Δ·Ͱ੩ిՃ଎‫ͯ͠ͱث‬ҎԼͷೋͭͷํ͕ࣜ޿͘࠾

1 ͸͡Ίʹ

༻͞Ε͍ͯΔɻຊߨٛ͸ɺ௒఻ಋۭಎͷ‫ڀݚ‬։ൃʹ͓͚Δਓࡐҭ• ίοΫΫϩϑτɾ΢Υϧτϯ‫ܕ‬Ճ଎‫ث‬੒Λ໨ࢦͯ͠ɺ௒఻ಋۭಎʹؔ͢Δ‫ج‬ຊతͳ஌ࣝΛղઆ͢Δ΋ͷͰ͋ΔɻຊߘͰ͸ஶऀ͕‫ܞ‬Θ͍ͬͯΔ• όϯσɾάϥʔϑ‫ܕ‬Ճ଎‫ث‬‫ڞ‬໐प೾਺͕ 1.3 GHz ͷ TESLA ‫ܕ‬௒఻ಋۭಎΛҎԼͰίοΫΫϩϑτɾ΢Υϧτϯͱύϯσɾά೦಄ʹ͓͍ͯઆ໌Λߦ͏ʢਤ 1 ࢀরʣɻ͜ͷ TESLAϥʔϑʹΑΔ੩ిՃ଎ͷ‫ݪ‬ཧʹ͍ͭͯ؆୯ʹઆ໌͢‫ۭܕ‬ಎ͸ ILC ‫ܭ‬ըʹ͓͚Δిࢠ/ཅిࢠՃ଎ʹ͓Δɻ͍ͯ࢖༻͞ΕΔՃ଎‫ث‬ίϯϙʔωϯτͰ͋Γɺ૝ఆ͞Ε͍ͯΔϏʔϜͷ଎౓͸ β = 1ɺۭಎ‫ܗ‬ঢ়͸ఆࡏ೾ପԁۭಎͰ͋Δɻ؆୯ͳߏ଄Ͱ͋Γɺද໘ॲཧ
ٕज़΋ཱ֬͞Ε͍ͯΔͨΊɺຊߘͰઆ໌͢Δ্Ͱద
͍ͯ͠Δɻ͜ΕΒΛ೦಄ʹ͓͍ͯຊߨٛΛߦ͏ɻ࠷ॳʹ࠷΋ॳ‫͞༻࠾ʹظ‬Ε͍ͯͨख๏Ͱ͋Δ੩ిՃ଎͍ͭͯઆ໌͢Δɻ࣍ʹɺ‫ݱ‬୅ͷՃ଎‫ث‬ՊֶͰ༻͍Β
ΕΔߴप೾Ճ଎ͷ‫ݪ‬ཧ͓Αͼ‫͍ͯͭʹૅج‬આ໌͢Δɻ͜ͷষͷ࠷‫Ͱޙ‬௨ৗͷৗ఻ಋۭಎͱ௒఻ಋۭಎ
ͷ࠷େՃ଎ޯ഑ͱফඅΤωϧΪʔͷ۩ମతͳൺֱΛߦ͏ɻ࣍ʹ௒఻ಋۭಎͷӡసɺ੡࡞๏ͷ֓ཁʹ͍ͭͯઆ໌͢Δɻ࣍ʹ௒఻ಋۭಎͷੑೳΛൃ‫͢ش‬ΔͨΊʹॏཁͱͳΔද໘ॲཧͷ֓ཁʹ͍ͭͯઆ໌͢Δɻ࣍
ʹۭಎੑೳΛ੍‫͢ݶ‬ΔཁҼʹ͍ͭͯઆ໌͢Δɻ࠷‫ޙ‬ʹ KEK ͰߦΘΕ͍ͯΔ௒఻ಋۭಎͷੑೳͷධՁํ๏ʹ͍ͭͯઆ໌͢Δɻա‫ڈ‬ͷ oho Ͱ΋௒఻ಋۭಎ
ʹ͍ͭͯͷղઆ͕͋Δ [2, 3, 4, 5, 6, 7]ɻ‫ܥ‬౷తʹ௒఻ಋۭಎʹ͍ͭͯษ‫͢ڧ‬Δʹ͸ Hasan ͷ‫ڭ‬Պॻ

[8, 9] ΛಡΉ͜ͱΛ‫ק‬ΊΔɻ

ਤ.2ίοΫΫϩϑτɾ΢Υϧτϯ‫ܕ‬Ճ଎‫༻Ͱث‬͍ΒΕΔঢѹճ࿏ͷి‫ؾ‬ճ࿏ਤ [10]ਤ.1

TESLA shape Superconducting Cavity [1]·ͣɺਤ 2 ʹίοΫΫϩϑτɾ΢Υϧτϯճ࿏ͷి‫ؾ‬ճ࿏ਤΛࣔ͢ɻਤ 2 ͷి‫ؾ‬ճ࿏ʹަྲྀΛҹՃ

2 ੩ిՃ଎

ͨ͠ͱ͖ɺμΠΦʔυ͸ͦͷ੔ྲྀ࡞༻ʹΑΓ‫ۃ‬ੑͷՙిཻࢠΛి৔Λ༻͍ͯՃ଎͢Δ૷ஔΛՃ଎‫ͱث‬มԽʹԠͯ͡։ด͢ΔεΠονͷΑ͏ʹৼΔ෣͏ɻ

͍͏ɻ੩ి৔Λ༻ཻ͍ͯࢠΛՃ଎͢Δํ๏͕ྺ࢙త

͜ͷաఔΛଓ͚Δ͜ͱͰશͯͷίϯσϯαʹిՙ͕ʹ࠷΋ૣཻ͘ࢠՃ଎Λ࣮‫͢ݱ‬ΔࡍʹऔΓೖΕΒΕνϟʔδ͞Εଓ͚Δ͜ͱͱͳΔɻަྲྀͷిѹৼ෯Λͨɻ͜ͷՃ଎‫ث‬͸੩ిՃ଎‫ݺͱث‬͹ΕΔɻ‫ࢸʹࡏݱ‬

Vp ɺஈ਺Λ N ͱ͢Δͱɺ࠷ऴతʹ্ஈ͔ΒԼஈʹ
1７－ 1

͔͚ͯిҐࠩ ∆V ∼ 2N Vp ͕ൃੜ͢Δɻ͜ΕΛ༻ϯσɾάϥʔϑ‫ܕ‬Ճ଎‫ث‬ͷಈ࡞‫ݪ‬ཧͰ͋Δɻ

ཻ͍ͯࢠΛՃ଎͢Δɻ

੩ిՃ଎‫ث‬͸࣭ྔͷҟͳΔΠΦϯͰ΋؆୯ʹՃ଎Ͱ͖ɺ͜ͷ఺ʹ͓͍ͯ‫Ͱޙ‬ड़΂Δߴप೾Ճ଎ํࣜΑΓऔΓѻ͍ʹ༏Ε͍ͯΔͱ‫͑ݴ‬Δɻͨͩ͠ɺ੩ిѹΛ༻͍͍ͯΔͨΊඇৗʹ์ి͠΍͘͢ɺͦͷରࡦͱͯ͠Ճ଎؅ͷ಺෦ʹ SF6 ͳͲͷઈԑੑͷΨεʢͦͷଟ͘͸༗ಟʣͰ෧͡੾Γʹ͢Δඞཁ͕͋Δɻͨͩ͠ɺͦΕͰ΋ͳ͓์ిΛ཈͑Δ͜ͱ͸Ͱ͖ͳ͍ͨ
Ίɺ҆શͳϨϕϧ·ͰՃ଎ి৔Λ཈͑Δඞཁ͕͋Δɻ͜ͷΑ͏ͳഎ‫ʹܠ‬ΑΓɺ੩ిՃ଎‫ Ͱث‬20 MVҎ্ͷՃ଎Λߦ͏͜ͱ͸ෆՄೳͰ͋Δɻ·ͨɺ੩ిՃ଎‫ث‬͸ిҐͷߴ͍ଆ͔Β௿͍ଆ΁ՙిཻࢠΛՃ଎͢Δ΋ͷͰ͋ΔͨΊɺ֎෦͔ΒҾ͖ೖΕཻͨࢠΛ࠶ͼ֎෦΁ͱՃ଎͢Δ͜ͱ͸Ͱ͖ͳ͍ɻ͕ͨͬͯ͠ɺ
੩ిՃ଎͸‫ݪ‬ཧతʹγϯΫϩτϩϯͳͲͰߦΘΕΔԁ‫ي‬ಓΛඳཻ͘ࢠΛಉ͡৔ॴͰ‫܁‬Γฦ͠Ճ଎͢Δ
ʮଟஈՃ଎ʯʹద༻Ͱ͖ͳ͍͜ͱΛҙຯ͢ΔɻҎ্ೋͭͷཧ༝ʹΑΓɺ‫ݱ‬୅ͷߴΤωϧΪʔՃ଎‫ݧ࣮ث‬Ͱ੩ిՃ଎‫ث‬͸΄ͱΜͲ࢖༻͞Ε͍ͯͳ͍ɻ
ਤ.3ϰΝϯάϥʔϑʹΑΔঢѹ‫ߏػ‬ͷ໛ࣜਤ [10]3 ߴप೾Ճ଎ͷ‫ૅج‬ύϯσɾάϥʔϑ‫ܕ‬ͷՃ଎‫ث‬ͷ‫ݪ‬ཧ͸ҎԼͷ௨Γɻ੩ి༰ྔ͕ C Ͱ͋Δු༡ͨ͠ಋମʹిՙ Q Λ੩ిՃ଎ʹ୅͑ͯී‫ํͨ͠ٴ‬๏͕प‫ظ‬తʹมԽ͢

= Q
C ͱͳ

Δߴप೾ి৔Λ༻ཻ͍ͯࢠΛՃ଎͢Δํ๏Ͱ͋ΓɺΔ͔Βɺଳిͤͨ͞ઈԑϕϧτΛίϯϕϠʔࣜʹ઀͜ͷํࣜΛ࠾༻ͨ͠Ճ଎‫ث‬͸ߴप೾Ճ଎‫ݺͱث‬͹Ε஍ଆ͔ΒૹΓ͜Ή͜ͱͰ Q Λ௥Ճͯ͠Ճ଎ిѹ V

Δɻಋମͷน໘Ͱғ·ΕͨதۭͷϚΠΫϩ೾‫ৼڞ‬ճΛಘΔɻίϯσϯαͱͯ͠͸Ұ෦ʹ݀ͷ։͍ͨۚଐ

࿏ͷ಺෦ʹಛఆͷप೾਺ͷి࣓೾ͷΤωϧΪʔΛ‫ٿ‬ମΛߟ͑ɺͦ͜ͷதΛ௨ΔΑ͏ʹϕϧτίϯϕ

஝ੵ͠ɺͦͷి৔੒෼Λ༻ཻ͍ͯࢠΛՃ଎͢ΔɻҎϠʔΛճసͤ͞Δɻۚଐ‫ٿ‬ମͷ൓ରଆΛ઀஍ଆͱఆ

߱ɺຊߘͰ͸͜ͷΑ͏ͳཻࢠՃ଎ʹ࢖༻͢ΔϚΠΫٛ͠ɺ͜͜ͰిѹΛ਑ʹҹՃͯ͠์ిͤͯ͞ϕϧτϩ೾‫ثৼڞ‬ͷ͜ͱΛʮՃ଎ۭಎʯͱ‫Ϳݺ‬ɻՃ଎ۭಎ

Λଳిͤ͞Δɻ‫ٿ‬ମଆͰ΋ϕϧτͷද໘ʹ઀৮͢Δͷ‫ڞ‬໐प೾਺͸ͦͷੇ๏ʹΑܾͬͯఆ͞Εɺۭಎ಺Α͏਑Λ৳͹͓͖ͯ͠ɺిՙΛճऩͰ͖ΔΑ͏ʹ͢ʹରԠ͢Δप೾਺ͷి࣓೾͕ఆࡏ೾ͱͯ͠ൃੜ͢

Δɻۚଐ‫ٿ‬ମʹ͸͕ۭ͍͍݀ͯΔ΋ͷͷɺ੩ిःณ

Δɻ͜ͷͱ͖ɺۭಎ಺ʹ͸༷ʑͳϞʔυͷఆࡏ೾͕ʹΑͬͯిՙ͸‫ٿ‬ମͷ֎ଆʹ෼෍͢Δɻ͜ͷঢ়ଶͰྭ‫͢ى‬Δ͜ͱ͕ՄೳͰ͋ΔɻҎԼͰ͸ɺಛʹཻࢠΛ‫ٿ‬ମͷதΛ௨ΔΑ͏ʹϕϧτίϯϕϠʔΛճసଓ͚

Ճ଎͢Δ͜ͱʹద͍ͯ͠Δਐߦํ޲ʹͷΈి৔੒෼Δ͜ͱͰɺۚଐ‫ٿ‬ମͷ֎ଆද໘ʹిՙ Q ͕஝ੵ͞Λ࣋ͭి࣓৔ͷϞʔυΛߟ͑Δɻۭಎͷ࣠ํ޲ʢ=ΕΔ͜ͱͱͳΔɻ͜ΕʹΑΓɺ࠷ऴతʹ‫ٿ‬ମͷද໘ཻࢠͷਐߦํ޲ʣʹ͸‫ڞ‬໐प೾਺ʹԠͨ͡ߴप೾ి

=Q
C৔͕೾ଧ͍ͬͯΔɻ͜Ε͕੾ΓସΘΔλΠϛϯάʹ

͕ൃੜ͢Δɻ͜ΕΛ༻ཻ͍ͯࢠͷՃ଎Λߦ͏ͷ͕ύಉ‫֎ͯ͠ظ‬෦͔Β‫܈ࢠཻͨ͠ࡏہ‬ͷմΛೖࣹ͢Ε

͋ͨ͑Δͱ͖ɺ͜ͷಋମͷిҐ V ͸ VͰఆٛ͞ΕΔ੩ి༰ྔ C Λ༻͍ͯՃ଎ిѹ V

2

７－ 2

͹ɺߴप೾ి৔ʹΑΔ࿈ଓతͳՃ଎͕࣮‫͖Ͱݱ‬Δɻ
͜Ε͕ߴप೾Ճ଎ͷ‫ݪ‬ཧͰ͋Δɻ
ߴप೾ి৔͸Ұप‫ظ‬ฏ‫Ͱۉ‬θϩͱͳΔͨΊɺ੩ి৔Λ༻͍Δ৔߹ͱൺ΂ͯ์ిʹର͢Δ଱ੑ͕޲্
͢Δɻ͜ΕʹΑΓɺՃ଎ޯ഑ͷ޲্ʢ=୹͍Ճ଎‫ث‬

ਤ.4௕ʣΛ࣮‫͖Ͱݱ‬ɺSF6 ͳͲͷ༗ಟੑͷઈԑΨεͷऔϐϧϘοΫεۭಎΓѻ͍͔Βղ์͞ΕΔ͜ͱͱͳΔɻ·ͨɺߴप೾Ճ
଎ͰଟஈՃ଎͕ՄೳͰ͋Δ͜ͱ͸‫ݪ‬ཧతʹࣗ໌Ͱ͋Δɻ‫ݱ‬୅ͷߴΤωϧΪʔ෺ཧֶ࣮‫ݧ‬ͷ‫ૅج‬Λఏ‫͢ڙ‬ρε⃗div B = 0
⃗ =
div E

ΔγϯΫϩτϩϯͷՃ଎‫ث‬ίϯϙʔωϯτͱͯ͠࠾༻͞Ε͍ͯΔɻ͜Ε͕‫ݱ‬୅ʹ͓͍ͯߴप೾Ճ଎͕޿

⃗⃗ = ⃗j + ε ∂ E
rotH
∂t
∂B
⃗ =−
rotE
∂t

͘࠾༻͞Ε͍ͯΔॴҎͱͳΔɻ‫ݪ‬ཧతʹཻࢠ͸࣭ྔʹԠͯ͡Ճ଎ͷ͞Ε΍͕͢͞ҟͳΔɻILC ͕λʔήοτ͢Δిࢠͱཅిࢠͷ࣭ྔ͸ 511 keV ͱඇৗʹ͍ܰͨΊɺཻࢠ͸͙͢͞·ޫ଎ʹՃ଎͞ΕΔɻͦ

(1)
(2)
(3)
(4)

⃗ ͸ి৔ϕΫτϧɺB⃗ ͸࣓৔ϕΫτϧɺ
͜͜ͰɺEΕΏ͑ɺՃ଎ۭಎͷ௕͞Λௐ੔͢Δඞཁ͸ಛʹੜ⃗͡j ͸ిྲྀີ౓ɺε ͸༠ి཰ɺµ ͸ಁ࣓཰ɺρ ͸ిՙີ⃗ = µH⃗ ͷؔ܎͕͋Δɻ
౓Ͱ͋Δɻ·ͨ B

ͳ͍ɻͨͩ͠ɺϛϡΦϯҎ্ͷ࣭ྔͷཻࢠΛՃ଎͢Δࡍ͸ɺཻࢠͷೖࣹͱߴप೾ి৔ͱͷಉ‫ظ‬ΛऔΔͨΊʹۭಎͷ௕͞ΛΤωϧΪʔ͝ͱʹௐ੔͢Δඞཁ͕·ͨɺohm ͷ๏ଇ͸ҎԼͰ͋Δɻ͋Δɻ

⃗⃗j = σ E(5)‫ݪ‬ཧతʹ‫͑ݴ‬͹ɺՃ଎ۭಎͱ༷ͯ͠ʑͳ‫ܗ‬ঢ়ͷ΋͜͜Ͱɺσ ͸ۚଐͷి‫఻ؾ‬ಋ཰Ͱ͋Δɻ

ͷΛ࠾༻Ͱ͖ΔɻͦͷΑ͏ͳ೚ҙͷ‫ܗ‬ঢ়ͷۭಎ಺෦ͷి࣓৔෼෍͸ɺి࣓৔ղੳιϑτ΢ΣΞʢANSYS,͔͜͜ΒҎԼͷ೾ಈํఔ͕ࣜಋ͔ΕΔʢۭಎ಺ͷSUPERFISH ͳͲʣΛ༻͍ͯ maxwell ํఔࣜΛղρ ͕ 0 ͱԾఆ͍ͯ͠Δʣɻ

͘͜ͱͰධՁͰ͖Δɻ௚ํମ΍ԁ౵ͳͲͷ୯७ͳ‫ܗ‬ঢ়ͷ৔߹Ͱ͋Ε͹ maxwell ํఔࣜΛղ͍ۭͯಎ಺
ͷి࣓৔෼෍ͷղੳղΛಘΒΕΔɻ

⃗
⃗
∂2E
∂E
+ µε 2
∂t
∂t
2⃗
⃗
H
∂
∂
H
⃗ = µσ+ µε 2∆H∂t∂t⃗ = µσ∆EҎԼͰ͸ਤ 4 ͷΑ͏ͳ൒‫ ܘ‬a Ͱ௕͞ d ͷԁ౵‫ܗ‬ͷۭಎʢ͍ΘΏΔ pilbox ۭಎʣͷ಺෦ͰಘΒΕΔి࣓೾෼෍ͷղੳղͷදࣜΛ༩͑Δɻ

(6)
(7)

্ࣜΛ൒‫ ܘ‬a ௕͞ d ͷԁ౵‫ܗ‬ͷಋମͷ‫ڥ‬ք৚݅·ͣɺmaxwell ํఔࣜ ͸ҎԼͰ͋Δɻ

Λߟྀͯ͠ղ͘͜ͱʹΑΓۭಎ಺෦ͷి࣓৔෼෍
ͷղੳղ͕ಘΒΕΔɻ͢ͳΘͪɺಋମද໘͸౳ిҐ໘Ͱ͋ΔͨΊ Eϕ (r = a) = 0, Ez (r = a) = 0 ͓Αͼ Eϕ (z = 0, d) = 0, Er (z = 0, d) = 0 ͕੒ཱ͢ΔɻҰൠʹɺۭಎ಺෦͕தۭͰಉ࣠‫ܗ‬ঢ়Ͱͳ͍৔߹
ͷి࣓৔෼෍͸ɺి৔͕ۭಎͷ࣠ํ޲ʹ௚ަ͢Δղ
ͱ࣓৔͕௚ަ͢Δղͷೋ௨ΓʹͳΔɻલऀͷి࣓৔

3

７－ 3

෼෍Λ TE modeɺ‫ऀޙ‬Λ TM mode ͱ͍͏ɻզʑ

Λ͍࣋ͬͯΔɻm, n, p ͱͯ͠ m′ , n′ , p′ ΛબΜ͕ͩ‫ڵ‬ຯ͕͋Δͷ͸ి৔͕ਐߦํ޲ʹ޲͘৔߹Ͱ͋ͬ

࣌ʹಘΒΕΔ‫಺ثৼڞ‬෦ͷి࣓৔ͷ෼෍Λ TM n′ͨʢ‫͑׵͍ݴ‬Ε͹ Hz = 0ʣɻͦ͜ͰɺҎԼͰ͸ TM

m′ p′ Ϟʔυͱ͍͏ɻm ͱ p ͸ 0 Ҏ্ɺn ͸ 1 Ҏmode ͷΈߟ͑Δ͜ͱͱ͢Δɻ͜ͷ৚݅ͷ΋ͱͰԁ্Ͱͳͯ͘͸ͳΒͳ͍ɻ͜͜Ͱɺm,n,p ͷ૊͸࠷௿౵‫ܕ‬ͷ಑ମ಺෦ͷి࣓৔෼෍Λ‫ٻ‬ΊΔͱҎԼͷղੳ࣍ʹબΜͰ͠·͔ͬͯ·Θͳ͍ɻͦ͜ͰɺҎ߱Ͱ͸ղ͕ಘΒΕΔɻ

TM010 Ϟʔυͷి࣓৔Λར༻ཻͯ͠ࢠՃ଎Λߦ͏͜ͱΛ૝ఆ͢Δɻ γϛϡϨʔγϣϯιϑτ΢ΣΞ

Er = −mnr)cos (mθ + ϕ)a( pπ )
z exp (iωmnp t)
× cosdͰ‫ ͨ͠ࢉܭ‬TM010 Ϟʔυͷి࣓৔෼෍Λਤ 6 ͱ 7
ʹࣔ͢ɻ

(8)
Bessel FunctionJn(x)Ez = E0 Jm

(ρ

(ρ r)
mpπ a
mn
′
cos (mθ + ϕ)
E0 J md ρmna( pπ )× sin
z exp (iωmnp t) (9)dHr = iε0 ωmnp

Hθ = iε0 ωmnp

J0

0.8

J1
J2

0.6

J3
J4

0.4
0.2
0

(ρ r)
pπ a2
mn
sin (mθ + ϕ)Eθ =E0 J m2d ρmna( pπ )× sin
z exp (iωmnp t) (10)dHz = 0

1

−0.2
−0.4
0

1

2

3

ਤ.5

(11)

4

5

6

7

8

9

10
x

ϕοηϧؔ਺

(ρ r)
a2 m
mn
E0 Jm
cos (mθ + ϕ)
2
ρmn r
a
( pπ )× cos
z exp (iωmnp t) (12)
d
(ρ r)
mn
′
sin (mθ + ϕ)
E 0 Jmρmna( pπ )× sin
z exp (iωmnp t) (13)daωmnp = c

√(
ρ

mn

a

)2

+

( pπ )2dਤ.6ߴप೾ి৔Λ༻͍ͯՃ଎͕ߦΘΕΔؔ܎্ɺՃ଎͜͜ͰɺJm ͸ m ࣍ͷ Bessel ؔ਺ʢਤ 5 ࢀরʣɺ′Jm
͸ͦͷඍ෼ɺρmnϐϧϘοΫεۭಎ಺෦ͷి৔෼෍ [11](14)͸ͦͷ n ൪໨ͷࠜΛද͢ɻΤωϧΪʔ͸ৼ෯ʹ‫཭ڑ‬Λ͔͚ͨྔͱΠίʔϧʹ͸

m,n,p ͸֤Ϟʔυͷి࣓৔෼෍Λಛ௃෇͚Δ཭ࢄͳΒͳ͍ɻ͜ͷޮՌ͸ time transit factor T ͱ‫ݺ‬తͳ੔਺Ͱ͋Γɺm ͕ճసํ޲ͷઅͷ਺ɺn ͕‫ܘ‬͹ΕΔ܎਺Λ༻͍ͯɺҎԼͷΑ͏ʹද‫͞ݱ‬ΕΔɻํ޲ͷઅͷ਺ɺp ͕࣠ํ޲΁ͷઅͷ਺ΛܾΊΔҙຯ

4

７－ 4

P0 =

1
Rs
2

∫

S

|H⃗// |2 dA(20)

͜͜ͰɺH⃗// ͸ۭಎͷද໘ʹฏߦͳ࣓৔ͷ੒෼ (θํ޲) Ͱ͋Δɻ
஝ੵΤωϧΪʔ U ͱଛࣦύϫʔ P0 Λ༻͍ۭͯಎ‫ثৼڞ‬ͷಛੑΛද͢ແෛՙ Q ஋ Q0 ΛఆٛͰ͖Δɻਤ.7ϐϧϘοΫεۭಎ಺෦ͷ࣓৔෼෍ [11]Q0 = U ω/P0

(21)

·ͨɺQ0 ͸ҎԼͷΑ͏ʹม‫͖Ͱܗ‬Δɻ

T =

∫ g/2

E0 cos (ωt)dz/

−g/2

∫ g/2

E0 dz (15)

−g/2

∫ g/2

ωz
cos ( )dz
= 1/g
v
−g/2
∫ g/2
2πz
)dz
= 1/g
cos (
βλ
−g/2
=

∫
⃗ 2 dVω 21 ε0 V |H|
Q0 = 1 ∫⃗ 2
2 Rs S |H| dA∫
ωε0 Hθ 2 dV
∫ 2
=
Rs
Hθ dA
= G/Rs

(16)
(17)

πg
sin ( βλ
)

(18)

πg
)
( βλ

(22)
(23)
(24)

͜͜ͰɺG ͸ఆ͔ٛΒ໌Β͔ͳΑ͏ʹۭಎ‫ثৼڞ‬͜͜Ͱɺg ͸ۭಎͷՃ଎Ϊϟοϓɺβ = v/c Λҙͷ‫ܗ‬ঢ়ʹΑͬͯͷΈܾ·ΔྔͰ͋ΔɻQ0 ΛଌఆͰ

ਤ͍ͯ͠Δɻ͜͜ʹ g = λ2 ͱ v = c Λ୅ೖ͢Δͱɺ

͖Ε͹γϛϡϨʔγϣϯʹΑܾͬͯఆͨ͠ G ͱͷsin ( π2)
= 0.637 ΛಘΔɻRF ి৔Λ༻͍ͨՃ଎ʹ͸(π2)ൺΛऔΔ͜ͱͰߴप೾ද໘఍߅Λಋग़Ͱ͖Δɻ

͜ͷϑΝΫλʔ͕͔͔Δ͜ͱΛߟྀ͓ͯ͘͠ඞཁ͕
͋Δɻ

‫ݟͰޙ‬ΔΑ͏ʹۭಎͷ֤ύϥϝʔλͷଌఆ஋Λ૊Έ߹ΘͤΔ͜ͱͰՃ଎ޯ഑ Eacc ΛܾఆͰ͖Δɻͦ

ҎԼͰۭಎ‫ثৼڞ‬ͷಛੑΛද͢ࡍʹศརͳύϥͷࡍʹ༗༻ͳྔͱͯ͠ҎԼͷγϟϯτΠϯϐʔμϯϝʔλΛྻ‫͢ڍ‬Δɻ

ε Rsh ͕ఆٛ͞Ε͍ͯΔɻ

·ͣɺۭಎ಺෦ʹ஝ੵ͞ΕΔ RF ͷΤωϧΪʔRsh =U ͸ҎԼͷΑ͏ʹද‫͖Ͱݱ‬Δɻ

V
P0

(25)

͜͜ͰɺV ͸ۭಎͷ্࣠ి৔ʹΑͬͯఆٛ͞ΕΔ

U=

1
µ0
2

∫

V

⃗ 2 dV =
|H|

1
ε0
2

∫

V

⃗ 2 dV|E|

ిҐͰ͋Δɻ

(19)࣍ʹɺۭಎ‫ثৼڞ‬ͷ಺෦ʹ༠‫͞ى‬Εͨి࣓৔ͷ·ͨɺRsh ͱ Q0 ͷൺ͸෼ࢠͱ෼฼ͱ΋ʹి৔ͷϞʔυ͸ maxwell ํఔࣜʹैͬͯද໘ʹిྲྀΛ༠‫͞ڧ‬ͷΈʹґଘܾͯ͠·ΔͨΊɺ͜Ε΋ۭಎͷઃ‫ܭ‬‫͢ى‬Δ͕ɺ͜Ε͸ۭಎ಺นͷߴप೾ද໘఍߅ Rs ͱʹΑͬͯͷΈܾ·ΔྔͱͳΔɻ

݁߹ͯ͠ҎԼͷࣜͰද͞ΕΔΤωϧΪʔଛࣦ P0 Λ

Rsh
V2
=
Q0
ωU

ੜΉɻ

5

７－ 5

(26)

·ͨɺՃ଎ి৔ Eacc ͱ࠷େද໘ి৔ Epk ΍࠷·ͰۚଐΛྫྷ٫͢Δͱ͋ΔԹ౓఺Ͱ૬సҠ͕ੜͯ͡େද໘࣓৔ Bpk ͱͷൺ཰΋ۭಎͷੑೳΛࣔ͢ύϥి‫ؾ‬఍߅ͷ‫ͳܹٸ‬ফࣦ͕ੜ͡Δͱಉ࣌ʹ֎෦͔ΒͷϝʔλͰ͋Δɻ࣓ྗઢ͕ःஅ͞ΕΔޮՌ͕ੜͣΔɻલऀͷಛੑ͸‫׬‬શಋిੑɺ‫ऀޙ‬͸‫׬‬શ൓࣓ੑʢ͋Δ͍͸ϚΠεφʔ

Epk
Eacc

(27)

Bpk
Eacc

(28)

ޮՌʣͱ‫ݺ‬͹Ε͓ͯΓɺ͜ͷಛҟతͳ૬సҠ‫ݱ‬৅͸௒఻ಋʢsuperconductivityʣͱ‫ݺ‬͹ΕΔɻઌ΄Ͳग़͖ͯͨʮৗ఻ಋʯ(normalconductivity) ͱ͸௒఻ಋͰ͸ͳ͍ঢ়ଶͷ͜ͱΛҙຯ͍ͯ͠ΔɻҎ߱Ͱ͸ɺศ

Epk
Eacc ͕খ͍͞΄ͲՃ଎ۭಎͷද໘͔Βిք์ग़
Bpk
ిࢠ͕์ͨΕʹ͘͘ͳΔɻ·ͨɺ Eacc͕খ͍͞΄རͷͨΊ௒఻ಋసҠ͢ΔԹ౓Λ Tc ͱද‫͢ه‬ΔɻԾ

ͲɺՃ଎ۭಎͷද໘࣓৔͕ऑ͘ͳΔɻ͢Ε͹ද໘఍߅͕θϩͱͳͬͯߴप೾ଛࣦ΋θϩʹʹ௒఻ಋࡐྉ͔Β੒ΔۭಎΛ੡࡞͠ɺ‫ۃ‬௿ԹͰӡ༻
ͳΔͱ‫ظ‬଴͞ΕΔɻҎ߱ɺ͜ͷΑ͏ͳۭಎΛ௒఻ಋྫͱͯ͠ɺEUV ۭಎʹର͢Δۭಎ‫ܗ‬ঢ়ͱ্࣠ͷۭಎͱ‫Ϳݺ‬ɻ࣮ࡍ͸௒఻ಋۭಎʹ͸θϩͰͳ͍ߴप

Ճ଎ి৔ͱද໘ి৔ͱද໘࣓৔ͱͷൺֱϓϩοτΛ

೾ද໘఍߅͕ੜͣΔɻͨͩ͠ɺͦͷ஋͸ৗԹͷಔͱ

ਤ 8 ʹࣔ͢ɻද໘࣓৔͸੺ಓ෦෇ۙͰɺද໘ి৔

ൺ΂Δͱ 10 ສഒҎ্௿͍ͨΊɺ΍͸Γ௒఻ಋۭಎ

͸ Iris ෦Ͱ࠷΋‫ͳ͘ڧ‬ΔɻTESLA shape ۭಎͰΛ༻͍Δ໌֬ͳϝϦοτ͕ଘࡏ͢ΔɻҰൠʹɺ௒఻Epk
͸ EaccBpk
͸ 2ɺ Eacc

ಋۭಎͷߴप೾ද໘఍߅͸Թ౓ґଘੑΛ΋߲ͭͱͦ͸ 4.3 ఔ౓Ͱ͋Δɻ

͏Ͱͳ͍߲ʹ෼ղ͞ΕΔɻલऀ͸༗‫ݶ‬Թ౓Ͱඞͣଘ
ࡏ͢Δ೤తʹྭ‫͞ى‬Εͨ४ཻࢠ (ΫʔύʔϖΞͰ͸ͳ͍ৗ఻ಋిࢠ) ͷϚΠΫϩ೾‫ٵ‬ऩʹ‫ى‬Ҽ͢Δ΋ͷ
Ͱ͋ΓɺBCS ఍߅ͱ‫ݺ‬͹ΕΔɻ͜ͷͱ͖ϚΠΫϩ೾‫ٵ‬ऩʹ‫د‬༩͢Δྭ‫ى‬४ཻࢠͷ਺͸ϘϧπϚϯҼࢠʹൺྫ͢Δɻ͕ͨͬͯ͠ɺTc ͕ߴ͍෺࣭ΛબͿͱྭ‫ى‬४ཻࢠͷ਺͕‫ͯͬݮ‬ද໘఍߅͕௿͘ͳΔɻԹ౓ʹґଘ͠ͳ͍߲ʹ͍ͭͯͷৄࡉ͸‫ޙ‬ड़͢Δɻ
௒఻ಋۭಎͷੑೳ͸௒఻ಋࡐྉͷ෺ੑͰܾ·Δྟք࣓৔଱ੑʹΑͬͯ΋੍‫͞ݶ‬ΕΔɻҰൠʹɺ֎෦͔Β௒఻ಋࡐྉʹ࣓৔͕ঃʑʹ‫ͳ͘ڧ‬ΔΑ͏ʹҹՃ͍ͯ͘͠ͱɺ͸͡Ί͸‫׬‬શ൓࣓ੑʹΑͬͯ௒఻ಋମͷ

ਤ.8

EUV ۭಎͷ‫ܗ‬ঢ়ͱՃ଎ి৔ͱද໘ి৔ͱ
ද໘࣓৔ͷൺֱϓϩοτ [3]಺෦΁ͷ࣓ଋͷ৵ೖ͕ःஅ͞Ε͍ͯΔ͕ɺ͋Δ࣓৔ͷ‫ʹ͞ڧ‬ୡͨ࣌͠఺Ͱ௒఻ಋମ಺΁ͷ࣓ଋͷ৵ೖ͕
ੜͣΔɻ࣓ଋͷ৵ೖΛ‫ͨ͠ڐ‬ஈ֊ͰҰ‫ʹؾ‬௒఻ಋঢ়

4 ߴप೾Ճ଎ۭಎͷੑೳ∫ଶ͕Ұ‫ʹؾ‬ഁΕΔ΋ͷΛୈ̍छ௒఻ಋମɺͦ͏Ͱͳ⃗ 2|H|
dA Ͱද͞ΕS 2Rs

͍΋ͷΛୈ̎छ௒఻ಋମͱ‫Ϳݺ‬ɻ͸͡Ίʹ࣓ଋͷ৵

ΔɻP0 Λ཈͑Δʹ͸ Rs Λখ͘͢͞Ε͹Α͍ɻ࠷

ೖ͕ੜͣΔ࣓৔ͷ‫͞ڧ‬ͷ͜ͱΛ࣓ଋ৵ೖ։࣓࢝৔ͱ

΋ࣗવͳൃ૝͸Ճ଎ۭಎΛۚଐͷ͏ͪ࠷΋ද໘఍߅‫͢ͱͱ͜Ϳݺ‬Δɻ࣓ଋ৵ೖ։࣓࢝৔ͷ‫͞ڧ‬͸ද໘ͷͷ௿͍ಔͰίʔςΟϯά͢Δ͜ͱͰ͋Ζ͏ɻຊߘͰ

ϙςϯγϟϧোนͷ༗ແʹΑͬͯมԽ͢Δɻ؆୯ͷ͸ओʹ͜ͷΑ͏ͳߴप೾ଛࣦͷগͳ͍ಔ੡ͷՃ଎ۭͨΊͦΕΛθϩͱΈͳ͢ͱɺͦΕ͸೤ྗֶతྟք࣓

ಎΛৗ఻ಋۭಎͱ‫͢ʹͱ͜Ϳݺ‬ΔɻҰํͰɺ‫ۃ‬௿Թ

৔ Hc (T ) ͱ‫ݺ‬͹ΕΔྔʹҰக͢ΔɻҰํͰɺୈ̎छ

Ճ଎ۭಎͷߴप೾ଛࣦ P0 ͸

6

７－ 6

௒఻ಋମͰ͸࣓ଋ৵ೖ։࣓࢝৔ʹ౸ୡͯ͠΋Ұ‫ʹؾ‬Λ Pb ϝοΩͨ͠΋ͷ͕ΠλϦΞͷࠃཱ‫࠾Ͱॴڀݚ‬ৗ఻ಋసҠ͸‫͜ى‬Βͳ͍ɻ·ͣ͸࣓ଋͷҰ෦৵ೖΛ༻͞Εͨྫ͕͋Δ͕ɺ͜ͷΑ͏ͳ Pb ੡ͷ௒఻ಋۭ‫ͨ͠ڐ‬ৗ఻ಋͱ௒఻ಋͷࠞ߹ঢ়ଶʢ͋Δ͍͸Ӕࢳঢ়ಎ͸࠷େՃ଎ޯ഑͕௿͘ɺੑೳ͕‫ܦ‬೥ྼԽ͢Δͱ͍ଶ‫ڞ‬Α͹ΕΔʣΛ‫ܗ‬੒͢Δɻୈೋछ௒఻ಋମͰ΋࣓͏େ͖ͳ໰୊͕֬ೝ͞Ε͍ͯΔɻҰํͰɺୈೋछ௒

ଋ৵ೖ։࣓࢝৔ͷ‫͞ڧ‬͸ද໘ͷϙςϯγϟϧোนͷ఻ಋମΛ༻͍ͯ௒఻ಋۭಎΛ੡଄͢Δ৔߹Ͱ͸ɺ‫ݱ‬༗ແʹΑͬͯมԽ͢ΔͨΊɺ؆୯ͷͨΊͦΕΛθϩࡏ΄΅શͯͷۭಎʹ͓͍ͯߴ७౓ͷόϧΫχΦϒ͕ͱࢥ͏͜ͱʹ͢ΔͱɺͦΕ͸Լ෦ྟք࣓৔ Hc1 (T )฼ࡐͱͯ͠༻͍ΒΕ͍ͯΔɻԼ෦ྟք࣓৔ͱసҠԹͱ‫ݺ‬͹ΕΔྔʹҰக͢Δɻ͞Βʹ࣓৔Λ‫͍ͯ͘͠ڧ‬౓͕७ۚଐதͰ࠷΋ߴ͍ͨΊߴ͍Ճ଎ిքͱ௿͍ද

͘ͱୈೋछ௒఻ಋମͷද໘Ͱ͸ৗ఻ಋ૬ͷྖҬ͕໘఍߅Λཱ྆Ͱ͖ɺ·ͨɺൺֱతՃ޻͕͠΍͘͢‫ܦ‬ঃʑʹ޿͘ͳ͍͖ͬͯɺ࠷ऴతʹද໘Λ‫׬‬શʹ෴͍೥ྼԽ͠ͳ͍޻ֶతͳϝϦοτ͕ଘࡏ͢Δ͜ͱ͕ཧਚͯ͘͠ৗ఻ಋసҠΛ‫͢͜ى‬ɻୈೋछ௒఻ಋମʹ͓

༝Ͱ͋ΔɻՃ଎ۭಎͷੑೳ͸ओʹ͸ߴप೾ද໘఍߅

͍ͯ௒఻ಋಛੑ͕‫׬‬શʹࣦΘΕͯ͠·͏࣓৔ͷ‫͞ڧ‬ͱ࠷େՃ଎ిքʹΑܾͬͯఆ͞ΕΔɻҎԼͰৗ఻ಋ

Λ্෦ྟք࣓৔ Hc2 (T ) ͱ‫Ϳݺ‬ɻ௒఻ಋମͷ֎෦࣓ۭಎͱχΦϒ੡ͷ௒఻ಋۭಎͷ࠷େՃ଎ిքͱߴप

৔ʹର͢ΔԠ౴͸ɺॎ࣠ʹ൓࣓ੑɺԣ࣠ʹ֎෦࣓৔೾ද໘఍߅Λൺֱ͠Α͏ɻͷ‫͞ڧ‬ΛͱͬͨϓϩοτͰද͢͜ͱ͕Ͱ͖Δɻਤ 9·ͣɺৗ఻ಋۭಎͷߴप೾ද໘఍߅͸ҎԼͷࣜͰʹͦͷΑ͏ͳϓϩοτΛ༩͑Δɻͳ͓ɺୈೋछ௒఻ද͞ΕΔɻಋମͷ‫ۂ‬ઢͱԣ࣠Ͱඳ͘໘ੵΛҰఆͱͯ͠ୈ 1 छ௒఻ಋମͷ‫ۂ‬ઢͱಉ࣓͡৔ґଘੑΛඳ͘͜ͱͰୈೋछ
௒఻ಋମͷ೤ྗֶతྟք࣓৔ Hc ΛఆٛͰ͖Δɻ

Rs =

√

ωµ
2σ

(29)

͜͜Ͱɺω ͸֯प೾਺ɺµ ͸ಁ࣓཰ɺσ ͸ۚଐͷి‫఻ؾ‬ಋ཰Ͱ͋Δɻ
্͔ࣜΒ σ ͕ߴ͍΄Ͳߴप೾ද໘఍߅Λ௿͘Ͱ
͖Δ͜ͱ͕Θ͔Δɻ͜Ε͕ৗ఻ಋۭಎͷ฼ࡐͱͯ͠
ਤ.9

࠷΋ σ ͷߴ͍ۚଐͰ͋Δߴ७౓ͷಔ͕༻͍ΒΕΔ൓࣓ੑʢॎ࣠ʣ vs ֎෦࣓৔ʢԣ࣠ʣͷؔ܎ɻ

ࠨ͕ୈ 1 छ௒఻ಋମͷ৔߹ɺӈ͕ୈ 2 छ௒఻ಋମཧ༝Ͱ͋Δɻ

ͷ৔߹ɻ[2]Ұํɺৗ఻ಋۭಎͷ࠷େՃ଎ిք͸ҎԼͷΑ͏ʹ
ୈ 1 छ௒఻ಋମΛ༻͍ͨ௒఻ಋۭಎͷ৔߹ɺද໘

ͯ͠༩ΒΕΔɻ্ड़ͨ͠௨Γɺߴप೾Ճ଎‫ث‬ͷ์ి࣓৔͕࣓ଋ৵ೖ։࣓࢝৔ʹ౸ୡͨ͠ஈ֊Ͱ௒఻ಋۭ

ʹର͢Δ҆ఆੑ͸੩ిՃ଎‫ͱث‬ൺ΂Δͱஶ͘͠ߴ͍

ಎͱͯ͠ͷ‫ػ‬ೳ͕ࣦΘΕΔɻ͜Ε͸ࣗ໌Ͱ͋ΔɻҰ΋ͷͷɺͦΕͰ΋ͳ͓‫׬‬શͳ҆ఆੑΛ֫ಘͰ͖ͳ͍

ํɺୈ̎छ௒఻ಋମΛ༻͍ͨ৔߹ʹ͸ɺ௚‫ײ‬తʹ͸͜ͱʹཹҙ͢Δඞཁ͕͋ΔɻҰൠʹɺ์ి vs ද໘࣓ଋ͕Ұ෦͔͠৵ೖ͍ͯ͠ͳ͍ঢ়ଶͳΒ·ͩੑೳ͕࣓৔ͷؔ܎͸प೾਺ʹԠͯ͡มԽ͢Δɻೋຕͷ‫ۃ‬൘ҡ࣋Ͱ͖ΔΑ͏ʹࢥ͑Δ͔΋͠Εͳ͍ɻͨͩ͠ɺ࣮

ؒͷ์ి‫ݱ‬৅Λཧ࿦తʹղੳͨ݁͠Ռ͔Βɺಔද໘ࡍ͸ͦ͏Ͱ͸ͳ͘ɺ࣓ଋ͕Ұ෦Ͱ΋৵ೖͨ͠ஈ֊Ͱ

ʹ͓͚Δද໘ి৔ͱ์ి‫ݱ‬৅ͷؔ܎Λදͨ͠‫ࣜݧܦ‬ۭಎੑೳ͸ࣦΘΕΔɻྺ࢙తʹ͸ɺୈҰछ௒఻ಋମ

ͱͯ͠ҎԼͷ Kilpatrick ͷ์ి‫ݶ‬ք͕༩͑ΒΕͯΛ༻͍ͯ௒఻ಋۭಎΛ੡଄ͨ͠ࣄྫͱͯ͠ಔͷ಺໘

͍Δʢਤ 10 ࢀরʣ [12]ɻ

7

７－ 7

f = 1.64

(

E
E0

)

)
(
E0
[MHz]
exp −8.5E(30)

Eacc maximum [MV/m]

͜͜ͰɺE0 = 1 MV/m Ͱ͋Δɻ

100
80
60
40

1.3 Kilpatrick

ਤ.11

20
0
0

2000

ਤ.10

4000

6000

8000
10000
Frequency [MHz]ද໘఍߅ͷԹ౓ґଘੑͷϓϩοτ [13]Λ࢝Ί௿Թ௒఻ಋମ͸ s ೾௒఻ಋʹ෼ྨ͞Ε͍ͯ
Δ͕ɺͦͷ४ཻࢠͷঢ়ଶີ౓ (DOS) ͸ίͷࣈ‫ܕ‬ͷ

1.3 Kilpatrick vs Frequency

Ϊϟοϓ͕։͍͍ͯΔ (ਤ 12)ɻ௒఻ಋମͷ BCS ఍্ࣜ͸์ిʹ҆ఆͳ࠷େද໘ి৔ͷ‫͞ڧ‬Λද͢ɻ߅ͷ‫ݯى‬͸ɺ༗‫ݶ‬Թ౓Ͱ͸ඞͣଘࡏ͍ͯ͠ΔΪϟοৗ఻ಋۭಎͷ࠷େՃ଎ޯ഑͸ɺ͜ͷ࠷େද໘ి৔͕

ϓͷӈଆ΁ͱ೤తʹྭ‫͞ى‬Εͨ४ཻࢠʹΑΔϚΠΫ

ൃੜ͍ͯ͠Δ࣌ͷ্࣠ͷՃ଎ి৔ͷ‫͔͞ڧ‬Β‫·ٻ‬ϩ೾‫ٵ‬ऩʹΑΔ΋ͷͰ͋ΔɻΪϟοϓͷ୩ͷӈଆͷΔɻ͕ͨͬͯ͠ɺप೾਺͕ߴ͍΄Ͳ࠷େՃ଎ޯ഑͸ྭ‫ى‬४ཻࢠͷ਺͸ϘϧπϚϯҼࢠʹൺྫ͓ͯ͠Γɺ

ߴ·Δؔ܎ʹ͋Δɻ࣮ࡍ͸ Kilpatrick ͷ์ి‫ݶ‬քͦΕ͸Թ౓ΛԼ͛Δͱࢦ਺ؔ਺తʹ‫ݮ‬গ͢Δɻͨ͠

ͰԾఆ͞Ε͍ͯΔಔද໘ͷঢ়ଶʢද໘ૈ͞ͳͲʣ͸͕ͬͯද໘఍߅͸ΪϟοϓͷӈͱࠨͷΤωϧΪʔࠩ‫ݱ‬୅ͷද໘ॲཧٕज़Λ༻͍ͯಘΒΕΔͦΕΑΓ͸∆ Λ༻͍ͯ Rs ∝ exp (ʵ∆/kT ) ͱॻ͚ΔɻΪϟοΔ͔ʹྼΔɻͦ͜ͰɺJ-PARC RFQ ΍ DTL Ͱ͸ϓ͸௒఻ಋసҠԹ౓͔Β཭ΕΔ΄Ͳ޿͕Δɻͨ͠

Kilpatrick ͷ์ి‫ݶ‬քͰ༧‫͞ݴ‬ΕΔ࠷େද໘ి৔ͷ͕ͬͯɺ७ۚଐதͰ࠷΋ Tc ͷߴ͍χΦϒͷද໘఍੍‫ݶ‬ΑΓ 1.3 – 1.8 ഒఔ౓ߴ͍ද໘ి৔ΛԾఆͯ͠߅͕཈͑ΒΕΔͷ͸ࣗ໌Ͱ͋Δɻऑ͍࣓৔ʹରͯ͠Ճ଎‫ث‬ͷӡస͕ߦΘΕ͍ͯΔɻ

ͷΈͷ݁ՌͰ͋Δ͕ɺRRR ͷߴ͍όϧΫχΦϒͷ

RBCS ͷԹ౓ґଘੑ͸ҎԼͷ൒‫ࣜݧܦ‬Λ༻͍ͯදͤ
Δ͜ͱ͕෼͔͍ͬͯΔɻ

ҎԼͰ௒఻ಋۭಎͷߴप೾ද໘఍߅ͱ࠷େՃ଎ి
քͷؔ܎ʹ͍ͭͯ‫ه‬ड़͢Δɻ
௒఻ಋମͷߴप೾ද໘఍߅͸ɺҎԼͷΑ͏ʹԹ౓

RBCS =

ґଘੑΛ΋߲ͭͱͦ͏Ͱͳ͍߲ʹ෼ղͰ͖Δɻ

Rs = RBCS + Rres

(

−4 1

2 × 10

T

(

f
1.5

)2

exp

(

−17.67T))(32)

͔͜͜ΒɺBCS ఍߅͸ 2 K, 1.3 GHz Ͱ 11 nΩ(31)ͱ‫͖Ͱࢉܭ‬Δɻ

࣮ྫΛਤ 11 ʹࣔ͢ɻ͜͜ͰɺRBCS ͸ࢦ਺ؔ਺తͳԹ౓ґଘੑΛ߲࣋ͭͰ BCS ఍߅ͱ‫ݺ‬͹ΕΔɻ࢒ཹ఍߅͸ɺද໘ʹ͓͚Δෆ७෺ͳΓ௒఻ಋసҠ

Rres ͸ఆ਺߲Ͱ࢒ཹ఍߅ͱ‫ݺ‬͹Ε͍ͯΔɻ χΦϒ࣌ʹۭಎද໘ʹτϥοϓ͞Εͯ͠·ͬͨ‫࣓ڥ؀‬৔͕

8

７－ 8

ͱʹΑͬͯಋग़Ͱ͖Δɻ2 K ͷϔϦ΢Ϝྫྷౚ‫ػ‬ͷআ೤ޮ཰͸ 3-5 kW/W ఔ౓Ͱ͋Δ͔Βɺ͜ͷΑ͏ʹͯ͠ྫྷౚ‫ྗిػ‬Λಋग़ͯ͠ৗ఻ಋۭಎͷߴप೾ଛࣦ
ͱൺ΂Δͱɺ௒఻ಋۭಎͷํ͕ AC ফඅిྗ͕ 90ഒҎ্গͳ͍͜ͱ͕ཧղ͞ΕΔɻ
ۭಎ಺෦ͷද໘࣓৔ͷ‫͕͞ڧ‬χΦϒͷ࣓ଋ৵ೖ։
࣓࢝৔Λ௒͑ͨஈ֊Ͱۭಎ಺໘ʹ࣓৔͕৵ೖ͢Δɻ
஝ੵ͞ΕΔి࣓ΤωϧΪʔ͕େ͖͘ͳΔ΄Ͳද໘ਤ.12࣓৔ͷ‫͞ڧ‬͸޲্͢Δɻ࣓ଋ͕௒఻ಋମʹҰ෦Ͱ΋χΦϒͷ४ཻࢠͷঢ়ଶີ౓ɻ୩ͷؒͷΪϟ

৵ೖ͢ΔͱͦΕ͸ۭಎ಺෦ͷߴप೾࣓৔ʹΑͬͯ

οϓ͸ 2∆ ʹ૬౰͢Δɻ [14]ࠨӈʹ༳ΒΕͯൃ೤͠ɺपғͷԹ౓Λ޲্ͤͯ͞͞
Βʹ௒఻ಋಛੑΛ௿Լͤ͞Δ ... ͱ͍͏αΠΫϧ͕‫ݪ‬Ҽͱͳͬͯੜ͡Δɻ‫࣓ڥ؀‬৔ʹΑͬͯੜ͡Δ࢒ཹ‫܁‬Γฦ͞Εͯ࠷ऴతʹഁյతͳ࣓ଋͷ৵ೖʢӔࢳઇ఍߅Λ Rmag ͱද‫͢ه‬Δͱɺͦͷप೾਺ґଘੑ͸Ҏ่ʣ͕ੜ͡Δɻ͜ͷ‫ݱ‬৅͸௒఻ಋഁյ΍ΫΤϯνͱԼͷࣜͰද͞ΕΔ [8]ɻRmag = 0.3Hext‫ݺ‬͹ΕΔɻΫΤϯν͕ੜ͡Δͱ௒఻ಋۭಎͱͯ͠͸√fͦΕҎ্ੑೳΛҡ࣋͢Δ͜ͱ͕ࠔ೉ͱͳΔɻ͜Εʹ

(33)ΑΓɺ࠷େՃ଎ޯ഑͕ఆٛ͞ΕΔ͜ͱͱͳΔɻͨͩ

͜͜ͰɺRmag ͸ [nΩ]ɺf ͸प೾਺ [GHz]ɺHext

͠ɺۭಎද໘ʹԿ͔ಛผͳ໰୊͕͋ͬͨ৔߹͸ͦΕ͸τϥοϓ͞Εͨ֎৔ͷ‫[ ͞ڧ‬mG] ͷ࣍‫ݩ‬Λ࣋ͭɻΑΓ΋΋ͬͱऑ͍࣓৔Ͱ௒఻ಋഁյ͕ੜ͡Δ͜ͱͱ

1.3 GHz Ͱ͸ 1 mG τϥοϓ͞Ε͚ͨͩͰ΋ 1 nΩͳΔɻͦͷ‫ߏػ‬ͷৄࡉ͸‫ޙ‬ड़͢Δɻͷ‫د‬༩͕͋Δ͜ͱ͕Θ͔Δɻ͜ΕΛ 2 K ͷ BCS
ઌड़ͨ͠ͱ͓Γɺۭಎͷ‫ܗ‬ঢ়ͰՃ଎ޯ഑ Eacc ͱ఍߅ͱಉఔ౓ʹ཈͑Α͏ͱࢥ͏ͱ‫࣓ڥ؀‬৔Λ਺ mG࠷େද໘࣓৔ Bpk ͷؒʹରԠؔ܎͕ੜͣΔɻ࣓ଋʹ཈͑Δඞཁ͕͋Δͱͷ݁࿦͕ಘΒΕΔɻ

৵ೖ։࣓࢝৔Λ Bv ͱఆٛ͢ΔͱɺҎԼͷΑ͏ʹද‫͖Ͱݱ‬ΔͩΖ͏ɻҎԼͰ f = 1 GHz Ͱ 300 K ͷಔͷද໘఍߅ͱ௒
఻ಋχΦϒ (2 K) ͷද໘఍߅Λൺֱ͠Α͏ɻ300 Kͷಔͷද໘఍߅͸ 8.1 mΩɺ2 K ͷ௒఻ಋ Nb ͷද

Bv =໘఍߅͸൒‫͔ࣜݧܦ‬Β 7.8 nΩ Ͱ͋Δɻ࢒ཹ఍߅ͷ

Bpk
Eacc,max
Eacc

TESLA shape cavity ͷ ৔ ߹ ͸‫د‬༩Λେ͖Ίʹ‫ੵݟ‬΋ͬͯ 10 nΩ ͱͯ͠΋ɺ௒఻

(34)
Bpk
Eacc

= 4.3

ಋۭಎͷߴप೾఍߅ͷํ͕ 45 ສഒҎ্௿͍͜ͱ͕

[MV/mT] Ͱ͋Δɻ࣓ଋ৵ೖ։࣓࢝৔͸ 170 – 200

Θ͔Δɻৗ఻ಋۭಎͰ͸্‫ه‬ͷද໘఍߅ʹൺྫͨ͠mT Ͱ͋ΔͷͰɺTESLA-shape ۭಎͷ࠷େՃ଎ޯ

ߴप೾ଛࣦ͕ੜ͡ɺ֎෦ͷߴप೾‫͔ݯ‬Β౤ೖ͞Εͨ഑͸ 40 – 46 MV/m ʹ૬౰͍ͯ͠Δɻ͜Ε͕෺ੑΤωϧΪʔ͕Ұ෦ফඅ͞Εͯ͠·͏͜ͱʹͳΔɻ͜

Ͱܾ·ΔχΦϒͷ࠷େՃ଎ޯ഑Λ༩͑Δؔ܎ࣜͰ͋

Ε͸ৗ఻ಋۭಎͰ͸͜ͷ෼ͷ AC ফඅిྗ͕ඞཁ

Δɻ

Ͱ͋Δ͜ͱΛҙຯ͢ΔɻҰํɺ௒఻ಋۭಎͰ͸ߴप೾ଛࣦ͸΄΅θϩͰ͋Δ΋ͷͷɺߴप೾ଛࣦ૬౰෼

ҰํͰɺৗ఻ಋۭಎͷ࠷େՃ଎ޯ഑͸ Kilpatrickͷද໘ൃ೤ΛϔϦ΢Ϝྫྷౚ‫ػ‬Λ༻͍ͯআ೤͢ΔͨΊͷ์ి‫ݶ‬քʹΑ੍ͬͯ‫͞ݶ‬ΕΔɻਤ 10 Λࢀর͢Δ

ͷӡ༻ిྗ͕ඞཁͰ͋Δɻ͜Ε͸ɺ௒఻ಋۭಎͷ಺ͱɺৗ఻ಋۭಎ͕์ిʹ҆ఆͳ࠷େද໘ి৔͸प෦ͷߴप೾ଛࣦͱྫྷౚ‫཰ޮྗిػ‬Λֻ͚߹ΘͤΔ͜೾਺ 10 GHz Ͱ 120 MV/m Ҏ্ͱͳΔɻͨͩ͠ɺ

9

７－ 9

͜Ε͸࠷େද໘ి৔ʹ͗͢ͳ͍ͨΊɺ͔͜͜Β͞ΒʹՃ଎ి৔΁ͷম͖௚͕͠ඞཁͱͳΔɻ؆୯ͷͨϏʔϜӡసʹ͓͍ͯ͸ɺΫϥΠΦϞδϡʔϧͷ֎

Epk
ΊɺTESLA-shape ۭಎͷ Eacc
=2 Λ༻͍Δͱɺ10෦ͷߴप೾‫͔ݯ‬Β͔Β಺෦ͷ௒఻ಋۭಎʹରͯ͠GHz Ͱୡ੒Մೳͳ࠷େՃ଎ޯ഑͸ 60 MV/m ͱͳߴप೾ిྗ͕౤ೖ͞ΕΔɻ͜͜Ͱɺߴप೾‫ͯ͠ͱݯ‬Δɻ͕ͨͬͯ͠ɺप೾਺ΛߴΊΔ͜ͱͰχΦϒ੡ͷ͸ɺಛʹߴΤωϧΪʔ࣮‫ͰͲͳݧ‬େిྗͷߴप೾ి௒఻ಋۭಎΛ্ճΔ஋Λୡ੒Ͱ͖Δ͜ͱ͕ཧղ͞ΕྗΛ‫͖Ͱڅڙ‬ΔΫϥΠετϩϯ͕༻͍ΒΕΔ͜ͱ͕

Δɻ௒఻ಋۭಎͱൺ΂Δͱද໘఍߅͸େ෯ʹѱ͍ͨଟ͍ɻͨͩ͠ɺϏʔϜύϫʔ͕গͳͯ͘΋Α͍৔߹ΊɺύϧεΦϖϨʔγϣϯ͔͠Ͱ͖ͳ͍ͷ͸ࣗ໌Ͱ͸ߴप೾‫҆ͯ͠ͱݯ‬Ձͳ൒ಋମΞϯϓͰ୅༻Ͱ͖Δ

͋Δɻ

৔߹΋͋Δɻ͜Ε͸ɺ௒఻ಋۭಎ͸ߴप೾ଛࣦ͕‫ۃ‬Ίͯগͳ͍͜ͱʹΑͬͯߦ͑Δ΋ͷͰ͋Δɻߴप೾

5 ௒఻ಋՃ଎ۭಎͷӡసిྗͷ఻ૹʹ͸ಋ೾؅͕༻͍ΒΕΔͷ͕ҰൠతͰ͋Δɻಋ೾؅಺෦Ͱ์ి͕සൃ͢Δ৔߹͸಺෦Ληϥ௒఻ಋՃ଎ۭಎΛ༻͍ͨϏʔϜՃ଎ͷ֓೦ਤΛਤϛοΫ૭ͳͲͰ۠੾ͬͯઈԑੑͷ SF6 ͷΨεͰຬ

13 ʹ༩͑Δɻ

ͨ͢͜ͱ͕͋Δɻۭಎʹߴप೾ిྗΛ౤ೖ͢ΔͨΊʹΞϯςφ͕ಥͬࠐ·ΕΔʢೖྗΧϓϥʔͱ‫Ϳݺ‬ʣɻߴप೾ిྗͷΈۭಎͱಋ೾؅ͷؒΛ௨աͰ͖ΔΑ
͏ɺۭಎͱಋ೾؅ͷؒ͸ηϥϛοΫ૭Ͱ࢓੾ΒΕ͍ͯΔɻۭಎ಺෦΁ͷߴप೾ిྗͷ఻ૹ͸൓ࣹ཰θϩͰ͸ߦ͑ͳ͍ɻͦ͜Ͱɺಋ೾؅ͷؒʹ͸൓ࣹ೾Λ҆શʹফ‫͢ڈ‬ΔͨΊͷαʔΩϡϨʔλʔ͕ઃ͚ΒΕ͍ͯΔɻ‫ڞ‬໐प೾਺ͷௐ੔ͷͨΊʹ͸ۭಎΛԡͨ͠ΓҾͬுͨΓͯ͠Θ͔ͣʹม‫ͤ͞ܗ‬Δप೾਺νϡʔφʔʹΑ࣮ͬͯ‫͞ݱ‬Ε͍ͯΔɻ҆ఆͳϏʔϜՃ଎
ਤ.13

Λ௒఻ಋ

௒఻ಋՃ଎ۭಎΛ༻͍ͨϏʔϜՃ଎ͷ֓೦ਤ [2]ۭಎʹ࣮ͯ‫͢ݱ‬ΔͨΊʹɺߴप೾ిྗΛ҆ఆԽͤ͞ΔͨΊͷ LLRF ͱ‫ݺ‬͹ΕΔ੍‫ͱܥޚ‬प௒఻ಋঢ়ଶΛอͭͨΊʹۭಎ͸ӷମϔϦ΢ϜΛຬ೾਺νϡʔφʔͷ੍‫͞૷࣮͕ܥޚ‬Ε͍ͯΔɻϏʔϜͨͨ͠༰‫͞૷಺ʹث‬ΕΔɻӷମϔϦ΢ϜͷԹ౓͸͕௨ա͢ΔࡍͳͲʹՃ଎ۭಎͷ಺෦ʹ͸ۭಎͷ‫ৼڞ‬

4.2 K ͔ 2 K ʹબ୒͞ΕΔ͜ͱ͕ଟ͍ɻ2 K ͢Δप೾਺Ҏ֎ͷߴௐ೾΋ྭ‫͞ى‬Εͯ͠·͏͜ͱ͔ΒɺͨΊʹ͸༰‫಺ث‬ͷ‫ݮ‬ѹ͕ඞཁʹͳΔɻ·ͨɺ֎෦͔

ͦΕΛআ‫͢ڈ‬ΔͨΊͷ HOM μϯύʔͱ‫ݺ‬͹ΕΔΒͷ೤৵ೖΛःஅ͢Δ໨తͰɺ͜ͷ༰‫ث‬ͷ֎ଆ͔Β‫಺͕ߏػ‬แ͞Ε͍ͯΔɻ·ͨɺӷମϔϦ΢Ϝ͸௒఻͞Βʹେ͖ͳஅ೤૧ʹΑͬͯ෴ΘΕΔ͜ͱͱͳΔɻಋۭಎͷߴप೾ଛࣦͱΫϥΠΦϞδϡʔϧ಺෦΁ͷۭಎੑೳ͸௒఻ಋసҠ࣌ͷ‫࣓ڥ؀‬৔ͷτϥοϓʹΑ

೤৵ೖྔͷೋͭͷ೤Λड͚ͯৠൃ͍ͯͨ͘͠Ίɺ͢Γ௿Լͯ͠͠·͏ͨΊɺۭಎͷ͙͢֎ଆʹ࣓‫ؾ‬γʔ͙ͦ͹ʹϔϦ΢ϜΨεΛճऩͯ͠࠶ͼӷԽ͢Δྫྷౚ

ϧυΛઃஔ͢Δɻ͜ͷΑ͏ʹͯ͠૊·Ε͍ͯΔҰ࿈‫͕ػ‬ઃஔ͞ΕΔɻӡస࣌ʹ͸ΫϥΠΦϞδϡʔϧΛͷϢχοτ͸ΫϥΠΦϞδϡʔϧͱ‫ݺ‬͹ΕΔɻӷମྫྷౚ‫ͱػ‬௚݁ͯ͠೤ෛՙΛߟྀ͠ͳ͕ΒӷମϔϦ΢ϔϦ΢Ϝ͸‫ؾ‬Խ͢Δͱମੵ͕ 700 – 800 ഒʹ૿େ͢Ϝͷঢ়ଶΛ੍‫͢ޚ‬Δɻ͜ͷΑ͏ʹͯ҆͠ఆͳϏʔϜ

ΔͨΊɺͦͷऔΓѻ͍͸೔ຊʹ͓͍ͯ͸ߴѹΨεอՃ଎Λ࣮‫͢ݱ‬Δɻ҆๏ʹ४‫ͨ͠ڌ‬΋ͷʹ͢Δඞཁ͕͋Δɻͦ͜Ͱɺߴ
ѹΨεอ҆๏ͷ৹ࠪΛύεͰ͖Δ΄Ͳ‫ͳ݈ؤ‬ΫϥΠΦϞδϡʔϧΛઃ‫ܭ‬ɾ੡଄͢Δඞཁ͕͋Δɻ

10

７－ 10

6 ௒఻ಋۭಎͷ੡଄

7 ۭಎͷද໘ॲཧ

ҎԼͰ͸จ‫[ ݙ‬15] ʹ‫͖ͮج‬௒఻ಋۭಎͷ੡଄޻֎෦࣓৔͸௒఻ಋঢ়ଶͷχΦϒද໘ʹରͯ͠͸ϩఔͷྲྀΕʹ͍ͭͯઆ໌͢Δɻ·ͣɺ൘ް 2.8 mm Ͱϯυϯ௕ఔ౓ͷ 40–50 nm ΄Ͳ͔͠ਁಁ͠ͳ͍ͨ֎‫ ܘ‬260 mm ͷߴ७౓ͷχΦϒԁ൘ʹରͯۚ͠‫ܕ‬Ίɺ࠷ද໘ͷ௒఻ಋಛੑ͕௒఻ಋۭಎͷੑೳͨΔ࣓Λ༻͍ͨϓϨε੒‫ʹܕ‬ΑΔਂߜΓՃ޻Λߦ͍ɺϋʔଋ৵ೖ։࣓࢝৔ʢ࠷େՃ଎ి৔ʣͱද໘఍߅ΛܾΊϑηϧΛ੡࡞͢Δɻ࣍ʹɺͦͷΞΠϦε෦ΛిࢠΔɻ௒఻ಋۭಎ͸ड͚ೖΕ࣌ͷ··Ͱ͸े෼ʹੑೳϏʔϜ༹઀ʹΑͬͯ઀߹ͯ͠μϯϕϧ‫ܗ‬ঢ়ʹ࢓্͕ൃ‫͕ͱ͍͜ͳ͖Ͱش‬෼͔͍ͬͯΔɻ͕ͨͬͯ͠ɺ

͛Δɻͭ͗ʹɺΞΠϦε෦ͷϋʔϑηϧ෦ͷม‫ʹܗ‬௒఻ಋۭಎͷੑೳΛे෼ʹൃ‫͢ش‬ΔͨΊʹ͸࠷ද໘

ର͢Δ‫౓ڧ‬ΛߴΊΔͨΊΞΠϦε෦֎ଆʹ‫ڧ‬Ίྠͷঢ়ଶΛ࠷దԽ͢Δද໘ॲཧ޻ఔ͕‫ۃ‬ΊͯॏཁͰ͋

Λ઀߹ͨ͠‫ޙ‬ɺҟͳΔμϯϕϧͷ੺ಓ෦ಉ࢜Λిࢠ

Δɻઌड़ͨ͠௨ΓɺχΦϒද໘ʹই΍ҟ෺͕ࠞೖ͠

ϏʔϜ༹઀ʹΑΓ઀߹͠࿈݁͢Δɻ͜ͷΑ͏ʹ͍ͯͯͨ͠ΓઑͬͨՕॴ΍༹઀͕ܽؕ͋ΔͱੑೳͷྼԽ

9-cell ۭಎ·Ͱଟ࿈Խ͍ͯ͘͠ɻࢀߟͷͨΊ STF-1

͕ੜ͡Δɻද໘ॲཧʹ͸͜ΕΒͷই΍ܽؕ΍ઑͬͨ

༻ 9-cell ௒఻ಋۭಎͷ੡࡞޻ఔͷࡍʹࡱӨ͞ΕͨՕॴΛআ‫ͯ͠ڈ‬ฏ‫ͳ׈‬ද໘ΛಘΔ໨త΋͋Δɻ

ը૾Λਤ 14 ʹࣔ͢ɻ‫ࡏݱ‬ɺҎԼʹࣔ͢ඪ४తͳද໘ॲཧϨγϐ͕௒఻ಋۭಎʹରͯ͠ࢪ͞ΕΔ͜ͱ͕Ұൠతͱͳͬͯ

ۭಎΛ੡଄͢Δࡍʹબ୒͞ΕͨిࢠϏʔϜ༹઀৚͍Δɻ݅͸ෆ७෺ͷࠞೖ΍ද໘ܽؕͷൃੜΛ๷ࢭ͢ΔͨΊʹಛʹॏཁͰ͋ΔɻిࢠϏʔϜ༹઀ͷ։ઌͷްΈௐ

1. ଟྔిղ‫ݚ‬ຏʢ100–200µmʣ

੔ɺ։ઌ໘ͷਗ਼ড়ԽɺϏʔϜύϥϝʔλͷ࠷ద҆ఆ

2. ਅۭ࿍ʹ͓͚ΔߴԹ೤ॲཧʢ800–900 ◦ C, 3৚݅ྖҬͷ֦େɺ૷ஔͷਗ਼ড়Խ‫ڥ؀‬ɺδά૊Έཱͯ࣌ͷਗ਼ড়؅ཧͳͲ͕ॏཁͰ͋Δɻ‫׬‬੒ۭͨ͠ಎ͸ɺਅۭϦʔΫࢼ‫ݧ‬ɺ‫ݧࢼີؾ‬ɺࡾ࣍‫ੇݩ‬๏‫ࠪݕ‬Λ΁ͯɺप೾਺ଌఆɺిք෼෍ଌఆɺްΈ෼෍ଌఆͳͲͷड

hoursʣ
3. ۭಎͷ಺໘‫ࠪݕ‬ʢ໰୊ൃ֮ͷ৔߹͸‫ݚॴہ‬ຏ౳ʹΑΔܽؕ෦ͷআ‫ڈ‬ʣ

4. ࢓্͛ిղ‫ݚ‬ຏʢ10–20µmʣೖ‫ߦ͕ࠪݕ‬ΘΕΔ͜ͱͱͳΔɻͦͷ‫ޙ‬ɺ‫ج‬ຊతͳੑ

5. ௒Ի೾ચড় (15 min)ೳʹ໰୊͕ͳ͍ͱ൑அ͞Εͨஈ֊Ͱۭಎͷ੡଄ͷड

6. ௒७ਫߴѹચড়ʢ3–6 hoursʣ͚ೖΕ‫ࠪݕ‬͸‫ͳͱྃ׬‬Δɻ

7. ΫϦʔϯϧʔϜʹۭͯಎͷ૊Έཱͯ
8. ௿ԹϕʔΩϯά (120 ◦ C, 48 hours)
1 ͱ 4 ͸ۭಎද໘ΛԜತͷͳ͍‫׈‬Β͔ͳද໘ʹ࢓
্͛ΔͨΊͷ޻ఔͰ͋Δɻ͜ͷ޻ఔʹ͓͍ͯද໘ͷԚΕ΍ܽؕɺઑͬͨՕॴͳͲͷૈ͞ͷӨ‫ڹ‬͸େ෯ʹ؇࿨͞ΕΔɻ3 ͸ిղ‫ݚ‬ຏ͚ͩͰ͸ରॲͰ͖ͳ͍໨
ͩͬͨܽؕΛআ‫͢ڈ‬ΔͨΊʹඞཁͳ޻ఔͰ͋Δɻඞ
ཁͰ͋Ε͹͜ͷஈ֊ͰΞΠϦε෦ͷ‫ݚ‬ຏͳͲ΋ߦΘΕΔɻ5 ͱ 6 ͱ 7 ͸ۭಎ಺෦΁ͷΰϛͷࠞೖΛ๷͍Ͱిք์ग़ʹΑΔੑೳྼԽΛ๷͙͜ͱ͕໨తͰ͋

ਤ.14

Δɻ௒७ਫͷߴѹચড়ʹΑۭͬͯಎ಺෦͔ΒΰϛΛۭಎͷ੡࡞աఔ [15]ୟ͖མͱͨ͋͠ͱɺ֎෦͔Βͷΰϛͷࠞೖ͕ͳ͍Α͏ࡉ৺ͷ஫ҙΛ෷͍ͳ͕ΒΫϦʔϯϧʔϜʹۭͯಎ

11

７－ 11

ʹଌఆ༻ͷϑϥϯδ෦ͱΞϯςφ෦ΛऔΓ෇͚͍ͯ͘ɻ2 ͸ΞχʔϧʹΑۭͬͯಎ಺෦ʹ‫ٵ‬ଂ͞ΕͨਫૉΛ์ग़ͤ͞ɺ‫ۃ‬௿Թࢼ‫ʹ࣌ݧ‬༗֐ͳ௒఻ಋମͨΔχΦϒਫૉԽ෺͕ੜ͡ΔྔΛ‫ݮ‬Βͨ͢Ίʹඞཁͳ޻
ఔͰ͋Δɻ8 ͸ߴిքʹ͓͚Δද໘఍߅ͷஶ͍͠૿େΛ཈͑ΔͨΊʹඞཁͳ޻ఔͰ͋Δɻ௚લͷిղ‫ݚ‬ຏͰ‫ٵ‬ଂ͞ΕͨਫૉΛ֦ࢄͤͨ͞Γɺද໘ͷࢎԽບΛ֦ࢄͤͯ͞χΦϒਫૉԽ෺ͷੜ੒Λ཈੍͢Δ͜ͱʹΑΓɺిքੑೳΛ޲্͢Δͱ͞ΕΔɻ͜͜Ͱɺి
ղ‫ݚ‬ຏͷ࣮ࢪ͕‫ܗ‬ঢ়ʹΑͬͯࠔ೉ͳ৔߹͸Խֶ‫ݚ‬ຏ͕ࢪ͞ΕΔ͜ͱ͕͋Δɻ͜ΕΒͷද໘ॲཧΛࢪͨ͋͠ͱɺ͍ΘΏΔ‫ۃ‬௿ԹͰͷۭಎੑೳଌఆͷͨΊͷిքੑೳࢼ‫ߦ͕ݧ‬ΘΕΔɻ

8 ௒఻ಋۭಎͷੑೳධՁ

ਤ.15

௒఻ಋۭಎͷੑೳ͸Ճ଎ిք E ͱද໘఍߅ Rs

ͨͯଌఆͰ༻͍ΒΕΔయ‫ܕ‬తͳηοτΞο

ϓͷճ࿏ਤ [8]ʹΑͬͯࢦඪ͞ΕΔɻRs ͸ి৔ʹґଘͯ͠มԽ͢
Δ‫ݧܦ‬తͳࣄ࣮͕͋Δɻ·ͨɺRs ͸ Q0 ஋ͱ‫্ܗ‬

͢ΔͨΊʹ༗༻ʹͳΔͷ͕ҎԼͷෛՙ Q ஋ (QL )ҼࢠΛ༻͍ܾͯఆ͢Δ͜ͱ͕Ͱ͖ΔɻҎ্ΑΓɺۭͰ͋ΔɻಎͷੑೳධՁΛߦ͏ͱ͸͢ͳΘͪɺԣ࣠ʹిք E
ɺॎ࣠ʹిքґଘੑͷ͋Δ Q0 (∝1/Rs ) ΛऔͬͨQL =Q0 -E curve Λ࡞੒͢Δ͜ͱͰ͋ΔɻҎԼͰ͸ۭಎͷੑೳදͷͨΊͷͨͯ‫ిܕ‬քੑೳଌఆࢼ‫ݧ‬ʢͨͯଌUω
P0 + Pe + Pt

(35)ෛՙ Q ஋ͷ෼฼ʹ͸ۭಎͳ͍ͰࣦΘΕΔશͯͷఆʣͷ‫ݪ‬ཧʹ͍ͭͯઆ໌͢Δɻύϫʔͷ߹‫ܭ‬ΛऔΔɻ౤ೖύϫʔ͕ 0 ͷ৔߹ͷۭಎ಺෦ͷΤωϧΪʔ‫ݮ‬ਰ཰͸ dU/dt = −(P0 + Pe +·ͣɺͨͯଌఆͰ༻͍Δయ‫ܕ‬తͳηοτΞοϓͷ

Pt ) ͱද͞ΕΔɻ͕ͨͬͯ͠ɺ͜ΕΛ QL Λ༻͍ͯճ࿏ਤΛਤ 15 ʹ༩͑Δ͜ͱͱ͠ɺ͜ͷγεςϜʹ

ॻ͖௚ͯ͠ඍ෼ํఔࣜΛղ͘͜ͱͰɺҎԼͷΑ͏ͳ͓͍ͯଌఆ͞ΕΔύϫʔͱۭಎੑೳʹඞཁͳύϫʔ

U (t) ͷ࣌ؒൃలͷղ͕ಘΒΕΔɻΛද 1 ͷΑ͏ʹఆٛ͢ΔɻPf ɺPr ɺPt ͸ύϫʔϝʔλͱํ޲ੑ݁߹‫ػ‬ɺαʔΩϡϨʔλΛ૊Έ߹Θ

U (t) = U (0) exp (−ωt/QL )ͤΔ͜ͱͰධՁͰ͖ΔɻҰํɺ Pe ͸ Pr′ ͱࠞ߹͢(36)ΔͨΊͦΕ୯ମͰύϫʔϝʔλͰ͸ධՁͰ͖ͳ͍͜

U (t) ͕ U (0) ͱൺֱͯ͠ 1/2 ·Ͱ‫ݮ‬ਰ͢Δ࣌ؒͱʹ஫ҙΛཁ͢Δɻ‫ޙ‬ड़͢ΔΑ͏ʹ Pe ͷධՁ͸ඇΛ τ1/2 ͱද‫͢ه‬ΔͱɺͦΕΛ༻͍ͯ QL ͸ҎԼͷৗʹॏཁʹͳΔͨΊͻͱ޻෉ඞཁͱͳΔɻΑ͏ʹද͞ΕΔɻۭಎ‫͠ʹثৼڞ‬͹Β͘ߴप೾ిྗΛ౤ೖͯ͠ఆৗ

QL = 2πfঢ়ଶʹͨ͠‫ޙ‬ɺ౤ೖύϫʔΛ੾Δ͜ͱͰۭಎ಺෦ʹ

τ1/2
ln(2)

(37)

஝ੵ͞ΕͨΤωϧΪʔ͕ࢦ਺ؔ਺తʹ‫ݮ‬গ͍ͯ͘͠

͜ΕΑΓɺۭಎͷύϫʔ͕ 1/2 ʹͳΔ·Ͱͷ༷࣌ؒࢠΛ‫؍‬ଌͰ͖Δɻ͕ͨͬͯ͠ɺdU /dt ∝ −U ͷ

τ1/2 Λ‫ٻ‬ΊΔ͜ͱͰ QL ΛධՁͰ͖Δ͜ͱͱͳΔɻ

ؔ܎͕͋Δɻ͜ͷΑ͏ͳࢦ਺ؔ਺తͳ‫ݮ‬ਰྔΛධՁ

12

７－ 12

P0

ۭಎͷۚଐนͰ୯Ґ࣌ؒ͋ͨΓʹࣦΘΕΔΤωϧΪʔPfΤωϧΪʔ౤ೖέʔϒϧʹ୯Ґ࣌ؒ͋ͨΓʹ౤ೖ͞ΕͨΤωϧΪʔPr′

Pf ͷ͏ۭͪಎଆʹ୯Ґ࣌ؒ͋ͨΓʹ൓ࣹ͞ΕͨΤωϧΪʔPe

୯Ґ࣌ؒ͋ͨΓʹΤωϧΪʔ౤ೖ༻Ξϯςφ͔Β‫্͍͛ٵ‬ΒΕΔΤωϧΪʔPr

ΤωϧΪʔ౤ೖέʔϒϧ͔Βۭಎଆʹ์ͨΕΔΤωϧΪʔPt୯Ґ࣌ؒ͋ͨΓʹ pickup Ξϯςφ͔Β‫্͍͛ٵ‬ΒΕΔΤωϧΪʔ
ද.1ۭಎੑೳͷධՁʹඞཁͳΤωϧΪʔͷ෼ྨۭಎ‫ڞ͕ثৼڞ‬໐ঢ়ଶʹ͋Δͱ͖ɺ֤ύϫʔͷؒʹ͸ҎԼͷؔ܎͕੒ཱ͢Δʢਤ 16 ࢀরʣɻ

Pe
P0
Pt
βt =
P0
Ppick
βpick =
P0
βf =

(39)
(40)
(41)

Pe ʹؔ࿈͢Δ βf Ҏ֎ͷ݁߹౓͸ύϫʔϝʔλΛ༻͍ͯධՁͰ͖Δɻ·ͨɺ ೖྗέʔϒϧଆʹછΈग़͢ύϫʔ Pe ͱͦΕҎ֎ͷۭಎ಺෦Ͱͷଛࣦύϫʔͷൺ β ∗ ͱͯ͠ҎԼΛఆٛ͢ΔɻPe
P0 + Pt= βf /(1 + βt )

β∗ =

(42)
(43)

ଞํɺۭಎ‫ثৼڞ‬ͷ౳Ձճ࿏໛‫ܕ‬Λ༻͍ͨ‫͔ࢉܭ‬Β β ∗ Λ Pr ͱ Pf Λ༻͍ͯҎԼͷΑ͏ʹද‫͖Ͱݱ‬Δ͜ͱ͕෼͔͍ͬͯΔɻ
ਤ.16

ۭಎ‫֤ͱثৼڞ‬ύϫʔͷؒͷؔ܎
∗

β =

1+
1−

√

√

Pr /Pf
Pr /Pf

or

1−

1+

√

√

Pr /Pf
Pr /Pf(44)

্ࣜͷϓϥεϚΠφε͸ҎԼͷΑ͏ʹܾΊΔɻ·P0 = Pf − Pr − Ptͣɺߴप೾ΤωϧΪʔΛ౤ೖ͢ΔΞϯςφͷਂ͞Λ(38)ௐ੔ͯ͠൓ࣹ͕‫ۃ‬গͱͳΔҐஔΛ୳Δɻ͔ͦ͜Βɺ͜ΕʹΑΓɺ֤ύϫʔΛύϫʔϝʔλͰଌఆ͢Δ

ΞϯςφΛਂ͘ೖΕΔͱ൓ࣹ͕େ͖͘ͳΔঢ়ଶɺ͋͜ͱʹΑΓ P0 ͕‫·ٻ‬Δɻ

Δ͍͸Ҿ͖ൈ͘ͱ൓ࣹ͕େ͖͘ͳΔঢ়ଶʹͳΔɻલऀΛΦʔόʔΧοϓϦϯάɺ‫ऀޙ‬ΛΞϯμʔΧοϓ֤ύϫʔͱ P0 ͷൺ β ͱͯ͠ҎԼͷྔΛఆٛϦϯάͱ͍͏ɻ෼ࢠ͕ ਖ਼ͳͷ͕Φʔόʔɺෛͳͷ͕ΞϯμʔͰ͋Δɻβ ∗ ͸ύϫʔϝʔλͰଌఆՄೳ

͢Δɻ

13

７－ 13

Ͱ͋ΔͨΊɺ͜ͷࣜΛ௨ͯ͡ βf ΛධՁͰ͖Δ͜ͱύϫʔϝʔλͰଌఆ͢Δ͜ͱʹΑΓ Eacc Λ‫ٻ‬Ίͯ

ʹͳΔɻ

Pt
͍ΔɻͦΕͱಉ࣌ʹ P0 Q0 = Pt Qt ⇒ Q0 = Qt P
0ͷؔ܎ࣜΛ༻͍ͯ Q0 Λ‫ٻ‬Ί͍ͯΔɻ͜Ε͕ Q-E
͜͜·ͰͰఆٛͨ݁͠߹౓Λ༻͍Δ͜ͱͰ QL Λଌఆͷ‫ݪ‬ཧͰ͋ΔɻҎԼͷΑ͏ʹද‫͖Ͱݱ‬Δɻ

9 ௒఻ಋۭಎͷੑೳͷ੍‫ݶ‬

QL = Q0 ×1/(1 + βf + βt )(45)‫ࢸʹࡏݱ‬Δ·ͰੵΈॏͶۭͨಎՊֶͷ஌‫͔ݟ‬Βɺ͔͜͜Β Q0 ͓Αͼද໘఍߅ Rs ΛධՁͰ͖ΔΑ

௒఻ಋۭಎͷੑೳ͕༷ʑͳཧ༝ʹΑͬͯϦϛοτ͞Εͯ͠·͏͜ͱ͕໌Β͔ʹͳ͍ͬͯΔɻҎԼͰ୅ද͏ʹͳΔɻ

తͳ 6 ͭͷ‫ݪ‬ҼΛྻ‫͢ڍ‬Δɻ࣍ʹɺEacc ͷධՁʹ͍ͭͯઆ໌͢ΔɻҰൠʹɺՃ

1. ෺ੑͰܾ·ΔΫΤϯν (Ideal performance)

଎ޯ഑ Eacc ͸Ճ଎ʹΑͬͯ֫ಘͰ͖ΔΤωϧΪʔ

2. ਫૉප (Hydrogen Q-disease)V ͱՃ଎͞ΕΔ࣮ޮతͳ௕͞ deﬀ ͷੵͰද͞ΕΔ

3. ϚϧνύΫλ (Multipacting)ɻ͜ΕΛ γϟϯτΠϯϐʔμϯε RQshʹద༻͢Δ
0

4. ిք์ग़ిࢠ (Field emission)ͱՃ଎ޯ഑͸ҎԼͷΑ͏ʹද‫͖Ͱݱ‬Δɻ

5. ද໘ܽؕͷଘࡏ (Thermal breakdown)
6. High Field Q-slope

V2
Rsh
=
ωU
Q0
Rsh
(Eacc deﬀ )2
=
⇒
P0 Q0
Q0
√
Rsh
P0 Q0
⇒ Eacc deﬀ =
Q0
√
Rsh
1
P0 Q0
⇒ Eacc =
deﬀ
Q0
√
Rsh
1
Pt Qt
=
deﬀ
Q0
√
= Z Pt Qt(46)্‫ه‬ͷ‫ݪ‬ҼʹΑͬͯੜͣΔಛ௃తͳ Q-E curveΛൺֱͨ͠ਤΛਤ 17 ʹࣔ͢ɻ

(47)
(48)
(49)
(50)
(51)

্ࣜΑΓՃ଎ి৔ Eacc ͸γϛϡϨʔγϣϯ͔Β‫·ٻ‬Δఆ਺ Z ͱ√

P0 Q0 ΋͘͠͸√

ਤ.17 ༷ ʑ ͳ ‫ ݪ‬Ҽ Ͱ ۭ ಎ ͕ ੑ ೳ ͞ Ε Δ Q-E
curve ͷൺֱ [16]Pt Qt ͷੵͱͯ͠ද͞ΕΔɻ্ࣜʹ QL ͔Β‫ٻ‬Ίͨ P0 ͱ Q0 ΋
͘͠͸ Pt ͱ Qt Λ౰ͯ͸ΊΔ͜ͱͰ Eacc ΛධՁ͢ҎԼͰ֤ʑͷཁҼʹ͍ͭͯઆ໌͢Δɻ

9.1 ෺ੑͰܾ·Δ੍‫ݶ‬Δ͜ͱ͕ՄೳͰ͋Δɻ͔͠͠ͳ͕ΒɺQL ͷଌఆ͸͕͔͔࣌ؒΔ্ɺ౤ೖΤωϧΪʔͷΦϑ࣌ʹ RF ੍ઌड़ͨ͠Α͏ʹɺཧ૝తͳද໘Λ΋ͬͨ௒఻ಋۭ

‫ޚ‬γεςϜͷ‫ڞ‬໐ঢ়ଶ͕֎Εͯ͠·͏͜ͱ͕͋ΓɺಎͰ͸ͦͷ࠷େՃ଎ޯ഑ʹؔͯ͠෺ੑͰܾ·Δྟքͦͷ৔߹ʹ࠶ͼߴप೾‫ݯ‬ͷग़ྗΛ‫ڞ‬໐ঢ়ଶʹ௥ਵ࣓͞৔ʹΑΔ্‫͕ݶ‬ଘࡏ͢ΔɻχΦϒͷ৔߹ɺԼ෦ྟ

ͤΔͨΊͷ࡞‫͕ۀ‬ඞཁʹͳΔͳͲɺ൥Θ͕͋͠͞Δɻ

ք࣓৔ͱͯ͠ Hc1 ΛऔΔͱ 170 mT ఔ౓ɺϙςϯͦ͜Ͱɺ࣮ࡍͷ Eacc ͷଌఆͰ͸ QL ͷଌఆ͔Β Qt

γϟϧোน·Ͱߟྀͨ͠ superheating field ΛͱΔΛܾఆ͓͖ͯ͠ɺͭ͗ʹ্ࣜʹ͓͍ͯ Z ͱ Qt ͕ͱ 200 mT ఔ౓ͱͳΔɻ͜Ε͸ TESLA-shape ۭͱ΋ʹෆมͰ͋ΔͱΈͳͯ͠࢒Δ།Ұͷม਺ Pt ΛಎͰ 40 – 46 MV/m ʹ૬౰͢Δɻ෺ੑͰܾ·Δ੍

14

７－ 14

‫ݶ‬ͷΈ͕ޮ͍͍ͯΔͷͰ͋Ε͹ɺۭಎ͸͜ͷลΓ·਺ഒΛຬͨ࣌͢ʹ૿෯͢ΔɻϚϧνύΫλʹؔͯ͠Ͱ͸ΫΤϯνͤͣʹ࣋ͪ‫͑ת‬Δ͸ͣͰ͋Δɻ

͸ɺ์ग़͞Εͨిࢠ͕‫ݩ‬ͷ৔ॴʹ໭Δաఔͱೋ఺ؒ

9.2 ਫૉප

ͰিಥΛ‫܁‬Γฦ͢աఔ͕ߟ͑ΒΕΔɻཻࢠͷ‫ي‬ಓͷۭಎ͸੡࡞͕‫ྃ͞׬‬ΕΔ·ͰͷؒɺχΦϒࡐྉͷ֓೦ਤΛਤ 18 ͷ (a) ͱ (b) ʹࣔ͢ɻԁ౵࣠ରশͷ੡଄ʹ൐͏ిࢠϏʔϜ༹ղɺ஁଄Ճ޻ɺϓϨεՃ޻ɺpilbox ۭಎͷ৔߹Ͱ͸ࢸΔॴͰϚϧνύΫλ์ి੾࡟Ճ޻ɺిࢠϏʔϜ༹઀ͳͲ͕ࢪ͞ΕΔɻͦΕΏ͕ੜͣΔՄೳੑ͕͋Γɺۭಎੑೳ੍͕‫͞ݶ‬ΕΔେ͖

͑ɺۭಎ͸ड͚ೖΕ࣌ʹ಺෦ʹଟྔͷਫૉΛཷΊࠐͳ‫ݪ‬Ҽͱͳ͍ͬͯΔɻϚϧνύΫλͷରࡦͱͯ͠͸ΜͰ͓ΓɺͦΕ͸ྫྷ٫࣌ʹपลͷχΦϒͱ݁߹ͯ͠

ೋͭ͋Δɻͻͱͭ͸ɺϚϧνύΫλ์ిΛ௕࣌ؒ‫ܧ‬௒఻ಋసҠԹ౓͕ 1.4 K ͷਫૉԽχΦϒΛ‫ܗ‬੒͢ଓͯ͠ࡐྉͷ࣋ͭೋ࣍ిࢠ์ग़܎਺ΛྼԽͤ͞Δ͜

Δɻ͜Ε͸௒఻ಋۭಎͷయ‫ܕ‬తͳӡసԹ౓ 2 – 4.2

ͱͰ͋Δɻ͜ͷաఔ͕‫ܧ‬ଓ͢Δ͏ͪʹ౸ୡՄೳͳՃ

K Ͱ͸ৗ఻ಋʹա͗ͳ͍ͨΊɺपΓͷ௒఻ಋిࢠͷ଎ిք͕ঃʑʹߴ·͍͖ͬͯɺ࠷ऴతʹೋ࣍ిࢠ์

ॿ͚ΛआΓͯԾͷ௒఻ಋಛੑΛࣔ͢ɻ͜ͷΑ͏ͳ͍ग़܎਺͕ 1 ҎԼͱͳΔஈ֊·Ͱ౸ୡ͢ΔͱϚϧνΘ͹௿‫ڃ‬௒఻ಋମ͕࠶ͼৗ఻ಋʹసҠ͢Δද໘࣓৔ύΫλ੍͕ѹ͞Εͨ͜ͱͱͳΔɻ͜ͷΑ͏ͳঢ়ଶ͸ͷ‫͞ڧ‬͸αΠζʹൺྫͯ͠ऑ͘ͳΔ͜ͱ͕஌ΒΕͯҰൠʹʮϓϩηε͞ΕͨʯͳͲͱ‫ݺ‬͹ΕΔɻୈೋͷ͍Δɻ͕ͨͬͯ͠ɺՃ଎ిքΛ޲্ͯ͠ද໘࣓৔͕

ରࡦͱͯ͠͸ɺପԁ‫্ܗ‬ͷۭಎΛ࠾༻͢Δ͜ͱͰ͋‫ͳ͘ڧ‬Δʹै͍ɺਫૉԽχΦϒ͕ৗ఻ಋసҠΛ‫͜ى‬ΔɻୈҰͷϝϦοτͱͯ͠ɺ͜ͷΑ͏ͳପԁ‫ܗ‬ͷδͯ͠ද໘఍߅ͷ૿Ճ͕΋ͨΒ͞ΕΔͱߟ͑ΒΕ͍ͯΦϝτϦͰ͸ϚϧνύΫλ͕૿෯͢ΔྖҬ͕‫ݶ‬ΒΕΔɻ͜ͷΑ͏ͳഎ‫ʹܠ‬ΑΓɺड͚ೖΕ࣌ͷ··ͷঢ়ΔɻୈೋͷϝϦοτͱͯ͠ɺೋ࣍ిࢠͷ‫ي‬ಓ͕࠷ऴଶͰ͸ɺ௒఻ಋసҠ࣌ʹαΠζͷେ͖ͳਫૉԽχΦతʹϚϧνύΫλͷൃੜ৚݅Λຬͨ͞ͳ͍੺ಓ෦ʹϒ͕‫ܗ‬੒͞ΕɺՃ଎ి৔͕਺ MV/m Λ௒͑ͨஈ֊ूଋ͞ΕΔͱ͍͏࢓૊Έ͕උ͑ΒΕ͍ͯΔ͜ͱͰ͋Ͱ Q ஋ͷ‫ݮͳܹٸ‬গ͕ੜ͡ɺͦΕҎ্ͷߴप೾ύ

Δʢਤ 18 (c) ࢀরʣɻϫʔ౤ೖ͸ෆՄೳͱͳΔɻ͜ͷ໽հͳ‫ݱ‬৅͸ਫૉප(Hydrogen Q-disease) ͱ‫ݺ‬͹Ε͍ͯΔɻਫૉප͸ରࡦͱͯ͠ 600 – 900 ◦ C 3 hours ͷߴԹΞχʔϧΛࢪ͢͜ͱ͕༗ޮͰ͋Δɻۚଐத͔Βਫૉ͕์ग़͞
Εɺྫྷ٫࣌ʹۭಎද໘Ͱ‫ܗ‬੒͞Εͯ͠·͏ਫૉԽ෺
ͷαΠζΛ‫ʹܹٸ‬཈੍Ͱ͖Δɻ͜ΕʹΑΓɺ౸ୡՄೳͳՃ଎ిքͷඈ༂తͳ޲্͕‫ظ‬଴Ͱ͖Δɻ

9.3 ϚϧνύΫλ
ۭಎ಺෦ʹඬ͏Ӊ஦ઢ΍ిք์ग़ిࢠͳͲ͸ߴप೾ి৔ͰՃ଎͞Εͯนʹিಥͯ͠ೋ࣍ిࢠΛ์ग़͢

ਤ.18 (a) pillbox ۭಎ಺ͷ 1 ࣍ͷ multipacting. (b) 2 ࣍ͷ multipacting. [8] (c) ପԁۭಎʹΑΔվળͷޮՌ. [17]. (͜ͷը૾͸ҎԼͷจ‫͔ݙ‬ΒҾ༻͠·ͨ͠ [2]).

Δɻೋ࣍ిࢠ์ग़܎਺͸਺ keV ͷΤωϧΪʔͰ์ग़܎਺͕ >1 Λຬͨ͢ɻ͜ͷ৔߹ɺۭಎ಺෦ʹඬ͏ిࢠ͕Ճ଎͞Εͯର޲͢Δࡐྉද໘ʹিಥͯ͠ೋ
࣍ిࢠ์ग़Λ༠ൃ͠ɺͦΕΒ͕·ͨ‫ݩ‬ͷࡐྉද໘ʹ

9.4 ిք์ग़ (Field Emission)໭ͬͯೋ࣍ిࢠΛ์ग़͢ΔաఔΛ‫܁‬Γฦ͢͜ͱʹΑΓ์ग़ిࢠͷ਺͕ࢦ਺ؔ਺తʹ૿෯͞Εۭͯಎ಺ۭಎ಺෦ͷද໘ి৔ʹΑͬͯిք์ग़ిࢠ͕์ग़

෦ͷΤωϧΪʔ͕‫ٵ‬ऩ͞Εɺ࠷ऴతʹԹ౓্ঢʹΑ͞ΕΔɻ͜Ε͕ۭಎ಺ʹඬ͏ͱ༨‫ͳܭ‬ΤωϧΪʔϩΔΫΤϯνΛੜͣΔɻ͜ͷ‫ݱ‬৅ΛϚϧνύΫλ์ిεΛট͘ɻ·ͨɺిք์ग़ిࢠ͕นʹিಥ͢Δͱൃ

ͱ͍͏ɻϚϧνύΫλ͸িಥ͢Δִ͕ؒप‫ظ‬ͷ൒੔೤ۭͯ͠ಎੑೳ͕௿Լ͠ɺ࠷ऴతʹ͸ΫΤϯν͕ੜ

15

７－ 15

ͣΔɻిք์ग़ిࢠ͸ Eacc ͕େ͖͘ͳΔ΄Ͳଟ͘์ग़͞ΕΔΑ͏ʹͳΔɻ·ͨɺද໘ʹಥ‫ى‬΍ΰϛ͕
͋Δͱද໘ి৔͕૿෯͞ΕΔͨΊɺ͜ͷӨ‫͕ڹ‬ඈ༂తʹߴ·ΔɻͦΕʹΑΔి৔ͷ૿෯ҼࢠΛ βFN ͱ
͢Δɻ͜ͷͱ͖ɺిք์ग़ిࢠͷిྲྀ͸ҎԼͷࣜͷΑ͏ʹද‫͖Ͱݱ‬Δ [8]ɻI(E) ∝ (βFN E)2.5 exp(−BFN ϕ3/2
βFN E

)

(52)

͜͜ͰɺE ͸ද໘ి৔ͷ‫͞ڧ‬ɺϕ ͸෺࣭ͷ࢓ࣄؔ
਺ɺβFN ͸ද໘ͷಥ‫ʹͲͳى‬ΑΔ‫ॴہ‬తͳి৔ͷ૿

ਤ.20

෯౓ɺBFN = 6.83×103 Ͱ͋Δɻ਺ µm ‫ڃ‬ͷۚଐߴѹ௒७ਫચড়ͷηοτΞοϓ [8]ύʔςΟΫϧͷଘࡏΛԾఆ͢Δͱ βFN ͸਺ඦഒʹ
ߴ·Δɻ͜ͷΑ͏ͳΤϛολʔͷը૾ͷྫΛਤ 19

ޮͰ͋ΔɻಛʹϔϦ΢ϜΛॆరۭͨ͠ಎ಺ʹߴप೾ʹ༩͑ΔɻిྗΛ౤ೖͯ͠ΤϛολΛ༹ղͤ͞Δํ๏ʹ͍ͭͯ͸࣮੷͕͋ΓɺϔϦ΢Ϝϓϩηεͱ‫ݺ‬͹Ε͍ͯΔ[19]ɻ·ͨɺۭಎ಺෦Ͱ࠷େͷද໘ి৔͕ൃੜ͢Δ
ͷ͸ Iris ෦Ͱ͋ΔͨΊɺIris ෦Λ‫ػ‬ց‫ݚ‬ຏ͢Δ͜
ͱͰ field emission ͷ౓߹͍Λվળͨ͠ࣄྫ͕͋Δ[20]ɻୈࡾʹɺࣜ 52 ͸ม਺ͱͯ͠࢓ࣄؔ਺Λ࣋ͭͨΊɺ͜ΕΛ޲্ͤ͞Δ͜ͱͰిք์ग़ిࢠͷྔΛ཈੍͢Δ͜ͱͰ͋Δɻۙ೥஫໨͞Ε͍ͯΔ΋ͷʹϓ
ϥζϚϓϩηεͱ‫ݺ‬͹ΕΔख๏͕͋Δɻۭಎ಺෦ΛNe ͱ CO2 ౳ͷࠞ߹ΨεͰຬͨͯ͠ߴप೾ిྗΛ౤ೖͯ͠ి࣓৔ͷ mode Λྭ‫͠ى‬ɺ֤ηϧ͝ͱʹϓϥζϚΛൃੜۭͤͯ͞ಎ಺นΛ෴͏༗‫ػ‬෺ͱࢎԽ
ਤ.19ϑΟʔϧυΤϛογϣϯͷΤϛολͷྫ [18]ບΛ࡟͗མͱ͢ɻ͜ΕʹΑΓɺχΦϒຊདྷͷ෺ੑ͕ൃ‫͞ش‬Ε࣮ͯޮతͳ࢓ࣄؔ਺͕޲্͢Δͱ‫ظ‬଴͞Ε

feild emission ͷରࡦͱͯ͠͸ɺୈҰʹ‫ॴہ‬తͳ

Δɻۙ೥ LCLS-II ͷ࿮૊ΈͰϓϥζϚϓϩηεͷ

ి৔Λඈ༂తʹߴΊΔӨ‫ڹ‬ͷ͋ΔۚଐύʔςΟΫϧ‫͕ڀݚ‬ਐΈɺ࣮ࡍʹ field emission ΛվળͰ͖ͨྫ

ͷࠞೖΛ๷͙͜ͱͰ͋ΔɻۭಎΛਗ਼ড়ʹ૊Έ্͛Δ

ʹ͍ͭͯใࠂ͞Ε͖͍ͯͯΔ [21]ɻͨΊʹɺਤ 20 ͷΑ͏ͳηοτΞοϓͰߴѹ௒७ਫ

9.5 ද໘ܽؕ

Λ༻͍ͯ಺໘Λೖ೦ʹચড়͢Δɻͦͷ‫ޙ‬ɺ௚ͪʹΫۭಎද໘ͷܽؕ΍ෆ७෺Ͱͷ‫ॴہ‬తͳൃ೤ʹΑͬϦʔϯϧʔϜʹ࣋ͪࠐΜͰਗ਼ড়ͳ‫ۭͰڥ؀‬ಎͷ૊Έͯੜ͡Δ௒఻ಋഁյ͸ۭಎੑೳΛ੍‫͢ݶ‬Δେ͖ͳཱͯΛߦ͏ɻୈೋʹి৔Λඈ༂తʹߴΊΔޮՌͷ͋ཁҼͱͳΔɻۭಎͷද໘࣓৔͕࠷େͱͳΔͷ͸੺ಓΔද໘ͷಥ‫ى‬Λͳͨ͘͢Ίɺද໘ૈ͞Λ௿‫ͯ͠ݮ‬ฏ

෦Ͱ͋Δ͕ɺ͜͜͸ిࢠϏʔϜ༹઀ͷෆ‫׬‬શͳՕॴ‫্͛࢓ʹ׈‬Δ͜ͱͰ͋ΔɻͦͷͨΊʹిղ‫ݚ‬ຏΛߦ΍ಥ‫͕ى‬ଘࡏ͢ΔՄೳੑ͕࠷΋ߴ͍৔ॴͰ͋Δɻ·͍ɺۭಎ಺෦ͷಥ‫ى‬Λ௿‫ͤ͞ݮ‬Δɻ·ͨɺߴप೾ి

ͨɺͦ͏Ͱͳ͘ͱ΋ɺۭಎද໘ʹ͸‫ॴہ‬తʹෆ७෺ྗΛ౤ೖۭͯ͠ಎද໘ͷΤϛολΛ༹͔͢͜ͱ΋༗ͷ‫ؚ‬༗ྔ͕ଟ͍ՕॴͳͲଘࡏ͢ΔՄೳੑ͕͋Δɻۭ

16

７－ 16

཰ κ ͱ RRR ͷؔ܎͸ҎԼͷࣜͰ༩͑ΒΕΔ [4]ɻಎͷిք‫ݚ‬ຏʹΑͬͯ͜ͷΑ͏ͳܽؕ෦͸࡟͗མ
ͱͤΔՄೳੑ͕͋Δ΋ͷͷɺ‫ݧܦ‬తʹ͸ͦΕ͚ͩͰ͸े෼Ͱ͸ͳ͍ɻͦ͜Ͱిք‫ݚ‬ຏͷલʹۭಎͷ಺໘‫ॴہ‬తͳ‫ػ‬ց‫ݚ‬ຏʹΑΓ͜ΕΛআ‫͢ڈ‬Δɻ࣮ࡍʹۭρ(300K)ρTcκ(4.2K) = RRR/4 [W/m·K]ಎ಺෦ʹଘࡏ͍ͯͨܽؕ͠ͷը૾ͷྫΛਤ 21 ʹ༩্ࣜΑΓɺRRR ΛߴΊΔ΄Ͳۭಎੑೳ͕ߴ·Δ

RRR =‫ࠪݕ‬Λߦͬͯܽؕͷ༗ແΛ୳ࡧ͠ɺൃ‫ͨ͠ݟ‬৔߹͸

͑Δɻ

(54)
(55)

͜ͱ͕ཧղ͞ΕΔɻͨͩ͠ɺRRR ΛߴΊΔ΄Ͳۭಎͷ‫ػ‬ցతͳ‫౓ڧ‬͸௿Լ͢Δɻ͜Ε͸ӷମϔϦ΢ϜΛ༻͍ͯྫྷ٫͕ߦΘΕ͍ͯΔχΦϒ੡ͷ௒఻ಋۭಎ
ʹͱͬͯେ໰୊Ͱ͋ΔɻͳͥͳΒ͹ɺӷମϔϦ΢Ϝ͸‫ؾ‬Խ͢Δͱମੵ͕ 700–800 ഒʹ๲Ε্͕ΔͨΊɺͦͷऔΓѻ͍͸ߴѹΨεอ҆๏ͷద༻ର৅Ͱ͋ΔɻΏ͑ʹɺ௒఻ಋۭಎͷ੡଄ʹ͓͍ͯ͸ߴѹΨεอ҆๏ͷ৹ࠪΛύεͰ͖Δ΄Ͳͷ‫͕͋౓ڧ‬Δ͜ͱΛอূ
͢Δඞཁ͕͋ΔɻRRR ∼ 300 ͷόϧΫχΦϒࡐͳΒߴѹΨεอ҆๏ͷ‫ج‬४Λ໰୊ͳ͘ύεͰ͖Δɻͦ
͜Ͱɺ௒఻ಋۭಎ͸͜ͷఔ౓ͷ७౓ͷχΦϒࡐΛ༻
ਤ.21

ද໘ܽؕͷྫ

͍ͯ੡଄͞ΕΔͷ͕ҰൠతͰ͋Δɻจ‫[ ݙ‬2] Ͱ͸ෆ७෺͕‫ڽ‬ॖͨ͠Օॴʢܽؕʣ͕‫ݪ‬࠷‫ʹޙ‬ɺ্ࣜʹ۩ମతͳ਺஋ΛೖΕͯ Hdefect ΛҼͰۭಎੑೳ͕௿Լ͢Δ࢓૊Έʹؔ͢Δ୯७ͳϞσ

ධՁ͢ΔɻӷମϔϦ΢ϜͷԹ౓͕ 2 Kɺa ͕ 50ϧʹΑΔධՁ͕༩͑ΒΕ͍ͯΔɻ൒‫ ܘ‬a Ͱද໘఍µmɺ ৗ఻ಋͷ఍߅͕ Rn =

߅ Rn Λ΋ͭৗ఻ಋͷද໘ܽؕʹΑͬͯ௒఻ಋഁյ

= 300 ͷ Nb ͷ೤఻ಋ཰͕ 75W/(mK) Ͱ͋Δͱ͠

͕ൃੜ͢Δද໘࣓քͷ‫ ͞ڧ‬Hdefect ͷؔ܎ࣜ͸ҎԼͯ Hdefect ΛධՁ͢Δͱ 82.6 mT ΛಘΔɻ͜Ε͸Ͱ༩͑ΒΕΔɻχΦϒࡐྉ͕࣋ͭຊདྷͷԼ෦ྟք࣓৔ 170 mT ͷ

Hdefect =

√

10 mΩ

ɺ RRR

2/5 ఔ౓͔͠ͳ͍ɻ
4κ (Tc − THe )
aRn

(53)
௒఻ಋχΦϒࡐͷ७౓Λ্͛ͯܽؕΛ௿‫͠ݮ‬ɺܽ͜͜Ͱɺκ ͸χΦϒͷ೤఻ಋ཰ɺTc ͸χΦϒͷస͕ؕൃ‫͞ݟ‬Εͨ৔߹ʹ͸‫ػ‬ց‫ݚ‬ຏʹΑͬͯ‫ॴہ‬తʹҠԹ౓ɺTHe ͸௒఻ಋۭಎΛྫྷ٫͍ͯ͠ΔӷମϔϦআ‫͢ڈ‬Δ͜ͱʹΑΓɺۭಎੑೳΛ༗ޮʹ޲্Ͱ͖Δ

΢ϜͷԹ౓Ͱ͋Δɻ

͜ͱ͕ཧղ͞ΕΔɻ

9.6

High Field Q-Slope͜ͷࣜ͸ɺෆ७෺͕ଟ͍ܽؕͷ͋ΔՕॴ͸‫ۃ‬௿Թ্‫ه‬ͷΑ͏ͳੑೳ޲্ͷରࡦΛࢪͨ͠‫Ͱޙ‬΋ɺߴͰ΋ৗ఻ಋͰൃ೤͠΍͍ͨ͢Ίɺ࣮ޮతͳ࣓ଋ৵ೖ

͍Ճ଎ి৔ʹ͓͍ͯ Q ஋ͷஶ͍͠‫ݮ‬গ͕ੜ͡Δ͜

։࣓࢝৔͕௿Լͯ͠͠·͏͜ͱΛҙຯ͍ͯ͠Δɻ·ͱ͕࣮‫ݧ‬తʹ໌Β͔ͱͳ͍ͬͯΔɻ͜ͷΑ͏ͳߴిͨɺ೤఻ಋ཰ κ ͕௿͍΄ͲɺͦͷΑ͏ͳൃ೤ՕॴͷքଆͰͷ Q ஋ͷ‫ݮ‬গΛ High Field Q-Slope ͱ‫ݺ‬೤ΛऔΓ͖Εͣʹੑೳ͕௿Լ͢Δ͜ͱΛҙຯ͍ͯ͠ͿɻHigh Field Q-Slope ͷରࡦͱͯ͠ɺ110–120 ౓Δɻͷ਺े࣌ؒʢҰൠతʹ͸ 48 ࣌ؒʣͷ௿ԹϕʔΩϯάΛࢪ͢͜ͱ͕༗ޮͰ͋Δɻ͜ΕʹΑΓɺQ-dropҰൠʹɺχΦϒͷ७౓ͱ RRRɺ͓Αͼɺ೤఻ಋ͕ճ෮ͯ͠ΫΤϯν͕ੜͣΔ·Ͱߴ͍ Q ஋Λҡ࣋

17

７－ 17

Ͱ͖ΔޮՌ͕‫ݱ‬ΕΔɻ͜ͷ‫ʹߏػ‬͸ද໘ࢎԽບͷ֦

Technology and Applications”, (J. Wiley &ࢄ΍ਫૉྔͷ‫ݮ‬গͳͲ͕ޮ͍͍ͯΔͱߟ͑ΒΕ͍ͯ

Sons, New York, 2008)Δɻ࣮ྫΛਤ 22 ʹࣔ͢ɻ[10]

ಕ ெ Ұ (KEK), “General Introduction

to Particle Accelerator Systems”, Soken-dai
Core Curriculum, Fall, 2018 Introduction to
Accelerators II - Week 2 (2018/10/25)[11] G. Burt, “Introduction to RF Cavities for
Accelerators”[12] W. D. Kilpatrick, Rev. Sci. Instr. 28 (1957)824[13] ക৿݈੒, “௒఻ಋՃ଎ۭಎͷੑೳ޲্ʹ޲͚ٕͨज़։ൃ”, ௿Թ޻ֶ, 2019 ೥ 54 ‫ ר‬4 ߸

p.267–274[14] ‫ٱ‬อ‫޾ؽ‬, “௒఻ಋՃ଎ۭಎͷ෺ཧͱ՝୊ɺͦ
ͯ͠ੑೳ޲্΁ͷཧ࿦తࣔࠦ –৽‫ࢀن‬ೖͷ༠ਤ.22

௿ Թ ϕ ʔ Ω ϯ ά ʹ Α Δ High Field Q–

͍–” , ௿Թ޻ֶ 54(4) 275 – 282, 2019 ೥ 7 ݄

Slope ͷճ෮ [22]20 ೔[15] Ճ‫ݹ‬Ӭ࣏, “௒఻ಋۭಎΛ༻͍ͨՃ଎‫ث‬ͷ‫ݱ‬ঢ়ͱల๬”, 2019 ೥ 54 ‫ ר‬4 ߸ p. 257-266

ࢀߟจ‫ݙ‬[16] Hasan Padamsee, “50 years of success for[1] Detlef Reschke, “CHALLENGES IN ILC

SRF accelerators - a review”, 2017 Super-

SCRF TECHNOLOGY”, APAC 2007, Raja

cond. Sci. Technol. 30 053003

Ramanna, MOOPMA01[17] U.Klein and D.Proch, Proc. of Future Pos-[2] ࡕҪ ‫ࢤ׮‬,ʮ7. ௒఻ಋۭಎʯ, ߴΤωϧΪʔՃ

sibilities for Electron Accelerators, Char-଎‫ث‬ηϛφʔ OHO, 2015.

lottesville, N1 (1979)[3] ‫ڐ‬൹ ଠ࿠,ʮ7. ௒఻ಋۭಎʯ, ߴΤωϧΪʔՃ[18] Hasan Padamsee and Jens Knobloch , “The଎‫ث‬ηϛφʔ OHO, 2017.

Nature of Field Emission From Microparti-[4] Ճ‫ ݹ‬Ӭ࣏,ʮ7. ௒఻ಋՃ଎ۭಎͷ‫ૅج‬ʯ, ߴΤcles and the Ensuing Voltage Breakdown”,

ωϧΪʔՃ଎‫ث‬ηϛφʔ OHO, 2014.

SRF 981021-14[5] ໺‫ ޱ‬मҰ,ʮ5. ௒఻ಋۭಎʯ, ߴΤωϧΪʔՃ[19] C. E. Reece, M. Drury, M. G. Rao and଎‫ث‬ηϛφʔ OHO, 2011.

V. Nguyen-Tuong, “Improvement of the op-[6] ക৿ ݈੒,ʮ7.SC ճऩϥΠφοΫʯ, ߴΤωϧ

erational performance of SRF cavities viaΪʔՃ଎‫ث‬ηϛφʔ OHO, 2008.

in situ helium processing and waveguide[7] ‫ݹ‬୩‫و‬ষ,ʮ6. ௒఻ಋՃ଎ۭಎͷ‫ૅج‬ʯ, ߴΤωvacuum processing’,’ Proceedings of theϧΪʔՃ଎‫ث‬ηϛφʔ OHO, 2006.

1997 Particle Accelerator Conference (Cat.

[8] Hasan Padamsee, Jens Knobloch , and Tom

No.97CH36167), 1997, pp. 3105-3107 vol.3

Hays, “RF Superconductivity for Accelera-[20] ໖؏ ޹ಓɼ౉ᬑ कɼઋ೾ ஐߦ, et al., “೔ཱ੡tors”, (J. Wiley & Sons, New York, 1998)࡞ॴʹ͓͚Δ 9 ηϧ௒఻ಋՃ଎ۭಎͷ։ൃঢ়

[9] Hasan Padamsee, Jens Knobloch , and Tom‫”گ‬, ୈ̕ճ೔ຊՃ଎‫ֶػ‬ձ೥ձ, p.1165–1167,

Hays, “RF Superconductivity:

Scinence,

THPS09118

７－ 18

[21] Giaccone, et al., “PLASMA PROCESSINGTO REDUCE FIELD EMISSION IN LCLSII 1.3 GHz SRF CAVITIES”, SRF2019,
Dresden, Germany, FRCAB[22] B. Visentin, “Q-Slope at high gradients: review of Experiments and theories”, in Proc.
11th workshop on RF Supercond., Travemunde, Germany, pp. 199 - 205 ,2003.

19

７－ 19