡜࡞ࡗ࡚࠸

ࡼࡿ᭱ᑠ஧஌ἲࢆ⏝࠸ࡿࠋࡿࠋᚑࡗ࡚ࠊࡇࢀ௨ୖ㧗ḟࡢᅛ᭷࣮ࣔࢻࢆ⪃៖ᚓࡽࢀࡓ SVD ᅛ᭷࣮ࣔࢻ 8 ಶࢆ Fig. 4-9 ୗ࡟♧

ࡍࡿᚲせࡣ↓࠸ࠋࡲࡓ MODE13 ࡛ࡣࠊ౛࠼ࠊ኱

ࡍࠋྛᯟ࡛ࠊᶓ㍈ࡣ㍈᪉ྥ఩⨨ Z ࡛ࠊ⦪㍈ࡣ༙ᚄࡁ࡞ᙉᗘㄗᕪ(30%)ࡀ࠶ࡗ࡚ࡶࠊ0.3ppm ௨ୗࡢ☢

᪉ྥ఩⨨ R ࡜ࡋ࡚ࠊFOV ࡜ CB ࠾ࡼࡧ FL 㟁ὶࡢሙㄗᕪ࡛ࡋ࠿࡞ࡃࠊ↓ど࡛ࡁࡿࠋᚑࡗ࡚ࠊ

఩⨨ࢆ♧ࡋ࡚࠸ࡿࠋྛᯟࡢྑഃ࡟ࡣ Step-1 ࡢ

MODE11 ࡲ࡛ࡣṇ☜࡟ㄪᩚࡍࡿࡀࠊMODE13 ࡣ

SVD ᅛ᭷࣮ࣔࢻࢆ♧ࡋࠊᕥഃ࡟ Step-2 ࡢ SVD ᅛ☢▼ࡢ〇సᛶࢆ⪃៖ࡋ࡚ㄪᩚ㺃タィࡍࡿ[10]ࠋ

᭷࣮ࣔࢻࢆ♧ࡋ࡚࠸ࡿࠋྛᯟࡢୖ㒊࡟ࡣ㟁ὶศᕸࡢᇶᗏࢆ♧ࡍࠋࡲࡓࠊୗ㒊ࡢ༙෇ᙧ㒊࡟ࡣ☢
ሙศᕸࡢᇶᗏࢆ♧ࡍࠋྛᯟࡢୖ㒊࡟ࡣᅛ᭷࣮ࣔ

ᅗ 4-10 MC-CB タ⨨఩⨨⛣ື࡟㛵㐃ࡋࡓ SVD ᅛ᭷࣮ࣔࢻࠋᩥ⊩ 10, Fig. .8 ࡼࡾᘬ⏝10㸫 24

4.4. ᕳࡁ⥺ᩘࡢ㞳ᩓ໬(Step-3)

ࡗࡓࠋᕳࡁ⥺᪉ἲ࠿ࡽ⪃࠼࡚ࠊᒙᩘ(༙ᚄ᪉ྥ)ࡣ
ẖ࡟ᩚᩘ໬ࡍ

അᩘ࡜ࡋ࡚࠸ࡿࡓࡵࠊ༙ᚄ᪉ྥࡢᕳࡁᩘ㑅ᢥࡀࡿ ࠋ ᑟ య ࡢ⤒ 㦂 ☢ ሙ ࡸ㟁 ※ ࠊ Ọ ஂ㟁 ὶ ࢫ ࢖ ࢵ

iCB ㉳☢ຊ࡟୚࠼ࡿᙳ㡪ࡣ≉࡟኱ࡁ࠸ࠋࡇࡢࡓ

ࢳࠊࡑࢀ࡟ࢡ࢚ࣥࢳ᫬ࡢ㟁ᅽࡸᑟయࡢ

ࡵࠊrCB ࠿ࡽ iCB ࡛⢭ᗘⰋࡃ㉳☢ຊ࡜᩿㠃ᙧ≧ࢆ

Step-3 ࡛ࡣᑟయࡢᕳࡁᩘࢆ CBᗘୖ᪼࡞࡝ࡢタィ㡯┠ࢆ⪃៖ࡋࡓୖ࡛ࠊᑟయᚄ࡜⣲⥺ㄪᩚࡍࡿࡇ࡜ࡣ㞴ࡋ࠸ࠋ㟁ὶࢆỴࡵࠊᕳࡁ⥺㓄⨨ࠊᕳࡁ⥺ᩘ(ᚑࡗ࡚ CB ᩿ࡇࡢ⌮⏤࡛ࠊiCB ࢆ rCB ࡜ྠࡌ఩⨨࡟⨨ࡃ࡜ࠊ㠃ᙧ≧)ࢆタィࡍࡿࠋࡇࡢẁ㝵࡛ࡣࠊྛ CB ࡢᕳࡁᆒ୍ᗘࡣຎ໬ࡍࡿࠋFig. 4-10 ࡢᅛ᭷࣮ࣔࢻ࡟ࡘ࠸

ᩘࡣᩚᩘ໬ࡉࢀ࡚࠸ࡿࡢ࡛ࠊiCB ࡜࿧ࡪࡇ࡜࡟ࡍ

࡚ࠊࡑࡢᙉᗘࢆㄪᩚࡍࡿࠋCB ⛣ືࢆ⛣ືࡉࡏ࡚

ࡿࠋStep-3 ࡛ࡣࠊiCB ࡢ᩿㠃ᙧ≧ࡣỴࡲࡗ࡚࠸ࡿ

ᘧ(4-7)ࡢࡼ࠺࡟ Step-1 ࡢᅛ᭷࣮ࣔࢻᙉᗘ࡟ྜࢃࡏ

ࡢ࡛ࠊ఩⨨(༙ᚄ఩⨨ R,࡜㍈᪉ྥ఩⨨ Z)ࡢࡳࡢኚ

ࡿࠋࡑࡢ⤖ᯝࠊTable᭦࡟ࡼࡾ☢ሙศᕸࢆ᭱㐺タィࡍࡿࠋ᭷࣮ࣔࢻᙉᗘࢆ෌⌧ࡍࡿࠋࡇ࠺ࡋ࡚ࠊiCB ఩⨨ࢆ

4-5 ࡢࡼ࠺࡟ Step-3 ࡲ࡛ᅛ

Fig. 4-10 ࡟ࡣ Step-3 ࡛ࡢᅛ᭷࣮ࣔࢻࢆ♧ࡍࠋ6ㄪᩚࡍࡿ࡜ࠊⰋዲ࡞ᆒ୍ᗘࢆ෌⌧࡛ࡁࡿࠋMC-

ಶࡢ CBࠊ12 ಶࡢ⮬⏤ᗘ࡛ࠊ6 ಶࡢ㍈ᑐ⛠ SVD ᅛ

CB ᩘࡢ 6 ಶ࡜ࡋ࡚࠸ࡿࡢ࡛ࠊወᩘ␒ྕ࡛ 6 ␒┠᭷ ࣔ ࣮ ࢻ ࢆᣢ ࡘ ࠋ ࡇ ࢀࡽ ࡢ ☢ ሙ ศᕸ ᇶ ᗏ ࡶ ࠊ

࡜࡞ࡿ 11 ␒┠ࡢᅛ᭷࣮ࣔࢻᙉᗘࡲ࡛ࡣṇ☜࡟ㄪ

Step-1 ࡢᇶᗏ࡜࡯ࡰྠࡌศᕸࢆᣢࡘࡢ࡛ࠊᙉᗘࢆ

ᩚฟ᮶ࡿࠋ13 ␒┠ᅛ᭷࣮ࣔࢻᙉᗘࡣṇ☜࡞ㄪᩚ

Step-1 ࡢᅛ᭷࣮ࣔࢻᙉᗘ࡟ྜࢃࡏࡿࠋࡉࡽ࡟㧗ḟࡣฟ᮶࡞࠸ࡀࠊTable 4-2 ࡢࡼ࠺࡟ᐤ୚ࡣᑠࡉ࠸ࡢ

ࡢᅛ᭷࣮ࣔࢻࡣㄪᩚࡉࢀ࡞࠸ࡀࠊᑠࡉ࡞☢ሙ࡛࡛ࠊ኱ࡁ࡞ᝏ໬࡟ᐤ୚ࡋ࡞࠸⛬ᗘࡢ್࡟཰ࡵ࡚

࠶ࡿࡓࡵࠊᆒ୍ᗘ࡬ࡢᙳ㡪ࡣᴟࡵ࡚ᑠࡉ࠸ࠋ
Table 4-5 ྛ Step ࡛ࡢᅛ᭷࣮ࣔࢻᙉᗘ
10 Table VI ࢆཧ⪃)(ᩥ⊩[13],

Table 4-4 ࡣ,Step-2 ࠿ࡽ Step-3 ࡬ࡢᑟయ⪃៖࡛ᕳࡁ⥺᪉ἲ࡜᩿㠃ᙧ≧ࢆỴࡵࡓ㐣⛬ࢆ♧ࡍࠋᕥഃ࡟ rCB(Step-2 ࡢ⤖ᯝ)ࡢ᩿㠃ᑍἲ࡜ࠊᑟయ᩿㠃ᑍἲ࡜ᕳࡁ⥺ᵓ㐀ࢆỴࡵࠊStep-3 ࡢ iCB ᩿㠃ᑍἲ࡜

No.

Homog. FLs+SC-CBs rCBs, PirCB, iCBs, PiiCB,
3.0 T ( Pi3T ) (PiFL, Step-1) (Step-2)(Step-3)

1

2.9980E+00 2.9980E+00 2.9980E+00 2.9980E+00㉳☢ຊࢆ♧ࡋࡓࠋࡇࡢ⾲ࡢ౛ࡣࠊᑟయ⣲⥺㟁ὶ

31.0948E-01

1.0948E-01 1.0948E-01

1.0948E-01

ࢆ 1000.5A ࡜኱ࡁࡃࡋ࡚࠸ࡿࠋ㏻ᖖࡢ MRI ☢▼5

7.8752E-03

7.8752E-03 7.8752E-03

7.8752E-03

࡛ࡣ 500A ๓ᚋ࡛࠶ࡿࠋࡇࢀࡣࠊ㞳ᩓ໬ࡢᙳ㡪ࢆ

77.0249E-04

7.0249E-04 7.0249E-04

7.0687E-04

኱ࡁࡃࡋࠊiCB ㉳☢ຊࢆ㞳ᩓ໬ࡋ࡚ࡶṇ☜࡞☢ሙ

96.9938E-05

6.9938E-05 6.9938E-05

6.9938E-05

タィ(ᆒ୍☢ሙࡀᚓࡽࢀࡿ)ࡀྍ⬟࡞ࡇ࡜ࢆ♧ࡍࡓ

11

7.4356E-06

7.4359E-06 7.4357E-06

7.4357E-06

ࡵ࡛࠶ࡿࠋࡇࡢ౛࡛ࡣࠊiCB ࡢ᩿㠃ࡀ rCB ࡜ྠ⛬

13
F13
ᆒ୍ᗘ

8.205E-07 -1.163E-07 -1.148E-07
1.0
-0.14
-0.14
0.0 ppm
0.928 ppm
0.937 ppm

-7.641E-08
No tuning
0.906 ppm

ᗘࡢࢧ࢖ࢬ࡟࡞ࡿࡼ࠺࡟ᑟయ࡜ᕳࡁ⥺ᵓ㐀ࢆỴࡵ࡚࠸ࡿࡀࠊiCB ࡜ rCB ࡛᭱኱ 10kA ࡢᕪ␗ࡀ࠶
ࡿࠋࡇࡢࡓࡵࠊiCB ࢆ rCB ࡜ྠࡌ఩⨨࡟㓄⨨ࡋࡓሙྜ࡛ࡣᆒ୍ᗘࡣᝏ࠸ࠋࡇࡢ౛࡛ࡣ 909ppm ࡛࠶ὀ㸸ᩘ್ࡣᕥ࠿ࡽࠊ᏶඲୍ᵝ☢ሙ࡟ᚲせ࡞ᅛ᭷࣮ࣔࢻᙉᗘࠊࡑ
ࢀ࡟ Step-1, -2, -3 ࡛ᐇ⌧ࡋࡓᅛ᭷࣮ࣔࢻᙉᗘ࡛࠶ࡿࠋF13 ࡣ 13␒┠ࡢᙉᗘㄪᩚࡢࣃ࣓࣮ࣛࢱࠊᆒ୍ᗘࡣ 40cm ⌫㠃ୖࡢ್ࠋ

Table 4-4 Step-2(rCB)࠿ࡽ Step-3(iCB)࡬ࡢ㟁ὶ㞳ᩓ໬ࡢ౛(ཧ⪃ᩥ⊩[13],10 Table IV ࢆᘬ⏝)ModelsCBs

rCB placements(F13=-0.13)
rCB Sizes(mm)

Radial Axial
MC10/11 64.2 220.0
MC20/21 29.5 154.3
MC30/31 22.1 150.0
SC10/11 42.0 144.8

Conductor sizes

Amp-turns Radial
(kAT)
(mm)
2117.9820.3
594.6-1094.8

2.05
1.85
1.85
1.85

Axial
(mm)

iCB (IPS = 1000.5 A)
Winding turns
Radial Axial Lack

3.25
3.00
3.00
3.00

10㸫 25

32
16
12
22

66
52
50
50

iCB sizes (mm) CB-Total Amp-turns
(kAT)
turns

Radial Axial-2
65.6 214.5-2
29.6 156.0-2
22.2 156.0-240.7 150.0

2110
830
598
1098

2111.1
830.4
598.3-1098.6

࠸ࡿࠋ㈇ࡢ್࡟࡞ࡗ࡚࠸ࡿཎᅉࡣࠊSC ࡟ࡼࡿ☢

࡟ᑐᛂࡋࡓ㉳☢ຊ㓄⨨ࡣṇ☜࡟ࡣỴࡵࡽࢀ࡞࠸

ሙࡢᙳ㡪࡛࠶ࡿࠋ

ࡢ࡛ࠊ㧗ḟᡂศࡀ୙ṇ☜࡟࡞ࡿ[36]ࠋ୍᪉ࠊSVDࢆ౑࠺➹⪅ࡢᥦ᱌ᡭἲ࡛ࡣ☢ሙศᕸ࡜㉳☢ຊ㓄⨨ࡀᑐᛂࡋ࡚࠾ࡾࠊ㧗ḟᡂศ࡟ࡼࡿㄗᕪ☢ሙࡶࡑࡢ኱ࡁࡉࢆᢕᥱ࡛ࡁࡿࠋࡲࡓࠊTSVD ࡛ࡣࠊᘧ(2-7)ࡢࡼ࠺࡟పḟᡂศ࠿ࡽຍ⟬ࡍࡿࡢ࡛ࠊồࡵࡿゎࡣࠕ㟁ὶᙜࡓࡾࡢ☢ሙᙉᗘࡀᙉ࠸ࠖࡢ᮲௳
ࢆྵࡴࠋࡑࡢࡓࡵࠊᑠࡉ࠸㉳☢ຊ࡛ࠊᚲせ࡞㉳☢ຊ㓄⨨ࢆỴࡵࡿࡇ࡜ࡀฟ᮶ࡿ࡜⪃࠼࡚࠸ࡿࠋ
ࡉࡽ࡟ࠊ㕲࡞࡝☢ᛶᮦᩱࢆྵࡴయ⣔࡛ࡶᛂ⏝ྍ⬟࡞ࡇ࡜ࡣཧ⪃ᩥ⊩[38]࡛♧ࡋ࡚࠸ࡿࠋ
௨ୖࡢ㆟ㄽࡣࠊࡼࡾ୍⯡ⓗ࡟౑ࢃࢀ࡚࠸ࡿỈᖹ ☢ ሙ ᶵ ࡢ☢ ሙ タ ィ ࡜ࡋ ࡚ ㆟ ㄽ ࡋࡓ ࡀ ࠊ ྠ ࡌFig. 4-11 ᮏᡭἲ࡛ồࡵࡓ㉳☢ຊ㓄⨨ࠋᕥࡣ
Step-2 ࡢ⤖ᯝࠊྑࡣᕳࡁᩘࢆᩚᩘ໬ࡋࡓ
Step-3 ࡢ⤖ᯝࠋᩥ⊩[10], Fig.10(a)ࡼࡾᘬ⏝TSVD ᛂ⏝ࡢ⪃࠼࡛ᆶ┤☢ሙᶵ{㛤ᨺᆺ MRI}ࡢ☢
ሙタィ[39]ࢆ⾜࠸ࠊ〇ရ໬ࡋ࡚࠸ࡿࠋ ࡇࡢ㛤ᨺᆺᶵࡣ 1.2T ࡢ☢ሙ࡛࠶ࡾࠊ〇ရฟⲴ㛤ጞᚋ 10 ᖺࢆồࡵࡓ㉳☢ຊ㓄⨨౛ࢆ Fig. 4-11 ࡟♧ࡍࠋᕥഃ㉸࠼ࡿࡀࠊࡇࢀ௨ୖࡢ☢ሙᙉᗘࢆᣢࡘ㛤ᨺᆺᶵࡣ Step-2 ࡢ⤖ᯝࠊྑഃࡣ Step-3 ࡢ⤖ᯝ࡛࠶ࡿࠋ࡜

ࡣᮍࡔᏑᅾࡋ࡞࠸ࠋTSVD ࡢ⪃࠼࡛☢ሙタィࡋࡓ

ࡶ࡟ 3.0T±1.5ppm ࡢ☢ሙᙉᗘ➼㧗⥺ࡀᆒ୍☢ሙࢆࡓࡵࠊ௚ࡢ᪉ἲ࡟ẚ࡭࡚ᑠࡉࡵࡢ㉳☢ຊ࡛タィ

ᚲせ࡜ࡍࡿ㡿ᇦࢆつ๎ⓗ࡟ྲྀࡾᅖࢇ࡛࠶ࡾࠊ௙

࡛ࡁࡓࡇ࡜ࡀዌຌࡋࡓ࡜⪃࠼࡚࠸ࡿࠋࡲࡓࠊ௨

ᵝࡢᆒ୍☢ሙศᕸࡀᚓࡽࢀ࡚࠸ࡿࠋ

ୖࡢ㆟ㄽࡣ෇ᙧࢥ࢖ࣝࢆ⏝࠸ࡓ☢▼࡟ࡘ࠸࡚ࡢ

௨ୖࡢ㉳☢ຊ㓄⨨タィᡭἲ࡛౑⏝ࡍࡿ SVD ᅛ㆟ㄽ࡛࠶ࡗࡓࡀࠊࢥ࢖ࣝᙧ≧ࡀ෇ᙧ࡛↓ࡃࠊࣞ᭷࣮ࣔࢻࡣ 5㹼7 ಶࡢ㍈ᑐ⛠࣮ࣔࢻ࡛࠶ࡿࠋ2n-1࣮ࢫࢺࣛࢵࢡᆺ࡛࠶ࡗ࡚ࡶ TSVD ฼⏝࡛ࠊᆒ୍☢

ࡢወᩘ␒ྕ࡛࠶ࡿࡀࠊn ࡀ㸯኱ࡁࡃ࡞ࡿ࡜ࠊ≉␗ሙࢆࡶࡘ☢▼ࡢ☢ሙタィࡀྍ⬟࡛࠶ࡿࡇ࡜ࡶ♧್(ࡇࡇ࡛ࡣ T/m ࡢ༢఩)ࡣ⣙㸯᱆ᑠࡉࡃ࡞ࡾࠊྠ

ࡋ࡚࠸ࡿ[40]ࠋ

ࡌ኱ࡁࡉࡢ㟁ὶ࡛ࡶࠊⓎ⏕ࡍࡿ☢ሙࡣ㸯᱆ᑠࡉࡃ࡞ࡗ࡚࠸ࡃࠋࡇࡢࡓࡵࠊn=7(MODE13)࡛ࡣࠊ

4.5. 㕲ⰺᆺ MRI ☢▼ࡢሙྜ

n=1 ࡢ⣙ 1/106 ࡢ≉␗್࡛࠶ࡾࠊⓎ⏕࡛ࡁࡿ☢ሙ

MRI ☢▼࡛ࡣ㕲ⰺࢆ฼⏝ࡋࡓ☢▼ࡶ࠶ࡿࠋᆶ

ᙉᗘࡣ 1ppm ௨ୗ࡛࠶ࡿࠋࡲࡓࠊ୺ࢥ࢖ࣝᩘ࡜ n┤☢ሙᆺ࡟࠶ࡾࠊỌஂ☢▼ࡶࡋࡃࡣ㉸ఏᑟࢥ࢖ࡢ㛫࡟ࡣᐦ᥋࡞㛵ಀࡀ࠶ࡿࡇ࡜ࡶࢃ࠿ࡗࡓࠋ

ࣝࢆ㉳☢ຊ※࡜ࡋ࡚࠸ࡿࠋ᧜ീ✵㛫࡛☢ሙศᕸ୍᪉ࠊ[35]࡞࡝ࡢ௚ᡭἲ࡛ࡣࠊᆒ୍ᗘ࡜㉳☢

ࢆ୍ᵝ࡜ࡍࡿࡓࡵ࡟ࠊ㕲ⰺࡢ᧜ീ㡿ᇦ࡟ᑐྥࡋ

ຊ(AT)ࢆ⤌ࡳྜࢃࡏࡓ್ࢆ᭱ᑠ໬ࡍࡿ᪉ἲࢆ࡜ࡿ

ࡓ㠃࡟ࡣࠊพฝࢆᣢࡕࠊ୍ᵝ࡞☢ሙࢆࡘࡃࡿࠋ

ࡀࠊ᭱ᛴ㝆ୗἲࡸ࢔ࢽ࣮ࣜࣥࢢ࡛⾜࠺ࠋࡇࡢሙ

ࡇࢀࡲ࡛࡟ㄝ᫂ࡋࡓ TSVD ṇ๎໬ࢆᇶ♏࡟ࠊ㕲ⰺྜࠊStep-1 ࡛❧࡚ࡓィ⏬࠿ࡽ㞳ࢀ࡚ゎࢆồࡵࠊᚲࡢพฝࢆタィ࡛ࡁࡿ[38]ࡢ࡛ࠊ⡆༢࡟ㄝ᫂ࡍࡿࠋ

ࡎࡋࡶィ⏬㏻ࡾࡢゎ࡟࡞ࡽ࡞࠸ࡇ࡜ࡸࠊ㉳☢ຊィ⟬య⣔ࡣ Fig. 4-12 ࡛ࠊ௒ᅇࡶ༙ᚄ᪉ྥ(R ʊ㓄⨨(CB ᩘ࡞࡝)࡜ồࡵࡿ☢ሙࡢ㛵ಀࡀᢕᥱࡋ㞴㍈᪉ྥ(Z)ࡢ 2 ḟඖ࡛࠶ࡿࠋࡓࡔࡋ㺂㍈᪉ྥࡣ⣬㠃

࠸Ⅼ࡟ၥ㢟ࡀ࠶ࡿ࡜⪃࠼࡚࠸ࡿࠋࡲࡓࠊᚑ᮶ࡢ

⦪᪉ྥ࡛ࠊZ ㍈࠾ࡼࡧ☢ሙࡢ᪉ྥࡣ⣬㠃ୖ᪉ྥࢆከࡃࡢ☢▼タィࡸࢩ࣑ࣥࢢィ⟬࡛ࡣࠊ[36㸪37]ࡢ

ྥ࠸࡚࠸ࡿࠋࡇࡢ㕲ⰺ࡛ࠊ┤ᚄ 0.38m ࡢ᧜ീ㡿ᇦࡼ࠺࡟ࠊ᧜ീ㡿ᇦࡢ☢ሙศᕸࢆ⌫㠃ㄪ࿴㛵ᩘ࡟(FOV: Field Of View)ࢆᣳࡴୖୗࡢ Z=±0.375m㹼

ᒎ㛤ࡋࠊ᭱పḟ㸦ᆒ୍☢ሙ㸧௨እࡢ㡯ࢆ㞽࡟㏆

0.450m ࡛㕲ⰺ࡟พฝࢆࡶ࠺ࡅ࡚ࠊFOV ࡢ☢ሙࢆ࡙ࡅࡿࡼ࠺࡟⥺ᙧィ⏬ἲࡸ࢔ࢽ࣮ࣜࣥࢢἲ࡛㉳୍ᵝ࡟㏆࡙ࡅࡿࠋ

☢ຊ㓄⨨ࢆㄪᩚࡍࡿࠋࡋ࠿ࡋࠊྛ⌫㠃ㄪ࿴㛵ᩘ

10㸫 26

FOV͹ࣕ৖‫(ࢋܯ‬3Dඉત‫)ࢋܯܙ‬Z [mm]‫܃‬Εศ͢‫ࢋܯ‬

750

Yoke

Cylinder450 Convexoconcave
Coil
375 Calculation plane
500
FOVĳPP2500

R [mm]
3000‫ۋ‬Ҳౕʃ
No.
‫ࣕࠫޣ‬৖

Yes‫܃‬Εศ͢
‫ࢋܯ‬श྅

‫ࣕࠫޣ‬৖͹ึਜ਼Ͷචགྷ͵ࣕ‫ـ‬Ϡʖϟϱφ෾ා(DUCAS‫)ࢋܯ‬ࣕ‫ـ‬Ϡʖϟϱφїరྖ(ࣕ‫ۅ‬໚Ԟದ)

Fig. 4-14 FOV ࡛☢ሙศᕸࢆ୍ᵝ࡜ࡍࡿ㕲ⰺᙧ≧ࢆồࡵࡿ⧞ࡾ㏉ࡋィ⟬ᡭ㡰Calculation plane
Convexoconcave Coil(MM)ࢆ♧ࡍ࡜⌮ゎࡍࡿࡇ࡜ࡶฟ᮶ࡿࠋࡑࡢࡓ
ࡵࠊFOV ࡢ☢ሙࡀ୍ᵝ࡜࡞ࡿࡼ࠺࡟ DUCAS ࡛ồ
Fig. 4-12 㕲ⰺࡢ᧜ീ㡿ᇦᑐྥ㠃࡟ᮏᡭἲ࡛ồࡵࡓ MC-CB ఩⨨ࠋᕥࡣ Step-2 ࡢ⤖ᯝࠊ㉳☢
ຊ(A)ࡣᐇᩘ࡛㐃⥆್ࠊྑࡣᕳࡁᩘࢆᩚᩘ໬ࡋࡓ Step-3 ࡢ⤖ᯝࠋᩥ⊩ 37, Fig.1 ࡼࡾᘬ⏝㕲ⰺࡢኚᙧ㔞ࢆ⟬ฟࡍࡿ࡟ࡣࠊDUCAS[41]ࢆ

ࡵࡓ MM ศᕸࢆࠊ㕲ⰺᙧ≧࡟᥮⟬ࡍࡿ࡜┠ᶆࡢ฼⏝ࡍࡿࠋDUCAS ࡣࢫࢸ࣮ࣛࣞࢱᆺ᰾⼥ྜ⿦⨨ィ⟬⤖ᯝ౛ࢆ Fig. 4-15 ࡟♧ࡋࡓࠋࡇࡢሙྜࠊ50ࡢࢥ࢖ࣝᙧ≧ࢆタィࡍࡿࡓࡵ࡟㛤Ⓨࡉࢀࡓィ⟬

ᅇࡢ⧞ࡾ㏉ࡋィ⟬࡛☢ሙศᕸࢆ୍ᵝ໬ࡍࡿ㕲ⰺᡭἲ࡛ࠊ┠ᶆ☢ሙࢆ෌⌧ࡍࡿࡼ࠺࡟᭤㠃ୖࡢ㟁ࡢพฝᙧ≧ࡀᚓࡽࢀ࡚࠸ࡿࠋࡲࡓࠊ๓⠇ࡲ࡛ࡢὶ⤒㊰(ᚑࡗ࡚ࠊࢥ࢖ࣝᙧ≧)ࢆ⟬ฟࡍࡿࠋィ⟬ࣔỈᖹ☢ሙ࡟㛵ࡍࡿ᳨ウ࡜ྠᵝࡢࠊ☢ሙศᕸࡢᙉ

ࢹࣝࡢᇶᮏࣔࢹࣝࢆ Fig. 4-13 ࡟♧ࡍࠋ㟁ὶ㠃ࢆ୕ᙅࡢᶍᵝࡀⓎ⏕ࡋ࡚࠸ࡿࡀࠊTSVD ィ⟬࡟౫Ꮡࡋゅせ⣲ࡢ㞟ྜ࡛⾲⌧ࡋࠊ⠇Ⅼࡢ㟁ὶ࣏ࢸࣥࢩࣕ

ࡓᶍᵝ࡛࠶ࡿࠋ๓⠇࡛ࡣ Fig. 4-4 ᭱ୗ㒊ࠊᅛ᭷ࣔࣝ Ti ࡟ࡼࡾ㠃㟁ὶࢆ⾲⌧ࡋࠊ㟁ὶ࣏ࢸࣥࢩࣕࣝࡢ

࣮ࢻ 7 ಶ฼⏝࡟┦ᙜࡋࡓ☢ሙศᕸ࡜࡞ࡗ࡚࠸ࡿࠋ

್ࢆ┠ᶆࡢ☢ሙࢆ෌⌧ࡍࡿࡼ࠺࡟ࠊTSVD ṇ๎໬௨ୖࡢࡼ࠺࡟ࠊTSVD ฼⏝࡛㕲ᚰᙧ≧ࢆ┠ᶆ☢

࡜᭱ᑠ஧஌ἲ࡛ࠊỴࡵࡿࠋDUCAS ࡢヲ⣽ࡣཧ⪃ሙ࡟ྜࢃࡏ࡚ኚᙧࡉࡏࡿࡇ࡜ࡶྍ⬟࡛࠶ࡿࡇ࡜

ᩥ⊩[41]࡟ㆡࡿࠋ

ࡀゎࡗࡓࠋࡇࡢ⪃࠼᪉ࡶ g-2/EDM ☢▼ࡢタィ࡟㟁ὶ࣏ࢸࣥࢩࣕࣝࡣ⠇Ⅼࡢ࿘ࡾ࡟࿘ᅇࡋ࡚࠸

☢ሙ࡟㏆࡙࠸࡚࠸ࡃࡇ࡜࡟࡞ࡿࠋࡇࡢ⧞ࡾ㏉ࡋィ⟬ᡭ㡰ࢆ Fig. 4-14 ࡟♧ࡋࡓࠋ┠ᶆ࡜ࡍࡿᆒ୍ᗘ
ࡀᚓࡽࢀࡿ࡜ィ⟬ࡣ⤊஢࡛࠶ࡿࠋ

౑ࡗ࡚⾜ࡃࠋ

ࡿ㟁ὶ್࡜ࡶ⌮ゎ࡛ࡁࠊ⠇Ⅼࡢ☢Ẽ࣮࣓ࣔࣥࢺ

Fig. 4-15 ⧞ࡾ㏉ࡋィ⟬(ᕥ)࡛ᚓࡽࢀࡓ㕲㠃ࡢพฝ࡜☢ሙศᕸ(ྑ㸸38cm-DSS ࡛ 4.6ppm)

Fig. 4-13 DUCAS ࡢ㠃㟁ὶィ⟬ࣔࢹࣝ

10㸫 27

4.6. ☢ሙࢩ࣑ࣥࢢ

⏝ࡋࠊṧࡾࡢ 12 ᮏࡣࢃࡎ࠿࡞㕲∦ࡢࡳ㓄⨨ࡍࡿ☢ሙタィࡀⰋዲ࡟⾜ࢃࢀ࡚࠸࡚ࡶࠊタ⨨ᚋ࡟

ヲ⣽㸦fine㸧ࢩ࣑ࣥࢢ࡟฼⏝ࡍࡿࠋᚋ⪅࡛ࡣ☢▼ᚓࡽࢀࡿ☢ሙ࡟ࡣㄗᕪ☢ሙࡀΰධࡋࠊ୍ᵝ☢ሙࡢᾘ☢࣭ບ☢సᴗࡀ୙せ࡜ࡋ࡚ࠊసᴗ㔞๐ῶ࡜ࡣࡍࡄ࡟ࡣᚓࡽࢀ࡞࠸ࠋMRI ☢▼ࢆ౛࡟ྲྀࡿ

ඹ࡟ࠊࡼࡾ☢ሙ⢭ᗘࢆྥୖ࡛ࡁࡿࠋ࣏ࢣࢵࢺ୰࡜ࠊタ⨨┤ᚋ࡛ࡣᩘⓒ㹼1000ppm ࡟㐩ࡍࡿࠋ┠ᶆࡢ㕲㔞ࡣᯈᯛᩘࡢኚ᭦࡛ࠊᚲせ㔞࡟㏆ఝࡋࠊ☢

ࡢ ᆒ ୍ ᗘ ࡜ࡣ ᠱ ࡅ 㞳 ࢀ࡚ ኱ ࡁ ࡞ ㄗᕪ ☢ ሙ ࡛ ࠶Ẽ࣮࣓ࣔࣥࢺࡢ኱ࡁࡉࢆㄪᩚ࡛ࡁࡿࠋMRI ⏝☢

ࡿࠋࡑࡇ࡛ࠊ☢▼タ⨨ᚋࠊ౑⏝㛤ጞ๓࡟☢ሙࢩ▼࡛㏻ᖖ౑࠺㕲ࢩ࣒∦ࡢ᭱ᑠ༢఩ࡣ 0.06cc ࡛࠶ࡿࠋ࣑ࣥࢢ(ㄗᕪ☢ሙࡢ⿵ṇ)ࢆ⾜࠺ࠋࡑࡢ౛ࢆᮏ⠇࡛

ࡋ࠿ࡋࠊ0.2ppm ࢆ┠ᣦࡍሙྜ࡟ࡣࡼࡾ⣽࠿ࡃ☢

ࡣ⤂௓ࡍࡿࠋ௨ୗ࡛ࠊᆒ୍ᗘࡣᘧ(1-1)ࡢᐃ⩏࡛ሙࢆㄪᩚࡍࡿࡓࡵ࡟ࠊ㕲 0.01cc ┦ᙜ(0.017Am2)⛬࠶ࡿࠋᗘࡢࢩ࣒∦ࢆ᭱ᑠ༢఩࡜ࡋ࡚౑࠺ᚲせࡀ࠶ࡿ[8]ࠋ

ㄗᕪ☢ሙࡢཎᅉࡣࠊタィ᫬ࡢ୸ࡵㄗᕪࠊ☢▼ᅗ୰ࡢ୰ኸࡣ☢ሙィ 㠃(MFMS: Magnetic Fieldࡢ⤌ࡳ❧࡚ㄗᕪࠊࡲࡓᘓᒇ㕲ᮦࡢ☢໬࡞࡝࡟ࡼ

Measurement Surface)࡛࠶ࡿࠋ㠃ࡣ୕ゅせ⣲࡜⠇ࡿタ⨨⌧ሙࡢ⎔ቃ☢ሙ(ྵᆅ☢Ẽ)ࡀཎᅉ࡛࠶ࡿࠋ

Ⅼ࡛ᵓᡂࡉࢀࡿᅗ࡟࡞ࡗ࡚࠸ࡿࡀࠊ⠇Ⅼࡣ☢ሙᚑࡗ࡚ࠊ☢▼タ⨨᫬࡟ࡣ⢭ᗘⰋࡃࡇࡢㄗᕪ☢ሙィࢆ⿵ṇ(௨ᚋࠊࢩ࣑ࣥࢢ࡜ゝ࠺)ࡍࡿᚲせࡀ࠶ࡿࠋ࡟┦ᙜࡍࡿࠋཧ⪃ᩥ⊩ࡢ[12]࡜]13]࡛ࡣࠊࡑࢀࡒ

ࡲࡓࠊ౑⏝㛤ጞᚋ࡛ࡶࠊᆒ୍ᗘࡀຎ໬ࡋࡓሙྜ

ࢀࠊ768 ࡜ 576 Ⅼࡢ఩⨨࡛☢ሙࢆィ ࡋ࡚࠸ࡿࠋ

࡟ࡣࠊಖᏲ᫬࡞࡝࡟ࢩ࣑ࣥࢢࢆ⾜࠺ࠋᆒ୍☢ሙ

MRI ࡢ᧜ീ✵㛫(FOV)ࡣ 40㹼50cm-DSV ⛬ᗘࡢ㡿ࢆᚲせ࡜ࡍࡿ᧜ീ✵㛫ࡢ࿘ᅖ࡟☢Ẽ࣮࣓ࣔࣥࢺ

ᇦ࡛࠶ࡿࡀࠊከᩘࡢィ(MM)ࢆศᕸ㓄⨨ࡉࡏࠊࡑࡢ MM ࡀసࡿ☢ሙ࡛ࠊഛࡋࠊ✵㛫ⓗ࡟⣽࠿ࡃㄪᩚฟ᮶ࡿᵓ㐀࡜ࡋ࡚࠸ㄗᕪ☢ሙࢆ⿵ṇࡍࡿࠋMM ࡢⓎ⏕※ࡣࠊ☢ሙ୰࡛ࡿࠋ௨ୗ࡛ࡢィ ☢ሙࡣ 40cm-DSS 㠃ୖ࡛ࡢィ☢໬ࡋࡓ㕲∦ࢆ౑࠺ࡇ࡜ࡀከ࠸ࠋࡲࡓࠊ㕲∦௨್࡛࠶ࡿࠋ

Ⅼ(MFMP: Magnetic Field Measurement Point)

Ⅼ࡜ MM 㓄⨨఩⨨ࢆ‽እ࡟ࠊᑠࢥ࢖ࣝ⩌ࢆ⏝࠸ࡿࢩ࣒ࢥ࢖ࣝࠊỌஂ☢
▼ࠊ࡞࡝ࡀ࠶ࡿࠋ☢໬㕲∦ࡢ MM ࢆ౑࠺ࢩ࣑ࣥ
ࢢࢆཷືⓗࢩ࣑ࣥࢢ(Passive shimming)࡜࿧ࡪࠋཧ
⪃ᩥ⊩[12, 13]ࡢ᪉ἲࡶཷືⓗࢩ࣑ࣥࢢ࡛࠶ࡿࠋ
ࡇࡢ᪉ἲࡣከᩘࡢ఩⨨࡛ MM(㕲∦)ࢆ㓄⨨ฟ᮶ࡿࡢ࡛ࠊ✵㛫ⓗ࡟⣽࠿ࡃ☢ሙㄪᩚࢆ⾜࠺ࡇ࡜ࡀฟ
᮶ࡿࠋMRI ☢▼࡛ࡣ୍⯡ⓗ࡟౑ࢃࢀࠊg-2/EDM ࡛ࡶࡇࡢ᪉ἲࢆ୺࡟౑࠺ࠋ
ᮏ⠇࡛౑⏝ࡍࡿ☢ሙࢹ࣮ࢱࡣࠊJ-PARC ෆ࡛ࠊ
MuSEUM ᐇ㦂⏝࡟⏝ពࡋ࡚࠸ࡿ෌฼⏝ MRI ☢▼࡛࠶ࡿࠋィ 㠃ࡣ 40cm-DSS ࡛࠶ࡿࠋ4.6.1.

ࢩ࣑ࣥࢢᶵᵓ

Fig. 4-16 ࢩ࣒ࢺࣞ࢖࡜☢ሙィ㠃ࡢ㓄⨨౛ࠋ

Fig. 4-16 ࡣ MRI ☢▼ࡢࢩ࣑ࣥࢢయ⣔࡛࠶ࡿ [13]ࠋ
㏻ᖖ 24 ᮏࡢࢩ࣒ࢺࣞ࢖ࢆᣢࡘࡀࠊᅗࡣࡑࡢ࠺ࡕ

4.6.2. ⧞ࡾ㏉ࡋࡢࢩ࣑ࣥࢢసᴗ

ࡢ 12 ᮏࢆ෇⟄≧࡟㓄⨨ࡋࡓᅗ࡛࠶ࡿࠋࡑࢀࡒࢀ
࡟ࡣ 24 ಶࡢ࣏ࢣࢵࢺࡀ࠶ࡿࠋྜィ 576 ಶࡢ࣏ࢣࢵࢺࡀᏑᅾࡍࡿࠋ
࣏ࢣࢵࢺ࡟㕲∦㸦ⷧᯈ㸧ࢆ㓄⨨ࡍࡿࠋࢩ࣒ࢺ
ࣞ࢖ 24 ᮏࡢ࠺ࡕࠊ12 ᮏࢆ⢒(coarse)ࢩ࣑ࣥࢢ࡟฼

Fig. 4-17 ࡟ࡣࢩ࣑ࣥࢢసᴗࡢᡭ㡰ࢆ♧ࡋࡓࠋ☢
ሙࢆィࡋࠊࡑࡢ☢ሙศᕸ࡟ࡘ࠸࡚ࠊᆒ୍ᗘࢆ

ㄪ࡭ࠊᆒ୍ᗘࡣ୙༑ศ࡞ሙྜ࡟ࡣࢩ࣑ࣥࢢィ⟬(Shimming Calculation)ࢆ⾜࠸ࠊࡑࡢ⤖ᯝ࡟ᇶ࡙࠸
࡚ࢩ࣒∦ࢆ㓄⨨ࡍࡿࠋ

10㸫 28ᐇ㝿ࡢࢩ࣑ࣥࢢసᴗ࡛ࡣࠊィ࡟ࢩ࣒∦ᐜ㔞࡟ㄗᕪࡣ࠶ࡿࡓࡵࠊ୍ᅇࡢࢩ࣑ࣥ
ࢢసᴗ࡛ࡣࠊ┠ᶆࡢ☢ሙᆒ୍ᗘ࡟ࡣ฿㐩࡛ࡁ࡞࠸ ࠋ ࡇ ࡢ ㄗᕪ ࢆ ⿵ ࠺ ࡼ࠺ ࡟ ⧞ ࡾ ㏉ࡋ స ᴗ ࡜ ࡞ࡿࠋ౛[13]࡛ࡣ 3 ᅇࡢ⧞ࡾ㏉ࡋసᴗ࡛࠶ࡿࡀࠊJPARC ࡛ィ⏬ࡋ࡚࠸ࡿᆒ୍ᗘࡣࠊMRI ࡼࡾ⣙୍᱆ᑠࡉ࠸್࡛࠶ࡿࡢ࡛ࠊ⧞ࡾ㏉ࡋసᴗᅇᩘࡣቑ࠼
ࡿ࡜⪃࠼࡚࠸ࡿࠋ
ࡇࡢ⧞ࡾ㏉ࡋసᴗࡢ୰࡛ࠊࢩ࣑ࣥࢢィ⟬ࡣ㔜せ࡞㡯┠࡛࠶ࡿࠋィ%ER = %0ࠊィ⟬ࠊࡑࢀ

☢ሙࡀධຊ࡛ࠊࢩ࣒∦㓄⨨ࡀฟຊ࡛࠶ࡿࠋࡇࡢෆᐜࢆḟ࡟⤂௓ࡍࡿࠋ

%MS

(4-9)

ࢆ⿵ṇࡍࡿࢩ࣒∦㓄⨨ࢆィ⟬ࡍࡿࠋࡇࡇ࡛ࠊ%0
࡜ %MS ࡣࠊࡑࢀࡒࢀࠊ┠ᶆ☢ሙ࡜ィ☢ሙ࡛࠶ࡿࠋᮏ㡯ࡢࢩ࣑ࣥࢢィ⟬ࡢㄝ࡛᫂ྲྀࡾᢅ࠺☢ሙ࡛ࠊࢩ࣑ࣥࢢ๓ࡢ☢ሙศᕸࡣࠊ40cm-DSS 㠃࡛ࠊ
Fig. 4-18 ࡢࡶࡢ࡛࠶ࡿࠋୗഃ࡛☢ሙࡀపࡃ࡞ࡗ࡚
࠾ࡾࠊ᭱኱᭱ᑠࡢᕪࡣ 693ppm ࡜኱ࡁ࡞ㄗᕪ☢ሙࡀ࠶ࡿࠋᐇ㝿ࡢࢩ࣑ࣥࢢ࡟ࡘ࠸࡚ࠊࢩ࣑ࣥࢢィ⟬ἲࢆ୰ᚰ࡟ㄝ᫂ࡍࡿࠋ
ࢩ࣑ࣥࢢィ⟬ࡢయ⣔ࡣ Fig. 4-19 ࡛࠶ࡿࠋィ 㠃
ࡣ 40cm-DSS ࡛ࠊࡇࡇ࡛ࡢ☢ሙィ ್࠿ࡽࢩ࣑ࣥ
ࢢィ⟬ࡢ⤖ᯝ࡟ᚑࡗ࡚ࠊࢩ࣒ࢺࣞ࢖ࡢ MM ኱ࡁYes☢▼タ⨨䚸ບ☢ᚋ䝅䝭䞁䜾సᴗ㛤ጞࡉࢆㄪᩚࡍࡿࠋࡇࡇ࡛ࠊᗙᶆ⣔ࡣ㍈᪉ྥࢆ Z ㍈࡜Magnetic field measurementࡋࠊỈᖹࠊᆶ┤᪉ྥࢆࡑࢀࡒࢀࠊX, Y ᪉ྥ࡜ࡋ࡚

Good homogeneity h(0) ?
No

Return to repeatసᴗ⤊஢

Shimming calculation(HiSHIM䠖High accuracy SHIMming)
Ramp-down is necessary ?

Yes

No

䝅䝮∦㓄⨨సᴗ

Ramp-down
Iron piece placements
Ramp-upFig. 4-17 ࢩ࣑ࣥࢢసᴗࡢᡭ㡰ࠋ☢ሙศᕸࡀ┠ᶆࡢᆒ୍ᗘࢆᚓࡿࡲ࡛⧞ࡾ㏉ࡋసᴗࢆ⾜࠺ࠋᩥ⊩ 13, Fig.1 ࡼࡾᘬ⏝4.6.3.

Fig. 4-18 ࢩ࣑ࣥࢢ๓ࡢㄗᕪ☢ሙศᕸࠋ࣓ࣝ
࢝ࢺ࣮ࣝᅗἲ࡛⾲♧ࠋᡴⅬ㡿ᇦࡣప☢ሙ㒊
ศࠋ40cm-DSS 㠃࡛ࡢィ ☢ሙ࡛࠶ࡿࠋ

ࢩ࣑ࣥࢢィ⟬

ࢩ࣑ࣥࢢ࡛┠ᶆ࡜ࡍࡿ☢ሙศᕸࡣ㺂☢▼㍈᪉ྥࢆྥࡁࠊ୍ᵝ࡞☢ሙᙉᗘศᕸ࡟㏆࠸☢ሙ࡛࠶ࡾࠊ
☢ሙࡢ㍈᪉ྥ Z ᡂศࢆࠊࢩ࣑ࣥࢢィ⟬࡛ࡶᢅ࠺ࠋ
MRI ⿦⨨ࡢࡼ࠺࡞୍ᵝ࡞☢ሙ࡛ࡣࠊࡇࢀࡣⰋ࠸
㏆ఝ࡛࠶ࡿ[13]ࠋࡑࡢ⤖ᯝࠊࢩ࣑ࣥࢢィ⟬࡛ % ࡣࠊεϞφϪ΢͹ࣕ‫ـ‬Ϡʖϟϱφ(రฤ)εϝϱή໚ࣕ৖‫ܯ‬଎఼
ࣕ৖඲Ճ఼(MFEP)YZ☢ሙホ౯Ⅼࡢ Z ᪉ྥ☢ሙᡂศ࡛ᵓᡂࡉࢀࠊ
X% **= (--------,‫ככ‬, --------)

(4-8)

੫ࣕ৖%
(1.70T)࡛࠶ࡿࠋୖῧ࠼Ꮠࠕ**ࠖࡣ☢ሙࡢ✀㢮ࢆ⾲⌧ࡋࠊ┠ᶆ☢ሙ TG, ィ ☢ሙ MS, ㄗᕪ☢ሙ ERࠊࢩ࣒∦

Djࡢ☢Ẽ࣮࣓ࣔࣥࢺ MM ࡼࡿ☢ሙ M, ࡛࠶ࡿࠋࢩ࣑ࣥࢢィ⟬࡛ࡣࠊㄗᕪ☢ሙ %ER

Fig. 4-19 ࢩ࣑ࣥࢢィ⟬య⣔ࠋ㍈᪉ྥࡀ Z ᪉
ྥ࡛ࠊ;< ࡣࠊỈᖹࠊᆶ┤᪉ྥࠋ

10㸫 29☢ሙ࠿ࡽࠊィ(T)㠃ࡢෆഃࡢ☢ሙศᕸ࡬ࡢෆᤄィ⟬[42, 43]ࢆ฼

☢ሙࢆ෌⌧ࡍࡿࡼ࠺

࡟ࠊ௬᝿㉳☢ຊ㓄⨨㠃(ࡇࡇ࡛ࡣ 60cm-DSS)࡟௬
᝿ⓗ࡟☢Ẽ࣮࣓ࣔࣥࢺ MM ศᕸࢆ⟬ฟࡋࠊࡑࡢ
MM ศᕸ࡛☢ሙศᕸࢆ⟬ฟࡋ࡚࠸ࡿࠋ
ࢩ࣒∦ࡀసࡿ☢ሙࡣ MM ࡢసࡿ☢ሙ࡛ࠊj ␒┠
Pj ࡀ i ␒┠఩⨨࡟సࡿ☢ሙ EMi ࡜ࡋ࡚,EMi=(10-7){3(Pj㺃Uij)Uij/rij2 Pj}/rij3,(1.2T, 40cm௜‫ܚ‬field camera, AV =1.19991006)

୉DTŘ>εϞฤྖଁՅ

1.0E-04
1.0E-05
1.0E-06

0.2 ppm=0.34PT

1.0E-07
1.0E-08

0

25
50
75
100
125
Truncation SVD eigenmode number DT

150

Fig. 4-20 ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ 0T ࡜ṧᕪ☢
ሙࡢ㛵ಀࠋࢩ࣑ࣥࢢィ⟬࡛ồࡵࡓ᥎ᐃ
್ࠋ0.2ppm ௨ୗ࡟ࢩ࣑ࣥࢢࡍࡿ࡟ࡣ 0T=69 ࡀጇᙜࠋ(4-10)

࡛ィ⟬࡛ࡁࡿࠋࡇࡇ࡛ࠊUij ࡣ j ␒┠ࢩ࣒∦࠿ࡽࠊi ␒┠ィ Ⅼ࡬ࡢ఩⨨࣋ࢡࢺ࡛ࣝ࠶ࡿࠋࡇࡢ࠺ࡕ
ࡢ㍈᪉ྥᡂศ bZi ࢆ฼⏝ࡋ࡚ࢩ࣑ࣥࢢࢆ⾜࠺ࠋ୍᪉ࠊ࣏ࢣࢵࢺ࡟㓄⨨ࡉࢀࡓ㕲∦ࡣ☢ሙ࡜ྠࡌ㍈
᪉ྥ(Z ᪉ྥ)࡟ྥࡁࠊ㣬࿴☢໬(㕲 1cc = 1.71Am2)
ࢆᣢࡘࠋࡘࡲࡾࠊ

2020/07/07ࣰ଎ࣕ৖͖Δࢋड़

MT= 69ࡋࠊ

MuSEUM ᐇ㦂㡿ᇦࡢ 20cm ┤ᚄ-30cm 㛗ࡢᴃ෇య⾲㠃࡬ෆᤄィ⟬ࡋࡓࠋィ693 ppm

1.0E-03
Residual magnetic field amplitude⏝ࡋࡓࠋࡇࡇ࡛ࡣࠊ40cm-DSS ࡛☢ሙィ

1.0E-02εϝϱή࠸ࡿࠋᐇ㝿ࡢࢩ࣑ࣥࢢ࡛ࡣࠊィ࡛࠶ࡿࡀࠊTSVD ࢆ⏝࠸࡚=

(4 െ 16)࡛࠶ࡿࠋຍ⟬ࡣᅛ᭷࣮ࣔࢻ࡟ࡘ࠸࡚≉␗್Pj = (0.0, 0.0, Mj)(4-11)

࡛࠶ࡿࠋᛂ⟅⾜ิ A ࡢせ⣲ࢆࠊᘧ(4-10)ࡢ༢఩
MM ࠶ࡓࡾࡢ☢ሙ࡜⪃࠼ࡿ࡜ࠊAij = (10-7){3Zij2/rij2 1.0}/rij3,

2
k[T/Am ] 㝆㡰࡟,ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ k=MT ࡲ࡛⾜࠺ࠋYk ࡜ Xk ࡣࡑࢀࡒࢀࠊ0 ࡜ % ࡢ k ␒┠ᅛ᭷ศᕸࠋࢩ࣑ࣥࢢᚋࡢண᝿ṧᕪ☢ሙ %RE ࡣࠊ%RE= %ER –σ(4-12)()= %ER - A0 (MT )࡛ ࠶ ࡾ ࠊj ␒ ┠ ఩ ⨨ ࡢ ༢ ఩ ☢ Ẽ ࣔ ࣮ ࣓ ࣥ ࢺ(4-17)(1.0Am2)ࡢ㍈᪉ྥᡂศࡀ i ␒┠ MFEP ࡟సࡿ☢ሙ࡛࠶ࡿࠋࡇࡢࢩ࣑ࣥࢢィ⟬ἲ࡛ࡣࠊ┠ᶆ☢ሙᙉࡢ㍈᪉ྥᡂศᙉᗘ࡛࠶ࡿࠋࡇࡇ࡛ࠊZij ࡣ Uij ࡢ㍈

ᗘ B0 ࡜ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ MT ࢆࠊ┠ᶆ☢ሙ᪉ྥ Z ᡂศ࡛࠶ࡿࠋࡲ࡜ࡵࡿ࡜ࠊࢩ࣒∦ࡀసࡿ☢

ศᕸ(±0.1ppm ௨ෆࡢ☢ሙኚື࡛ࠊᆒ୍ᗘ 0.2ppm)

ሙ %M ࡣࠊ

ࡀᚓࡽࢀࡿࡼ࠺࡟Ỵࡵࡿᚲせࡀ࠶ࡿࠋࡇࡢ᪉ἲ
ࢆཧ⪃ᩥ⊩[8, 44]ࡢ 0.2ppm ࢆᐇ⌧ࡋࡓࢩ࣑ࣥࢢ᫬
%M = A0(4-13)

ࡢ☢ሙࢆ౑ࡗ࡚ࠊḟ࡟ㄝ᫂ࡍࡿࠋ
๓࣮࣌ࢪࡢ Fig. 4-18 ࡣࠊࢩ࣑ࣥࢢ๓ࡢィ࡜᭩ࡅࡿࠋࡇࡢᘧࡣ᭱ึ࡟᭱ᑠ஧஌ἲࡢㄝ᫂ࡢ

㠃ෑ㢌ࡢᘧ(2-1)࡜ྠࡌᙧ࡛࠶ࡾࠊ%ER ࢆ⿵ṇࡍࡿࠊ

(40cm-DSS)ୖࡢ☢ሙศᕸࢆ࣓ࣝ࢝ࢺ࣮ࣝᅗἲ࡛

0 㓄⨨ࢆồࡵࡿࡓࡵ࡟➹⪅ᥦ᱌ࡢࢩ࣑ࣥࢢィ⟬⾲♧ࡋࡓࠋࡇࡢ☢ሙศᕸࡣࠊ20-30cm ᴃ෇య⾲㠃࡛ࡣࠊ᭱ᑠ஧஌ἲࢆ TSVD ṇ๎໬࡛ゎࡃࠋ➨ 2 ❶࡟ෆᤄィ⟬ࡍࡿ࡜ࠊ341ppm ࡛࠶ࡿࠋࡇࡢ☢ሙศ࡛ㄝ᫂ࡋࡓィ⟬ἲࢆ฼⏝ࡍࡿࠋᕸ࡟ࢩ࣑ࣥࢢィ⟬ࢆᐇ⾜ࡋࠊᘧ(4-17)࡛ồࡵࡓ MT࡜ṧᕪࡢ㛵ಀࡀ Fig. 4-20 ࡛ࠊṧᕪ☢ሙศᕸ %RE ࠿

2 ஌ㄗᕪ㸻(%ER - A0)2ĺ᭱ᑠ

(4-14)

ࡽࠊḟᘧ࡛ồࡵࡓ peak-to-peak ್ࢆ⾲♧ࡋࡓࠋ

࡜ࡍࡿ 0 ࡣࠊ0 = (AtA)-1At%ER((4-15)

10㸫 30

)=

(

) െ

(

) (4-18)

40cm-DSS ࡣィ㠃࡛࠶ࡿࡀࠊෆᤄィ⟬࡛ 20-

30cm ࡢᴃ෇య⾲㠃࡟ࡘ࠸࡚ࡶ⾲♧ࡋࡓࠋ

4-17 ࡢࡼ࠺࡟⧞ࡾ㏉ࡋసᴗ࡜࡞ࡿࠋ⧞ࡾ㏉ࡋసᴗẖ࡟ୖグࡢ᳨ウࢆ⾜࠺ࡇ࡜࡟࡞ࡿࠋ

୍⯡࡟ࠊMT ࢆ኱ࡁࡃࡍࡿ࡜ᆒ୍ᗘࡣⰋዲ࡟࡞

ཧ⪃࡟ཧ⪃ᩥ⊩[13]ࡼࡾ,࿘ᅇ᪉ྥ࡟୍ᵝ࡞ᇶᮏࡿࡀࠊ౑⏝ࡍࡿ㕲∦㔞ࡣቑຍࡍࡿࠋࡑࡢࡓࡵࠊ

ᅛ᭷࣮ࣔࢻ࡟ࡘ࠸࡚ࠊࢩ࣑ࣥࢢ࡟ᚲせ࡞㕲㔞ࢆ┠ᶆᆒ୍ᗘࢆ‶ࡓࡍ⠊ᅖ࡛ᑠࡉ࡞ MT ࢆ㑅ᢥࡍ♧ࡋࡓ(Table 4-6)ࠋᇶᮏᅛ᭷࣮ࣔࢻࡣ 4.1 ⠇ࡢ MRIࡿࠋࡇࡇ࡛ࡣ MT =69 ࢆ㑅ᢥࡍࡿࠋ☢▼ࡢ☢ሙタィ࡛㆟ㄽࡋࡓᅛ᭷࣮ࣔࢻ࡜࡯ࡰྠ

ḟ࡟ࠊࡇࡢ MT=69 ࡛┠ᶆ☢ሙᙉᗘࢆỴࡵࡿᅗࡌ࡛࠶ࡿࠋࢩ࣒ࢺࣞ࢖࡟㓄⨨ฟ᮶ࡿ㕲㔞ࡣ

ࡀࠊFig. 4-21 ࡛࠶ࡿࠋMT ࡜ࢩ࣑ࣥࢢィ⟬࡛⟬ฟ

2000cc ௨ୗ࡛࠶ࡾࠊ⾲୰࡛ 7 ␒┠௨㝆ࡢᅛ᭷࣮ࣔ

ࡋࡓᆒ୍ᗘࡢண᝿್ࢆࣉࣟࢵࢺࡋ࡚࠸ࡿࠋࢩ࣒

ࢻࡣࢩ࣑ࣥࢢ࡛ࡁ࡞࠸࡜ゝ࠼ࡿࠋ౑⏝☢▼ࡢ୺∦ࡢ᭱ᑠ༢఩ࡢ 3 ✀㢮࡛♧ࡋࡓࠋ㏻ᖖࡢ MRI ☢

ࢥ࢖ࣝᩘࡣ 6 ಶ࡛࠶ࡾࠊ7 ␒┠௨㝆ࡢᅛ᭷࣮ࣔࢻ

2▼࡛⏝࠸࡚࠸ࡓ㕲∦ 0.06cc(0.103Am ), MuSEUM

ࡣ☢▼タィ࡛ࡣ⪃៖ࡉࢀ࡚࡞࠸࡜⪃࠼ࡿࠋB0 ࡟ᐇ㦂⏝࡟⏝ពࡋࡓ Ni ∦ 0.036cc(0.017Am2), ࡑࢀ࡟ࡶ౫Ꮡࡍࡿࡢ࡛ࠊṇ☜࡞㆟ㄽ࡟ࡣฟ᮶࡞࠸ࡀࠊ7↓㝈ᑠࡢሙྜ࡛࠶ࡿࠋཧ⪃࡟ࠊ㕲ࡢ㣬࿴☢໬ࡣ␒┠௨ୖࡢḟᩘࡢ㧗࠸ᅛ᭷࣮ࣔࢻࡣᐇ㝿ୖࢩ࣑

2.15T ࡛ࠊNi ࡣ 0.60T ࡜ࡋࡓࠋࣥࢢ࡛ࡁ࡞࠸ࡇ࡜ࡀゎࡿࠋࢩ࣒㕲ࡣ☢ሙࢆ୺࡟పୗࡉࡏࡿࡢ࡛ࠊ┠ᶆ☢
Table 4-6 ࿘ᅇ᪉ྥ୍ᵝ࡞ᅛ᭷࣮ࣔࢻࡢࢩ࣑ࣥࢢ࡟ᚲせ࡞ࢩ࣒㕲∦㔞ࡢ౛([13]ࡼࡾᘬ⏝)ሙࡣ㧗ࡵࡢ᪉ࡀࠊࢩ࣒∦㔞ࡀᑡ࡞ࡃ࡞ࡿࠋ୍᪉
࡛ࠊ㧗ࡍࡂࡿ࡜ࢩ࣒∦㓄⨨ࡢゎࡀ↓ࡃ࡞ࡿ(ࡘࡲError
Estimatediron
2D basic Eigenmode eigenmodestrength
volumeeigenmode
No.
No. i
M2Di
PiER (T) Vol(i) (cm3)1
15.963E-5
5.114E+1
2
7
3.588E-5
6.819E+1
3
21
4.916E-5
2.986E+24492.057E-5
4.728E+25735.440E-6
5.154E+2697
2.142E-6
8.886E+2
7121
1.889E-6
3.621E+3
81451.750E-6
1.714E+4
9175
8.021E-7
5.073E+4ࡾ ☢ ໬ ᪉ ྥࢆ ☢ ሙ ࡢ ㏫᪉ ྥ ࡜ ࡍ ࡿゎ ࢆ ฟ ຊ ࡍࡿ)ࠋࡲࡓࠊᚲせ௨ୖ࡟Ⰻዲ࡞ᆒ୍ᗘࢆồࡵࡿ࡜ࠊ㐣኱㔞ࡢࢩ࣒∦ࢆᚲせ࡜ࡍࡿࡇ࡜࡟࡞ࡿࠋ
ࡑࡢࡓࡵࠊ࡛ࡁࡿࡔࡅᑡ࡞࠸㕲㔞࡛ࠊᚲせ࡞ᆒ୍ᗘࢆᐇ⌧ࡍࡿࡼ࠺࡟ࠊB0, MT ࢆỴࡵࡿࠋࡑࡢព
࿡࡛ࠊB0>1.199685T ࡣጇᙜ࡛ࡣ࡞࠸ࠋ
୍᪉ࠊ㕲∦ 0.06cc ࡀ᭱ᑠ༢఩ࡢሙྜࠊ୍∦ࡢ㓄⨨࡛ኚ໬ࡍࡿ☢ሙࡀ኱ࡁ࠸ࡢ࡛ࠊ0.2ppm ࡟ࡣ฿㐩࡛ࡁ࡞࠸ࠋࡋ࠿ࡋࠊNi 0.036cc ࡣ 0.2ppm ௨ୗࡢゎࡀ࠶ࡿࠋ౛࠼ࡤࠊB0=1.199680T ࡢࡼ࠺࡟㑅ᢥ

4.6.4. ࢩ࣑ࣥࢢసᴗࡢᐇ⾜ࡍࡿ࡜Ⰻ࠸⤖ᯝࢆ୚࠼ࡿࠋᐇ㝿ࡢࢩ࣑ࣥࢢࡣ Fig.

1.0

MT= 69㕲㔞NG䝅䝭䞁䜾୙ྍ

0.6

0.2

0.0
1.19950࡛ࡁࠊ⏝ពࡋࡓ☢ሙࢩ࣑ࣥࢢࡢᢏ⾡ࡀࠊJ-PARC
8.0E-04

0.8

0.4

ᐇ⾜࡛ࠊJ-PARC ࡛┠ᣦࡍ 0.2ppm ࡢᆒ୍ᗘࡀᐇ⌧1.2E-03㈇㕲㔞

㕲∦0.06cm3 (0.103Am2)
ᆒ୍ᗘ
Ni0.036cm3 (0.017Am2,㕲∦䛾1/6)

1.19960

1.19965

1.19970࡚࠾ࡃࠋ௨ୖࡢᡭἲ࡟ࡼࡿࢩ࣑ࣥࢢィ⟬࡛ࠊMuSEUM

0.0E+00

0.5 Gaussᐇ㦂௙ᵝࡢ 20-30cm ᴃ෇య࡛ 0.2ppm ࢆ┠ᣦࡍࢩ࣑ࣥࢢ⾜࠸ࠊ┠ᶆࡢᆒ୍ᗘ࡟฿㐩ࡋ࡚࠸ࡿࠋFig.

-4.0E-04↓㝈ᑠ༢఩䝅䝮∦1.19955

4.0E-04ᐇ㦂࡟ᑐᛂ࡛ࡁࡿࡇ࡜ࢆ☜ㄆࡋࡓࡇ࡜ࢆ⤂௓ࡋྜィ䝅䝮㕲㔞(m3)ᆒ୍ᗘ(20-30cmᴃ෇య⾲㠃) (ppm)௨ୖࡢ⪃࠼࡟ࡼࡿࢩ࣑ࣥࢢィ⟬࡜ࢩ࣑ࣥࢢࡢ
920cc = 7.3kg

1.19975

4-22 ࡣ⧞ࡾ㏉ࡋసᴗ࡟ࡼࡿᆒ୍ᗘࡢపୗࢆ♧ࡋ࡚

-8.0E-04
1.19980࠸ࡿࠋࢩ࣑ࣥࢢ๓࡛ࡣࠊ20-30cm ᴃ෇య⾲㠃࡛┠ᶆ☢ሙᙉᗘB0 (T)Fig. 4-21 ᆒ୍ᗘ࡜┠ᶆ☢ሙࡢ㛵ಀࢆࠊ␗࡞ࡿ
㕲㔞᭱ᑠ༢఩࡛♧ࡍࠋ0.2ppm ௨ୗ࡟ࢩ࣑ࣥࢢ
ࡍࡿ࡟ࡣ 0.017Am2(Ni 0.036cc ┦ᙜ)⛬ᗘ௨ୗࡢ᭱ᑠ༢఩ࡢࢩ࣒∦࡜ࡍࡿᚲせࡀ࠶ࡿࠋ

391ppm ࡢᆒ୍ᗘ࡛࠶ࡗࡓࡀࠊࢩ࣑ࣥࢢᚋ࡟ࡣ
0.16ppm ࡟ฟ᮶ࡓࠋ

10㸫 315 ᅇ┠ࡲ࡛ࡣ᭱ᑠࢩ࣒∦༢఩ࢆ㕲 0.06cc ࡛࠶ࡀࠊ඲࡚ᴃ෇యࡢእ࡟࠶ࡾࠊᮇᚅࡋࡓⰋዲ࡞ᆒ

ࡾࠊࡇࡢẁ㝵࡛ࡣ 0.5ppm ⛬ᗘ࡛೵⁫ࡋࡓࠋ6㸪7

୍ᗘࡀᚓࡽࢀࡓ࡜ゎࡿࠋࡑࡋ࡚ࠊ0.2ppm ࡢ☢ሙᅇ┠ࡣ Ni 0.036cc ࢆ᭱ᑠ༢఩࡜ࡋ࡚ࠊ0.16ppm ࢆᆒ୍ᗘࢆᐇ⌧ࡍࡿࡓࡵࡢࢩ࣑ࣥࢢᢏ⾡ࡣࠊࡇࢀ㐩ᡂࡋ࡚࠸ࡿࠋࢩ࣑ࣥࢢィ⟬࡟ࡼࡿண

ࡲ࡛࡟㏙࡭ࡓᡭἲ࡛ᑐᛂྍ⬟࡜⤖ㄽ࡛ࡁࡿࠋ

࡜▩┪

ࡋ࡞࠸ࠋ

4.6.5. ཷືࢩ࣑ࣥࢢࡢ㞴ࡋ࠸☢ሙࢩ࣑ࣥࢢィ⟬ࡸࢩ࣒∦ᐜ㔞࡟ࡣࠊྜィࡍࡿ࡜
᭱኱ 7.5%ࡢࢩ࣒∦㔞ࡢィ⟬࣭㓄⨨ㄗᕪࡀ࠶ࡿ࡜

᪤࡟ 2.3 ⠇࡜ 4.1 ⠇࡛㏙࡭ࡓࡼ࠺࡟ࠊMRI ☢▼᥎ᐃࡋ࡚࠸ࡿࠋࡇࡢࡓࡵ࡟ࠊ1㸪3 ᅇ┠࡜ 6 ᅇ┠ࡢࡢࡼ࠺࡟ࠊᆒ୍☢ሙࢆⓎ⏕ࡍࡿ☢▼ࡢ☢ሙタィᆒ୍ᗘࡢኚ໬ࡀ኱ࡁ࠸᫬࡟ࡣࠊண᝿࡜ᐇ㝿࡜ࡀ࡛ࡣࠊ㍈࡟ᖹ⾜࡞☢ሙᡂศ(BZ)ࢆᢅ࠺ࠋࡋ࠿ࡋࠊ

ࡸࡸ஋㞳ࡋ࡚ࡃࡿࠋࡋ࠿ࡋࠊ⧞ࡾ㏉ࡋసᴗ࡜ඹィ ☢ሙ BMS ࡣ MFEP ࡛ィ ࡉࢀࠊ|MS

ࡶྵࡲࢀࠊୗグࡢ㛵ಀࡀ B , BZ,࡟ࡇࡢ஋㞳ࡀゎᾘࡉࢀࡿࡇ࡜ࡀゎࡿࠋ| (<< |BZ|)

ࡢ㛫࡟ࠊ

Fig. 4-23 ࡟ࡣࠊᐇ㝿࡟ࢩ࣑ࣥࢢసᴗࢆ⾜ࡗࡓ⤖=ᯝࠊᚓࡽࢀࡓ☢ሙศᕸࢆ♧ࡍࠋ㍈᪉ྥ-ᆶ┤᪉ྥࡢ☢ሙᙉᗘศᕸࢆ 0.1ppm ẖࡢ➼㧗⥺࡛♧ࡋ࡚࠸+؄ࡣࠊࢩ࣑ࣥࢢィ⟬࡟ධຊࡢ㛵ಀࡀ࠶ࡿࠋࡇࡢ

ࡉࢀࠊBZ ࡜ࡋ࡚ᢅࢃࢀࡿࠋࡓ࡜࠼

1000

/

Ꮡᅾࡋࡓ࡜ࡋ࡚ࡶࠊ0.5(100

ᆒ୍ᗘ(ppm)}, (4-19){1 + 0.5

ࡀ 7 ࢞࢘ࢫ

)ࡣ 0.1ppm ࡼࡾᑠࡉࡃࠊࡇࡢᕪ␗ࡣ᳨▱ࡉࢀ࡞࠸ࡲࡲࠊࢩ࣑ࣥࢢィ

10<0.06cc/Pocket⟬ࡉࢀࡿࠋࡲࡓࠊཷືⓗ࡟☢໬ࡋࡓ MM ࡛ࡣᡂศࢆ⿵ṇࡍࡿࡇ࡜ࡶ㞴ࡋ࠸ࠋࡑࡢࡓࡵࠊ

ࡣ࡜ࡣ↓㛵ಀ࡟ࢩ࣑ࣥࢢసᴗࡀ㐍ࡵࡽࢀࡿࠋࡘࡲ

1ࡀ༑ศ୍ᵝ࡟ࢩ࣑ࣥ

ࡾࠊࢩ࣑ࣥࢢࡢ⤊஢ᚋ(
0.1
0

1

2

3

4

5

6

7

ࢢࡉࢀࡓᚋ)࡛ࡶࠊ

⧞䜚㏉䛧సᴗᅇᩘ

Fig. 4-22 ࢩ࣑ࣥࢢ⧞ࡾ㏉ࡋసᴗ୰ࡢᆒ୍ᗘ

ᡂศࡣṧࡿࡇ࡜࡟࡞ࡿࠋMaxwell ᪉⛬ᘧ࠿ࡽ⪃ᐹࡍࡿ࡜ୗグࡢࡼ࠺࡟࡞
ࡿࠋ㟁ὶࡢᏑᅾࡋ࡞࠸㡿ᇦ࡞ࡢ࡛ࠊ
=0 ĺ

=െ

= 0 ĺ

=

,

+
and

(4-20),=

࡛࠶ࡿࠋ༑ศࢩ࣑ࣥࢢࡉࢀࡓ☢ሙ࡛ࡣࠊ(4-21),,

ࡣ࡯ࡰ㞽࡛࠶ࡿ(< 0.1ȣT/0.1m). ࡑࡋ࡚ࠊ

࡜
,

࡜

+

ࡶ㞽࡛࠶ࡿࠋࡋ࠿ࡋࠊࡇࡢ

ᘧ࡟ධࡗ࡚࡞࠸ BX, BY ᡂศ࡛ࠊ
ࡍࡿ

=

ࢆ‶㊊

ᡂศࡣࠊࢩ࣑ࣥࢢᚋ࡛ࡶṧࡿࡇ࡜࡟࡞

ࡿࠋࡇࡢ☢ሙࡣࠊ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ{0, 0,

Fig. 4-23 ࢩ࣑ࣥࢢᚋࡢṧᕪ☢ሙศᕸࢆ୰ᚰ☢
ሙ࠿ࡽ 0.1ppm ẖࡢ➼㧗⥺࡛⾲♧ࠋᴃ෇ࡣ
MuSEUM ᐇ㦂㡿ᇦ⾲㠃ࠋ๓➼㧗⥺ࡀᴃ෇ࡢእ࡟࠶ࡾࠊᆒ୍ᗘࡣ 0.2ppm ௨ୗ࡛࠶ࡿࠋ

ĳ X, Y)} ࡛⾲ࡉࢀࡿ BX=

࠾ࡼࡧ BY=㺎‫ (׎‬, ) =

+

(

cos

sin

࡛࠶ࡾࠊ

), (4 െ 22)࡛࠶ࡿࠋ‫ (׎‬, )ࡣ఩⨨(X, Y) ࡛ࡢ࣋ࢡࢺ࣏ࣝࢸࣥ
ࢩࣕࣝࡢ Z ᡂศ(ణࡋࠊZ ᪉ྥ࡟୍ᵝ)࡛࠶ࡿࠋ(X,10㸫 32Y) ࡣ(R, )ᗙᶆ࡜ࡢ㛵ಀࡣ X=Rcos , Y=Rsin ࡛࠶
ࡣ(X, Y)ࡢ᪉఩࡜ X ㍈࡜ࡢゅᗘ࡛࠶ࡿࠋn ࡣᩚᩘ࡛࠶ࡿࠋn=0 ࡛ࡣ‫ (׎‬, )ࡾࠊR ࡣ R= ξ,+⤊஢ᚋ࡛ࡣࠊィ 㠃ୖ࡛ࡣ±0.1ppm ௨ෆࡢ᣺ᖜ࡛
୍ᵝ࡞☢ሙ࡜࡞ࡿࠋࡋ࠿ࡋࠊᘧ(4-23)࡛ n൒2 ᡂศࡢᙳ㡪ࡀ࠶ࢀࡤࠊZ=0 ௜㏆࡛ࡣࢩ࣑ࣥࢢ㠃ࡼࡾᙅ
࠸|B|࡜࡞ࡿࠋᘧ(4-23)☢ሙࡢࡓࡵ࡟☢ሙࡀᙅࡃ࡞
ࡿ Z ㍈௜㏆࡛ࡶࠊィ 㠃࡟㏆࠸࡜ࡇࢁ࡛ࡣࠊࢩ࣑
ࣥࢢ࡟ࡼࡾࡣ୍ᵝ໬ࡉࢀࡿࠋࡑࡢ⤖ᯝࠊ☢▼୰
ᚰ(R=0.0, Z=0.0)௜㏆࡛ࡣࠊィ㠃ࡼࡾᙅ࠸☢ሙ࡜࡞ࡿࠋ౛࠼ࡤࠊ10 ࢞࢘ࢫࡢ||(n൒2)ࡀᏑᅾࡍ

ࡿ࡜ࠊࢩ࣑ࣥࢢᚋ࡛ࡣ☢▼୰ᚰ࡜ィ
࡟ࠊ0.17ppm ࡢᕪ␗{0.5(

Fig. 4-24 %X, %Y ᡂศ{ᘧ(4-21)}☢ሙࡢ☢ຊ⥺ࢆᕥ࠿ࡽ Q=1, 2,3 ࡛♧ࡍࠋ▮༳ࡣ☢ሙ᪉ྥࠋ

/

㠃ࡢ☢ሙ

)}ࡀᏑᅾࡍࡿࡇ࡜

ࡀண᝿ࡉࢀࠊࡇࡢᕪ␗ࡣ᳨ฟ࡛ࡁࡿࠋ
ࡶ࠺୍ࡘࡢ᳨ฟ࣭⿵ṇἲࢆᥦ᱌ࡍࡿࠋࡇࡢ᪉
ἲࡣࠊࡣᐃᩘ࡜࡞ࡾࠊ☢ሙ(BX, BY)ࡣ㞽࡛࠶ࡿࠋ
ᘧ(4-22)࡟ࡘ࠸࡚ࠊపḟ(n=1, 2, 3)࡛ CC=0 ࡢศᕸࢆ Fig. 4-24 ࡟♧ࡋࡓࠋ‫➼ࡢ׎‬㧗⥺࡛♧ࡋ࡚࠾ࡢ᳨ฟἲ࡟ࡶ࡞ࡿࠋ

ࡣ Fig. 4-24 ࡢ☢

ሙࡢຍ⟬࡛࠶ࡿࠋ୍⯡ⓗ࡟పḟ(n=1, 2)ᡂศࡢᙉ
ࡉࡀ኱ࡁ࠸࡜⪃࠼ࡿࠋࡑࡇ࡛ࠊ6 ᮏ௨ୖࡢ Z ᪉ྥࡾ ࠊ ☢ ຊ ⥺࡛ ࡶ ࠶ ࡿ ࠋ☢ ሙ ࡢ ᪉ ྥࡶ ♧ ࡋ ࡚ ࠸㟁ὶࡀ FOV ࢆྲྀࡾᅖࡴࡼ࠺࡟➼㛫㝸࡛㓄⨨ࡋࠊࡿࠋ ࡇࡢ࣋ࢡࢺ࣏ࣝࢸࣥࢩࣕࣝ࡟ࡼࡿ☢ሙࡣࠊ

㟁ὶ㓄ศࢆ

|

|‫ן‬

Ii = Icos(nș+Į)(4 െ 23)(4-24)

࡛࠶ࡾࠊn=1(ࢲ࢖࣏࣮ࣝᡂศ)௨እ࡛ࡣࠊ༙ᚄ࡟

࡜ࡋ࡚ࠊI ࡜ Į ࢆࠊヨ⾜㘒ㄗ࡟࡞ࡿࡀࠊn=1, 2 ࡟౫Ꮡࡋࠊᆒ୍ᗘ࡟ᙳ㡪ࡍࡿྍ⬟ᛶࡀ࠶ࡿࠋࡇࢀ

ࡘ࠸࡚ࠊኚ໬ࡉࡏࡿࠋ㍈(Z)᪉ྥ㟁ὶࡣࠊࢆ㑊ࡅࡿ࡟ࡣࠊඛグࡢࡼ࠺࡟ 7 ࢞࢘ࢫ௨ୗࡢ|

|

㠃ࡢ☢ሙ

ࢆᙅࡃฟ᮶ࡿሙྜࠊࡘࡲࡾࠊᘧ(4-19)ࡢᣓᘼෆ➨࡛࠶ࡿࡇ࡜ࢆ☜ㄆࡍࡿᚲせࡀ࠶ࡿࠋࡇࡢࡼ࠺࡞☢ሙࡢⓎ⏕※ࢆ⪃ᐹࡍࡿࠋn=1 ࡢ☢
ሙࡣࠊィࢆⓎ⏕ࡍࡿࡢ࡛ࠊヨ⾜㘒ㄗࡍࡿ࡜ィᡂศ

㍈࡜☢▼㍈ࡀᖹ⾜࡛࡞࠸ሙྜࠊᐜ᫆

࡟Ⓨ⏕ࡍࡿࠋ7 ࢞࢘ࢫࡣ MuSEUM ᐇ㦂ࡢ 1.7T ࡢ☢ሙ࡛ࡣࠊ0.024 ᗘࡢ㍈᪉ྥࡢᕪ࡛Ⓨ⏕ࡍࡿࠋࡋ

2 㡯ࢆᑠࡉࡃࡍࡿሙྜࡶ࠶ࡿࠋࡇࢀࡀ

ᡂศࢆ⿵ṇฟ᮶ࡓሙྜ࡛࠶ࡿࠋMRI ⏝☢▼࡛ࡣࠊᡂศࡢᙳ㡪ࡣᑠࡉ࠸࡜⪃࠼ࡿࡀࠊg-2/EDM ☢▼࡛ࡣ↓ど࡛ࡁ࡞࠸ྍ⬟ᛶࡶ࠶ࡿࡢ࡛ࠊFig. 4-24 ࡢᵝ࡞☢

࠿ࡋࠊᆒ୍ᗘ࡟ࡣᙳ㡪ࡋ࡞࠸ࡓࡵࠊၥ㢟࡜ࡣ࡞ሙࢆᡴࡕᾘࡍࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖ࢆ⏝ពࡍࡿィ⏬

ࡽ࡞࠸ࠋn=2 ࡢᅄᴟ☢ሙᡂศࡣࠊCB ࡢ㠡ᆺኚᙧ࡛࠸ࡿࠋḟ❶࡛෌ᗘヰࡍࠋ

࡛Ⓨ⏕ࡍࡿྍ⬟ᛶࡀ࠶ࡿࡀࠊ±0.25mm ࡢኚᙧ࡛4.7. MRI ☢▼㟼☢ሙタィࡢࡲ࡜ࡵࡶ 4 ࢞࢘ࢫ⛬ᗘ(50cm-DSS ୖ)࡜ィ⟬࡛ࡁࡿࠋࡇࢀ
ࡣࠊ1.7T ࡢィ ☢ሙ࡛ࡣࠊ0.03ppm ࡢᙳ㡪࡛ࡋ࠿ᮏ❶࡛ࡣࠊ୍ᵝ☢ሙࢆⓎ⏕࡛ࡁࡿ㉳☢ຊ㓄⨨࡞࠸ࠋࡲࡓࠊᐇ㝿ࡢ CB 〇㐀࡛ࡇࡢࡼ࠺࡞ኚᙧࡣ

ࢆࠊTSVD ṇ๎໬࡛ồࡵࡿ MRI ⏝☢▼ࡢ☢ሙタィ㉳ࡇࡾ㞴࠸ࠋ

ᢏ⾡࡟ࡘ࠸࡚ㄝ᫂ࡋࡓࠋ3 ࡘࡢ Step ࡛㉳☢ຊ㓄⨨ᡂศࡢᙳ㡪ࡣࠊ஦ᐇୖࠊၥ㢟ࢆタィࡍࡿࠋSVD ࡣ㟁ὶศᕸ࠿ࡽ᧜ീ㡿ᇦ࡟┦࡜ࡣ࡞ࡽ࡞࠸࡜ᮇᚅ࡛ࡁࡿࠋࡋ࠿ࡋࠊ௨ୗ࡛ࡑ

ᙜࡍࡿ㡿ᇦ(FOV)⾲㠃࡟సࡿ☢ሙ࡬ࡢᛂ⟅⾜ิ࡟ࡢ᳨ฟἲ࡜⿵ṇἲࢆᥦ᱌ࡍࡿࠋ

ᑐࡋ࡚ᐇ⾜ࡋ࡚࠸ࡿࠋ

௨ୖࡢᵝ࡟ࠊ

|࠿ࡽࡢᙳ㡪ࡀᑠࡉ࠸

Step-1 ࡛ࡣࠊ෇⟄≧࡟ከᩘ㓄⨨ࡋࡓ⥺㍯㟁ὶࡢࡇ࡜ࢆ☜ㄆࡍࡿࡓࡵ࡟ࠊࢩ࣑ࣥࢢ⤊஢ᚋ࡟ࠊ୰

㟁ὶศᕸࢆࠊFOV ࡟┦ᙜࡍࡿ㡿ᇦ࡛ࠊᆒ୍☢ሙᚰ㒊ࡢ☢ሙᙉᗘࢆィ㠃࡛ࡢ☢ሙࢆⓎ⏕ࡍࡿࡼ࠺࡟ࠊ⟬ฟࡍࡿࠋ≉␗್(T/A)ࡢ኱

ᙉᗘ࡜ẚ㍑ࡍࡿࡇ࡜ࡀⰋ࠸࡜⪃࠼ࡿࠋࢩ࣑ࣥࢢ

ࡁ࡞ᅛ᭷࣮ࣔࢻ࠿ࡽ୍ᵝ☢ሙ࡟ᚲせ࡞ᙉᗘ࡛ຍ

ᐇᶵ☢ሙ࡛ࠊᆒ୍ᗘ࡟|ࡋࠊ☢ሙィ

10㸫 33⟬ࡍࡿࠋᅛ᭷࣮ࣔࢻᩘࢆቑຍࡉࡏࡿ࡜ࠊ☢ሙࡢ㝈ࡽࢀࡓ᫬㛫࡜⣬㠃ࡢࡓࡵࠊヲࡋ࠸ㄝ᫂ࡣฟ

୍ᵝ࡞㡿ᇦࡀᗈࡲࡿࠋࡲࡓࠊ㟁ὶࣆ࣮ࢡᩘࡣຍ

᮶࡞࠿ࡗࡓࡀࠊタィィ⟬ࡢᴫ␎ࢆឤࡌ࡚㡬ࡅࡓ⟬ᅛ᭷࣮ࣔࢻᩘ࡟୍⮴ࡍࡿࠋ࡜ᮇᚅࡋࡲࡍࠋࡉࡽ࡟ࠊ⯆࿡࠶ࡿேࡣཧ⪃ᩥ⊩

Step-2 ࡛ࡣࠊ๓ Step ࡛ồࡵࡓ㟁ὶศᕸ࡛ࣆ࣮ࢡ

ࢆㄞࢇ࡛㡬ࡅࡿࡇ࡜ࢆᮇᚅࡋࡲࡍࠋ

࡜࡞ࡗࡓ఩⨨࡟ࢥ࢖ࣝࣈࣟࢵࢡ(CB)ࢆ㓄⨨ࡍࡿࠋ௨ୖࡢᢏ⾡ࡣ⌧ᅾ‽ഛ୰ࡢ g-2/EDM ࡢ☢▼タ

CB ࡢ᩿㠃ᙧ≧ࡣࠊStep-1 ࡛ồࡵࡓᅛ᭷࣮ࣔࢻᙉ

ィࡸ☢ሙㄪᩚ࡟฼⏝ࡋ࡚࠸ࡃィ⏬࡛ࠊ㐍ࡵ࡚࠸ᗘࢆ෌⌧ࡍࡿࡼ࠺࡟ࠊㄪᩚࡍࡿࠋࡇࡢ Step-2 ࡛ࡣࠊࡲࡍࠋྛ CB ࡢ㟁ὶࡣ㐃⥆್࡜ࡋ࡚࠸ࡿࠋ
Step-3 ࡛ࡣࠊCB ᩿㠃࡟ᑟయࡢᕳࡁ⥺ᵓ㐀ࢆ⪃៖ࡍࡿࠋᑟయࢆ㑅ᢥࡋࠊStep-2 ࡢ CB ᩿㠃࡟㏆࠸᩿ 㠃 ᙧ ≧ ࢆ෌ ⌧ ࡍ ࡿ ࡼ࠺ ࡟ ᕳ ࡁ ⥺ᵓ 㐀 ࢆ ᝿ ᐃࡋࠊ༙ᚄ࡜㍈᪉ྥ఩⨨ࢆᚤㄪᩚࡋ࡚ࠊStep-1 ࡢᅛ᭷࣮ࣔࢻᙉᗘࢆ෌⌧ࡍࡿࡼ࠺࡟ࡍࡿࠋồࡵࡓ㉳☢ຊ㓄⨨ࡀࠊᗄఱᏛⓗ࡞タィ௙ᵝࠊ⤒㦂☢ሙ࡞࡝ࡢᑟయ௙ᵝ࡜▩┪ࡍࡿ࡞ࡽࡤࠊᚲせ࡟ᛂࡌࡓ
Step ࠿ࡽ෌᳨ウࢆ⾜࠺ࠋ㕲 yoke ࢆྵࡴయ⣔࡛ࡶࠊᮏ❶ࡢ⪃࠼᪉ࡀ㐺⏝ྍ⬟࡛࠶ࡿࡇ࡜ࡶㄝ᫂ࡋࡓࠋ
௨ୖࡢᡭἲ୍࡛ᵝ☢ሙࢆⓎ⏕࡛ࡁࡿ㉳☢ຊ㓄⨨ࢆタィ࡛ࡁࡿࠋࡋ࠿ࡋࠊᐇ㝿ࡢ☢▼࡛ࡣࠊ⤌ࡳ❧࡚ㄗᕪࡸタ⨨⟠ᡤࡢ࿘ᅖࡢ㕲ᮦ࡞࡝ࡢᙳ㡪࡞࡝࡟ࡼࡿㄗᕪ☢ሙࡀྵࡲࢀࠊ☢▼タ⨨┤ᚋ࡟ࡣ タ ィ ☢ ሙࡢ ࡼ ࠺ ࡞ ୍ᵝ ☢ ሙ ࡣ ᐇ⌧ ࡛ ࡁ ࡚ ࡞࠸ࠋࡑࡢࡓࡵࠊ౑⏝㛤ጞ๓࡟☢ሙࢩ࣑ࣥࢢࢆ⾜࠸ࠊタィ☢ሙ࡟㏆࠸୍ᵝ☢ሙ࡟ࡍࡿࠋ
➹⪅ࡀᥦ᱌ࡋ࡚࠸ࡿࢩ࣑ࣥࢢᡭἲࡣࠊࡸࡣ
ࡾࠊTSVD ṇ๎໬฼⏝ࡢࢩ࣑ࣥࢢィ⟬ࢆ୰ᚰ࡜ࡍ
ࡿᡭἲ࡛࠶ࡿࠋᩘⓒⅬࡢࢩ࣒ࢺࣞ࢖࣏ࢣࢵࢺ࡟
㓄⨨ࡍࡿࢩ࣒∦(ከࡃࡣ㕲∦)ࡢ☢Ẽ࣮࣓ࣔࣥࢺ
MM ࠿ࡽᩘⓒⅬࡢ FOV ⾲㠃☢ሙ࡬ࡢᛂ⟅⾜ิ࡟
SVD ࢆᐇ⾜ࡍࡿࠋㄗᕪ☢ሙࡢᡂศࢆᅛ᭷࣮ࣔࢻ
ࡢᡂศᙉᗘ࡛ᢕᥱࡋࠊᆒ୍ᗘ௙ᵝࢆ‶ࡓࡍ(ṧᕪ☢ሙࡢ᥎ᐃ್ࡀᑠࡉࡃ࡞ࡿ)ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ(MT)௨ୗࡢపḟᡂศࡢᅛ᭷࣮ࣔࢻࡢᙉᗘࢆᡴࡕ ᾘ ࡍ ࡼ ࠺ ࡟ MM ࢆ 㓄 ⨨ ࡍ ࡿ ࠋ ࡇ ࡢ ᡭ ἲ ࢆ
MuSEUM ᐇ㦂࡟฼⏝ணᐃࡢ MRI ☢▼☢ሙ࡟㐺⏝ࡋࠊJ-PARC ᐇ㦂࡛ᚲせ࡜ࡍࡿ 0.2ppm ࡢ☢ሙᆒ୍ᗘࢆᐇ⌧ࡋࡓࢩ࣑ࣥࢢヨ⾜ࢆㄝ᫂ࡋࡓࠋణࡋࠊ
MRI ౑⏝᫬࡟ẚ࡭ࢩ࣑ࣥࢢ࡛฼⏝ࡍࡿ᭱ᑠ༢఩
ࡢࢩ࣒∦ࢆࠊ1/6 ௨ୗ࡜ࡍࡿᚲせࡀ࠶ࡿࡇ࡜ࡶゎࡗࡓࠋ

10㸫 34

5.

J-2/EDM ☢▼ࡢ☢ሙタィࡇࡇ࡛ࡣࠊ࣑࣮ࣗ࢜ࣥࡢ⼺᪕ධᑕ[6]࡜୧❧ࡍࡿ㧗࢚ࢿࣝࢠ࣮ຍ㏿ჾ◊✲ᶵᵓ(KEK)࡛ࡣ࣑࣮ࣗ
࢜ࣥ(Muon)ࡢ␗ᖖ☢Ẽ⬟⋡/㟁Ẽ⬟⋡(g-2/EDM)ࢆ
⢭ᗘⰋࡃィࡍࡿィ⏬ࡀ࠶ࡾࠊᐇ㦂‽ഛࢆ㐍ࡵ

࡚࠸ࡿࠋMuon ࡢ g-2/EDM ࢆࠊᚑ᮶࡟ẚ࡭࡚⢭ᗘࢆྥୖࡉࡏ࡚ィ☢ሙศᕸ࡛ࠊ࣑࣮ࣗ࢜ࣥ⵳✚㡿ᇦࡢᆒ୍☢ሙࢆ☜ ಖ ࡛ ࡁ ࡿ☢ ሙ タ ィ ࠾ࡼ ࡧ ☢ ሙ ࡢㄪ ᩚ ⿦ ⨨ ࠊMuon ධᑕ㛵㐃ࡢ☢ሙࢆ⤂௓ࡍࡿࠋ
5.1. ୺☢ሙࡍࡿ[5, 6, 45, 46]ࡓࡵ࡟ࠊᐇ㦂✵㛫࡛ࡣ MRI ࡟ẚ࡭⣙ 1 ᱆Ⰻ࠸(ᆒ୍ᗘࡀᑠࡉ࠸)୍ᵝ☢ሙࢆồࡵࡿࠋࡇࢀࡲ࡛ㄝ᫂ࡋ࡚ࡁࡓ TSVDࢆ౑ࡗࡓ᭱ᑠ஧஌ἲ࡛ࡣࠊ฼⏝ࡍࡿᅛ᭷࣮ࣔࢻ
ࢆቑຍࡉࡏࡿࡇ࡜࡛ࠊᴟࡵ࡚Ⰻዲ࡞ᆒ୍ᗘࢆᣢ
ࡘ୍ᵝ☢ሙࢆⓎ⏕ྍ⬟࡞㉳☢ຊ㓄⨨ࢆタィ࡛ࡁࡿ ࠋ ࡲ ࡓ ࠊ☢ ሙ ࢩ ࣑ ࣥࢢ ࡶ ᐇ ⾜ ࡛ࡁ ࡿ ࡿ ࡜ ⪃࠼ࠊタィࢆ㐍ࡵ࡚࠸ࡿࠋࡑࡢタィ࡟ᚲせ࡞⥺㍯

Fig. 5-1 ࡣࡇࡢᐇ㦂࡛౑⏝ࡍࡿ㉸㟁ᑟ☢▼ࡢィ⏬ᴫせࢆ᩿㠃ᅗ࡛♧ࡋࠊTable 5-1 ࡟ࡣࠊ௙ᵝࢆ᭩࠸ࡓࠋࡇࡢ☢▼ࡢୖഃ࠿ࡽࠊ㕲࣮ࣚࢡࢆ㈏㏻ࡋ
ࡓ ධ ᑕ ⏝ ࡢ✰ ࠿ ࡽ ࣑ ࣮ࣗ ࢜ ࣥ ࣅ ࣮࣒ ࢆ ධ ᑕ ࡍࡿࠋࡇࡢ☢▼ࡣ㺂㉸ఏᑟࢥ࢖ࣝ࡟ࡼࡾ☢▼୰ᚰ㠃௜㏆࡛ࡣ 3. 0T ࡢ୍ᵝ☢ሙࢆⓎ⏕ࡍࡿࠋࡑࡢ୍ᵝ☢ሙ୰࡟ Muon ࢆ࿘ᅇࡉࡏ⵳✚ࡍࡿࠋ㟁ὶࡸ෇ᙧ CB ࡢ☢ሙ࡟ࡘ࠸࡚ࡶࠊ๓❶ࡲ࡛࡟ࠊ༑ศ࡞⢭ᗘࢆᣢࡘࡇ࡜ࢆㄝ᫂ࡋࡓࠋ
ࡇࡢࡼ࠺࡞⪃࠼࡜ࡇࢀࡲ࡛ㄝ᫂ࡋ࡚ࡁࡓ☢ሙタィᡭἲࢆ౑ࡗ࡚ࠊg-2/EDM ᐇ㦂࡛౑⏝ࡍࡿ㉸㟁ᑟ☢▼ࡢ㉳☢ຊ㓄⨨࣭☢ሙタィࢆ㐍ࡵ࡚࠸ࡿࠋ

Fig. 5-2 ࣑࣮ࣗ࢜ࣥࣅ࣮࣒ࡽࡏࢇධᑕࡢ㌶㐨ᴫᛕࠋᩥ⊩[6], Fig.1 ࡼࡾᘬ⏝ࠋ
ධᑕ㌶㐨ࡢᴫᛕࢆ Fig. 5-2 ࡟♧ࡋࡓࠋୖ㒊࠿ࡽධᑕࡋࡓ Muon ࡣࠊ☢ሙ୰࡛࿘ᅇࡋ࡞ࡀࡽ㍈᪉ྥ࡟⛣ືࡍࡿࡀࠊ☢▼ࡢ୰ኸỈᖹ㠃௨እ࡛ࡣ☢ሙࡢ BR ᡂศࡀᏑᅾࡋࠊࡇࡢ☢ሙ࠿ࡽཷࡅࡿ㍈᪉ྥຊ࡛ᚎࠎ࡟ Z ᪉ྥ㏿ᗘࢆῶ㏿ࡍࡿࠋࡑࡋ࡚ࠊ୰ᚰ
Fig. 5-1 ࣑࣮ࣗ࢜ࣥ⵳✚☢▼ࡢィ⏬᩿㠃ᅗࠋ㠃ࡢ Muon ⵳✚㡿ᇦ࡟฿㐩ࡋࡓࢱ࢖࣑ࣥࢢ࡛ࠊBR
ࣃࣝࢫ☢ሙ࡟ࡼࡾ Muon ㍈᪉ྥ⛣ືࢆṆࡵ࡚ࠊ⵳✚ࡍࡿࠋMuon ࢆ୍ᵝ☢ሙ୰࡟⵳✚ࡍࡿࡇ࡜ࡀ୺

Table 5-1 Muon ⵳✚☢▼(MSM)ࡢ௙ᵝ
Parameters
Magnetic field strength
Homogeneity (BZ)
Area with Homogeneous
magnetic fieldn-index of weak focus field
Radial magnetic fieldcomponent BR
Current drive

Values
3.0 T< 1.0 ppm (0.2 ppm 2D)
R: 0.318 m to 0.348m
Z: -0.05 m to +0.05 m
0.0 to 3.0E-4
BR > -1.0E-4 Tࡓ ࡿ ᙺ ┠ ࡛࠶ ࡿ ࡜ ゝ ࠺ࡇ ࡜ ࠿ ࡽ ࠊࡇ ࡢ ☢ ▼ ࢆ
MSM(Muon Storage Magnet)࡜௨ୗ࡛ࡣ࿧ࡪࠋ
ࡇࡢ MSM ࡟ࡣࠊᆒ୍☢ሙࡀ㔜せ࡛࠶ࡿ MRI ☢
▼࡜ඹ㏻࡞≉ᚩࡀ᭷ࡿࡢ࡛ࠊMRI ☢▼ࡢ☢ሙタィ࡛ㄝ᫂ࡋࡓ୕ࡘࡢ Step ࢆ౑ࡗ࡚タィࡍࡿ[7,10]ࠋ

Persistent mode10㸫 355.1.1. Step-1
᭱ึ࡟ࠊ࡝ࡇ࡟㉳☢ຊ(㟁ὶࠊ☢ᛶయ)ࢆ㓄⨨ࡍ
࡭ࡁ࠿?ࢆᢕᥱࡍࡿࡓࡵ࡟ࠊ⥺㍯㟁ὶࢆከᩘ㓄⨨ࡋ᳨࡚ウࡍࡿ(Fig. 4-1, Step-1 ࡜ྠᵝ)ࠋStep-1 㛤ጞ᫬࡛Ỵࡲࡗ࡚࠸ࡿࡇ࡜ࡣୗグࡢ 3 㡯┠࡛࠶ࡿࠋ(i) ᚑ᮶௨ୖࡢィ⢭ᗘࢆᚓࡿࡓࡵࠊⰋዲ࡞☢

ሙᆒ୍ᗘࡀᚲせ࡛ࠊ୰ᚰ༙ᚄ 33.3cm ࡛ᖜ
3.0cm, ㍈᪉ྥ㧗ࡉ 10.0cm ࡢ෇⟄㡿ᇦ(࣑࣮ࣗ࢜ࣥ⵳✚㡿ᇦ)࡛㍈᪉ྥ☢ሙ BZ=3.0T±0.1ppm(ᆒ୍ᗘ 0.2ppm)ࡢ⠊ᅖ࡛࠶ࡿࠋ
(ii) ධᑕ㡿ᇦ࡛ࡣ㍈᪉ྥ⛣ື㏿ᗘࢆᙅࡵࡿࡼ࠺

ᅗ 5-3(a) Muon ⵳✚☢▼ࡢᴫᛕ᳨ウ 1
ᩥ⊩[7], Fig.2 ࡜ Fig.4 ࡼࡾᘬ⏝࡟ࠊBR>0 ࡀᚲせ࡛࠶ࡿࠋ(iii) ㉸ఏᑟ☢▼࡛࠶ࡾࠊMRI ☢▼ᢏ⾡ࢆᛂ⏝ࡍࡿࠋỌஂ㟁ὶ࣮ࣔࢻ࡛㐠㌿ࡋࠊNbTi ㉸ఏᑟ⥺ࢆ⏝࠸ࠊᑟయࡢ᭱㧗☢ሙࢆ 5.5T ௨ୗ࡛ࠊ125A/mm2 ⛬ᗘ࡜ࡍࡿࠋ
ୖグࡢ᮲௳ࢆ‶ࡓࡍ㉳☢ຊ㓄⨨ᴫᛕࢆ᥈⣴ࡍࡿ
ࡓࡵ࡟ࠊMRI ☢▼タィ࡜ྠᵝࡢࢫࢸࢵࣉ㸦Fig. 41 ཧ↷㸧ࢆ⤒࡚ࠊ☢▼ࡢ㉳☢ຊ㓄⨨ᴫᛕࢆỴࡵࡿࠋMRI ࡛ࡣᆒ୍☢ሙࡢ௙ᵝࡀ㔜せ࡛࠶ࡗࡓࡀࠊࡇࡇ࡛ࡣࠊࡉࡽ࡟(ii)ࡢ BR ௙ᵝࢆ᳨ウࡍࡿᚲせࡀ࠶ࡿࠋ(iii)ࡣࠊMRI ☢▼ᵝࡢ㉸㟁ᑟ☢▼ࡢᑟ
య௙ᵝ࡜ࡋ࡚⪃࠼ࡓ㡯┠࡛࠶ࡿࠋ
Step-1 ࡛ࡣヨ⾜㘒ㄗ᳨࡛ウࡏࡊࡿࢆᚓ࡞࠸ࠋ

Fig. 5-3(b) Muon ⵳✚☢▼ࡢᴫᛕ᳨ウ 2ࠋ
ᩥ⊩[7], Fig.2 ࡜ Fig.4 ࡼࡾᘬ⏝✀ࠎࡢ㉳☢ຊ㓄⨨఩⨨ࡢೃ⿵ࢆ࠸ࡃࡘࡶヨࡍࡇ࡜࡟࡞ࡿࠋᐇ㦂⿦⨨ᮏయ(ࣅ࣮࣒㌶㐨ࢲࢡࢺࠊ⵳
✚ᐜჾࠊ᳨ฟჾࠊ➼)ࢆ⪃៖ࡍࡿ࡜ࠊMuon ㌶㐨࣭⵳✚㡿ᇦ࠿ࡽࡣࠊ㞳ࢀ࡚㓄⨨ࡍࡿᚲせࡀ࠶ࡿࠋ୍᪉ࠊ࠶ࡲࡾ࡟㞳ࢀࡿ࡜ࠊ☢ሙศᕸࡢㄪᩚࡀ㞴ࡋࡃࠊᮏ㡯ࡢ᭱ึ࡟᭩࠸ࡓ 3 㡯┠ࡢ᮲௳ࢆ‶ࡓࡏ࡞ࡃ࡞ࡿ࡜ඹ࡟ࠊᚲせ௨ୖࡢ☢▼〇సࢥࢫࢺࡢ
ቑ኱࡟࡞ࡿࠋࡇࡢ⫼ᬒ࡛ࠊከᩘࡢ㉳☢ຊ㓄⨨᱌ࢆ᳨ウࡋࡓࡀࠊMRI ☢▼ࡢ☢ሙタィ࡟㛵㐃ࡋ࡚
㛤Ⓨࡋࡓᡭἲࡢ Step-1 ࡣ᭷ຊ࡞ᡭἲ࡛࠶ࡗࡓࡇ࡜
ࡣᙉㄪࡍࡿࠋ
ヨ⾜㘒ㄗࡋࡓ୰࡛ࠊ௦⾲ⓗ࡞ 2 ࡘࡢ᱌ࢆ⤂௓ࡍ
ࡿࠋFig. 5-3(a)࡜ Fig. 5-3(b)࡛࠶ࡿࠋMSM ࡢ Step1 ࡢᴫᛕ᳨ウࢆ⾜ࡗࡓ⥺㍯㟁ὶ(FL: Filament Loop)ࢆ♧ࡍࠋFig.5-3(a)࡛ࡣࠊ෇⟄≧࡟⥺㍯㟁ὶࢆ㓄⨨ࡋ࡚࠸ࡿࠋ୍᪉ࠊFig. 5-3(b)࡛ࡣࠊᆒ୍☢ሙ㡿ᇦࢆྲྀࡾᅖࡴࡼ࠺࡟⥺㍯㟁ὶࢆ㓄⨨ࡋ࡚࠸ࡿࠋ

㛗᪉ᙧࡀ Muon ⵳✚㡿ᇦ࡛࠶ࡿࡀࠊࡑࢀࢆྲྀࡾᅖ
ࡴࡸࡸ኱ࡁ࡞ᴃ෇ࡢ⾲㠃࡟ MFEPs ࢆ⨨࠸࡚࠸ࡿࠋ㧗ḟᡂศࢆᢕᥱࡋ᫆ࡃࡍࡿࡓࡵ࡛࠶ࡿࠋ
Fig. 5-3(c)࡟ࡣࠊᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕ MT ࢆỴࡵࡿࡓࡵࡢࠊᘧ(2-13㹼15)ࢆ฼⏝ࡋࠊᆒ୍ᗘ࡜
MT(ᐇᩘ࡛࠶ࡿ)ࡢ㛵ಀࢆ♧ࡋࡓࠋFig. 5-3(c)࠿ࡽ
ࡣࠊ(a)ࠊ(b)ࡢ࡝ࡕࡽ࡛ࡶᆒ୍ᗘࡣᐇ⌧࡛ࡁࡿ࡜᥎ᐃ࡛ࡁࡿࠋ(a)࡛ࡣ MT=10.4(10 ␒┠ࡲ࡛ࡢ඲࡚
࡜ࠊ11 ␒┠ࡢ 40%ࢆ฼⏝)࡛ࠊ(b)࡛ࡣ MT=10.1(10␒┠ࡲ࡛ࡢ඲࡚࡜ࠊ11 ␒┠ࡢ 10%ࢆ฼⏝)࡛ࠊᆒ୍ᗘࡣ 0.2ppm ࢆୗᅇࡿࠋࡇࡢᅗ࡛ࠊ5Ѝ6, 7Ѝ8, 9
Ѝ10 ࡢ㒊ศ࡛ࠊᆒ୍ᗘࡀᨵၿࡋ࡚࡞࠸⌮⏤ࡣࠊഅᩘ␒┠ࡢᅛ᭷࣮ࣔࢻ࡛ࡣࠊZ=0 㠃࡟ᑐࡋ࡚ࠊ཯
ᑐ⛠࡞㟁ὶ࣭☢ሙศᕸ࡛࠶ࡾࠊ฼⏝࡛ࡁ࡞࠸ࡓ
ࡵ࡛࠶ࡿࠋ

10㸫 36

࣮ࣔࢻࡢᚲせᙉᗘࡶᙅࡃ࡞ࡗ࡚࠾ࡾࠊẚ㍑ⓗ࡟Ⰻタᐃ࡞ၥ㢟࡜࡞ࡗ࡚࠸ࡿ{Fig. 5-3(b)ࡢሙྜ}ࠋ
☢ሙศᕸ࡟ᙳ㡪ࡀ኱ࡁ࡞఩⨨ࡣࠊ┤✚㡿ᇦࡢ༙ᚄ኱ഃࡢ఩⨨࡜ࠊ༙ᚄ᭱ᑠࡢ఩⨨ࡢୖୗ㒊࡜ゎࡿࠋࡲࡓࠊMODE11 ࡣ 10%ࡢࡳࠊ཯ᫎࡉࢀࡿࡢ
࡛ࠊከࡃࡣ୍ᵝ☢ሙ࡟ᑐࡋ࡚ṧᕪ☢ሙ࡜ࡋ࡚ṧࡿࠋࡇࡢࡓࡵࠊMODE11 ࡢ☢ሙᙉᗘศᕸࡀࠊồࡵࡿ☢▼ࡢṧᕪ☢ሙ࡜ࡋ࡚ṧࡿࠋࡇࢀࡽࡢᅛ᭷
࣮ࣔࢻ࡛ࡣࠊồࡵࡿ☢ሙࡢᵓᡂ࡟ᚲせ࡞➢ྕࡣFig. 5-3(c) ᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕࡢ᳨ウࠋᑐ㇟᮲௳࠿ࡽወᩘ␒┠ᅛ᭷࣮ࣔࢻࡢࡳ౑⏝ࠋᩥ⊩[7],Fig.5(a)ࡼࡾᘬ⏝⪃ ៖ ࡉ ࢀ ࡚࡞ ࠸ ࠋ ࡇ ࡢࡓ ࡵ ࠊ ᐇ 㝿ࡢ ṧ ᕪ ☢ ሙࡣࠊMODE11 ࡢᡴⅬ㡿ᇦ(☢ሙࡀ㧗࠸㡿ᇦ)࡜㠀ᡴ

Fig. 5-3(c)ࡢ᳨ウ࠿ࡽᘧ(2-11)࡛㟁ὶศᕸ(ࡓࡔࡋࠊMT ࡣᐇᩘ࡜ࡋ࡚ 10.4 ࠾ࡼࡧ 10.1 ࡜ࡋ࡚)ࢆồࡵࠊ☢ሙศᕸࢆィ⟬ࡋࡓ⤖ᯝࡣࠊྛᅗࡢྑഃ࡟
♧ࡍࠋୖୗ࡟㉮ࡗ࡚࠸ࡿ⥺ࡣ➼☢᮰⥺(☢ຊ⥺࡛ࡶ࠶ࡿ)࡛࠶ࡾࠊ┤✚㡿ᇦ࠿ࡽᨺᑕ≧ࡢᶍᵝ࡟࡞ࡗ࡚࠸ࡿ⥺ࡣ☢ሙᙉᗘ➼㧗⥺࡛࠶ࡿࠋ3.0T ࡟ᑐࡋ୍࡚᱆ẖ(±0.1, 1.0, 10.0)࡟ࣉࣟࢵࢺࡋ࡚࠸ࡿࠋ
๓❶ࡢ MRI ☢▼☢ሙタィ࡜ྠᵝ࡟ᡴⅬ࡛♧ࡋࡓ☢ሙࡀ㧗࠸㡿ᇦ(B > 3.0 T)࡛࠶ࡾࠊ㉳☢ຊ※(CBs)࠿ࡽᆒ୍☢ሙ㡿ᇦ࡟ఙࡧࡿࠋཧ ⪃ ࡟ ࠊFig. 5-3(d)࡟ ࠊFig. 5-3(b)ࡢ 㓄 ⨨ ࡟ ࡼࡿࠊ11 ␒┠ࡲ࡛ࡢወᩘ␒(Z=0 㠃࡟ᑐࡋ࡚ᑐ⛠)ᅛ᭷࣮ࣔࢻࢆ♧ࡍࠋ࿘ᅖࢆᅖࡴ▮༳ࡀ㟁ὶศᕸ(༙ᚄ኱᪉ྥࡀṇ)ࢆ♧ࡋࠋ⵳✚㡿ᇦ࿘ᅖ࡟ࡣ☢ຊ⥺㸦➼☢᮰⥺㸧ࢆ♧ࡋࡓࠋMRI ☢▼ࡢሙྜ࡜ྠᵝ࡟ࠊ㧗ḟᡂศ࡯࡝≉␗್ࡣᑠࡉࡃ࡞ࡿࡀࠊᅛ᭷

Ⅼ㡿ᇦࡀ㏫࡜࡞ࡗ࡚ࡃࡿࠋ
ࡇࡢ 2 ࡘࡢೃ⿵࡛ࡣࠊタィ᮲௳ࡢ㡯┠(ii)࡛ࠊ
Muon ධᑕ㌶㐨ୖࡢ BR>0 ࡀ㔜せ࡜࡞ࡿࠋFig. 53(c)࡟ࡣࠊ㌶㐨ୖࡢ BR ࡢ᭱ᑠ್ࡶ♧ࡋࡓࠋFig. 53(a)ࡢሙྜ࡟ࡣࠊBR<0 ࡀ㌶㐨ୖ࡟Ꮡᅾࡍࡿ஦ࢆ♧ࡋ࡚࠾ࡾࠊ౑⏝࡛ࡁ࡞࠸㉳☢ຊ㓄⨨࡛࠶ࡿ࡜⌮ゎ࡛ࡁࡿࠋࡑࡢ⌮⏤࡟ࡘ࠸࡚ㄝ᫂ࡍࡿࠋ㟁 ὶ ࡢ ↓ ࠸ 㡿 ᇦ ࡛ ࡣ ࠊrot%=0 ࡼ ࡾ ࠊdBZ/dR=dBR/dZ ࡛࠶ࡿࠋdBZ/dR>0 ࡛࠶ࢀࡤࠊdBR/dZ>0 ࡶᚓࡽࢀࠊୖୗᑐ⛠࡛࠶ࡿࡓࡵࠊ㉥㐨㠃࡛ BR=0 ࡛࠶ࡿࡓࡵࠊ㡯┠(ii)ࡀồࡵࡿ BR>0 ࡢ☢ሙࡀᚓࡽࢀ
ࡿࠋ2 ࡘࡢᅗ{Fig. 5-3(a), Fig.5-3(b)}࡛ࠊR=0.333m
ࢆ Muon ࡢධᑕ㌶㐨࡟㏆࠸࡜⪃࠼ࡿ࡜ࠊࡇࡢ⥺ࡢ఩⨨ࡼࡾ༙ᚄࡀ኱ࡁ࡞࡜ࡇࢁ࡟☢ሙࡢ㧗࠸㡿ᇦࡀᚲせ࡛࠶ࡿࠋࡇࡢព࿡࡛ࠊᡴⅬ㡿ᇦࡀࠊ
R=0.333m ࡼࡾ኱ࡁ࡞఩⨨࡟ᚲせ࡛࠶ࡿࠋFig. 5-3(d) MSM ࡢᴫᛕタィ࡟⏝࠸ࡓ SVD ᅛ᭷࣮ࣔࢻࠋྛࣇ࣮࣒࡛ࣞࠊ୰ᚰ㒊ࡢ➼㧗⥺ࡣ➼☢᮰⥺(☢ຊ⥺)ࠊ࿘㎶ࡢ▮༳ࡣ⥺㍯㟁ὶࡢ㟁ὶศᕸ(༙ᚄ኱ഃࡀṇ㟁ὶ)ࠊ᭱ୖ㒊࡟ MODE ␒ྕࠊ3 ಶࡢᐇᩘࡣୖ࠿ࡽࠊ≉␗್ࠊ3.0T ᐇ⌧ࡢࡓࡵࡢ࣮ࣔࢻᙉᗘࠊศᕸࡢ peak-to-peak ್ࠋഅᩘ␒ᅛ᭷࣮ࣔࢻࡣ
཯ᑐ⛠࡛࠶ࡾ୙౑⏝ࠋᩥ⊩[7]Fig.5(b)ࡼࡾᘬ⏝10㸫 37

5.1.2.

ࡇࡢ᮲௳࡛⪃࠼ࡿ࡜ࠊFig. 5-3(a)࡛ࡣࠊZ<0.60m

Step-2 ࠾ࡼࡧ Step-3࡛ ༙ ᚄ ࡢ ᑠࡉ ࠸ ࡜ ࡇ ࢁ࡟ ☢ ሙ ࡢ 㧗࠸ 㡿 ᇦ ࡀ ࠶

SVD ᅛ᭷࣮ࣔࢻศᕸᙉᗘࡣࠊ㕲 yoke ࡸ CB ࢆࡾࠊdBZ/dR =dBR/dZ<0 ࡛࠶ࡾࠊ㡯┠(ii)ࡀ‶ࡓࡉ⏝࠸࡚タィࡍࡿ☢▼࡟࠾࠸࡚ࡶࠊ⥺㍯㟁ὶ࡛ồࢀ࡞࠸ࠋ୍᪉ࠊFig. 5-3(b)࡛ࡣࠊ☢ሙࡢ㧗࠸㡿ᇦࡵࡓ Step-1 ࡢᅛ᭷࣮ࣔࢻ࡛ࡑࡢᙉᗘ{ᘧ(2-12)㸸Pk

ࡀ඲㡿ᇦ(Z = 0.0㹼1.1 m)࡛ࠊR=0.333m ࡼࡾ༙ᚄࡢ

= Xkt%TG/np}ࢆồࡵࠊStep-2, Step-3 ࡛ࡶᅛ᭷࣮ࣔࢻ

኱ࡁ࡞఩⨨࡟࠶ࡾࠊdBZ/dR =dBR/dZ>0 ࡜࡞ࡿࠋᙉᗘࡀ෌⌧ࡉࢀࡿࡼ࠺࡟㉳☢ຊ(CB ཬࡧ㕲 yoke)

BR>0 ࢆྍ⬟࡜ࡋ࡚࠸ࡿࠋ

ࢆ㓄⨨ࡍࡿࠋࡇࢀࡣ MRI ⏝☢▼࡜ྠࡌ⪃࠼᪉࡛௨ୖࢆࡲ࡜ࡵࡿ࡜ࠊ෇⟄≧ࡢ⥺㍯㟁ὶ㓄⨨࠶ࡿࡀࠊࡇࡇ࡛ࡣࠊCB ఩⨨ᙧ≧ࡔࡅ࡛࡞ࡃࠊ㕲{Fig. 5-3(a)}࡛ࡣࠊMuon ධᑕ㌶㐨ࡢ඲㡿ᇦ࡛ BR>0yoke ࡢᙧ≧ࡶㄪᩚࡍࡿࠋࡋ࠿ࡋࠊࡇࡢ 2 ࡘࡢ Step࡜ࡍࡿ᮲௳(ii)ࢆᐇ⌧࡛ࡁ࡞࠸ࠋࡋ࠿ࡋࠊFig. 5-

࡛ࡣࠊ᳨ウࡣ┤⥺ⓗ࡛ࠊヨ⾜㘒ㄗࡣ↓࠸ࠋࡘࡲ3(b)ࡢࡼ࠺࡟⥺㍯㟁ὶࡀ⵳✚㡿ᇦࢆྲྀࡾᅖࡴࡼ࠺

ࡾࠊศᕸ㟁ὶࡢ Step-1 ⤖ᯝࢆࠊ㞳ᩓ㓄⨨ࡢ CB ࡜࡟㓄⨨ࡋ࡚࠾ࡃ࡜᮲௳(ii)ࢆᐇ⌧࡛ࡁࡿࠋ༙ᚄᑠ

㕲 yoke ࡟⨨ࡁ᥮࠼ࠊ㓄⨨ࡢᚤㄪᩚ࡛ࠊSVD ᅛ᭷ഃ࠿ࡽ⵳✚㡿ᇦ࡟ྥ࠿ࡗ࡚ࠊỈᖹ㠃௜㏆࡛☢ሙ࣮ࣔࢻᙉᗘࢆㄪᩚࡍࡿࡢࡳ࡛࠶ࡿࠋ

ࡢ㧗࠸㡿ᇦࢆⓎ⏕ࡍࡿࠋࡇࢀ࡟ࡼࡾࠊBR<0 ࢆస

Fig. 5-5 ࡣ Step-2 ࡢ᭱ึ࡟ィ⏬ࡋࡓ 2D(༙ᚄ R,

ࡗ࡚࠸ࡓ☢ሙࡢ㧗࠸㒊ศࡀࠊR=0.333m ࡢ㏆ഐ࠿㍈᪉ྥ఩⨨ Z)㉳☢ຊ㓄⨨࡛࠶ࡿࠋ▮༳ࡣࠊṧᕪࡽࡣ↓ࡃ࡞ࡿࡓࡵ࡛࠶ࡿࠋ

ࡢ㟁ὶศᕸ࡛࠶ࡾࠊࡇࡢṧᕪ㟁ὶࡣᅛ᭷࣮ࣔࢻ

Step-1 ࡛ࡣࠊࡇࡢࡼ࠺࡞᳨ウࡋ࡚ Fig. 5-3(b)ࡢ

ᙉᗘࡢㄪᩚࢆ⤊஢ࡋࡓẁ㝵࡛ࡣ㞽࡟㏆࡙ࡃࠋࡇ☢ሙศᕸ࡜㉳☢ຊ(⥺㍯㟁ὶ)㓄⨨ࢆᴫᛕタィ⤖ᯝࡢẁ㝵ࡢ⪃࠼᪉ࡣ MRI ☢▼ࡢ Step-2, Step-3 ࡜ྠ࡜ࡋࡓࠋ⵳✚㡿ᇦ௜㏆ࡢ☢ሙᙉᗘศᕸࢆ Fig. 5-4

ࡌ࡛࠶ࡿࠋFig. 5-6 ࡟ࡣ⧞ࡾ㏉ࡋィ⟬୰ࡢ཰᮰≧࡟♧ࡋࡓࠋ☢ሙᙉᗘ➼㧗⥺ࡣ 0.1, 1.0, 10.0 ppm ࡛ἣࢆ♧ࡋࡓࠋ2 ࡘࡢࢫࢸࢵࣉࢆྜࢃࡏ࡚ 7 ᅇࡢィ࠶ ࡿ ࡀ ࠊ ⵳✚ 㡿 ᇦ ࡟ ࡣධ ࡗ ࡚ ↓ ࡃࠊ ᆒ ୍ ᗘ ࡀ⟬࡛཰᮰ࡋࡓࠋ

0.2ppm ௨ୗ࡛࠶ࡿࠋ⥺㍯㟁ὶࡢ୍㒊ࡣࠊ㕲 yokeᚓࡽࢀࡓ㉳☢ຊ㓄⨨࡜☢ሙศᕸࡀ Fig.5-7 ࡛࠶ࡢ㓄⨨ࢆ᝿ᐃࡋ࡚࠸ࡿࠋStep-2 ௨㝆࡛ࡇࡢ☢ሙࢆࡿࠋᆒ୍ᗘࡣ peak-to-peak ್࡛ 0.13ppm(ྑୗᅗ)࡛

෌⌧ࡍࡿ㉳☢ຊ㓄⨨(㕲 yoke ࡜ CBs)ࢆồࡵࡿࠋ࠶ࡿࠋධᑕ㡿ᇦ࡟ BR<0 ࡣ↓࠸(ྑୖ)ࠋࡇࢀࡽ

Fig. 5-4 ⵳✚㡿ᇦ௜㏆ࡢ☢ሙᙉᗘศᕸࢆ 3.0T
±0.1㺂1.0, 10. 0ppm ࡢ➼㧗⥺࡛♧ࡍࠋᡴⅬ㡿ᇦࡣ☢ሙࡢ㧗࠸㒊ศࠋᩥ⊩[7], Fig. 6 ࢆᘬ⏝ࠋ

ᅗ 5-5 Step-2 ࡢึᮇ㓄⨨.
ᩥ⊩[7], Fig.7 ࡼࡾᘬ⏝.

10㸫 38

5.1.3.

Strengths of 9-th eigenmode
P9IR, P9CB, P9MG (T)Homogeneities
hR5x10, hS7x25 (ppm)

Iron pole change

rCB ĺ

iCB

ᐇ㝿ࡢ㕲 yoke ࡟ࡣࠊMuon ㏻㐣⏝ࠊࢩ࣒ࢺࣞ࢖

100ྲྀࡾฟࡋ⏝ࠊࡑࢀ࡟ࠊ෭෾ᶵ࡜ࡢ㛫࡟ᾮయ He ㍺

hS7x2510hR㕲 yoke ☢ሙ(3D)ࡢᢅ࠸

㏦ࣃ࢖ࣉ⏝ࠊ࡞࡝࡟ከࡃࡢ✰ࡀ㛤ࡃࠋࡇࢀࡽࡢ

5x10

1

✰ࡣᑐ⛠ᛶࢆ⪃࠼ࠊ඲࡚㺂☢▼㍈࿘ࡾ࡛ 4 ᅇᑐ⛠

0.1
1.2E-05 0

1

2

3

4

5

6

ࡢ㓄⨨࡜ࡋ࡚࠸ࡿࠋࡋ࠿ࡋࠊ☢ሙศᕸࡣ࿘ᅇ᪉

7

P9CB

8.0E-06ྥ࡟ࡶἼᡴࡘ 3D ☢ሙศᕸ࡛࠶ࡿࡀࠊ3D ☢ሙ࡛

P9MG

4.0E-06

ࡣࠊCB 㓄⨨ࢆㄪᩚฟ᮶࡞࠸ࠋࡇࡢࡓࡵࠊḟࡢᡭ

0.0E+00㡰࡛㕲 yoke ࢆྵࡵࡓ 3D ☢ሙࢆ 2D ໬ࡋ࡚ࠊ㉳☢

P9IR,-4.0E-06-8.0E-06
0

1

2

3

4

5

6

7

ຊ㓄⨨ࡢ᭱㐺໬ࢆ⾜ࡗ࡚࠸ࡿࠋ

Iterative step(1) 㕲 yoke ᙧ≧䛸 CB 㓄⨨䜢௬ᐃ䚹

Fig. 5-6 ⧞ࡾ㏉ࡋィ⟬(Step-2 & -3)ࡢ཰᮰≧ἣ.
ᩥ⊩[7], Fig.10 ࡼࡾᘬ⏝(2) 㠀⥺ᙧ 3D ☢ሙィ⟬䝁䞊䝗䛷☢ሙィ⟬䚹ࡣࠊ௙ᵝ᮲௳ࢆ‶ࡓࡋࠊᑟయ⤒㦂☢ሙ(5.0T)࡜㟁ὶᐦᗘࢆ NbTi ⥺ᮦ࡛ᐇ⌧ྍ⬟࡞㉸ఏᑟ☢▼࡛࠶ࡿࡇ࡜ࢆ☜ㄆ࡛ࡁࡓࠋ㕲 yoke ࡟ࡣ୰ᚰ㒊࡟ୖୗᑐ⛠࡞ pole(㕲)ࢆ㓄⨨ࡋࠊ5 ಶࡢ CBs ࡜࡜ࡶ࡟ࠊ
ᆒ୍☢ሙ㡿ᇦ࡜ࡑࡢ࿘㎶㒊ࡀ Step-1(Fig. 5-4)࡛ィ⏬ࡋࡓ☢ሙศᕸ࡜ྠᵝ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀࢃ࠿
ࡿࠋࡇࢀࡣࠊᘧ(2-12)ࡢᅛ᭷࣮ࣔࢻᙉᗘࢆྠ୍࡟

(3) ☢ሙศᕸ䜢࿘ᅇ᪉ྥ䛻ᖹᆒ໬䛧䛶 2D ☢ሙࠋ(4) 2D ☢ሙ䛾ᆒ୍ᗘ䜢☜ㄆ䚸Ⰻዲ䛺䜙⤊஢䚹(5) CB ☢ሙ %CB 䜢ィ⟬(2D ☢ሙ)䚹(6) 㕲 yoke ☢ሙ(2D)%IR 䜢(5)䛸(4)䛾ᕪ␗䛷⟬ฟ䚹(7) %CB+%IR 䛜 2D ୍ᵝ☢ሙ䛸䛺䜛 CB 㓄⨨䛻ㄪᩚ(8) ㄪᩚ CB 㓄⨨䛷 3D 㠀⥺ᙧሙィ⟬(9) CB 㓄⨨ྍ⬟ᛶ䜢☜ㄆĺ 3)or(1)䜈ᡠࠋ
ࡇࡇ࡛ࠊ(9)࡛ࡣࠊᑟయࡢ⤒㦂☢ሙࡸ඲యࡢ኱ࡁ

ࡋ࡚࠸ࡿࡓࡵ࡛࠶ࡿࠋ
⏝☢▼ࡢᐇ⌧ᛶࡉࢆࢳ࢙ࢵ ࢡࡍࡿࠋጇ ᙜ࡛↓ࡅࢀ ࡤࠊ෌ᗘ(1)ࡀ☜ㄆ࡛ࡁࡓࠋࡇࢀࢆཷࡅ࡚ࠊヲ⣽タィࡀ㐍ࡵ࡟ᡠࡾࠊ㓄⨨ࢆ෌⪃ࡍࡿࠋࡲࡓࠊCB 㓄⨨ୖ࡟ၥࡽࢀ࡚࠸ࡿࠋᐇᶵ࡛ᆒ୍☢ሙࢆᚓࡿࡓࡵ࡟㔜せ㢟ࡀ↓ࡅࢀࡤࠊ(3)࡟ᡠࡾࠊ(4)࡛ᆒ୍ᗘࢆㄪ࡭ࠊ

࡞ࢩ࣑ࣥࢢ࡟ࡣࠊMRI ☢▼⏝࡟ TSVD 㛤Ⓨࡋࡓ┠ᶆ࡟฿㐩ࡋ࡚↓ࡅࢀࡤࠊ⧞ࡾ㏉ࡋィ⟬ࢆ⥆ࡅ

TSVD ᛂ⏝ࡢࢩ࣑ࣥࢢィ⟬ᡭἲ(4.6 ⠇࡟グ㏙)ࢆ฼

ࡿ ࠋ(7)࡛ ࡣ ࠊ ᘧ(4-7)ࡢ ᵝ ࡟ ᅛ ᭷ ࣔ ࣮ ࢻ ᙉ ᗘ ࢆ⏝ࡍࡿணᐃ࡛࠶ࡿࠋ

Step-1 ࡛Ỵࡵࡓ್࡟ࠊᩘᅇࡢ⧞ࡾ㏉ࡋィ⟬{(7)ࡣ௨ୖࡢᵝ࡟ g-2/EDM ヲ⣽ィ㕲 yoke ࡢ↓࠸ MRI ☢▼ࡢ Step-2, Step-3 ࡜ྠ୍ィ⟬ἲ}࡛ࠊㄪᩚࡍࡿࠋࡍ࡛࡟ Step-1 ࡛☢ሙࡢᴫᛕタィࡣ⤊஢ࡋ࡚࠸ࡿࡢ࡛ࠊ(3)-(9)ࡢ⧞ࡾ㏉ࡋィ⟬ࢆ⥆ࡅࡿ࡜ࠊ┠ᶆࡢᆒ୍ᗘ(Step-1 ࡢᆒ୍ᗘ)࡟ᚲ
ࡎ㐩ࡍࡿࠋ
5.1.4. ☢ሙタィࡢ Update
Fig. 5-8 ࡣ⌧≧࡛⪃࠼࡚࠸ࡿ㕲 yoke ࡢᙧ≧ࢆ
180 ᗘศ࡛♧ࡋࡓࠋMuon ධᑕ⏝ࠊᾮయ He ㍺㏦⟶⏝ࠊࡑࢀ࡟ࢩ࣒ࢺࣞ࢖ࡢฟࡋධࢀ⏝࡟㈏㏻Ꮝࡀ
㓄⨨ࡉࢀ࡚࠸ࡿࠋ඲࡚ࠊ4 ᅇᑐ⛠࡜࡞ࡿࡼ࠺࡟ࠊ
ᅗ 5-7 g-2/EDM ☢▼ࡢ㉳☢ຊ㓄⨨᱌.
ᩥ⊩[7], Fig.11 ࡼࡾᘬ⏝.

ᚲせ࡛࡞࠸㈏㏻Ꮝ(ణࡋࠊࢣ࣮ࣈࣝ㏻㐣࡞࡝࡟౑࠺౑࠺ࡇ࡜࡟࡞ࡿ࡜ண᝿)ࡶタࡅ࡚࠸ࡿࠋ

10㸫 39

Table 5-2 Electromagnetic parameters
Parameters

M20210727 M20160422(July 2021)
ᩥ⊩[7]
5
5
1.6060 MAT 1.594 MAT
5.0071 MAT 4.988 MAT
5.39 T
4.99 T
10.5 cm
12 cm
0.079 ppm
0.13 ppm
0.720 m0.720 m0.070 m (in), 0.148 m (out)Number of CBs
Max. AT of a CB
Total Ampere-turnMax. B on conductor
0.3 mT Ber Z-position
Homogeneity
Pole face Z position
Pole radius
SC conductor size
1.40x2.10mm 1.53x2.21mm(Cu ratio 2.5)
Conductor current
417.15 A
417.88 A
B due to Iron yoke
0.47569 T
0.47871 T

Fig. 5-8 Update ࡋࡓ㕲 yoke ᙧ≧. ᩥ⊩[47],Fig. 2 ࡼࡾᘬ⏝ࡋ࡚㟁ὶᐦᗘ(1.7MA/m)࡜࡞ࡗ࡚࠸ࡿࠋࡇࢀࡽࡢ

ࡇࡢ㕲 yoke ࡟ᑐࡋ࡚ࠊࡇࢀࡲ࡛ㄝ᫂ࡋࡓ᪉ἲ
࡛ồࡵࡓ㉳☢ຊ㓄⨨࡜ 2D ෌ᵓᡂ☢ሙ(㕲 yoke ࡟ࡇ࡜ࡣࠊ㕲 yoke ☢ሙࢆ 2D ࡛෌⌧ࡍࡿ⥺㍯㟁ὶࡀጇᙜ࡟ồࡵࡽࢀ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋࡼࡿ☢ሙ)ࢆ Fig. 5-9 ࡟♧ࡍࠋ㕲 yoke ࡢෆ㠃(⵳✚ࡇ ࠺ ࡋ ࡚ ồ ࡵ ࡓ CB ⩌ ࡢ 㟁 ☢ ࣃ ࣛ ࣓ ࣮ ࢱ㡿ᇦഃ)࡟⥺㍯㟁ὶࢆከᩘ㓄⨨ࡋࠊ㕲 yoke ࡢ 2D

(M20210727)ࢆ Table 5-2ࠊTable 5-3 ࡟♧ࡍࠋཧ⪃ᖹᆒ໬☢ሙࢆ෌⌧ࡋ࡚࠸ࡿࠋ㟁ὶࢆỴࡵࡿࡓࡵ࡟ Fig. 5-7[7](M20160422)ࡢࣃ࣓࣮ࣛࢱࡶ♧ࡋ࡚࡟ࠊᕥᅗࡢᐇ⥺࡛ᅖࡲࢀࡓ㡿ᇦࡢィ⟬☢ሙࢆࠊ࠸ࡿࠋ୧⪅ࡢᕪ␗ࡣࠊFig. 5-8 ࡛ࡣ㕲 yoke ࡟㛤ࡅ࿘ᅇ᪉ྥᖹᆒ໬ࡋࡓ☢ሙ࡜ࡋ࡚ࠊ⏝࠸ࡓࠋ

࡚࠸ࡿ㈏㏻Ꮝࡣ Muon ධᑕཱྀ(8 ᮏ)ࡢࡳ࡛࠶ࡿࡀࠊ

R=0.45m ௜㏆ࡢ㟁ὶ್ࡢᒁᡤⓗ࡞ኚືࡣࠊࡇࡢ

Update ࡋࡓ Fig. 5-9 ࡛ࡣࠊFig. 5-8 ࡢ,㈏㏻Ꮝࡀቑ

௜㏆ࡢ㈏㏻Ꮝ(ࢩ࣒ࢺࣞ࢖࡜ Muon ධᑕ⏝)࡟ࡼࡿຍࡋࡓ㕲 yoke ᙧ≧ࡀ཯ᫎࡉࢀ࡚࠸ࡿࠋࡇࡢᙳ㡪㕲 yoke ࡢ☢ሙ࡬ࡢᐤ୚ࡢపୗࢆ཯ᫎࡋ࡚࠸ࡿࠋ

࡛ࠊUpdate ࡋࡓ㉳☢ຊ㓄⨨(M20220727)࡛ࡣࠊ㉳ࡲࡓࠊ୰ᚰୖୗࡢ࣏࣮ࣝ㒊࡛ࡣ☢Ẽ㣬࿴ࢆ཯ᫎ☢ຊࡀࢃࡎ࠿࡟ቑຍࡋࡓࠋࡋ࠿ࡋࠊ኱ࡁ࡞ኚ᭦
ࡣ࡞࠸ࠋTable 5-2 ࡢ᭱ୗ⾜࡟㕲 yoke ࡀసࡿ☢ሙࢆ᭩࠸࡚࠸ࡿࡀࠊ3.0T ࡢ࠺ࡕࠊ⣙ 15.86㸣ࡢ☢ሙࢆ㕲 yoke ࡀసࡗ࡚࠸ࡿࠋ㕲 yoke ࡣ୰ᚰୖୗ㒊࡟෇⟄✺㉳ᙧ≧(࣏࣮ࣝ࡜࿧ࡪ)ࢆᣢࡕࠊ㕲 yoke ࡟ࡼࡿ☢ሙࢆ༙ᚄᑠഃ࡛☢ሙࡀᙉࡃࡋ࡚࠸ࡿࠋࡇࡢ
⤖ᯝࠊStep-1 ࡛ィ⏬ࡋࡓ⵳✚㡿ᇦࡢ༙ᚄᑠഃ࡛☢
Table 5-3 CB parameters (M20210727)
Coil
BlocksFig. 5-9 Update 㕲 yoke ᙧ≧ࢆ཯ᫎࡋࡓ㉳☢ຊ㓄⨨࡜☢ሙศᕸࠋᕥ㸸☢ຊ⥺࡜☢ሙᙉᗘศᕸ
(ᡴⅬ㡿ᇦࡣ☢ሙࡢ㧗࠸㒊ศ)ࠊྑ㸸㕲 yoke ࡢసࡿ☢ሙࡢ☢ຊ⥺ࠋ▮༳ࡣ㕲 yoke ☢ሙࢆ෌⌧ࡍࡿ⥺㍯㟁ὶ. ᩥ⊩[47], Fig. 3 ࡼࡾᘬ⏝Current(kAT)

Position
Widht (m)Radius R (m) R-Width
Axial Z (m) Z-Width

Turns
RxZ
-Lack

MC10,11 1606.027 0.8274361 0.05487120 36x10(2CBs)±0.6330839 0.23561400 7-2
MC20,21 651.588 0.8261195 0.05182280 34x46(2CBs)±0.2294832 0.10129200 -2
MC30
(1CB)

10㸫 40491.820 0.8154354
0.0

0.03048400 20x59
0.12991800 -1

ሙࢆᙉࡃࡋࠊBR>0 ࢆ Muon ධᑕ㌶㐨ୖ࡛ᐇ⌧࡛ࡁࡀࠊ࿘ᅇ᪉ྥࡢಶࠎࡢ఩⨨࡛ࡢ☢ሙࢆぢࡿ࡜×࡚࠸ࡿࠋࡢࡼ࠺࡟ࠊ±8 T ࡛ࠊ࿘ᅇ᪉ྥ࡟☢ሙ࡟ศᕸࡀ᭷

5.1.5.

ࡿࠋࡇࡢศᕸࡣࠊ±0.1ppm ࡼࡾ኱ࡁ࠸ࡀࠊタ⨨

2D ෌ᵓᡂ☢ሙ࡜࿘ᅇ᪉ྥ☢ሙኚືᚋ࡟☢ሙࢩ࣑ࣥࢢࡍࡿࡇ࡜࡛ࠊ┠ᶆࡢᆒ୍ᗘ࡟

Fig. 5-9 ࡢᕥᅗࡣࠊ2D ☢ሙ࡛࠶ࡾࠊ⥺㍯㟁ὶࡢㄪᩚฟ᮶ࡿࡇ࡜ࡣ☜ㄆࡋ࡚࠸ࡿࠋ

㞟ྜ࡛☢ሙศᕸࢆ⾲⌧ࡋ࡚࠸ࡿࠋ㠀⥺ᙧィ⟬ࢆ⾜ࢃ࡞࠸ࡢ࡛ࠊ2D ࡛࠶ࡿࡀࠊ☢ሙศᕸࢆ㧗㏿࡟⟬ฟ࡛ࡁࡿࠋࡇࡢ⌮⏤࡛ࠊMuon ධᑕ᮲௳ࠊ࢟ࢵ
࣮࢝☢▼ࡢ㓄⨨఩⨨ࡢ᭱㐺໬࡞࡝ࡢධᑕ᮲௳ࡢ
᥈⣴࡟฼⏝ࡋ࡚࠸ࡿࠋࡑࡢࡓࡵࠊ2D ☢ሙࡢ෌ᵓᡂ⢭ᗘࢆ☜ㄆࡋ࡚࠸ࡿࠋ
Fig. 5-10 ࡣࠊ2D ෌ᵓᡂ☢ሙ(Fig. 5-9 ᕥ)࡜ 3D 㠀⥺ᙧ☢ሙࢆẚ㍑ࡋ࡚࠸ࡿࠋᅗ࡛‫ ࡣۑ‬3D ィ⟬್ࢆ࿘ᅇ᪉ྥ࡟ᖹᆒࡋࡓ್࡛࠶ࡿࠋࡇࡢ☢ሙࢆ෌⌧ࡍࡿࡼ࠺࡟ 2D ෌ᵓᡂ☢ሙࡢࡓࡵࡢ⥺㍯㟁ὶศᕸࢆỴࡵ࡚࠸ࡿࠋࡑࡢ⤖ᯝࠊ‫ ࡜ۑ‬2D ෌ᵓᡂ☢ሙ(ᐇᅗ 5-11 ⵳✚㡿ᇦࡢ☢ሙศᕸࣜࢵࣉࣝࠋ

⥺)ࡣࠊBR, BZ ඹ࡟ࠊࡼࡃ୍⮴ࡋ࡚࠸ࡿࠋࡋ࠿ࡋࠊ

×ࡣ࿘ᅇ᪉ྥ 10 ẖ࡜ࡢ☢ሙᙉᗘࠋ2D ᖹᆒ☢ሙ‫࡜ۑ‬෌ᵓᡂ☢ሙ(ᐇ⥺)ࡣⰋࡃ୍⮴ࡍࡿࠋ

Z>0.95m ࡛ࡣ Muon ධᑕ⏝ࡢ㈏㏻Ꮝ࡞࡝ࡢᙳ㡪࡛ࠊ࿘ᅇ᪉ྥ࡟ࣜࢵࣉࣝࡀ኱ࡁ࠸ࠋࡇࡢ௜㏆࡛
ࡣࠊMuon ධᑕ㌶㐨ࡢィ⟬࡟ࡣࠊ3D 㠀⥺ᙧ☢ሙィ

5.2. ㄪᩚ⿦⨨⟬ࡼࡿ☢ሙࢹ࣮ࢱࡀᚲせ࡛࠶ࡿࠋ

g-2/EDM ヲ⣽ィ ࢆ⾜࠺㠀ᖖ࡟ᆒ୍࡞☢ሙࢆᐇ

Fig. 5-11 ࡣ⵳✚㡿ᇦ௜㏆ࡢ☢ሙࢆ♧ࡋࡓࠋ࿘ᅇ

⌧ࡍࡿࡓࡵ࡟ࠊ0.2ppm ࡼࡾⰋዲ࡞ᆒ୍ᗘࢆᐇ⌧᪉ྥᖹᆒࡢ 2D ☢ሙࡣࠊ±0.1ppm ࡟ධࡗ࡚࠸ࡿ

࡛ࡁࡿ㉳☢ຊ㓄⨨࡜ࡋ࡚࠸ࡿ[7, 47]ࠋ㉳☢ຊ㓄⨨ࢆࠊMRI ⏝☢▼ࡢタィ࡛㛤Ⓨࡋࡓ≉␗್ศゎᛂ⏝ࡢ☢ሙタィࢆᛂ⏝ࡋ࡚タィࡋ࡚࠸ࡿࠋࡲࡓࠊ
ࡇࡢ☢ሙ࡟ᑐࡋ࡚ࠊMuon ࡢධᑕ᮲௳ࢆ᳨ウࡋ࡚࠸ࡿ[6, 49, 50]ࠋࡋ࠿ࡋࠊMRI ☢▼࡟㛵㐃ࡋ࡚ㄝ᫂ࡋࡓᵝ࡟ࠊタ⨨☢▼࡟ࡣ✀ࠎࡢㄗᕪ☢ሙࡀΰධࡍࡿࠋࡑࡢ
ࡓࡵࠊMRI ☢▼ྠᵝ࡟ࡇࡢㄗᕪ☢ሙࢆ⿵ṇࡍࡿᶵᵓࡣᚲ㡲[2, 51]࡛࠶ࡿࠋࡇࡢࡓࡵࠊཷືⓗࢩ࣑ࣥࢢᡭἲ[8, 13](ᙉ☢ᛶయࡢ☢ሙࢩ࣒∦ࢆ฼⏝)ࠊ⬟ືⓗࢩ࣑ࣥࢢἲ[51, 52]ࠊࡑࢀ࡟ࠊ㌶㐨ᚤㄪᩚ⏝ࡢࢫࢸ࢔ࣜࣥࢢ☢▼[53, 54]ࢆ᳨ウࡋ࡚࠸ࡿࠋ
5.2.1. ཷື☢ሙࢩ࣑ࣥࢢ
☢ሙ⿵ṇࡢᇶᮏⓗᡭ㡰ࡣࠊFig. 4-17 ࡜ྠࡌ࡛࠶
ࡿࠋࢩ࣑ࣥࢢ࡟౑࠺ᶵჾ࡟ࡘ࠸࡚ࠊTable 5-4 ࡟ㄝᅗ 5-10 2D ෌ᵓᡂ☢ሙ࡜ 3D 㠀⥺ᙧィ⟬⤖ᯝࡢẚ㍑ࠋZ<0.95m ࡛ࡣ୧⪅ࡣࡼࡃ୍⮴ࠋ㕲 yoke☢ሙࡀⰋࡃ෌⌧ࡉࢀ࡚࠸ࡿࠋ

᫂ࡋࠊ㓄⨨ᴫᛕࢆ Fig. 5-12(a), (b)࡟♧ࡍࠋᮏ㡯࡛ࠊཷືࢩ࣑ࣥࢢ࡟ࡘ࠸࡚ㄝ᫂ࡍࡿࠋ

10㸫 41ཷືࢩ࣑ࣥࢢ࡛ࡣࠊ⿵ṇ☢ሙⓎ⏕※ࡣᙉ☢ሙ(3.0 T)୰ ࡛ ☢ ໬ ࡋ ࡓ ᙉ ☢ ᛶ య ∦(㕲 ∦ ࡞ ࡝)࡛ ࠶ࡿࠋ☢໬࡟ࡼࡿ☢Ẽ࣮࣓ࣔࣥࢺࡀసࡿ☢ሙ࡛ࠊㄗᕪ☢ሙࢆ⿵ṇࡍࡿࡢࡀཷືⓗࢩ࣑ࣥࢢ࡛࠶ࡿ
(4.5 ⠇ཧ↷)ࠋ

Fig. 5-12(b) ࢩ࣒ࢺࣞ࢖㓄⨨ᅗ. ᕥ: %Z type ࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖,ྑ: %R type ࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖. ᩥ⊩[51], Fig. 2(b)ࡼࡾᘬ⏝.
ࡣࠊࡑࢀࡒࢀࠊ38mmȭࠊ90mmȭ࡛࠶ࡿࠋᚋ⪅(Coarse ⏝)ࡣບ☢᫬࡟ࡣ㛢Ṇࡍࡿࡀࠊfine ⏝ࡣࠊ㕲 yoke ࡟ࡼࡿ☢ሙࢆኚ໬ࡉࡏࡎ㧗⢭ᗘ࡞ࢩ࣑ࣥ
Fig. 5-12(a) ☢ሙィ 㠃(ෆ㒊෇⟄)࡜ࢩ࣒ࢺࣞ࢖(ゅᙧ)ࡢ㓄⨨. ᩥ⊩[51], Fig. 2(a)ࡼࡾᘬ⏝.

ࢢࢆᐇ⾜࡛ࡁࡿࡼ࠺࡟ࠊ㛤ཱྀ≧ែࢆಖࡘࠋ
ࢩ࣒ࢺࣞ࢖⏝✰ࡢ➃࡛ࡣࠊ✰ࡢ༙ᚄ⛬ᗘࡢ㊥㞳࡛ࠊ2.0Ѝ0T ࡟☢ሙ໙㓄ࡀᏑᅾࡋࠊࡑࢀࡒࢀࠊ

ཷືⓗࢩ࣑ࣥࢢࡢసᴗᡭ㡰ࡣࠊMRI ☢▼ࡢሙ
ྜ(Fig. 4-17)࡜ྠᵝ ࡛ࠊ ࢩ࣒∦ ࡢ㓄 ⨨ࢆ⟬ ฟࡍࡿࠊࢩ࣑ࣥࢢィ⟬ࡶ MRI ☢▼ࡢሙྜ࡜ྠᵝ࡟ࠊ

100T/m ࡜ 45T/m ⛬ᗘ࡜ぢ✚ࡶࡿࠋ☢ሙ໙㓄࡟ࡼࡾ㕲ࢩ࣒∦ࡢ MM(M [Am2])࡟ຍࢃࡿ☢ຊ ) ࡣࠊ

4.6.3 㡯ࡢࢩ࣑ࣥࢢィ⟬ᡭἲ[13]ࢆ⏝࠸ࡿィ⏬࡛࠸ࡿࠋࡇࢀࡽࡢᡭἲࡣࠊ᪤࡟ࠊᆒ୍ᗘ 0.2ppm ࡟ᑐᛂ࡛ࡁࡿᐇ⦼ࡀ࠶ࡿࡇ࡜ࡣᙉㄪࡋ࡚࠾ࡃࠋ
ࢩ࣒ࢺࣞ࢖࡟ࡣࠊTable 5-4 ୖ㒊ࡢࡼ࠺࡟ Coarse
࡜ fine ࡢ 2 ✀㢮ࢆ⏝ពࡋ࡚࠸ࡿࠋඹ࡟ᗄఱᏛⓗ㓄⨨ࡣ Fig. 5-12(a)࡜ྠᵝ࡛࠶ࡿࠋFine ⏝࡛ࡣ㓄⨨ฟ
3᮶ࡿ㕲㔞ࡣᑡ࡞࠸(5cm /1 ࣏ࢣࢵࢺ)ࠋCoarse ࡣ㕲㔞ࢆከࡃ౑࠸(85cm3/1 ࣏ࢣࢵࢺ)ࠊ☢ሙ⿵ṇࡢ⬟ຊࡣ኱ࡁ࠸ࠋ୍᪉ࠊࢩ࣒ࢺࣞ࢖ྲྀࡾฟࡋ⏝ࡢ✰)=‫׏‬%㺃0؆MSAT‫׏‬B,(5-1)

࡛,☢ሙ໙㓄࡜ࢩ࣒∦㔞࡟ẚ౛ࡍࡿࠋࡇࡇ࡛ࠊMSAT ࡣ㣬࿴☢໬ࡋࡓᙉ☢ᛶయࡢ☢Ẽ࣮࣓ࣔࣥࢺ
࡛ࠊ㕲∦ࡢయ✚ࡀ V cm3 ࡢሙྜࠊ1.71V[Am2]࡛࠶
ࡿࠋCoarse ࡛ 20cm3/࣏ࢣࢵࢺ࡛࠶ࢀࡤࠊ157kg ࡛࠶ࡾࠊfine ࡛ 1cm3/࣏ࢣࢵࢺࡢሙྜࡣࠊ17.5kg ࡛
࠶ࡿࠋMRI ☢▼࡛ࡣࠊࢩ࣒ࢺࣞ࢖ࡢྲྀࡾฟࡋ㒊
ศ࡛ࠊ2T/m ⛬ᗘࡢ໙㓄☢ሙ࡛࠶ࡿࡀࠊMuon ⵳✚⏝☢▼࡛ࡢ‫ࡣ ׏‬㠀ᖖ࡟኱ࡁ࠸ࠋ

Table 5-4 Tools of Precise Magnetic Field Shimming for J-2/EDM Magnet. ᩥ⊩[51], Table 1 ࡼࡾᘬ⏝.
Shimming Tools

Passive tools(magnetizediron pieces)

Coarse shimming shim-trays

Fine shimming shim-trays

BZ type shim-coils
Active tools 6 coils in longitudinal array(Shim-coils
BR type shim-coils
arrays)
6 coils in longitudinal array

Capacities(actual)

Roles and usage>3.50x104 cc(<6000 cc)

Rough shimming (shimming for high orderedeigenmodes) using large volumes of iron pieces withmagnet current ramp-down, and with iron-yoke ceilingremoved and reassemble.

<2000 cc(<100 cc)

Fine shimming (shimming for low ordered eigenmodes)
with magnetic field on and without iron-yoke ceilingremoved. Fe volume in a shim-pocket should be less than
1 cc.

3 Gauss BZ(1.0 kA)

In rotational direction, uniform, cosĬ and cos2Ĭ like
distributions can be corrected.

6 Gauss BR(1.0 kA)

In rotational direction, uniform, cosĬ and cos2Ĭ like
distributions can be corrected.

10㸫 42୍᪉࡛ࠊMuon ☢▼࡛ࡢ‫✰⏝࢖ࣞࢺ࣒ࢩࠊࡣ ׏‬ࡢ➃㒊࡟㞟୰ࡋ࡚࠸ࡿࡢ࡛ࠊಶࠎࡢ࣏ࢣࢵࢺࡢ
ࢩ࣒∦㔞࡜ࡑࡢ☢ຊࢆ⪃៖ࡍࡿࠋ⌧≧࡛ࡣᐇ㝿ࡢ ࢩ ࣒ ∦ 㔞ࡣ ୙ ᫂ ࡛ ࠶ࡿ ࡀ ࠊ ከ ࠸࣏ ࢣ ࢵ ࢺ ࡛ࡣࠊᑡ࡞ࡃ࡜ࡶ 20cm3 ⛬ᗘ௨ୖࡢ㔞ࡣ࠶ࡾᚓࡿ࡜
⪃࠼ࡿ࡜ࠊບ☢᫬ࡢྲྀࡾฟࡋࡣ㞴ࡋ࠸ࠋ୍᪉ࠊ
fine ࡛ࡣࠊ1 ࣏ࢣࢵࢺ࠶ࡓࡾ 1cm3 ௨ୗ࡟ฟ᮶ࢀ
ࡤࠊບ☢᫬࡛ࡶྲྀࡾฟࡋࡣྍ⬟࡜⪃࠼࡚࠸ࡿࠋ
௨ୖࡢ⪃࠼࠿ࡽࠊCoarse ࢩ࣑ࣥࢢ࡛ࡣࠊࢩ࣒ࢺ
ࣞ࢖ࢆྲྀࡾฟࡍ᫬ࡢ☢ຊࢆ㑊ࡅࡿࡓࡵ࡟ࠊᾘ☢
ࢆ⾜࠺ࠋࡑࡢୖ࡛ࠊ㕲 yoke ࡢኳ஭ࡢ୍㒊ࢆ๤ࡀࡋ࡚(᳨ウ୰)ࠊసᴗࢆᐇ⾜ࡍࡿࠋࡑࡢࡓࡵࠊ㕲yoke 㓄⨨ࡸ㟁ὶ್ࡢ෌⌧ᛶ࡟㞴Ⅼࡀṧࡿࠋࡇࢀ

Fig. 5-13 %Z ࢱ࢖ࣉࢩ࣒ࢥ࢖ࣝ࡟ࡼࡿ☢ሙࠋ6 ಶࡢ඲ࢥ࢖ࣝ࡟ 1.0kA ࢆ ㏻㟁ࡋࡓሙྜࡢࠊ☢ຊ⥺(ᕥ)࡜☢ሙᙉᗘ➼㧗⥺(ྑ)ࠋ

ࢆ㑊ࡅ࡚ࠊ᭱⤊ⓗ࡟Ⰻዲ࡞୍ᵝ☢ሙࢆᚓࡿࡓࡵ
࡟ࠊfine ⏝࡟ᑠࡉ࠸✰(┤ᚄ 38 mm)ࢆᖖ᫬㛤ࡅ࡚࠾ࡁ(Fig. 5-8 ཧ↷)ࠊfine ࢩ࣑ࣥࢢ୰ࡢ㕲 yoke ᧯సBR(ࢆ↓ࡃࡋ࡚ࢩ࣑ࣥࢢࡍࡿࠋ

୍᪉ࠊཷືࢩ࣑ࣥࢢࡢࡼ࠺࡞⣽࠿࠸☢ሙศᕸࡢ

Coarse ࠿ࡽ fine ࢩ࣑ࣥࢢ࡬ࡢ⛣⾜ࡣࠊࢩ࣒ࢺࣞ

)ᡂศ(BR ࢱ࢖ࣉ౑⏝)ࡢㄪᩚࡶྍ⬟࡛࠶ࡿࠋㄪᩚࡣฟ᮶࡞࠸ࠋ

࢖ࡢྲྀࡾฟࡋ࡟ᚲせ࡞ຊࡀ┠Ᏻ࡟࡞ࡿࡀࠊࢩ࣑

BZ ࢱ࢖ࣉࡢࢩ࣒ࢥ࢖ࣝࡣࠊZ=0.7m ௜㏆࡟㟁ὶࣥࢢィ⟬࡟ࡼࡾྛࢩ࣒࣏ࢣࢵࢺࡢ㕲㔞ࡀ 1 cc ௨ୗࢆ㓄⨨ࡋ࡚ࠊFig. 5-13 ࡢ☢ຊ⥺ࢆᣢࡘ☢ሙࢆⓎ⏕

࡛ Coarse-->Fine ࡟⛣⾜࡜⪃࠼࡚࠸ࡿࠋ

ࡍࡿࠋྑࡢ☢ሙᙉᗘࡣ 6 ಶࡢࢥ࢖ࣝ඲࡚࡟ 1.0kA

ࢩ࣒㕲ࡢ㓄⨨࡟ࡣࠊ2 ࡘࡢࢩ࣑ࣥࢢ㐣⛬ඹ࡟ࠊ

ࢆ㏻㟁ࡋࡓሙྜ࡛࠶ࡿࠋ୰ᚰ࡛ 3.03 ࢞࢘ࢫ(⵳✚᪤࡟ MRI ☢▼࡛ᆒ୍ᗘ 0.2ppm ࡟ᑐᛂ࡛ࡁࡿࡇ࡜

㡿ᇦ: 3.028㹼3.038 ࢞࢘ࢫ)࡛࠶ࡿࠋୖୗ㞳ࡋ࡚㓄ࢆ☜ㄆࡋࡓࢩ࣑ࣥࢢィ⟬ᡭἲ [8, 13, 44] ࢆ฼⏝ࡍ⨨ࡍࡿࡇ࡜࡛ࠊ⵳✚㡿ᇦ࡛ࡣ୍ᵝ࡟㏆࠸ BZ ศᕸࡿணᐃ࡛࠶ࡿࠋ

࡟࡞ࡿ(ᕥᅗࡢ☢ຊ⥺ཧ↷)ࠋ࿘ᅇ᪉ྥࡢ BZ ☢ሙࡢศᕸࢆㄪᩚࡍࡿࠋࡇࡢ᮲௳(3 ࢞࢘ࢫⓎ⏕)࡛ࠊ

5.2.2. ⬟ືⓗ☢ሙࢩ࣑ࣥࢢ

1 T ࡢ☢ሙ᣺ᖜࡀ࠶ࡾࠊᆒ୍☢ሙࢆ஘ࡋ࡚ࡋࡲ

⬟ືⓗࢩ࣑ࣥࢢ࡟ࡣࠊࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖

࠺ࠋࡑࡢࡓࡵࠊᆒ୍☢ሙ࡜ࡢ୧❧ࢆ⪃࠼ࡿ࡜ࠊ{Fig. 5-12(b)}ࢆ⏝࠸ࡿࠋ6 ಶࡢࢥ࢖ࣝࡀ⵳✚㡿ᇦ౑⏝⠊ᅖࡣ㝈ࡽࢀࡿ(1 ࢞࢘ࢫ⛬ᗘ௨ୗ)ࡀࠊBZ ᙉࢆྲྀࡾᅖࡳࠊ෇⟄≧࡟㓄⨨ࡉࢀࡿࠋྛࢥ࢖ࣝࡣ

ᗘࢆᚤㄪᩚ࡛ࡁࡿᶵ⬟ࢆᣢࡘࠋࡲࡓࠊᐇ㝿ࡢ⿦㟁※࡟᥋⥆ࡉࢀࠊ㟁ὶㄪᩚ࡟ࡼࡾ⬟ືⓗ࡟☢ሙ⨨㐠㌿࡛ࡣࠊཷືࢩ࣑ࣥࢢࡢ fine ࢩ࣑ࣥࢢᶵ⬟ࠊㄪᩚࢆ⾜࠺ࠋ

ᙅ㞟᮰☢ሙ࡜ేࡏ࡚୰ᚰ☢ሙᙉᗘࢆㄪᩚࡍࡿࡓ

ࢩ࣒ࢥ࢖ࣝࡣ☢ሙศᕸㄪᩚࡢ⮬⏤ᗘࡣᑡ࡞ࡵ࡟ࡶ౑⏝࡛ࡁࡿࠊ࡜⪃࠼࡚࠸ࡿࠋ

࠸ࠋ㕲∦㓄⨨ Pocket ࡀ coarse, fine ඹ࡟ 400 ಶᏑᅾ

BR ࢱ࢖ࣉࡢࢩ࣒ࢥ࢖ࣝࡀసࡿ☢ሙࡣࠊFig. 5-14

ࡍࡿࡢ࡟ᑐࡋ࡚ࠊࢩ࣒ࢥ࢖ࣝࡣ BR ࢱ࢖ࣉ(㍈࡟┤࡛࠶ࡿࠋ☢ሙࡢ᪉ྥࢆࠊ☢▼㍈࡟ᆶ┤࡞ᖹ㠃(X-Y஺ᡂศ☢ሙ⏝)ࠊBZ ࢱ࢖ࣉ(㍈᪉ྥᡂศ⏝)ඹ࡟ 6 ಶ㠃࡛ Z=0 ࡢ㉥㐨㠃) ୖ࡟ࠊ▮༳࡛♧ࡋ࡚࠸ࡿࠋྛ

࡛࠶ࡿࠋࡑࢀࡒࢀࠊ࿘ᅇ᪉ྥࡢ BR ࠾ࡼࡧ BZ ☢ሙᯟୖ࡟ࡣࠊ≉␗್ࢆ♧ࡍࠊ2.13E-5㹼3.79E-6[T/A]ศᕸࢆ 6 ಶࡢࢩ࣒ࢥ࢖࡛ࣝㄪᩚࡍࡿࠋྛࢥ࢖ࣝ᭱

࡛࠶ࡿࠋྛࢥ࢖࡛ࣝ᭱኱㟁ὶࡀ 1.0kA ࡛㝈ࡽࢀࡿ

኱ 1.0 kAT ࡛࠶ࡿࠋࡢ࡛ࠊྛ☢ሙࡢ᭱኱ᙉࡉࡣࠊ≉␗್ࡢẚ౛࡟ࡣᐇ㦂㛤ጞᚋ࡟Ⓨ⏕ࡋࡓㄗᕪ☢ሙࡢ⿵ṇࡸ☢ሙ࡞ࡽ࡞࠸ࡀࠊNo, 1 & 2 ࡛ࡣ 7 ࢞࢘ࢫ⛬ᗘࠊNo.6 ࡛ᙉᗘࡢᚤㄪᩚ࡟⏝࠸ࡿࠋࡲࡓࠊ⬟ືⓗ࡞ࡓࡵࠊࡣ 1 ࢞࢘ࢫ⛬ᗘ࡛࠶ࡿࠋࡇࡢ୰࡛ࠊNo. 1 ࡜ 2 ࡢ

10㸫 43ᅛ᭷࣮ࣔࢻࡣࠊ⵳✚㡿ᇦࢆ☢ຊ⥺ࡀ☢▼㍈࡟ᆶ

(1) ☢ሙタィ࡛チᐜࡋࡓ☢ሙศᕸࠊ┤࡟㏻㐣ࡍࡿ☢ሙ࡛࠶ࡿࠋᆒ୍ᗘ࡟ࡣᙳ㡪ࡋ࡞(2) ☢▼㍈࡟┤஺ࡋࡓ☢ሙᡂศ࠸ࠋ᳨ฟჾ࡜☢▼ࡢ㍈ࡀ┦஫࡟ഴ࠸࡚㓄⨨ࡉࢀ࡛࠶ࡿࠋࢩ࣑ࣥࢢࡣ☢ሙᙉᗘ|B|ࢆㄪᩚࡍࡿࡀࠊ

ࡿ࡜ࠊ᳨ฟჾ࠿ࡽぢ࡚ࠊBX ࡶࡋࡃࡣ BY ࡢ☢ሙࡀタィ᫬࡟ィ⏬ࡋࡓ☢ሙ௨ୖ࡟Ⰻዲ࡞☢ሙศᕸࢆᏑᅾࡍࡿࡼ࠺࡟ぢ࠼ࡿࠋMuon ࣅ࣮࣒఩⨨ࢆㄪᚓࡿࡇ࡜ࡣฟ᮶࡞࠸[13]ࠋᚑࡗ࡚ࠊࢩ࣑ࣥࢢᚋ࡛

࡭ࠊࡑࡢ᪉ྥࡁ࠿ࡽࠊBX, BY ࢆ᳨ฟ࡛ࡁࢀࡤࠊ

ࡶ Table 5-1 ࡢᆒ୍ᗘࢆ‶ࡓࡍ⠊ᅖ࡛☢ሙᙉᗘࡢFig.5-14 ࡢ☢ሙࢆ౑ࡗ࡚⿵ṇ࡛ࡁࡿ࡜⪃࠼࡚࠸ศᕸࡣṧࡾࠊࡇࢀࡀṧᕪ☢ሙ BRE ࡛࠶ࡿࠋࡋ࠿

ࡿࠋࡲࡓࠊ6 ␒┠ࡢ࿘ᅇ᪉ྥ୍ᵝ࡞ᡂศࡣࠊ࢝ࣉ

ࡋࠊ┠ᶆࡢ 0.2 ppm ௨ୗ࡜☢ሙタィࡉࢀ࡚࠸ࡿࡢ

ࢫ☢ሙ࡛࠶ࡿࠋBR ᡂศࢆ࿘ᅇ᪉ྥ୍ᵝ࡟Ⓨ⏕ࡍ࡛ࠊࡇࡢṧᕪ☢ሙࡣၥ㢟࡛ࡣ࡞࠸ࠋ

ࡿࡢ࡛ࠊ᭱኱࡛ BR=1 ࢞࢘ࢫ⛬ᗘ࡜ᑠࡉ࠸ࡀࠊ

୍᪉ࠊ(2)ࡢ

ࠊ

ᡂศࡣࠊ4.1 ⠇ࡢ☢▼タィࡸ 4.6.3

Muon ⵳✚㌶㐨ࡢ㍈᪉ྥ఩⨨ࡢㄪᩚ࡟฼⏝ࡍࡿ஦㡯ࡢࢩ࣑ࣥࢢィ⟬࡜ 4.6.5 ࡢṧᕪ☢ሙ࡛ㄝ᫂ࡋࡓ

ࡶ⪃࠼࡚࠸ࡿࠋ

ࡼ࠺࡟ࠊィࡀᅔ㞴࡛࠶ࡾࠊタィィ⟬࣭ࢩ࣑ࣥࢢィ⟬࡟ྵࡲࢀࡎࠊࡉࡽ࡟ࠊཷືࢩ࣑ࣥࢢ࡛ࡣ
ᡂศࡢࢩ࣑ࣥࢢࡣ㞴ࡋ࠸ࠋࡑࡢࡓࡵ࡟ࢩ࣑ࣥ
ࢢᚋ࡟ṧࡿ☢ሙ࡛࠶ࡿࠋࡇࡇ࡛ࡣࠊMSM ࡟㛵㐃ࡋࡓࠊタ⨨ㄗᕪࢆ᝿ᐃࡋࡓㄗᕪ☢ሙࡢィ⟬࡜ࢩ࣑ࣥࢢࢩ࣑࣮ࣗࣞࢩࣙࣥ(௨ୗ࡛ࡣ௬᝿ࢩ࣑ࣥࢢ)ࢆ㏻ࡋ࡚ㄝ᫂ࡍࡿࠋ
Fig. 5-15 ࡟ 3 ✀㢮ࡢ㕲 yoke タ⨨ㄗᕪࢆ♧ࡍࠋᕥ࠿ࡽࠊ(a)タィ≧ែࠊ(b)㕲 yoke ୖ᪉ኚ఩ 1mm, (c)ᶓኚ఩ 1mm, (d)ᅇ㌿ 0.05 ᗘࠊ࡛࠶ࡿࠋ࠸ࡎࢀࡢሙ
ྜࡶࠊ3000cm3 ௨ୗࡢࢩ࣒㕲∦࡛ BZ ☢ሙࡢᆒ୍ᗘ
Fig. 5-14 %R ࢱ࢖ࣉࢩ࣒ࢥ࢖ࣝ࡟ࡼࡿ☢ሙ. 6 ಶࡢࢥ࢖ࣝ ㏻㟁ኚ᭦࡟ࡼࡿ 6 ✀㢮ࡢ☢ሙศᕸ. ☢ሙ᪉ྥࢆ Z=0 㠃࡛ࡢ▮༳࡛♧ࡍ. ᩥ⊩[51], Fig. 6 ᘬ⏝.

0.2ppm (⵳✚㡿ᇦࡢ 3cm ᖜ x10cm 㧗ࡉࡢ㡿ᇦ)࡛
ࢩ ࣑ ࣥ ࢢ ࡛ ࡁ ࡿ ஦ ࡣ ☜ ㄆ ࡋ ࡓ ࠋ ᭱ ኱ ࡣ(b)࡛
2348.3ccm3 ࡛࠶ࡗࡓࠋࡲࡓࠊ(b)࡜(d)࡛ࡣ Fig. 4-24
࡛ࡶ㆟ㄽࡋࡓ

ࢣ࣮ࢫ(b)࡛ࡣࢩ࣑ࣥࢢᚋ࡛ࡶࠊ࿘ᅇ᪉ྥ඲య

5.2.3. ཷືࢩ࣑ࣥࢢࡢ㞴ࡋ࠸☢ሙ࡜ࡢ㛵㐃࡛㍈᪉ྥ(R ᪉ྥ)ࡢṧ␃☢ሙࡍ࡛࡟ࠊ4.6.5 㡯࡛㆟ㄽࡋࡓࡼ࠺࡟ࠊ☢▼㍈࡟ᆶ┤࡞☢ሙᡂศ

ࡀ-0.11㹼-0.16 ࢞࢘ࢫᏑᅾࡋࡓࠋg-2/EDM ヲ⣽ィ ᐇ㦂ࡣࠊ

ࡣࠊ㏻ᖖࡢࢩ࣑ࣥࢢ࡛ࡣㄪᩚ
n-index=1.5E-4{

ฟ᮶࡞࠸ࠋࡑࡢࡼ࠺࡞☢ሙࢆ Fig. 4-24 ࡟♧ࡋࡓ
ࡀࠊBR ࢱ࢖ࣉࡢࢩ࣒ࢥ࢖ࣝࡀసࡿ☢ሙ࡜ఝ࡚࠸
ࡿࠋ4.6.5 㡯࡛ᡂศ☢ሙࡀࠊᏑᅾࡍࡿࠋ

☢ሙᡂศࡢ᳨ฟ࣭⿵ṇἲࢆᥦ᱌

ࡋࡓࠋMRI ☢▼࡛ࡣᐇ㝿ୖၥ㢟࡜࡞ࡿࡇ࡜ࡣ↓= െ1.35E-3 T/m}

࡛ ⾜ ࢃ ࢀ ࡿ ண ᐃ ࡛ ࠶ ࡾ ࠊ-8.1mm㹼-11.9mm ࡢ
Muon ࿘ᅇ㌶㐨ࡢ㍈᪉ྥ఩⨨ࡢኚ఩ࢆ㉳ࡇࡍࠋࡇ࠸ ࡜ ㄝ ᫂ ࡋ ࡓ ࡀ ࠊ ḟ ⠇ ࡛ ㄝ ᫂ ࡍ ࡿ ࡼ ࠺ ࡟ ࠊg2/EDM ィ ⏝ࡢ MSM ࡛ࡣࠊ(5-2)

ᡂศࡢⓎ⏕ࡀ↓ど࡛ࡁ࡞࠸ሙྜࡶ࠶ࡿࠋࡑࡢ⿵ṇ࡟ࡣࠊBR ࢱ࢖ࣉࡢࢩ࣒ࢥ࢖ࣝࡀ฼⏝࡛ࡁࡿ࡜⪃࠼࡚࠸ࡿࠋ

Z
Iron-yoke

SC CBsX(a) No error(Design)

5.2.4. ཷືⓗ☢ሙࢩ࣑ࣥࢢ࡜ṧᕪ☢ሙ(b) 㕲yoke䛜
1mmୖ᪉⛣ື(c) 㕲yoke䛜
1mmᶓ᪉ྥ⛣ື(d) 㕲yoke䛜
0.05ᗘᅇ㌿

Fig. 5-15 3 ✀㢮ࡢ㕲 yoke タ⨨ㄗᕪࢩ࣑ࣥࢢసᴗᚋ࡛ࡶࠊୗグࡢ☢ሙࡣṧࡿࠋ

10㸫 44ࡢ⿵ṇ࡟ BR ࢱ࢖ࣉࢩ࣒ࢥ࢖ࣝࡢ☢ሙ࡛ Fig. 5-14

⥺ࡢ᪉ྥࡀࠊ☢ሙ᳨ฟჾ࡜ 0.002 ᗘ(0.038 mrad)ࡔ

ࡢ 6 ␒┠ࡢ☢ሙࡀ౑࠼ࡿ࡜⪃࠼࡚࠸ࡿࠋ

ࡅഴ࠸࡚࠸ࡿࡇ࡜࡟࡞ࡿࠋࡇࡢ≧ἣࢆᶍᘧⓗ࡟3(c)ࡣ 1947.5cm ࡢ㕲ࢩ࣒∦ࢆ౑ࡗࡓཷືࢩ࣑ࣥ

ㄗᕪ☢ሙࡢ☢ຊ⥺࡛⾲ࡍ࡜ Fig. 5-17 ࡛࠶ࡿࠋࢩ࣑

ࢢ࡟ࡼࡾࠊ⵳✚㡿ᇦ࡛ࡣࠊBZ ᆒ୍ᗘࡀ 31.1ppmЍ

ࣥࢢ๓࡛ࡣࠊㄗᕪ☢ሙࡣ㍈᪉ྥᡂศࢆᣢࡗ࡚࠸

0.11ppm, BR ࡢ᭱኱್ࡶ|BR|<28.3 TЍ|ࡿࡀࠊࢩ࣑ࣥࢢࢆ⾜࠺ࡇ࡜࡛ㄗᕪ☢ሙࡣ୺࡟|<0.36 Tᡂศ࡜࡞ࡿࠋ

࡜ฟ᮶ࡓࠋ༑ศᑠࡉ࠸ṧᕪ☢ሙ࡜ゝ࠼ࡿࠋ(d)࡛ࡣࠊ☢Ẽ㍈ࡢഴࡁࢆ⾲ࡍ☢ሙࢆ௬᝿ࢩ࣑ࣥࢢࡢ⤖ᯝࢆᚓࡓࠋFig. 5-16 ࡛ࡣࠊ㕲 yoke ࡟

Fiducial volume(d)ࡢ 0.05 ᗘ(0.87mrad)ࡢഴࡁࡀᏑᅾࡍࡿሙྜ࡟ࡘ

Shimming
operation

ER࠸࡚ࠊࢩ࣑ࣥࢢ๓(ㄗᕪ☢ሙ B )࡜ᚋ(ṧᕪ☢ሙBRE)ࢆ༙ᚄ 0. 333m ࡢ෇⟄㠃ୖ࡛♧ࡍࠋBZ ᡂศ࡜

Fig. 5-17 ࢩ࣑ࣥࢢ๓ᚋࡢㄗᕪ☢ሙᡂศ(BX, BY or BR)ᡂศࡀ࠶ࡿࡀࠊBZ ศᕸ(3.0 T ࡟ᑐ
ࡋ 0.1 ppmࠊ1.0 ppm ࡜ 10 ppm ࡟➼㧗⥺)࡜෇⟄㠃(b)࡜(d)࡛ࡣࠊཷືࢩ࣑ࣥࢢᚋ࡟ࠊㄗᕪ☢ሙࡢ࡟ᆶ┤࡛༙ᚄ᪉ྥࢆྥ࠸ࡓ☢ሙᡂศ BR ศᕸ(0.5 ࢞࠺ࡕ࢘ࢫẖࡢ➼㧗⥺)ࢆ♧ࡋ࡚࠸ࡿࠋᡴⅬ㡿ᇦ࡛ࡣࠊ࡞☢ሙࡢ⿵ṇ࡟ࠊBR-type ࢩ࣒ࢥ࢖ࣝࢆ౑࠺ࡇ࡜

BZER>0(ୖྥࡁ)ࠊ BR>0(እྥࡁ)࡛࠶ࡿࠋ

ࡀฟ᮶ࡿ࡜⪃࠼࡚࠸ࡿࠋチᐜᡂศ࡟ࡘ࠸࡚ࡢ

ᇶ‽ࡣᮍᐃ࡛࠶ࡿࡀࠊ౛࠼ࡤ

=7 ࢞࢘ࢫࡔ࡜ࠊ

ER

ୖഃࡢ B
RE

࡟ᑐࡋ࡚௬᝿ࢩ࣑ࣥࢢ࡛ồࡵࡓṧᕪᡂศࡀṧࡿࡇ࡜ࢆㄝ᫂ࡋࡓࡀࠊࡇࡢࡼ࠺

ࢆ Fig. 5-16 ୗ 㒊 ࡟ ♧ ࡋ ࡓ ࠋ 㕲 㔞 ࢆ|B|࡟ ᆒ ୍ ᗘ ࡢ チ ᐜ ☢ ሙ ᣺ ᖜ ࡟ ᑐ ࡋ ࡚ ᭷ ព ࡞

1623.7 cc ࡢ㕲∦ࢆ౑࠺ࡀࠊࣅ࣮࣒⵳✚㡿ᇦ࡛ࡣ

0.03ppm ࡢኚ໬ࢆ୚࠼ࡿࠋࡑࡢࡓࡵࠊ➹⪅ࡣࠊ☢ሙ B

0.07 ppm ࡢᆒ୍ᗘࡀᚓࡽࢀࡿ⤖ᯝ࡛࠶ࡿࠋࡋ࠿
ࡋࠊ<7 ࢞࢘ࢫࢆ୍ࡘࡢ┠Ᏻ࡜⪃࠼࡚࠸ࡿࠋ

ᡂศࡣṧᏑࡋࠊ⵳✚㡿ᇦ௜㏆࡛ࡣ Z ᪉ྥ఩⨨࡟౫Ꮡࡋ࡞࠸ᡂศ࡜࡞ࡿࠋ4.6.5 㡯࡛ㄝ᫂ࡋࡓࢩ࣑ࣥࢢࡢ㞴ࡋ࠸ᡂศࡀṧࡗࡓ⤖ᯝ࡛࠶ࡿࠋࡇࡢ౛࡛ࡣṧᕪ BRRE ࡣ±1.13 ࢞࢘ࢫ࡛ࠊ☢ຊ୍᪉ࠊ☢Ẽࢭࣥࢧ㸫ࡣ|B|ࢆィ
ศ㞳ࡋ࡚ィ

ࡋࠊ

ᡂศࢆ

ࡍࡿࡇ࡜ࡣ㞴ࡋ࠸ࠋࡋ࠿ࡋࠊ

0.01ppm(nmr ࢭࣥࢧ࡛ 1Hz ┦ᙜࠊ┦ᑐኚ໬㔞࡛࠶ࡿ)⛬ᗘࡢ☢ሙኚ໬ࢆィࡍࡿࡇ࡜ࡣྍ⬟࡜⪃࠼ࡿࠋࡑࡇ࡛ࠊ౛࠼ࡤ Fig. 4-24 ᕥࡸ Fig. 5-16
5-1 ྑୗࠊ
右下、
࠾ࡼࡧࠊFig. 5-17 ྑࡢࡼ࠺࡞☢▼㍈࡟ᆶ┤࡟☢ຊ⥺ࡀ㏻㐣ࡍࡿṧᕪᡂศࢆࠊBR-type ࡢࢩ࣒ࢥ࢖ࣝ
࡛ MODE1, MODE2 (Fig. 5-14 ᕥ➃)ࢆ౑ࡗ࡚ᡴࡕ
ᾘࡍࡇ࡜ࡀฟ᮶ࡿ࡜⪃࠼࡚࠸ࡿࠋ6 ಶࡢࢩ࣒ࢥ࢖
ࣝࡢ㟁ὶ㓄ศ , ࡀ☢ሙศᕸࢆỴࡵࡿࡢ࡛ࠊ
, = C1,1 + C2,2

(5-3)

࡜ࡋࠊC1, C2 ࢆヨ⾜㘒ㄗⓗ࡟ኚ໬ࡉࡏ࡚ࠊィ☢

ሙࡀࢃࡎ࠿࡟ᙅࡃ࡞ࡿ C1, C2 ࢆồࡵࡿ࡜ࡑࡢ᮲௳
࡛ࢲ࢖࣏࣮ࣝ

ᡂศࡀᡴࡕᾘࡉࢀࡓ࡜ุ᩿࡛ࡁ

ࡿࠋ୍᪉ࠊ1 ࢞࢘ࢫ࡟ࡶ‶ࡓ࡞࠸
Fig. 5-16 㕲ᚰኚ఩ࡢࢣ࣮ࢫ(d)࡟ࡼࡿㄗᕪ☢ሙ࡜ཷືࢩ࣑ࣥࢢ⤖ᯝ㺂 ୖ㸸ㄗᕪ☢ሙࠊୗ㸹ṧᕪ☢
ሙࠊ༙ᚄ 0. 333m ෇⟄ୖࡢ %R ศᕸࢆᒎ㛤ࡋ࡚♧ࡍ.
ᩥ⊩[51], Fig. 4, Fig.5(a)ࡼࡾᘬ⏝.

ᡂศࡔ࡜ࠊᘧ(5-3)࡛㆟ㄽࡋࡓ᪉ἲ࡛ࡣ㺂㞴ࡋ࠸ྍ⬟ᛶࡀ㧗࠸ࠋࡋ
࠿ࡋࠊFig. 5-15 ࡢࡼ࠺࡞㕲 yoke ࠿ࡽࡢㄗᕪ☢ሙࢆࢩ࣑ࣥࢢࡋࡓᚋ࡛ண

10㸫 45

ࡉࢀࡿ BR ᡂศࡢṧ␃ࡣࠊࣅ࣮࣒㍈᪉ྥ఩⨨࡟ᙳ㡪ࢆ୚࠼ࡿࠋᘧ(5-2)࡜ࡋ࡚タィࢆ㐍ࡵ࡚࠸ࡿࠋBZ ศᕸࡣࠊ఩⨨(R, Z)

ࡢᙅ㞟᮰☢ሙࡢሙྜࠊ

࡜ᣦᩘ n ࡟౫Ꮡࡋࠊᘧ(3-29)ࢆཧ⪃࡟ࡍࡿ࡜ࠊ

ࡣ Muon ࿘ᅇ Z ᪉ྥ఩⨨ࢆ-(b)ࡢṧᕪ☢ሙ

=

8.1mm㹼-11.9mm ኚ໬ࡉࡏࠊ
ࡣࠊ࿘ᅇ㠃ࢆ 0.004mrad(0.002 ᗘ)ഴࡅࡿ

(d)ࡢ

࡜ඹ࡟ࠊMuon ࡟࿘ᅇ࿘Ἴᩘ࡟ྠᮇࡋࡓ Z ᪉ྥ᣺

െ

( െ

=െ

ࢩ࣒ࢥ࢖࡛ࣝ⿵ṇ࡛ࡁࡿࠋ๓⪅(b)࡛ࡣࠊFig. 5-14

(5-6)࡛࠶ࡿࠋࡲࡓࠊᘧ(5-4)࠿ࡽࠊ

ືࢆⓎ⏕ࡉࡏࡿྍ⬟ᛶࠊࡀண᝿ࡉࢀࡿࠋࡇࢀࡽࡀ᳨ฟ࡛ࡁࢀࡤࠊBR-type

)+

(5-7)

࡛ࡶ࠶ࡿࠋࡇࡇ࡛ࠊR0, B0 ࡣ g-2/EDM ࡢ MSM ࡢࡢ 6 ␒┠ࡢᙉࡉࢆㄪᩚࡋ࡚ Muon ㌶㐨ࡢ Z ᪉ྥࢆ୰ᚰࣃ࣓࣮ࣛࢱ࡛ࡑࢀࡒࢀ 0.333m, 3.0T ࡛࠶ࡿࠋ୰ᚰ㠃(Z=0)࡟ᡠࡏࡿࠋࡲࡓࠊ(d)ࡢሙྜ࡛ࡶࠊヨᑟయ఩⨨ࡢ㓄⨨ሙᡤ࡟ࡣࠊ㓄⨨⢭ᗘࢆⰋࡃࡍ

⾜㘒ㄗ࡟࡞ࡿࡀࠊᘧ(5-3)ࡢ C1, C2 ࢆㄪᩚࡋ࡚ࠊᙳ

ࡿࡓࡵ࡟ࠊ5 ಶࡢ MC-CB ࡢᕳࡁᯟࢆ฼⏝ࡍࡿࠋ㡪ࡢ↓ࡃ࡞ࡿ᮲௳ࢆ᥈ࡍࠋ

ࡑࡢࡓࡵ࡟ࠊMC-CB ࡢෆഃ࡛ࠊMC-CB ࡢᨭᣢᵓ࡜ࡇࢁ࡛ࠊࢩ࣒ࢥ࢖ࣝ࡟ࡼࡿ☢ሙࡣࠊ≉࡟ᙉ㐀≀ࢆ฼⏝ࡋ࡚㓄⨨ࡍࡿࠋࡘࡲࡾࠊ༙ᚄࡣ

࠸㟁ὶ࡛౑⏝ࡋࡓሙྜࠊᆒ୍☢ሙࢆ஘ࡍ☢ሙ࡜

0.795m ࡛ Z=-0.750m㹼+0.750m ࡢ⠊ᅖ࡟㓄⨨ࡍࡿ࡞ࡿ࡜ண᝿ࡉࢀࡿࠋࡑࡢࡓࡵࠊࢩ࣒ࢥ࢖࡛ࣝ⿵

ィ⏬࡛࠶ࡿࠋ㟁ὶ್࡜㓄⨨఩⨨ࢆỴࡵࡿࡓࡵ࡟

ṇࡋࡓᚋ࡟ࠊ෌ᗘࠊfine ࢩ࣑ࣥࢢ࡛☢ሙࢆㄪᩚࡍ

ࡶࠊFig. 4-1 ࡢ᪉ἲࢆ౑࠺ࠋ
Step-1 ࡜ࡋ࡚ࠊR=0.795m ࡟⥺㍯㟁ὶ 50 ᮏࢆ㓄ࡿࡇ࡜࡟࡞ࡿ࡜⪃࠼࡚࠸ࡿࠋ

⨨ࡋ࡚ࠊ☢ሙホ౯Ⅼࢆ R=0.333m ୰ᚰ࡛ࠊ㧗ࡉ
5.3. Muon ධᑕ&⵳✚㛵ಀࡢ☢ሙⓎ⏕ᶵჾ

10.0cm ᖜ 3.0cm ࡢᴃ෇᩿㠃ୖ࡟☢ሙホ౯Ⅼࢆ㓄⨨

Muon ධᑕ࣭⵳✚࡟㛵㐃ࡋࡓ☢ሙ࡟ࡣࠊᙅ㞟᮰ࡋࡓࠋࡑࡢ⤖ᯝࠊᚓࡽࢀࡓ SVD ᅛ᭷ศᕸࢆ Fig.

☢ሙࠊ࢟ࢵ࣮࢝☢ሙࠊࡑࢀ࡟ࠊࢫࢸ࢔ࣜࣥࢢ☢

5-18 ࡟♧ࡍࠋR-Z ࡢ෇⟄ᗙᶆ࡛࠶ࡾࠊ▮༳࡛⥺㍯

ሙࡀ࠶ࡿࠋ᭱ᚋ࡟ࡇࢀࡽࢆㄝ᫂ࡍࡿࠋ

㟁ὶศᕸࠊ➼㧗⥺࡛☢ሙᙉᗘศᕸࢆ♧ࡋࡓࠋወᩘ␒┠ࡢ 4 ಶࡢ SVD ᅛ᭷࣮ࣔࢻࢆ♧ࡋࡓࠋ෌ྑ

5.3.1. ᙅ཰᮰☢ሙഃ(Candidate WFC)ࡣࠊStep-1 ࡢ᳨ウ࡛ᚓࡽࢀࡓ㟁ᙅ㞟᮰☢ሙࡣ WFC(WFC㸸Weak Focus Coilࠊᙅὶศᕸ࡜☢ሙศᕸ࡛࠶ࡿࠋࡇࡢศᕸࡣࠊTable 5-5㞟᮰☢ሙࢥ࢖ࣝ)࡛సࡽࢀࡿࠋ⵳✚㡿ᇦ࡛࣑࣮ࣗࡢ᳨ウ࡛ᚓࡓࠋࡇࡢ⾲࡛ࡣࠊFig. 5-18 ࡢᅛ᭷࣮ࣔ

࢜ࣥ㌶㐨ࢆࠊୖୗ᪉ྥ࡛Ᏻᐃ໬ࡉࡏࡿࡓࡵ࡟ຍ

ࢻࢆຍ⟬ࡍࡿ๭ྜࢆ᳨ウࡋ࡚࠸ࡿ{Fig. 5-3(c)ཧ

࠼ࡿ☢ሙ࡛࠶ࡿࠋ⌧ᅾࡢタィ࡛ࡣࠊ↷}ࠋᘧ(5-6)ࢆ෌⌧ࡍࡿ࡟ࡣຍ⟬๭ྜࡣ඲࡚ 1.0ࡀⰋ࠸ࡀࠊṧᕪ☢ሙࡢチᐜ⠊ᅖ࡛ࠊ㟁ὶࢆୗࡆ== െ1.35 × 10

[T/m]

(5-4)

ࡢᙅ㞟᮰☢ሙ࡛ࡢᐇ㦂ࡀணᐃࡉࢀ࡚࠸ࡿࠋࡇࡢ
໙㓄ࡣࠊ᪤࡟ 3.4 ⠇࡛㆟ㄽࡋࡓࡼ࠺࡟ࠊ㏆ఝⓗ࡟‫ן‬࡜ࡍࡿᣦᩘ n ࡛⾲ࡉࢀࡿࠋ᪤࡟ᘧ(3-27)ᘧ

࡛ᐃ⩏ࡀ♧ࡉࢀ࡚࠸ࡿࡀࠊ෌ᗘୗグ࡟♧ࡍࠋn=െ
g-2/EDM ィ

.

(5-5)

WFC ࡢ㏻㟁㟁ὶㄪᩚ࡛ࠊᣦᩘ n ࢆ 0㹼3.0x10(⨨ㄗᕪࡀ࠶ࢀࡤࠊㄗᕪ☢ሙࡀ኱ࡁࡃ࡞ࡿࡓࡵ࡛࠶ࡿࠋTable 5-5 ࠿ࡽࠊNo. 5 ࡜ 6 ࡛ࡣࠊṧᕪ☢ሙ
ࡣ+/-0.035ppm ⛬ᗘࡢ⠊ᅖ࡛࠶ࡾࠊᑠࡉ࠸࡜ุ᩿
ࡋ࡚ࠊ㟁ὶࡀࡼࡾᑠࡉ࠸ No.5 ࡛タィࢆ㐍ࡵࡿࡇ࡜࡟ࡋࡓࠋᐇ㦂࡛ࡣᘧ(5-4)ࡀᐃ᱁࡛࠶ࡿࡀࠊ
-3࡚࠾ࡁࡓ࠸ࠋࡇࢀࡣࠊ኱ࡁ࡞㟁ὶ࡛ࠊᑟయࡢタ

Fig. 5-18 ࠿ࡽゎࡿࡼ࠺࡟ࠊ㟁ὶศᕸࡢࣆ࣮ࢡࡣ
ṇ࣭㈇ేࡏ࡚ 7 ࢝ᡤ࡟࠶ࡾࠊࡇࡢ఩⨨࡟ᑟయࢆ㓄⨨ࡋ࡚ࠊFig.5-18 ࡜ྠ➼ࡢ☢ሙࢆసࡿࡓࡵࡢ SVDᅛ᭷ศᕸࡀࠊFig. 5-19 ࡛࠶ࡿࠋ࠾࠾ࡼࡑࠊ50 ᮏࡢ= 0㹼2.7x10 T/m)ࡢ⠊ᅖ࡛ኚ᭦ྍ⬟࡛࠶ࡿࠊ⥺㍯㟁ὶࡢሙྜ࡜ఝࡓ☢ሙศᕸ࡛࠶ࡿࠋTable 5-5
࡟ࡣ⥺㍯㟁ὶ 50 ᮏ࡜ 7 ᮏ࡛ࠊ౑⏝ࡍࡿᅛ᭷࣮ࣔ

10㸫 46

Fig. 5-18 ᙅ཰᮰☢ሙࢥ࢖ࣝࡢ☢ሙタィ࡟⏝࠸ࡓ SVD ᅛ᭷࣮ࣔࢻ, ⥺㍯㟁ὶ 50 ᮏࢻࢆ᳨ウࡋࡓ⤖ᯝࡶ♧ࡋࡓࠋᅛ᭷࣮ࣔࢻࡣࡑࢀ

ࡢ☢᮰࡛࠶ࡿࠋ0.333m ࡟ࡣࠊWFC ࡀసࡿ☢ሙࢆ

ࡒࢀࠊFig. 5-18 ࡜ Fig. 5-19 ࡟♧ࡋ࡚࠸ࡿࠋTable 5-▮༳࡛♧ࡋࡓࠋ☢ሙࡢ኱ࡁࡉᩘ್࡛♧ࡋࡓࠋࡲ

5 ࡢ᳨ウ⤖ᯝࡣࠊ୧⪅࡛㏆࠸⤖ᯝ࡛࠶ࡿࡀࠊ7 ᮏࡓࠊ୺ࢥ࢖ࣝ(MC10㹼MC30)௜㏆࡟᭩࠸ࡓᩘᏐ࡜࡛ࡢ᳨ウ⤖ᯝ࡛ྜィ㟁ὶ(⤯ᑐ್ࡢຍ⟬) ࡣࡸࡸᑠ▮༳ࡣ WFC ࡢ㟁ὶ(▮༳ࡣ㟁ὶ್࡟ẚ౛)࡛࠶

ࡉ࠸ࠋࡇࢀࡣࠊ50 ᮏ࡛ࡢ᳨ウ࡛ồࡵࡓ㟁ὶࣆ࣮ࢡ఩⨨ࡀࠊྠᵝࡢ☢ሙࢆⓎ⏕ࡍࡿ᫬࡟᭱ࡶຠ

Table 5-5 WFC ࡢ౑⏝ᅛ᭷࣮ࣔࢻ᳨ウ⋡ⓗ࡞఩⨨࡛࠶ࡿࡓࡵ࡛࠶ࡿࠋ7 ᮏ࡛ࡣศᕸ㟁ὶࢆ༑ศ࡟ࡣ⪃៖ࡉࢀ࡞࠸ࡢ࡛ࠊᐇ㝿࡟ࡣ㧗ḟᡂศࡢ☢ሙࡀⓎ⏕ࡋ࡚࠸ࡿࡀࠊ≉␗್(T/A ࡛ᕥୖ)ࡀᛴ㏿࡟ῶᑡࡍࡿࡇ࡜࠿ࡽ⪃࠼࡚ࠊࡑࢀࡽࡣᴟ
ࡵ࡚ᑠࡉ࠸࡜ゝ࠼ࡿࠋ௨ୖ࡛ᚓࡓ WFC ࡢ☢ሙศᕸࢆࠊFig. 5-20 ࡟♧ࡍࠋᕥഃ࡟ࡣࠊ☢᮰➼㧗⥺(☢ຊ⥺)ࢆࠊ5.0E-5Wb
ẖ(Z ࡢᑠࡉ࠸㡿ᇦ)ࠊ࠾ࡼࡧ 5.0E-4Wb ẖ(Z ࡢ኱ࡁ࡞㡿ᇦ)ࡢ➼㧗⥺࡛♧ࡋ࡚࠸ࡿࠋᡴⅬ㡿ᇦ࡛ࡣṇ

⥺㍯㟁ὶ 50 ᮏ⥺㍯㟁ὶ 7 ᮏྜィྜィ
No. ᅛ᭷࣮ࣔࢻ␒ྕ
㟁ὶ㟁ὶ
(0.1 T)(0.1 T)
1 3 5 7
(kA)
(kA)
3.47
1 1.0 1.0 0.0 0.0 -44.3㹼+57.2 3.43 -44.5㹼57.5
8.12 -22.3㹼30.6
8.71
2 1.0 1.0 0.5 0.0 -22.0㹼30.2
15.49 -3.85㹼3.66 17.74
3 1.0 1.0 1.0 0.0 -4.11㹼3.90
42.50 -2.08㹼2.26 36.32
4 1.0 1.0 1.0 0.5 -2.18㹼2.38
74.96 -1.03㹼1.15 62.02
5 1.0 1.0 1.0 0.9 -1.04㹼1.16
83.08 -0.84㹼0.87 68.44
6 1.0 1.0 1.0 1.0 -0.82㹼0.86
ຍ⟬๭ྜ

Fig. 5-19 ᙅ཰᮰☢ሙࢥ࢖ࣝࡢ☢ሙタィ࡟⏝࠸ࡓ SVD ᅛ᭷࣮ࣔࢻ, ⥺㍯㟁ὶ 7 ᮏ

10㸫 47ࡿࠋ▮༳ࡢ᰿ඖ࡟ࡣ‫ࢆڧ‬᭩࠸࡚࠸ࡿࡀࠊWFC ࢥ࢖ࣝ఩⨨࡛࠶ࡿࠋ୺ࢥ࢖ࣝࡢࡍࡄෆഃ࡟㓄⨨ࡍࡿࠋྑഃୖ࡟ࡣ☢ሙᙉᗘ(୺☢ሙ㸩WF ☢ሙ)ࡢ➼㧗⥺ࢆ 20 T ẖࡢ➼㧗⥺࡛♧ࡋࡓࠋᡴⅬ㡿ᇦ࡛ࡣ☢ሙࡀ㧗࠸(3.0T ௨ୖ)ࠋ➼☢ሙᙉᗘ⥺ࡣෆഃ࡟ฝ
ࡢᙧ࡛࠶ࡿࡀࠊᘧ(5-6)ࡢ➨ 3 㡯ࡢᙳ㡪࡛࠶ࡿࠋྑ
ୗ࡟ࡣࠊᘧ(5-6)࡜ᕥᅗࡢ㟁ὶ㓄ศ࡟ࡼࡿ☢ሙ࡜ࡢᕪ␗(ṧᕪ)ࢆ♧ࡋࡓࠋ᪤࡟ Table 5-5 ࡛ヰࡋ࡚࠸ࡿࡀࠊᑠࡉ࡞ṧᕪ☢ሙ࡛࠶ࡿࠋ
࡜ࡇࢁ࡛ࠊR=0.333m, Z=0.0m ࡢ Muon ⵳✚㡿ᇦ୰ᚰ࡛ WFC ☢ሙࡣ㸫0.405E-5T ࡜ࡋ࡚࠸ࡿࠋࡇࢀ
ࡣࠊ3D 㠀⥺ᙧィ⟬࡛㕲ᙳ㡪ࢆㄪ࡭ࡿ࡜ࠊࢃࡎ࠿
࡟ṇࡢ☢ሙࢆⓎ⏕ࡍࡿࡢ࡛ࠊࡑࡢᙳ㡪ࢆᡴࡕᾘࡍࡼ࠺࡟ࡋࡓࡓࡵ࡛࠶ࡿࠋ
Fig. 5-20 ⥺㍯㟁ὶ 7 ᮏ࡟ࡼࡿᙅ཰᮰タィ☢ሙ

WFC ࡣ MRI ☢▼ࡸ୺ࢥ࢖ࣝ⩌࡟ẚ࡭ࠊ᩿㠃ࡀᑠࡉ࠸ࠋࡑࡢࡓࡵࠊᙧ≧ࡢᙳ㡪ࡣᑠࡉ࠸ࡢ࡛ࠊ

5.3.2. ࢟ࢵ࣮࢝ࢥ࢖ࣝ

Step-2 ࡣ᳨ウࡋ࡞࠸ࠋ⌧ᅾࠊTable 5-6 ࡢᵝ࡟ࠊ7ಶࡢ⥺㍯㟁ὶࢆࠊ౑⏝ᑟయࢆ᝿ᐃࡋ࡚ࠊ⣲⥺㟁ὶ್ࠊᕳࡁ⥺ᵓ㐀ࢆỴࡵࠊStep-2 ࡢྛࢥ࢖ࣝ఩⨨ࡢᚤㄪᩚࢆ⾜ࡗ࡚࠸ࡿࡀࠊᮍ᏶࡛࠶ࡿࠋ
࠶࡜୍ࡘㄢ㢟ࢆヰࡋ࡚࠾ࡃࠋࡇࡢ WFC ࡢ㟁ὶ࡛ࠊZ=0 㠃ࡢࢥ࢖ࣝ-9.48kA ࡀ+0.2mm ఩⨨ኚ఩ࢆ㉳ࡇࡋ࡚࠸ࡿ࡜ࡍࡿ࡜ࠊ⣙+/-3.5 T ࡢㄗᕪ☢ሙ
ࢆⓎ⏕ࡍࡿࠋࡇࡢ⛬ᗘࡢタ⨨ㄗᕪࡣ࠶ࡾᚓࡿ
࡜⪃࠼ࡿࡀࠊࡇࡢㄗᕪ☢ሙࡣ⿵ṇࡍࡿᚲせࡀ࠶
ࡿࡢ࡛ࠊ3.0T ୍ᵝ☢ሙ࡟ࢩ࣑ࣥࢢࡋࡓୖ࡛ࠊᙅ཰ ᮰ ☢ ሙ ࢆຍ ࠼ ࡓ ሙ ྜࡸ ᙉ ᗘ ኚ ᭦ࡋ ࡓ ሙ ྜ ࡟ࡣࠊᙅ཰᮰☢ሙࡢ⌮᝿ⓗ࡞ศᕸ࠿ࡽࡢㄗᕪࢆ fineࢩ࣒ᶵ⬟࡜ࢩ࣒ࢥ࢖ࣝࢆ౑ࡗ࡚ㄪᩚࡍࡿࡇ࡜࡟
࡞ࡿ࡜⪃࠼࡚࠸ࡿࠋ

Muon ࡢ㍈᪉ྥ⛣ືࢆṆࡵࡿࡓࡵࡢ༙ᚄ᪉ྥ☢
ሙ BR ࢆ▷᫬㛫(100㹼500ns ᳨࡛ウ୰)Ⓨ⏕ࡍࡿࠋࡇࡢࡓࡵࠊྍ⬟࡞㝈ࡾᑠࡉ࡞࢖ࣥࢲࢡࢱࣥࢫ࡛࠶
ࡿࡇ࡜ࡀᮃࡲࡋ࠸ࡢ࡛ࠊࢱ࣮ࣥᩘࡣ᭱ᑠࡢ+/ 1ࢱ࣮࡛ࣥ࠶ࡿࠋࢥ࢖ࣝ࡜ゝ࠺ࡼࡾࠊ㖡ࡢ෇⟄≧ᵓ㐀≀࡛࠶ࡾࠊᶍᘧᅗࢆࠊFig. 5-21 ࡟♧ࡍࠋୖഃ࠿ࡽᨭᣢࡍࡿணᐃ࡛࠶ࡿࠋྛᑟయ࡟ࡣ᭱኱ 1kA⛬ᗘࡢ㟁ὶࡀࣃࣝࢫ(25Hz)࡛ὶࢀࡿࠋ▷᫬㛫࡞ࡓࡵࠊⓎ⇕㔞ࡣᑠࡉࡃࠊ㍽ᑕᨺ⇕࡛༑ศ࡛࠶ࡿࠋࡲ ࡓ ࠊ ☢ ሙ໙ 㓄 ࡀ ᑠ ࡉ࠸ 㡿 ᇦ ࡟ 㓄⨨ ࡉ ࢀ ࡿ ࡢ࡛ࠊ㟁☢ຊࡶᑠࡉ࠸ࠋࡓࡔࡋࠊ25Hz ࡛㏻㟁ࡉࢀࡿࡢ࡛ࠊࡇࡢ࿘Ἴᩘ࡜ඹ᣺ࡍࡿᵓ㐀ࡣ㑊ࡅࡿᚲせࡀ࠶ࡿࠋᑟయ࡟ࡣࠊ3mm㹼5mm ⛬ᗘࡢ㖡ᯈࢆ෇⟄≧࡟

Table 5-6 ᙅ཰᮰☢ሙ⏝ CB 㓄⨨(Q=1.5E-4)⥺㍯㟁ὶィ⟬
CB
CB
୰ᚰ఩⨨
㟁ὶ
␒
ྕ R(m) Z(m) Ii(kA)ຍᕤࡋ࡚⏝࠸ࡿィ⏬࡛࠶ࡿࠋࡇࡢᑟయࡢෆ㠃(༙ᚄᑠഃ㠃)ࡣࠊR=0.36m ࢆணᐃࡋࠊ㧗ࡉ఩⨨ࡣ㺂ୖᕳࡁ⥺ᩘᩚᩘ໬
ࢱ࣮ࣥᩘ ᩿㠃㉳☢ຊRxZ
RxZ (mm) kA
–Ḟᦆ

ᑟయ㛗
(m)

1 0.795 0.733 +10.363 4x37, -1 4.4x40.7 +10.290 734.3
2 0.795 0.400 -8.654 4x31, -1 4.4x34.1 -8.610 614.4
3 0.795 0.135 +7.280 4x26, -1 4.4x28.6 +7.210 514.5
4 0.795
0.0 -9.481 4x34, -1 4.4x37.4 -9.450 674.3
5 0.795 -0.135 +7.280 4x26, -1 4,4x28.6 +7.210 514.5
6 0.795 -0.400 -8.654 4x31, -1 4.4x34.1 -8.610 614.4
7 0.795 -0.733 +10.363 4x37, -1 4.4x40.7 +10.290 734.3

㹼ഃ ᑟ య ࡛+0.20m㹼+0.30m, ୗ ഃ ᑟ య ࡛-0.05m㹼-0.15m
0.15m ࡛࠶ࡿࠋ࢖ࣥࢲࢡࢱࣥࢫࡣ 2.02 H ࡜ィ⟬ࡋ࡚࠸ࡿࠋ⾲⓶ຠᯝࡀࠊࡸࡸ࢖ࣥࢲࢡࢱࣥࢫࢆῶ ᑡ ࡉ ࡏ ࡿ ຠ ᯝ ࢆ ᣢ ࡗ ࡚ ࠸ ࡿ ࠋ100ns ࡛ ࠊ0Ѝ
1.0kA ࡢ㟁ὶୖ᪼ࢆ⪃࠼ࡿ࡜ࠊ㧗㟁ᅽ 20-50kV ࡀ
ぢ㎸ࡲࢀࡿࡀࠊ࢟ࢵ࣮࢝ࢥ࢖ࣝࡢ㏻㟁᮲௳ࡣ᳨ウ୰࡛࠶ࡿࠋ

ᑟయ:1.1mmȭNiTi ㉸㟁ᑟ⥺ࢆ᝿ᐃ㺂ᐃ᱁ 70A, ᭱኱ 140A

10㸫 48

Fig. 5-22 ࡟ࡣ Muon ⵳✚㡿ᇦࡢ BR ☢ሙศᕸࢆ♧ࡋࡓࠋ୺☢ሙࡢ BR ࡣ⵳✚㡿ᇦ࡛ࡣ࡯ࡰ㞽࡛ࠊZ >࡜࡟࡞ࡿࠋࡇࡢ☢ሙ࡛ࠊMuon ࡢ㍈᪉ྥ⛣ືࢆṆࡵࡿࠋ

0.30m ࡛ࡣ኱ࡁࡃ࡞ࡿࠋࡇࢀ࡟ᑐࡋ࡚, ཰᮰☢ሙ

5.3.3. ⬟ື☢Ẽ㐽ⶸᆺࢫࢸ࢔ࣜࣥࢢ☢▼ࢆຍ࠼ࡿ࡜ࠊ⵳✚㡿ᇦ௜㏆࡛㈇ࡢ໙㓄ࢆᣢࡘ BRศ ᕸ ࡀ ฟ ᮶ࡿ ࠋ ࢟ ࢵ ࣮࢝ ☢ ሙ ࡣ ⵳✚ 㡿 ᇦ ࠿ ࡽMuon ࡢධᑕ࣭⵳✚ࡀ㡰ㄪ࡟⾜ࢃࢀࡿ☢ሙࢆᣢ

Z=0.20m ௜㏆ࡲ࡛ BR>0 ࡢ☢ሙࢆ▷᫬㛫Ⓨ⏕ࡍࡘ MSM ࢆタィࡋ࡚ࡁࡓࠋࡋ࠿ࡋࠊᐇ㝿ࡢ MSM

ࡿࠋࡇࡢ㡿ᇦ࡛ࡣࠊ௚࡟ BR ࢆᙉࡃ(1mT ⛬ᗘ)Ⓨ⏕࡟ࡣ✀ࠎࡢㄗᕪ☢ሙࡀΰධࡍࡿࠋ⵳✚㡿ᇦࡢ☢

ࡍ ࡿ ࡶ ࡢ ࡣ↓ ࠸ ࡢ ࡛ ࠊ࢟ ࢵ ࢝ ࣮ ㏻㟁 ୰ ࡣ ࠊ ࡯ሙ࡟ᑐࡋ࡚ࡣ☢ሙࢩ࣑ࣥࢢ⏝ࡢᶵჾ㸦ཷືࢩ࣑ࡰࠊ࢟ࢵ࣮࢝☢ሙࡢࡳࡀ BR ☢ሙࢆసࡗ࡚࠸ࡿࡇ

ࣥࢢᶵᵓ࡞࡝㸧ࢆ⏝ពࡋ࡚࠸ࡿࡀࠊMuon ධᑕ㌶㐨 ࡢ ᚤ ㄪ ᩚ ⏝ ࡟ ࡣ ࠊ ࢫ ࢸ ࢔ ࣜ ࣥ ࢢ ☢ ▼(SM:
Steering Magnet)ࢆࠊ㕲 yoke ࡟㛤ࡅࡓ Muon ධᑕ⏝㈏㏻Ꮝࡢ๓ᚋ࡟㓄⨨ࡍࡿィ⏬(Fig. 5-23)࡛࠶ࡿࠋ

Supported from upper sideᮏ㡯ࡢෆᐜࡣཧ⪃ᩥ⊩[53, 54]࡟ヲࡋ࠸ࠊࡑࡢᢤ

3.0 T

Support rods
(Insulator)⢋࡛ㄝ᫂ࡍࡿࠋヲࡋ࠸ィ⟬ᡭἲࡣࠊཧ⪃ᩥ⊩[14,
15, 28, 29, 41, 53, 54]ࢆཧ⪃࡟ࡍࡿ࡜Ⰻ࠸ࠋ

Upper conductor
Muons

Lower conductor
Fig. 5-21 ࢟ࢵ࣮࢝ࢥ࢖ࣝࡢ 2 ࡘࡢᑟయ㸦෇⟄ᯈ㸧࡜ Muon ⵳✚㡿ᇦ࡜ࡢ㛵ಀ

Deceleration

Muons

Acceleration
0.4

Fig. 5-23 ஧ࡘࡢ ASSM 㓄⨨ࢆ♧ࡍᶍᘧᅗ. ᩥ⊩[54],Fig.1 ࡼࡾᘬ⏝ࡇࡢ SM ࡣ࿘ᅖ࡜ࡢ☢Ẽⓗ┦஫స⏝࡟ࡼࡿㄗᕪ
☢ሙࢆ㑊ࡅࡿࡓࡵࠊ㧗☢ሙ(3.0T)୰࡛⢭ᗘⰋ࠸☢
Ẽࢩ࣮ࣝࢻᶵ⬟ࡀᚲせ࡛࠶ࡿࠋࡘࡲࡾࠊ⬟ື☢
Ẽ㐽ⶸ(AS: Active Shield)ᶵ⬟ࢆᣢࡘ ASSM(⬟ື

Magnet+Weak focus+Kicker field

0.1

0

-0.1
-0.0020.000

BR (T)

0.002☢ Ẽ 㐽 ⶸ ᆺ ࢫ ࢸ ࢔ ࣜ ࣥ ࢢ ☢ ▼: Active Shield
Steering Magnet)࡛࠶ࡿࠋࡲࡓࠊ⇕ⓗ࡞せᅉ࡟ࡼࡿ
0.29msCurrent

0.2

Conductor Z position
R=0.36m
R=0.36m

Vertical position Z (m)

0.3

Time

0.004

Fig. 5-22 Muon ⵳✚㡿ᇦ௜㏆ࡢ %R ☢ሙศᕸ

Flattop current
0.23msFig. 5-24 inner-ASSM ࡢ㏻㟁Ἴᙧ(25 Pulses/1 ⛊).
ᩥ⊩[54],Fig.2 ࡼࡾᘬ⏝.

10㸫 49

Table 5-7 Target specifications of ASSMs
Parameter
Inner-ASSM Outer-ASSM
BL product (Tm)
1.0E-3
4.0E-3Magnetic field direction
RadialRadial, axial
Control angle
Pitch
Pitch, rolling
Magnetic shied ( T)
< 1.0 at 0.2m < 1.0 at 0.3m
Joule heat Q (W)
<1.0
<10.0
OXWHUGLDPHWHU PPĭ
42.7
89.1
Beam Wall thickness (mm)1.5
2.1
TBD (Temporary SUS)
duct Material
Eddy current decay time te 0.0575 ms 0.166 ms
Allowable Diameter (mm)
<100
<200
size
Length (mm)
<200
<400

ㄗᕪ☢ሙࢆ㑊ࡅࡿࡓࡵ࡟ࠊⓎ⇕㔞ࢆᢚไࡍࡿ
ࡼ࠺࡟ J-PARC 㐠㌿࡟ྜࢃࡏࡓࣃࣝࢫ㐠㌿(25Hz)
ࢆ⾜࠺(Fig. 5-24)ࠋᮏ㡯࡛ࡣࠊASSM ࢆ☢Ẽタィᡭἲ࡜ඹ࡟⤂௓ࡍࡿࠋ

Fig. 5-25 2D ᳨ウ࡟ࡼࡿ ASSM ࡢ㟁ὶ࣭☢ຊ⥺.
ᩥ⊩[54],Fig.3 ࡼࡾᘬ⏝

Table 5-7 ࡣタィࡢ┠ᶆ௙ᵝ࡛࠶ࡿࠋ┠ᣦࡍ☢ሙࡿࠋ୺ࢥ࢖ࣝࡢ㟁ὶᐦᗘࡣ᭱኱ 21.1A/mm ࡛࠶(Muon ࡟ᚲせ࡞ BL ✚)ࢆࠊᑠࡉ࠸☢▼(☢Ẽ㐽ⶸᛶࡾࠊࡇࡢ⤖ᯝ࠿ࡽᑟయࢆ 1mm ᖜ(࿘ᅇ᪉ྥ)㹶

⬟ࠊⓎ⇕㔞ࡶྵࡴ)࡟Ⓨ⏕ࡍࡿࡇ࡜ࡀ㔜せ࡛࠶

2mm(༙ᚄ᪉ྥ)࡛ࠊ⣲⥺㟁ὶ 25A ࢆ㑅ᢥࡋࡓࠋࡲ

ࡿࠋ༑ศ࡞☢Ẽ㐽ⶸࢆᚓࡿ࡟ࡣ 3D ࡛ࡢࢩ࣮ࣝࢻ

ࡓࠊࡇࡢ⤖ᯝ࠿ࡽࠊᚲせ࡞㟁※࡜Ⓨ⇕㔞ࡶᴫ⟬ࢥ࢖ࣝࡢタィࡀᚲせ࡛࠶ࡿࡢ࡛ࠊࢫࢸ࣮ࣛࣞࢱ

ฟ᮶ࠊ≉ู࡞෭༷ࡸ㟁※ࡀᚲせ࡛࡞࠸ࡇ࡜ࡶᢕ

ᆺ᰾⼥ྜ⿦⨨ࡢࢥ࢖ࣝᙧ≧タィᢏ⾡(DUCAS)[41]ᥱ࡛ࡁࡓࠋࡇࡢ⤖ᯝࢆཷࡅࠊ3D ᳨ウ࡟㐍ࡴࠋ࡜⬟ື☢Ẽ㐽ⶸࢆᣢࡘ MRI ഴᩳ☢ሙࢥ࢖ࣝࡢタ

3D ᳨ウ࡛ࡣࠊDUCAS[41]࠾ࡼࡧ MRI ⏝ࡢ⬟ືィ ᡭ ἲ[14,15]ࢆ ᛂ ⏝ ࣭ 㐺 ⏝ ࡋ ࡓ ࠋ ࡇ ࡇ ࡛ ࡣ ࠊ☢Ẽࢩ࣮ࣝࢻഴᩳ☢ሙࢥ࢖ࣝࡢタィᡭἲ[14, 15,

inner-ASSM ࡢタィ࡟ࡘ࠸࡚ㄝ᫂ࡋ࡚࠸ࡃࠋ

28, 29]ࢆᛂ⏝ࡍࡿࠋFig. 5-26 ࡣ 3D ᳨ウ⏝ࡢィ⟬

ASSM ࡢ☢ሙタィࡣ 2 ࡘࡢẁ㝵࡟ศࡅ࡚㐍ࡵ࡚ࣔࢹ࡛ࣝ࠶ࡿࠋFig. 4-13 ࡛♧ࡋࡓ DUCAS ᳨ウ⏝࠸ࡿࠋࡲࡎࠊ2D(2 ḟඖ)࡛ࠊᑟయࡢ㑅ᢥࢆ㋃ࡵࠊ

ࡢ㟁ὶ⾲⌧ࣔࢹࣝࢆ౑࠺ࠋྛ⠇Ⅼࡢ㟁ὶ࣏ࢸࣥᴫ␎ࢆᢕᥱࡋࠊ3D タィ࡛ᐇ㓄⥺ࢆỴࡵࡿࠋ࠸ࡎ

ࢩ್ࣕࣝ T ࢆࠊྑᅗ MFEPs ࡛ BR=0 ࢆ‶ࡓࡍࡼ࠺ࢀࡢሙྜࡶࠊ୺ࢥ࢖ࣝ(┠ⓗࡢࢫࢸ࢔ࣜࣥࢢ☢ሙ

࡟ࠊTSVD ṇ๎໬ࢆ฼⏝ࡋ࡚Ỵࡵࡿࠋ୺ࢥ࢖ࣝࢆసࡿ)࡜ࢩ࣮ࣝࢻࢥ࢖ࣝࢆ┦஫࡟▩┪࡞ࡃタィࡍࡿࡓࡵ࡟ୗグࡢᡭ㡰ࢆ࡜ࡿࠋ(i)୺ࢥ࢖ࣝࡢ㟁ὶ㓄⨨ࠊ

(ii)୺ࢥ࢖ࣝࡢ☢ሙࢆ࿘㎶࡛ᡴࡕᾘࡍࢩ࣮
ࣝࢥ࢖ࣝࡢ㟁ὶศᕸィ⟬ࠊ

(iii)ࢩ࣮ࣝࢻࢥ࢖ࣝ☢ሙࢆ⪃៖ࡋ࡚୺ࢥ࢖
ࣝࡢ㟁ὶศᕸࢆ෌ィ⟬ࠊ

(iv)☢▼࿘ᅖࡢ☢ሙࢆ☜ㄆࡋࠊ༑ศᙅࡅࢀ
ࡤィ⟬⤊஢ࠊ኱ࡁ࠸ሙྜ࡟ࡣ(ii)࡟ᡠࡾ
⧞ࡾ㏉ࡋィ⟬ࠊࡇ࠺ࡋ࡚ࠊ2D タィ࡛ࠊ┤⥺㟁ὶศᕸࢆồࡵࡓ☢ሙタィ⤖ᯝࡀ Fig. 5-25 ࡛ࠊ☢ຊ⥺ࢆ♧ࡋ࡚࠸
ࡿࠋ100 ࢞࢘ࢫࡢ☢ሙࢆࠊ10cm ࡢ㛗ࡉ(⣬㠃ᆶ┤᪉ྥ)࡛Ⓨ⏕ࡍࡿࠋࢩ࣮ࣝࢻࢥ࢖ࣝእഃ࡟ࡣ☢ຊ⥺ࡀ₃ࢀ࡚↓ࡃࠊⰋዲ࡞☢Ẽ㐽ⶸࡀᚓࡽࢀ࡚࠸

Fig. 5-26 3D ASSM ☢ሙタィ᳨ウ⏝ィ⟬ࣔࢹࣝ. ᩥ⊩[54],Fig.4 ࡼࡾᘬ⏝10㸫 50Table 5-8 inner-ASSM ☢ሙタィࡢ᳨ウ⤖ᯝ ᩥ⊩[54], Table 2 ࡼࡾᘬ⏝Fig. 5-27 3D ᳨ウ࡟ࡼࡿ ASSM ࡢ㟁ὶ㓄⨨ୖ㸸㟁ὶ࣏ࢸࣥࢩࣕࣝศᕸࠊୗ㸸ᑟయ㓄⨨. ᩥ⊩[54],Fig. 6&7 ࡼࡾᘬ⏝.
(ᕥ)ࡣࠊ〇సࢆ⡆༢໬ࡍࡿࡓࡵ࡟ࠊ┤⥺ࢆᇶᮏ࡜ࡋࡓᕳࡁ⥺ᵓ㐀࡜ࡋࠊୗグࡢศᕸ࡜ࡋࡓࠋ
=σsin{(2 െ 1) } ( ),(5-8)ࡇࡇ࡛ࠊ ࡣࠊ(X, Y)఩⨨࣋ࢡࢺࣝ࡜ࠊX ㍈࡜ࡢゅᗘࠊT0 ࡣ 2D ࡛ࡢ᭱኱㟁ὶ࣏ࢸࣥࢩ್ࣕࣝ(㉳☢
ຊ)࡛ࠊ⧞ࡾ㏉ࡋィ⟬ࢆ C1 =1.0 ࡜ Cl = 0 (l=2 to 4)࡛㛤ጞࡋࠊ┠ᶆࡢ BL ࡀࣅ࣮࣒ࢲࢡࢺ᩿㠃ෆ୍࡛ᵝ࡜࡞ࡿࡼ࠺࡟ࠊCl (l=1 to 4)ࢆㄪᩚࡍࡿࠋ
ࡑࡢ⤖ᯝᚓࡽࢀࡓ㟁ὶ࣏ࢸࣥࢩࣕࣝศᕸࢆ Fig.
5-27 ୖ㒊࡟♧ࡍࠋ25A ẖࡢ➼㧗⥺࡛♧ࡋ࡚࠸ࡿࠋ
Fig. 5-27 ୗᅗ࡛ࡣࠊ
= 25.0 × (Parameter
2D design 3D design
P/S current (A)
25.0
25.0
Numb. of turns±22/12±25/12
Conductor (mm)Cu 1.0x2.0 Cu 1.0x2.0
Max.current density (A/mm)
21.1
20.8
Rough size (mm)ĭ-150L ĭ-164L
1.0E-30.996E-3
BL products (T㺃m)
Magnetic energy (J)0.01890.0322
EM
Inductio Inductance (mH)
60.4
100.3
n
Inductive voltage (V)
50.3
86.0
Resistance (W)
0.153
0.222
Resistive voltage (V)
3.83
5.55
Joule
loss
Heat generation (W)
0.60
0.87
with SS duct
25Hz
25Hz
Duct Joule loss (W)
1.0 (rough estimation)
64.1
91.6
Power Total voltage (V)supply Spec. plan
120V, 30A, >10kHz

ࡢ➼㟁ὶ࣏ࢸࣥࢩࣕࣝ⥺(➼㧗⥺)࡟ἢࡗ࡚㓄⨨ࡋࡓᑟయ఩⨨࡛࠶ࡿࠋm ࡣᕳࡁ⥺␒ྕ(ᩚᩘ)࡛࠶
ࡿࠋࢩ࣮ࣝࢻࢥ࢖࡛ࣝࡣ m<0 ࡛࠶ࡿࠋࡇࡇ࡛ࠊmࡣ୧➃㒊࡛ࡣࠊᑟయ㓄⨨ࢆᗈࡆ࡚࠸ࡿࡀࠊࡇࢀࡣ ࠊ ࢩ ࣮ ࣝࢻ ࢥ ࢖ ࣝ ➃㒊 ࡢ 㛤 ཱྀ 㒊ࢆ ⪃ ៖ ࡋ ࠊ
ASSM ඲య࡛☢Ẽ࣮࣓ࣔࣥࢺࡀ㞽࡜࡞ࡿࡼ࠺࡟ࢩ
࣮ࣝࢻࢥ࢖ࣝࡢ☢Ẽ࣮࣓ࣔࣥࢺࢆ኱ࡁࡃࡋࡓ⤖ᯝ࡛࠶ࡿࠋࡇࡢࡼ࠺࡟ࡋ࡚ồࡵࡓ inner-ASSM ࡢసࡿ☢ሙ
ࢆ Fig. 5-28 ࡟♧ࡍࠋᕥ࡟ࡣ ASSM ࡀసࡿ BL ್ࠊെ 0.5) ( ),(5-9)

BL = ‫׬‬.
.

,(5-10)

ศᕸࢆ᩿㠃ࡢ➼㧗⥺(1.0E-6 Tm ẖ)࡛♧ࡋࡓࠋ୰ᚰ࡛ࡣ 0.0996Tm ࡛࠶ࡾࠊ┠ᶆ್୍࡛ᵝ࡞ BL ✚ࡀ᩿㠃࡛ᚓࡽࢀࡿࡇ࡜ࡀゎࡿࠋྑഃ࡟ࡣࠊASSM
࿘㎶ࡢ☢ሙᙉᗘࢆ♧ࡋࡓࠋASSM ୰ᚰ࠿ࡽ 0.2m
㞳ࢀࡿ࡜ࠊ1 T ௨ୗࡢ☢ሙ࡛࠶ࡾࠊ༑ศ࡞☢Ẽࢩ࣮ࣝࢻࡀฟ᮶࡚࠸ࡿ࡜ุ᩿ࡋ࡚࠸ࡿࠋ
⌧≧ࡢタィ⤖ᯝࢆ Table 5-8 ࡟♧ࡍࠋ᭱⤊∧࡛ࡣ࡞࠸ࡀࠊタィᡭἲ࡜ࡋ࡚ࡣ༑ศ࡞⬟ຊ࡛࠶ࡿ࡜⪃࠼࡚࠸ࡿࠋouter-ASSM ࡢタィࡣ 2D ࡢࡳࡀ⤊Fig. 5-28 ☢ሙタィ⤖ᯝ ᕥ㸸ࣅ࣮࣒ࢲࢡࢺෆࡢ
BL ✚ศᕸ(%/=0.996E-3Tm ࡛+/-1 Tm ௨ෆࡢ᣺ᖜ)ࠊྑ㸸ASSM ࿘ᅖࡢ₃ࢀ☢ሙศᕸ. ᩥ⊩[54], Fig. 8 & 9 ࡼࡾᘬ⏝ࢃࡗ࡚࠸ࡿࡀࠊ௒ᅇ♧ࡋࡓ ASSM ࡢ 3D タィᡭἲࡣᛂ⏝࡛ࡁࡿ࡜⪃࠼࡚࠸ࡿࠋ

10㸫 51

5.4. g-2/EDM ☢▼☢ሙタィࡢࡲ࡜ࡵ࡚ࠊྜィ 62kAT ࡛ࠊn-index=1.5E-4 ࡢഴᩳ☢ሙࢆJ-PARC࣭㧗࢚ࢿࣝࢠ࣮ຍ㏿ჾ◊✲ᶵᵓ(KEK)ࡘࡃࡿࡼ࠺ TSVD ṇ๎໬࡛㉳☢ຊ㓄⨨ࢆỴࡵࡓࠋ࡛ࡣ࣑࣮ࣗ࢜ࣥ(Muon)ࡢ␗ᖖ☢Ẽ⬟⋡/㟁Ẽ⬟⋡ࢥ࢖ࣝᕳࡁ⥺ᵓ㐀࡟ࡘ࠸࡚タィ㐍⾜୰࡛࠶ࡿࠋ

(g-2/EDM)ࢆ⢭ᗘⰋࡃィࡍࡿᐇ㦂ࢆィ⏬ࡋ࡚࠾ㄗᕪ☢ሙࡣタ⨨ㄗᕪ࡟ᩄឤ࡛࠶ࡾࠊᐇᶵ࡛ࡣࠊ

ࡾࠊࡑࡢᐇ㦂࡛౑⏝ࡉࢀࡿ muon ⵳✚☢▼(MSM)ഴᩳ☢ሙࢆຍ࠼ࡿሙྜ࡟ࡣࠊ෌ᗘࡢ fine ࢩ࣑ࣥࡢタィ࡟ࡘ࠸࡚ㄝ᫂ࡋࡓࠋᮏ☢▼ࡣࠊmuon ⵳✚

ࢢࡀᚲせ࡟࡞ࡿ࡜⪃࠼࡚࠸ࡿࠋ

✵㛫࡛ࡣ MRI ࡟ẚ࡭⣙ 1 ᱆Ⰻ࠸(ᆒ୍ᗘࡀᑠࡉ࠸)࢟ࢵ࣮࢝ࢥ࢖ࣝࡣ࢖ࣥࢲࢡࢱࣥࢫࢆᑠࡉࡃࡍ

ᆒ୍ᗘ 0.2ppm ࡢ୍ᵝ☢ሙࡀᚲせ࡛ࠊmuon ࡢධࡿࡇ࡜ࡀᚲせ࡛ࠊⷧᯈ࣭෇⟄≧ࡢᑟయࢆ㟁ὶ᪉ᑕ࡟ࡣ⼺᪕ධᑕࢆ౑࠺஦ࡀ≉ᚩ࡛࠶ࡿࠋ2 ࡘࡢ≉ྥࡢ஫࠸࡟␗࡞ࡿ 2 ࡘ㓄⨨ࡋ࡚ 300-1000A ⛬ᗘᚩࢆᐇ⌧ࡍࡿ☢ሙศᕸࢆⓎ⏕࡛ࡁࡿ MSM ☢▼ࡢࡢ㟁ὶࢆὶࡍィ⏬࡛࠶ࡿࠋMuon ධᑕ࣭⵳✚࡟ᑐタィࢆ㐍ࡵࠊᐇ⌧ྍ⬟࡞㉳☢ຊ㓄⨨ࢆᣢࡕࠊỌࡋ࡚᭱㐺࡞㓄⨨ࢆồࡵ࡚࠾ࡾࠊ㐍⾜୰࡛࠶ࡿࠋ
ࢫࢸ࢔ࣜࣥࢢ☢▼ࡣࠊ☢▼ࡢධᑕ᪉ྥ࡜ࣅ࣮

ஂ㟁ὶ࣮ࣔࢻ࡛㏻㟁ࡍࡿ㉸㟁ᑟ☢▼ࡢ☢ሙタィ࣒఩⨨ࢆࠊMSM ධᑕ᫬࡟ᚤㄪᩚࡍࡿࠋ㕲 yokeࢆ⾜ࡗࡓࠋ
MRI ྠᵝ࡟ 3 ࡘࡢ Step ࡛☢▼タィࢆ⾜ࡗࡓࠋ࡟ࡣධᑕ⏝㈏㏻Ꮝࡀ⏝ពࡉࢀࡿࡀࠊࡑࡢ๓ᚋ࡟

ᆒ୍☢ሙ࡜ Muon ධᑕྍ⬟࡞༙ᚄ᪉ྥ☢ሙࢆᵓᡂ㓄⨨ࡉࢀࡿࠋ㕲 yoke ➼ࠊMSM ᵓ㐀≀ࡀ㏆ഐ࡟Ꮡ

ࡍࡿᚲせࡀ࠶ࡿࠋStep-1 ࡛ࡣࠊ☢▼඲యࢆそ࠺ᅾ ࡍ ࡿ ࡢ ࡛ࠊ ⬟ ື ☢ Ẽ㐽 ⶸ ࡢ ᶵ ⬟ࡀ ᚲ せ ࡛ ࠶㉳☢ຊ※ࡀ ᚲせ࡛᭷ࡿ ࡇ࡜ࡀゎࡗ ࡓࠋStep-2,

ࡿࠋࡑࡢࡓࡵࠊ⬟ື☢Ẽࢩ࣮ࣝࢻᆺࢫࢸ࢔ࣜࣥ

Step-3 ࡛ࡶࠊMRI ☢▼タィ࡜ྠᵝ࡞᳨ウ࡛࠶ࡿࢢ☢▼ (ASSM: Active Shield Steering Magnet) ࡛࠶

ࡀࠊMSM ࡛ࡣ㕲 yoke ᙧ≧ࢆྵࡵ࡚㉳☢ຊ㓄⨨ࡿࠋ㕲 yoke ࡢ⵳✚㡿ᇦഃ࡟㓄⨨ࡍࡿ inner-ASSM

ࢆ᭱㐺໬ࡋࡓࠋࡑࡢ⤖ᯝࠊMuon ⵳✚㡿ᇦ(༙ᚄ࡟ࡘ࠸࡚ࠊ3D ࡛ࢩ࣮ࣝࢻࢥ࢖ࣝࡲ࡛ྵࡵ࡚タィ

0.333m, ༙ᚄ᪉ྥᖜ 5cm, ㍈᪉ྥ㧗ࡉ 10cm)࡛ࠊ

ࡋࡓࠋMRI ⿦⨨࡛⏝࠸ࡿ⬟ື☢Ẽࢩ࣮ࣝࢻᆺഴ☢ ሙ ᙉ ᗘ 3.0T ࡛ ᆒ ୍ ᗘ 0.079ppm ࡢ ☢ ሙ ࢆᩳ☢ሙࢥ࢖ࣝ㸦ASGC: Active Shield Gradient field

5.0071MAT ࡢ㉳☢ຊ࡜ࠊ୰ᚰ㒊࡟✺㉳ᙧ≧(࣏࣮

Coil㸧 ࡢ タィ ᢏ ⾡ ࢆ ᛂ⏝ ࡋ ࡓ ࠋ Inner-ASSM ࡣࣝ)ࢆᣢࡘ㕲 yoke ࡛┠ᶆ☢ሙࢆᐇ⌧ࡍࡿ☢▼ࢆタ

1mTm ࡢ BL ✚ࢆᣢࡕࠊ୰ᚰ࠿ࡽ 0.2m 㞳ࢀࡓ఩⨨ィࡋࡓࠋ࡛ࡣ 1 T ௨ୗ࡟☢ሙ㐽ⶸ࡛ࡁࡿ ASSM ࢆタィฟᐇ㝿ࡢᐇ㦂࡛⪃࠼ࡽࢀࡿㄗᕪ☢ሙ࡟ᑐᛂࡍࡿ

᮶ࡿࡇ࡜ࢆㄝ᫂ࡋࡓࠋ
௨ୖࡢタィࡣ㐍ᒎ୰࡛࠶ࡾࠊヲ⣽タィࡀ㐍ࡴࡓࡵ࡟ᚲせ࡜ண᝿ࡉࢀࡿㄪᩚ⿦⨨ࡶタィࡋࡓࠋMuon ⵳✚㡿ᇦ࡟ࡣࠊMRI ⏝☢▼࡜ྠࡌࢩ࣑

࡜ࠊ☢ሙタィࡢᚤㄪᩚࡶ⾜࠺ࡇ࡜࡟࡞ࡿ࡜⪃࠼ࣥࢢィ⟬ἲࢆ฼⏝ࡍࡿィ⏬࡛ࠊ௬᝿ⓗࢩ࣑ࣥࢢ࡚࠸ࡿࠋࡲࡓࠊㄗᕪ☢ሙࡢ⿵ṇࡣࠊᐇᶵ࡛┠ᶆ(ࢩ࣑ࣥࢢࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ)ࢆ⾜ࡗࡓࠋ㍈᪉ྥ☢ሙࢆᐇ⌧ࡍࡿୖ࡛㔜せ࡛࠶ࡿ࡜⪃࠼ࠊྍ⬟࡞☢ሙࢆᆒ୍໬࡛ࡁࡿ஦ࡀ♧ࡉࢀࡓࠋࡋ࠿ࡋࠊ㕲⿵ṇᶵᵓࢆ௜ຍࡋ࡚࠸ࡃࠋ

yoke ࡢタ⨨ㄗᕪࡀࠊ㕲∦࡟ࡼࡿࢩ࣑ࣥࢢ࡛ࡣ⿵
ṇฟ᮶࡞࠸ࠊ㍈࡟ᆶ┤࡞☢ሙᡂศࢆⓎ⏕ࡋࠊṧᕪ☢ሙ࡜࡞ࡿࡇ࡜ࡀྍ⬟ᛶ࡜ࡋ࡚♧ࡉࢀࡓࠊࡇ
ࡢ⿵ṇ࡟ࡣࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖ࢆ⏝ពࡍࡿࠋ
Muon ධᑕ㛵㐃ࡢ☢ሙ࡜ࡋ࡚ࠊᙅ㞟᮰☢ሙࠊ࢟ࢵ࣮࢝☢ሙࠊࡑࢀ࡟ࠊࢫࢸ࢔ࣜࣥࢢ☢ሙࡀ࠶ࡿࡀࠊࡑࢀࡒࢀࠊ☢ሙタィࢆ㐍ࡵ࡚࠸ࡿࠋ
ᙅ㞟᮰☢ሙࢥ࢖ࣝ(WFC)ࡣࠊタ⨨ㄗᕪࢆ㍍ῶ࡛
ࡁࡿ࡜⪃࠼ࠊ୺ࢥ࢖ࣝࡢ┤ࡄෆഃ࡟ࠊᨭᣢᵓ㐀
ࢆඹ㏻࡟ࡋ࡚㓄⨨ࡍࡿࠋ7 ಶࡢᑠ CB ࢆ㓄⨨ࡋ10㸫 52

6. ࡲ࡜ࡵ
J-PARC ࡛‽ഛࡋ࡚࠸ࡿ g-2/EDM ⢭ᐦィ㐀ࡣ⪃៖ࡏࡎࠊCB ඲యࡢ㉳☢ຊࡣࠊ㟁ὶᐦᗘ
⏝☢

▼(MSM)ࡢ☢ሙタィ࡟ࡣࠊ᭱ᑠ஧஌ἲࢆᡴࡕษ
ࡾ≉␗್ศゎࡢ฼⏝ࡋ࡚ゎࡃᡭἲ(TSVD ṇ๎໬)ࢆ ౑ ࡗ ࡚ ࠊ㐍 ࡵ ࡚ ࠸ ࡿࠋ ࡑ ࡢ ࡓ ࡵࠊ ᮏ ㈨ ᩱ ࡛ࡣࠊ➨ 2 ❶࡛ᡭἲࡢᐃᘧ໬ࢆㄝ᫂ࡋࡓࠋ┠ᶆ☢ሙศᕸࠊᅛ᭷࣮ࣔࢻศᕸࠊᅛ᭷࣮ࣔࢻᙉᗘࠊᡴࡕ
ษࡾᅛ᭷࣮ࣔࢻ␒ྕࠊṧᕪ☢ሙࠊ෌ᵓᡂ㟁ὶࠊ෌ᵓᡂ☢ሙ࡟ࡘ࠸࡚ࠊᐃ⩏ࢆ㏙࡭ࡓࠋ
➨ 3 ❶࡛ࡣࠊ౛㢟ࢆゎࡃࡇ࡜࡛ࠊᡭἲࡢ⌮ゎࢆ㐍ࡵࡓࠋࡲࡎࠊィ⟬⢭ᗘࡢ☜ಖࡢࡓࡵ࡟ࠊ෇㟁ὶ(⥺㍯㟁ὶ)ࡢసࡿ☢ሙࡢィ⟬ἲࢆ☜ㄆࡋ࡚ࠊ12᱆ࡢ⢭ᗘ࡛⥺㍯㟁ὶ࡟ࡼࡿ☢ሙࡀồࡲࡗ࡚࠸ࡿ
ࡇ࡜ࢆ☜ㄆࡋࡓࠋࡑࡢୖ࡛౛㢟ࢆゎ࠸ࡓࠋ෇⎔య⣔࡛ࠊ෇⎔ෆ㒊࡟┠ᶆ☢ሙࢆ୚࠼ࡓࠋ」ᩘࡢ
✀㢮ࡢ┠ᶆ☢ሙࢆ୚࠼ࠊ෇⎔㠃ࢆ࿘ᅇ᪉ྥ࡟ὶ
ࢀࡿ㟁ὶࡢ࣏ࣟ࢖ࢲ᩿ࣝ㠃ศᕸࢆồࡵࡓࠋMaxwell ᪉⛬ᘧ࡟▩┪ࡋ࡞࠸┠ᶆ☢ሙࢆ୚࠼ࡿ
࡜ࠊᡴࡕษࡾᅛ᭷࣮ࣔࢻ␒ྕࢆ኱ࡁࡃࡍࡿࡇ࡜
࡛⢭ᗘⰋࡃ☢ሙࢆ෌ᵓᡂࡍࡿ㟁ὶศᕸࢆồࡵࡿࡇ࡜ࢆ♧ࡋࡓࠋ┠ᶆ☢ሙ࡜ࡋ࡚࣋ࢡࢺ࣏ࣝࢸࣥ
ࢩࣕࣝࡶྍ⬟࡛࠶ࡿࡇ࡜ࡶ♧ࡋࡓࠋణࡋࠊࡇࡢ
ሙྜࠊ㟁ὶ್ࢆ኱ࡁࡃࡍࡿ᮲௳ࡶ࠶ࡿࡢ࡛ὀព
ࢆせࡍࡿࠋ➨ 4 ❶࡛ࡣࠊ෇⟄ᆺࡢ඲㌟ MRI ⏝☢▼ࢆ᝿ᐃࡋࡓ㉳☢ຊ㓄⨨タィࢆ౛㢟࡜ࡋࡓࠋ᭱ึ࡟ࠊ▴ᙧ᩿㠃ࡢ෇ᙧࢥ࢖ࣝࡀసࡿ☢ሙࢆࠊ࢞࢘ࢫồ✚ἲࢆ౑࠼ࡤࠊ▷᫬㛫࡛⢭ᗘⰋࡃ☢ሙィ⟬࡛ࡁࡿࡇ࡜ࢆ♧ࡋࠊࡑࡢ᪉ἲࢆ☢ሙタィ࡟⏝࠸ࡓࠋMRI⏝☢▼ࡢ☢ሙタィࡣࠊ3 ࡘࡢẁ㝵ࢆ㏻ࡋ࡚⾜࠺ࠋ
Step-1 ࡛ࡣࠊ෇⟄≧࡟㓄⨨ࡋࡓ⥺㍯㟁ὶ⩌ࡢ㟁ὶศᕸࢆࠊ᧜ീ㡿ᇦ࡛☢ሙศᕸࡀ୍ᵝ࡟࡞ࡿࡼ࠺࡟㸦40cm-⌫㠃࡛ᆒ୍ᗘ 1ppm ⛬ᗘ㸧SVD ᅛ᭷ศᕸࢆ㔜ࡡྜࢃࡏ࡚ồࡵࡿࠋຍ⟬ࡋࡓᅛ᭷࣮ࣔ
ࢻᩘ࡟ᑐᛂࡋࡓ㟁ὶࡢࣆ࣮ࢡࡀ⌧ࢀࡓࠋ
Step-2 ࡛ࡣࠊࡇࡢ㟁ὶࣆ࣮ࢡ఩⨨࡟ࠊ▴ᙧ᩿㠃ࡢࢥ࢖ࣝࣈࣟࢵࢡ(CB)ࢆ㓄⨨ࡋࠊࡑࡢ᩿㠃ᙧ≧
ࢆࠊStep-1 ࡛ồࡵࡓ☢ሙศᕸࢆ෌⌧ࡍࡿࡼ࠺࡟ࠊ
CB ࡢ఩⨨࣭᩿㠃ᙧ≧ࢆㄪᩚࡋࡓࠋ☢ሙศᕸࡢ┠Ᏻ࡜ࡋ࡚ࠊᅛ᭷࣮ࣔࢻᙉᗘࢆ฼⏝ࡋࡓࠋStep-2 ࡛ࡣࠊCB ᩿㠃࡟୍ᵝ࡟㟁ὶࡀศᕸࡋ࡚ࠊᕳࡁ⥺ᵓ

(150-180A/mm2)ࢆಖࡕ㐃⥆ⓗ࡟ኚ᭦(▴ᙧࡢ᩿㠃✚ࢆኚ᭦)࡛ࡁࡿ࡜ࡋ࡚ࠊㄪᩚࡋ࡚࠸ࡿࠋ
Step-3 ࡛ࡣࠊᑟయࢆ㑅ᢥࡋࠊCB ෆࡢᕳࡁ⥺ᵓ㐀ࢆỴࡵࡿࠋStep-2 ࡛ࡢ㟁ὶᐦᗘࠊ᩿㠃ᙧ≧ࢆྍ⬟࡞㝈ࡾ෌⌧ࡍࡿࡼ࠺࡟ỴࡵࡿࡀࠊCB ㉳☢ຊࡣ㞳 ᩓ ್ ࡛ ࠶ࡾ ࠊ ྠ ࡌ ್࡟ ࡣ ฟ ᮶ ࡞࠸ ࠋ ౛ 㢟 ࡛
ࡣࠊ820.3kAЍ830.4kA ࡢ CB ࡶ࠶ࡾࠊᆒ୍ᗘࡣ
0.94Ѝ906ppm (40cm ⌫㠃)࡟ᝏ໬ࡋࡓࠋࡋ࠿ࡋࠊ
ࢥ࢖ࣝ఩⨨ࢆᚤㄪᩚ(2mm ௨ୗࡢ⛣ື)ࡍࡿࡇ࡜
࡛ࠊStep-1, Step-2 ࡢᆒ୍ᗘࢆ෌⌧࡛ࡁࡿࡇ࡜ࢆㄝ
᫂ࡋࡓࠋࡇࢀ࡟ࡼࡾࠊMRI ☢▼ࡢ☢ሙタィࡀ᏶஢ࡍࡿࠋ㕲 yoke ࢆ⏝࠸ࡿ MRI ⏝☢▼ࡶ࠶ࡿࠋࡑࡢ㕲yoke ᙧ≧ࢆⰋዲ࡞ᆒ୍ᗘࡢ☢ሙࢆⓎ⏕࡛ࡁࡿ㕲yoke ᙧ≧ࢆタィࡍࡿࠋࡇࡢタィ࡟ࠊTSVD ࡟ࡼࡿ᭱ᑠ஧஌ゎࢆ฼⏝ࡍࡿ DUCAS(Design tool Using
Current potential And Singular value decomposition)ࢆゎࡋ࡚ࠊ☢ሙタィ࡛ࡁࡿࡇ࡜ࢆ♧ࡋࡓࠋࡋ࠿ࡋࠊタ⨨ᚋࡢᐇᶵ࡛ࡣ✀ࠎࡢ⌮⏤࡛ㄗᕪ☢ሙࡀΰධࡍࡿࠋ1ppm ⛬ᗘ࡛タィࡋ࡚ࡶࠊタ⨨࣭ึບ☢┤ᚋࡢ☢▼࡛ࡣᩘⓒ ppm ࡟ᆒ୍ᗘࡀ
ᝏ໬ࡋ࡚࠸ࡿࠋࢩ࣑ࣥࢢసᴗࡀࠊࡑࡢㄗᕪ☢ሙࡢከ࠸☢ሙศᕸ࠿ࡽタィ☢ሙࢆ෌⌧ࡍࡿࠋ☢ሙ୰࡛☢໬ࡋࠊ☢Ẽ࣮࣓ࣔࣥࢺ(MM)ࢆᣢࡘᙉ☢ᛶయ(㕲ࢩ࣒∦)ࢆ㓄⨨ࡋ࡚ࠊࡑࡢ☢Ẽ࣮࣓ࣔࣥࢺࡀ
సࡿ☢ሙࢆ౑ࡗ࡚ㄗᕪ☢ሙࢆ⿵ṇࡍࡿࠋࡇࡢ㕲ࢩ ࣒ ∦ ࡢ 㓄⨨ ศ ᕸ ࢆ Ỵࡵ ࡿ ィ ⟬ 㸦ࢩ ࣑ ࣥ ࢢ ィ⟬㸧࡟ࡶࠊTSVD ṇ๎໬ࢆ฼⏝ࡋࡓࠋᡴࡕษࡾᅛ
᭷࣮ࣔࢻ␒ྕࡣࠊࢩ࣑ࣥࢢィ⟬࡛ண᝿ࡍࡿᆒ୍
ᗘࡀ༑ศ࡜࡞ࡿ␒ྕ࡜ࡋࡓࠋࡲࡓࠊ┠ᶆ☢ሙᙉᗘࡣࠊ౑⏝㕲㔞ࡀᑡ࡞࠸᮲௳࡜ࡋࡓࠋ
ᐇ㝿ࡢసᴗ࡛ࡣࠊࢩ࣑ࣥࢢ㛤ጞ᫬࡟ࡣከ㔞ࡢࢩ࣒∦ࢆ౑࠺ࡢ࡛ࠊ☢ຊࢆ኱ࡁ࠸ࠋࡑࡢࡓࡵࠊ
ᾘ☢࣭ບ☢ࢆకࡗ࡚ࢩ࣑ࣥࢢసᴗࢆ⾜࠺ࡀࠊ᭱ᚋࡢᚤㄪᩚ࡛ࡣ☢ሙࢆಖࡗ࡚సᴗ(fine ࢩ࣑ࣥࢢ)ࡋࡓࠋࡑࡢࡓࡵࠊࢩ࣒ࢺࣞ࢖ࢆ 2 ✀㢮࡟ศ㢮ࡋࠊࢩ࣒∦㔞ࡢᑡ࡞࠸ࢩ࣒ࢺࣞ࢖ࢆⰋ࠸࡟ࡋ࡚ࠊࢩ
࣑ࣥࢢసᴗࢆ⾜ࡗࡓࠋࡑࡢ⤖ᯝࠊMuSEUM ᐇ㦂࡟฼⏝࡛ࡁࡿⰋዲ࡞ᆒ୍ᗘࢆᐇ⌧࡛ࡁࡿࡇ࡜ࢆ
ㄝ᫂ࡋࡓࠋ

10㸫 53➨ 5 ❶࡛ࡣࠊg-2/EDM ⢭ᐦィᐇ㦂⏝ࡢ Muonᅾ ࡍ ࡿ ࡢ ࡛ࠊ ⬟ ື ☢ Ẽ㐽 ⶸ ࡢ ᶵ ⬟ࡀ ᚲ せ ࡛ ࠶⵳✚☢▼(MSM: Muon Storage Magnet)ࡢ☢ሙタィࡿࠋࡑࡢࡓࡵࠊ⬟ື☢Ẽࢩ࣮ࣝࢻᆺࢫࢸ࢔ࣜࣥ

ࢆㄝ᫂ࡋࡓࠋMRI ☢▼タィ࡛㛤Ⓨࡋࡓタィᡭἲࢢ☢▼ (ASSM: Active Shield Steering Magnet) ࡛࠶࡜ࢩ࣑ࣥࢢᡭἲࢆ㐺⏝ࡍࡿࠋMRI ྠᵝ࡟ 3 ࡘࡢࡿࠋ㕲 yoke ࡢ⵳✚㡿ᇦഃ࡟㓄⨨ࡍࡿ inner-ASSM

Step ࡛☢▼タィࢆ⾜ࡗࡓࠋᆒ୍☢ሙ࡜ Muon ධᑕ࡟ࡘ࠸࡚ࠊ3D ࡛ࢩ࣮ࣝࢻࢥ࢖ࣝࡲ࡛ྵࡵ࡚タィྍ ⬟ ࡞ ༙ ᚄ᪉ ྥ ☢ ሙ ࢆᵓ ᡂ ࡍ ࡿ ᚲせ ࡀ ࠶ ࡿ ࠋࡋࡓࠋMRI ⿦⨨࡛⏝࠸ࡿ⬟ື☢Ẽࢩ࣮ࣝࢻᆺഴ

Step-1 ࡛ࡣࠊ☢▼඲యࢆそ࠺㉳☢ຊ※ࡀᚲせ࡛᭷ᩳ☢ሙࢥ࢖ࣝ㸦ASGC: Active Shield Gradient fieldࡿࡇ࡜ࡀゎࡗࡓࠋStep-2, Step-3 ࡛ࡶࠊMRI ☢▼タ

Coil㸧 ࡢ タィ ᢏ ⾡ ࢆ ᛂ⏝ ࡋ ࡓ ࠋ Inner-ASSM ࡣィ࡜ྠᵝ࡞᳨ウ࡛࠶ࡿࡀࠊMSM ࡛ࡣ㕲 yoke ᙧ≧

1mTm ࡢ BL ✚ࢆᣢࡕࠊ୰ᚰ࠿ࡽ 0.2m 㞳ࢀࡓ఩⨨ࢆྵࡵ࡚㉳☢ຊ㓄⨨ࢆ᭱㐺໬ࡋࡓࠋࡑࡢ⤖ᯝࠊ

࡛ࡣ 1 T ௨ୗ࡟☢ሙ㐽ⶸ࡛ࡁࡿ ASSM ࢆタィฟMuon ⵳✚㡿ᇦ(༙ᚄ 0.333m, ༙ᚄ᪉ྥᖜ 5cm, ㍈᪉

᮶ࡿࡇ࡜ࢆㄝ᫂ࡋࡓࠋ

ྥ㧗ࡉ 10cm)࡛ࠊ☢ሙᙉᗘ 3.0T ࡛ᆒ୍ᗘ 0.079ppm☢▼ᮏయ௨እ࡟ࠊ㕲 yoke ࡛ᅖࡲࢀࡓ✵㛫࡟ࡢ☢ሙࢆ 5.0071MAT ࡢ㉳☢ຊ࡜ࠊ୰ᚰ㒊࡟✺㉳ࡣࠊ㟁Ꮚᑐࡢ᳨ฟჾࠊࡑࡢ㥑ື⏝㟁※(DC-DC ࢥᙧ≧(࣏࣮ࣝ)ࢆᣢࡘ㕲 yoke ࡛┠ᶆ☢ሙࢆᐇ⌧ࡍࡿࣥࣂ࣮ࢱ) ࠊ㟁ὶࢣ࣮ࣈࣝࠊnmr ࢭࣥࢧ࣮➼ࡢከ☢▼ࢆタィࡋࡓࠋ

ࡃࡀ㓄⨨ࡉࢀࡿࠋࡇࢀࡽࡣࠊㄗᕪ☢ሙࡢせᅉ࡜

MRI ⏝☢▼࡜ྠࡌࢩ࣑ࣥࢢィ⟬ἲࢆ฼⏝ࡍࡿ࡞ࡾᚓࡿࠋࡑࡢࡓࡵࠊ☢ᛶయࡢ୙౑⏝ࢆࠊ㓄⨨ィ⏬࡛ࠊ௬᝿ⓗࢩ࣑ࣥࢢ(ࢩ࣑ࣥࢢࡢࢩ࣑࣮ࣗࣞ

ࢆ࿘ᅇ᪉ྥ୍ᵝᛶࠊࢩࣙࣥ)ࢆ⾜ࡗࡓࠋࡑࡢ⤖ᯝࠊ㕲 yoke ࡢタ⨨ㄗᕪᕪ☢ሙせᅉࡢపῶ࡟ດࡵ࡚タィࢆ㐍ᒎࡉࡏ࡚࠸

ࡀࠊ㕲∦࡟ࡼࡿࢩ࣑ࣥࢢ࡛ࡣ⿵ṇฟ᮶࡞࠸ࠊ㍈ࡿࠋ࡟ᆶ┤࡞☢ሙᡂศࢆⓎ⏕ࡋࠊṧᕪ☢ሙ࡜࡞ࡿࡇ
࡜ࡀྍ⬟ᛶ࡜ࡋ࡚♧ࡉࢀࡓࠊࡇࡢ⿵ṇ࡟ࡣࢩ࣒ࢥ࢖ࣝ࢔ࣞ࢖ࢆ⏝ពࡍࡿࠋ
Muon ධᑕ㛵㐃ࡢ☢ሙ࡜ࡋ࡚ࠊᙅ㞟᮰☢ሙࠊ࢟ࢵ࣮࢝☢ሙࠊࡑࢀ࡟ࠊࢫࢸ࢔ࣜࣥࢢ☢ሙࡀ࠶ࡿࡀࠊࡑࢀࡒࢀࠊ☢ሙタィࢆ㐍ࡵ࡚࠸ࡿࠋ
ᙅ㞟᮰☢ሙࢥ࢖ࣝ(WFC)ࡣࠊタ⨨ㄗᕪࢆ㍍ῶ࡛
ࡁࡿ࡜⪃࠼ࠊ୺ࢥ࢖ࣝࡢ┤ࡄෆഃ࡟ࠊᨭᣢᵓ㐀
ࢆඹ㏻࡟ࡋ࡚㓄⨨ࡍࡿࠋ7 ಶࡢᑠ CB ࢆ㓄⨨ࡋ࡚ࠊྜィ 62kAT ࡛ࠊn-index=1.5E-4 ࡢഴᩳ☢ሙࢆࡘࡃࡿࠋタ⨨ㄗᕪ࡟ᩄឤ࡛࠶ࡾࠊᐇᶵ࡛ࡣࠊഴ
ᩳ☢ሙࢆຍ࠼ࡿሙྜ࡟ࡣࠊ෌ᗘࡢ fine ࢩ࣑ࣥࢢࡀᚲせ࡟࡞ࡿ࡜⪃࠼࡚࠸ࡿࠋ
࢟ࢵ࣮࢝ࢥ࢖ࣝࡣ࢖ࣥࢲࢡࢱࣥࢫࢆᑠࡉࡃࡍ
ࡿࡇ࡜ࡀᚲせ࡛ࠊⷧᯈ࣭෇⟄≧ࡢᑟయࢆ㟁ὶ᪉ྥࡢ஫࠸࡟␗࡞ࡿ 2 ࡘ㓄⨨ࡋ࡚ 300-1000A ⛬ᗘࡢ㟁ὶࢆὶࡍィ⏬࡛࠶ࡿࠋMuon ධᑕ࣭⵳✚࡟ᑐࡋ࡚᭱㐺࡞㓄⨨ࢆồࡵ࡚࠾ࡾࠊ㐍⾜୰࡛࠶ࡿࠋ
ࢫࢸ࢔ࣜࣥࢢ☢▼ࡣࠊ☢▼ࡢධᑕ᪉ྥ࡜ࣅ
࣮࣒఩⨨ࢆࠊMSM ධᑕ᫬࡟ᚤㄪᩚࡍࡿࠋ㕲 yoke࡟ࡣධᑕ⏝㈏㏻Ꮝࡀ⏝ពࡉࢀࡿࡀࠊࡑࡢ๓ᚋ࡟
㓄⨨ࡉࢀࡿࠋ㕲 yoke ➼ࠊMSM ᵓ㐀≀ࡀ㏆ഐ࡟Ꮡ

10㸫 54ᗘኚ໬ࡢᢚไࠊ࡞࡝ࠊㄗ



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