1 SuperKEKB ͷઃ‫ܦܭ‬Ң໰୊ͱ͞Ε͍ͯͨɻઃ‫ݕܭ‬౼ͷਐߦʹ൐͍ίώʔϨϯθϩ͔ΒͷҰൠͳՃ଎‫ث‬ઃ‫Ͱܭ‬͸ɺॳΊʹ֤छͷ‫ج‬ຊతͳੑೳࢦඪΛධՁ͢Δղੳతͳެࣜ΍؆қతͳධՁπʔϧΛ༻͍ͯɺ໨తʹԠͨ͡Ճ଎‫ث‬ύϥϝʔλ (Ϛγϯύϥϝʔλ) ͕બఆ͞ΕΔɻଓ͍ͯɺબఆ͞ΕͨϚγϯύϥϝʔλΛ࣮‫͢ݱ‬Δͷʹదͨ͠ޫֶ‫ܥ‬ͷ‫ج‬ຊߏ଄ (ి࣓ੴɾߴप೾ۭ಑ͷ഑ஔ) ͕બ୒͞ΕΔɻޫֶ‫ܥ‬ͷ‫ج‬ຊߏ଄͕ܾ·ͬͨ‫ޙ‬͸ɺॴ๬ͷϚγϯύϥϝʔλΛ࣮‫͢ݱ‬Δޫֶؔ਺ΛಘΔͨΊͷ‫ثػ‬഑ஔɾ‫ثػ‬ύϥϝʔλͷ࠷దԽΛߦ͍ɺ‫ثػ‬഑ஔҊʹ‫ثػͮ͘ج‬ઃ‫ͱܭ‬ઃ‫͞ܭ‬Ε࣓ͨ৔෼෍౳ͷޫֶϞσϧ΁ͷϑΟʔυόοΫɺޫֶϞσϧʹΑΔϏʔϜण໋΍ Luminosity ౳ͷੑೳධՁ΍҆ఆੑͷ‫ূݕ‬౳͕ߦͳΘΕɺੑೳ΍‫ثػ‬഑ஔͷվળ΍ίετ࡟‫ݮ‬ͷͨΊͷ࠶ઃ‫͕ؒ࣌ܭ‬ͷ‫͢ڐ‬‫ݶ‬ΓߦͳΘΕΔɻ
͔͠͠ɺ‫ߦݱ‬ͷ SuperKEKB Ճ଎‫ث‬ͷઃ‫ܭ‬͸༷ʑͳ֎తཁҼ͔Β͜͏ͨ͠ඪ४తͳઃ‫ܭ‬ϑϩʔͱҟͳΔ‫ܦ‬ҢΛ୧͍ͬͯΔɻSuperKEKB Ճ଎‫ث‬ͷ౰ॳҊ͸‫ߦݱ‬ͷ΋ͷͱେ͖͘ҟͳΓɺ2004 ೥ʹ·ͱΊΒΕͨ “Letterof Intent for KEKB Super B Factory”[1] ʹ༗ΔΑ͏౰࣌Քಇதͩͬͨ KEKB B-Factory Ճ଎‫ث‬ͷઃ‫ܭ‬Λ΋ͱʹɺόϯν௕ σz∗ ͱিಥ఺ਨ௚ϕʔλؔ਺ βy∗ Λ൒෼ʹॖখͭͭ͠ɺΫϥϒަࠩํࣜΛ༻͍ͯϏʔϜϏʔϜύϥϝʔλΛ͓͓Αͦ 2 ഒͷ ξy ∼ 0.2 ఔ౓·ͰߴΊɺ஝ੵిྲྀΛ 4 ഒʹ͢Δ͜ͱͰɺγϛϡϨʔγϣϯ৚݅ʹ΋ΑΔ͕ 2.5 ∼ 5.0 × 1035 cm−2 s−1 ఔ౓ͷϧϛϊγ
ςΟ1 Λ࣮‫͢ݱ‬Δͱ͍͏ίϯηϓτͰ͋ͬͨɻ࣮૷‫ܭ‬ը͸ɺিಥ఺෦ͷվ૷ͱਅۭνΣϯόʔ‫ߴͼٴ‬प೾ۭ಑ͷେిྲྀԽରԠΛߦͳ͏ͱ͍͏΋ͷͰɺিಥ఺ޫֶ‫ܥ‬ͷߏ଄͸ KEKB B-Factory Ճ଎‫ث‬ͷߏ଄Λ౿ऻ͠௿ βy∗ԽʹରԠ͢ΔͨΊʹɺਫฏ໘಺ͷަࠩ֯౓Λ 22mard͔Β 30mard ʹ޿͛ɺిࢠɾཅిࢠϏʔϜϥΠϯ‫ڞ‬௨ͷ௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴ (QCS) ͷઃஔҐஔΛিಥ఺ʹ޲
͚ͯ 40% ΄Ͳલਐͤ͞Δͱ͍͏΋ͷͰ͋ͬͨɻޫֶ
‫ܥ‬ͷύϥϝʔλͱͯ͠͸‫ͳ࣮ݎ‬ઃఆͰ͕͋ͬͨɺ͜ͷ࣌఺Ͱ͸·ͩ࠷ऴऩଋ‫ൃͰܥ‬ੜ͢ΔγϯΫϩτϩϯ์ࣹޫͷॲཧʹؔͯ͠ɺਅۭ༰‫ܥֶޫͱث‬ͷ੔߹ͷऔΕͨઃ‫׬͕ܭ‬੒͍ͯ͠ͳ͔ͬͨɻ·ͨɺߴप೾‫Ͱ͚ͩܥ‬֓ࢉ 73MW ΋ͷిྗΛཁ‫͢ٻ‬Δͱ͍͏ྗٕͳઃ‫ͳܭ‬ͨΊɺେిྲྀɾ୹όϯνӡసରԠͷߴप೾‫ثػ‬ɾਅۭ‫ثػ‬ͷ։ൃ೉౓͕ߴ͘ɺͭ͘͹Ωϟϯύεͷडి༰ྔ(125MW) ͔Βͷӡసిྗ֬อ΍ӡస‫ܦ‬අͷංେԽ͕
1 KEKB B-Factory Ճ଎‫ث‬ͷ࠷ऴੑೳͷ͓͓Αͦ 16 ഒ (16 ∼2 × 2 × 4)τγϯΫϩτϩϯ์ࣹ (CSR) ͕୹όϯνԽͷো֐ͱͳΔ͜ͱ͕൑໌ͨ͜͠ͱ΍ɺ2006 ೥ͷ KEKB B-FactoryՃ଎‫ث‬ͷ Crab Crossing Խվ૷ͱͦΕʹΑΔ࣮ূͰಘΒΕͨ Crab Crossing ͰͷϏʔϜϏʔϜύϥϝʔλ͕ξy ∼ 0.13 ఔ౓ͱࣄલͷϏʔϜϏʔϜγϛϡϨʔγϣϯ͔Β༧ଌ͞ΕΔ஋ 0.2 ʹൺ΂ͯ௿͍͜ͱ͔Β౰֘ઃ‫ܭ‬ҊͰ 2 × 1035 cm−2 s−1 Λӽ͑ΔϧϛϊγςΟͷ࣮‫ݱ‬͸೉͍͠ͱ‫͍ͨͯͬ·ڧ͕ํݟ‬ɻ͞ΒʹɺΠλϦΞΛத৺ͱͨ͠άϧʔϓ͔Β Large Piwinski Angle ͳিಥ఺ઃ‫ʹܭ‬ΑΔઃ‫ܭ‬ϧϛϊγςΟ1036 cm−2 s−1 ͷ࣮‫ݱ‬Λᨳͬͨ SuperB ‫ܭ‬ը͕ఏҊ͞Εͨ͜ͱΛ͏͚ͯɺ෺
ཧ࣮‫ݧ‬Λ୲౰͢Δ Belle άϧʔϓ͔Β͸࣮‫ܭݧ‬ըʹࢀՃ͢Δ෺ཧֶऀืू‫ڝ‬૪ʹෛ͚ͳ͍ͨΊʹΠλϦΞͷ
SuperB ‫ܭ‬ըͱ΄΅ಉ౳ͷઃ‫ܭ‬ϧϛϊγςΟΛ࣮‫͢ݱ‬Δ͜ͱΛ‫͘ڧ‬ཁ੥͞ΕΔঢ়‫ͨͬͳͱگ‬ɻ͜͏ͨ͠ঢ়‫گ‬ͷதɺ“KEKB Accelerator Review Committee” ͔Β΋
Large Piwinski Angle Λ༻͍ͨઃ‫ܭ‬ҊΛ‫ݕ‬౼͢΂͠ͱͷ౴ਃ͕͋Γɺ2007 ೥લ‫͔ޙ‬Β‫ݕ‬౼͕࢝·Γɺ2009೥ॳ಄ʹ KEKB τϯωϧ΁ͷ࣮૷Λલఏͱͨ͠ઃ‫ܭ‬࡞‫͕ۀ‬ຊ֨Խͨ͠ɻઃ‫ͯ͠ࡍʹܭ‬͸ɺ‫͢߹ڝ‬Δ SuperB‫ܭ‬ըͱͷ‫ڝ‬૪΍༧ࢉ֫ಘͷ‫͔఺؍‬Βɺ‫ݐ‬ઃ޻‫ظ‬ѹॖͱ‫ݐ‬ઃඅ࡟‫ݮ‬ͷͨΊʹ KEKB B-Factory Ճ଎‫͔ث‬Βͷτϯωϧྲྀ༻ͱՄೳͳ‫ݶ‬Γͦͷ··ϏʔϜϥΠϯΛ࠶ར
༻͢Δ2 ͜ͱ͕‫ٻ‬ΊΒΕͨɻ࠷ॳ‫ظ‬ͷઃ‫ࢼܭ‬Ҋ͸ SuperB ͷઃ‫ܭ‬Λࢀߟʹɺ8GeVߴΤωϧΪʔిࢠϦϯά (HER) ΞʔΫηϧͷ୹ηϧ
Խͱ 3.5GeV ௿ΤωϧΪʔཅిࢠϦϯά (LER) ओภ޲ి࣓ੴ௕ͷԆ௕ʹΑΔ௿ΤϛολϯεԽʹΑΓฏߧΤϛολϯεΛ 1nmrad ఔ౓·Ͱ௿ΤϛολϯεԽ͠ɺަࠩ֯ 60mrad ͷিಥ఺ʹ HER/LER ‫ڞ‬௨ͷ௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴΛઌ಄ʹͨ͠࠷ऴऩଋ‫ͱܥ‬ΠλϦΞ‫ܕ‬ͷ৭ऩࠩิਖ਼෦Λಋೖ͢Δͱ͍͏΋ͷͰ͋ͬͨɻ͜ͷࢼҊͷධՁ݁Ռ͔Β͸ҎԼͷ஌‫͕ݟ‬ಘΒΕͨɻHER/LER‫ڞ‬௨ͷ௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴΛ༻͍ͨઃ‫Ͱܭ‬͸ɺ࣠֎Λ௨ΔϏʔϜͷ‫ي‬ಓภ޲͕֯େ͖͗͢‫ط‬ઃͷτϯωϧ‫ڥ‬քʹऩ·ΔΑ͏ʹภ޲ͤ͞ΔͱɺͦΕʹ൐͏෼ࢄؔ਺
ͷൃੜͱฏߧΤϛολϯεͷੜ੒Ͱઃ‫ܭ‬ίϯηϓτ͕
ഁ୼͢ΔɻΠλϦΞ‫ܕ‬ͷΞʔΫηϧΛϕʔεʹͨ͠৭ऩࠩิਖ਼෦͸ɺ‫࣮ݱ‬తͳ࣓৔ઃఆͰิਖ਼ʹඞཁͳ෼ࢄ
ؔ਺Λ֬อ͢Δʹ͸‫཰ۂ‬൒‫͕ܘ‬େ͖͗ͯ͢ɺ‫ط‬ઃͷτϯωϧ‫ڥ‬քʹऩ·Βͳ͍ɻKEKB B-Factory Ճ଎‫ث‬ͷHER ΞʔΫηϧͰ͸ฏߧΤϛολϯε 5nmrad ఔ౓͕
2 ‫ݸ‬ผͷ‫ثػ‬Λ࠶ར༻ͯ͠΋ɺ࠶഑ஔ͢Δʹ͸૬Ԡͷ޻‫ͱظ‬ਓ݅අ͕ඞཁͱͳΔ８－ 1Լ‫Ͱݶ‬ɺ1nmrad ୆Λ࣮‫͢ݱ‬Δʹ͸ηϧ௕Λ 3/5 ʹॖখ௥Ճ͕ߦͳΘΕͨɻ݁Ռɺ࠷ऴऩଋ‫ܥ‬ͷ௒఻ಋి࣓ੴ

͢Δඞཁ͕༗ΔɻLER ΞʔΫηϧͷओภ޲ి࣓ੴΛՄγεςϜ͸ิঈιϨϊΠυΛ߹Θͤͯ 45 ‫ݸ‬ͷ௒఻ಋೳͳ‫ݶ‬Γ௕ͯ͘͠ฏߧΤϛολϯε 1nmrad ఔ౓ʹઃίΠϧΛ‫ؚ‬Ήෳࡶͳ΋ͷʹͳ͍ͬͯΔɻ·ͨɺ‫ثػ‬੡‫ͯ͠ܭ‬΋ɺόϯν಺ϏʔϜࢄཚ (intra-beam scattering)࡞ͷ։࢝‫ʹޙ‬͸ɺ੡࡞޻ఔͰ‫ൃ͕࡞ޡ‬ੜͨ͠ࡍʹ࠶੡ޮՌΛߟྀ͢Δͱ 3.5GeV Ͱ͸ 3nmrad ۙ͘·ͰྼԽ࡞ʹ൐͏ೲ‫ظ‬஗ԆΛආ͚ΔͨΊɺͦͷ··ઃ‫ʹܭ‬औΓͯ͠͠·͏ɻ

ࠐΉ౳ͷมߋ΋Ճ͑ΒΕɺ2018 ೥ 3 ݄ͷ SuperKEKB
Phase-II ίϛογϣχϯάͰब໾ͨ͠ɻ

͜͏ͨ͠஌‫ݟ‬Λ౿·͑ҎԼͷΑ͏ʹઃ‫ํܭ‬਑ͷमਖ਼͕ਤΒΕͨɻLER ͷ intra-beam scattering ରࡦͱͯ͠ɺ
ΤωϧΪʔͷඇରশ౓Λ 3.5GeV×8GeV ͔Β 4GeV×

7GeV(LER/HER) ΁‫ݮ‬Βͯ͠ intra-beam scattering Λ؇࿨͢Δͱͱ΋ʹɺฏߧΤϛολϯεͷઃ‫ܭ‬໨ඪΛ
3/5nmrad(LER/HER) ఔ౓·Ͱ؇ΊɺHER ʹؔͯ͠͸‫ط‬ઃͷΞʔΫ෦Λͦͷ··࠶ར༻͠ɺLER ʹؔͯ͠͸ओภ޲ి࣓ੴΛ 4m ‫ڃ‬ͷ΋ͷʹަ‫Ͱ্ͨ͠׵‬ϏʔϜύΠϓΛిࢠӢରࡦͷͨΊΞϯςνΣϯόʔ‫ܕ‬ͷ΋ͷʹ‫૷׵‬3 Λߦͳ͏ɻ৭ऩࠩิਖ਼෦͸ɺฏߧΤϛολϯεͷ
ઃ‫ܭ‬஋ʹए‫ׯ‬ͷ༨༟͕Ͱ͖ͨͷͰɺKEKB B-FactoryՃ଎‫ͱث‬ಉ༷ͷγέΠϯ‫ܕ‬Λ࠾༻͠ɺ྆Ϧϯάʹਫฏɾਨ௚ํ޲ͷ৭ऩࠩิਖ਼Λಋೖ͢Δɻ࠷ऴऩଋ‫ܥ‬ͷ௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴ͸ϏʔϜϥΠϯຖʹಠཱͤ͞ɺ࠷
લํʹઃஔ͢Δ LER ༻௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴ (QC1P)
ͱ HER ϏʔϜύΠϓؒͷΫϦΞϥϯεΛ֬อ͢ΔͨΊʹɺަࠩ֯Λ 83mrad ʹ૿΍্ͨ͠Ͱ QC1P ͷ࣓‫ؾ‬γʔϧυΛ࡟আ͢Δɻ͜ͷઃ‫ܭ‬มߋʹΑΓɺQC1P ͔Β HER ϏʔϜϥΠϯ΁ͷ࿙Ӯ࣓৔ʹΑΔӨ‫࢒͕ڹ‬Δ
͜ͱʹͳ͕ͬͨɺ࢛ॏ‫ۃ‬੒෼·Ͱ͸‫ي‬ಓɾޫֶ‫ܥ‬ઃ‫ܭ‬ͷҰ෦ͱͯ͠औΓࠐΈɺޫֶੑೳ্༗֐ͳߴ࣍ଟॏ‫ۃ‬੒෼ʹؔͯ͠͸ HER ϏʔϜύΠϓ্ʹ૬ࡴ༻ͷ௒఻ಋίΠϧΛ௥Ճ4 ͢Δɻ్தɺিಥ఺΁ͷ࢛ॏ‫ۃ‬Ӭ‫ٱ‬࣓ੴಋೖͳͲͷ೿ੜ‫ܕ‬ͷൺֱ‫ݕ‬౼Λߦͳ͍ͭͭɺ2010೥य़ࠒʹ͸‫ ߦݱ‬SuperKEKB Ճ଎‫ث‬ͷিಥ఺ઃ‫ܭ‬Ҋ [2]ͷ‫ͳͱܗ͕ܕݪ‬Γɺ2010 ೥‫ޙ‬൒ʹ͸௒఻ಋి࣓ੴͷઃ‫͔ࢉܭܭ‬ΒϑΟʔυόοΫ͞Ε࣓ͨ৔෼෍ΛऔΓೖΕͨՃ଎‫ث‬ϞσϦϯάͷߏஙͱੑೳධՁ͕࢝·͍ͬͯΔɻ࣓৔‫ࢉܭ‬Λ൓өͨ͠Ճ଎‫ث‬ϞσϧͷੑೳධՁ͸ɺ࣓৔‫ࢉܭ‬Ϟσϧͷվྑ΍Ճ଎‫ث‬ϞσϦϯάύϥϝʔλͷநग़ٕ๏ͷվྑͱฏߦͯ͠ߦͳΘΕɺਨ௚ํ޲ͷฏߧΤϛολϯεͷੜ੒‫ݪ‬ҼͱͳΔιϨϊΠυ࣠ͱϏʔϜ‫ي‬ಓͷΞϥΠϝϯτͷ‫ݟ‬௚͠΍ิঈιϨϊΠυ࣓৔෼෍ͷ࠷దԽɺ௒఻ಋ࢛ॏ‫࣓ిۃ‬ੴͷϑϦϯδ΍ຊମʹ‫د‬ੜ͢Δྗֶ‫ʹܘޱ‬ରͯ͠༗֐ͳଟॏ‫࣓ۃ‬৔Λ௿‫͢ݮ‬ΔͨΊͷίΠϧ‫ܗ‬ঢ়࠷దԽ΍ଟॏ‫ิۃ‬ਖ਼ίΠϧͷ
3 ϏʔϜύΠϓͷःஅप೾਺͕มΘΔͨΊɺϏʔϜҐஔϞχλʔ(BPM) ͷ৴߸ॲཧ‫ܥ‬ͷ࠶։ൃ͕ඞཁʹͳͬͨ
4 ͜ͷ࣓‫ؾ‬γʔϧυͷ࡟‫ݮ‬͸ɺ‫ʹޙ‬௒఻ಋి࣓ੴγεςϜͷઃ‫ܭ‬ΛෳࡶԽͤ͞ΔཁҼͷҰͭͱͳ͍ͬͯΔ

2

SuperKEKB ͷϚγϯύϥϝʔλͱিಥ఺ޫֶ‫ܥ‬Ψ΢ε෼෍͢ΔϏʔϜಉ࢜ͷিಥʹΑΔ Luminosityੑೳ͸ɺϏʔϜͷपճप೾਺ frev ɺόϯν਺ nb ɺόϯν಺ͷཻࢠ਺ N+ , N− ͱিಥ఺ͰͷϏʔϜͷ޿͕Γͷඪ४ภࠩ σx∗ , σy∗ Λ༻͍ͯҎԼͷΑ͏ʹද‫͞ݱ‬ΕΔɻ

L≡

N+ N− nb frev
4πσx∗ σy∗(1)͜͜Ͱɺपճप೾਺ frev ͸‫ي‬ಓ௕ (ʙτϯωϧप௕) ͱϏʔϜͷඈߦ଎౓ (ʙޫ଎) Ͱܾ·ΔͨΊɺτϯωϧͷ
࠶ར༻͕લఏͱ͢Δ SuperKEKB Ճ଎‫Ͱث‬͸΄΅ఆ਺Ͱ͋Δɻ·ͨɺόϯν਺ nb ͸ɺߴप೾Ճ଎ۭ಑ͷप೾਺ͱपճप೾਺ frev ͷൺ্͕‫Ͱݶ‬ɺKEKB B-FactoryՃ଎‫ث‬ͷߴप೾‫ܥ‬Λ࠶ར༻͢Δ SuperKEKB Ճ଎‫Ͱث‬͸্‫ ݶ‬5200 όϯνɺϏʔϜෆ҆ఆੑ౳͔Βͷӡ༻҆ఆੑΛߟྀ࣮ͨ͠༻্‫ݶ‬͸ 2500 όϯνఔ౓ͱ૝ఆ͞
Ε͍ͯΔɻ࢒Δઃ‫্ܭ‬มߋՄೳͳύϥϝʔλ͸ϏʔϜిྲྀ (I± = eN± nb frev ) ͱ૬ؔ͢Δ N± ͱিಥஅ໘ੵ∗ͷΈͰ͋Δɻ·ͨɺҟछిΛܾΊΔϏʔϜαΠζ σx,yՙಉ࢜Ͱ൓ߤিಥ͢ΔϏʔϜͰ͸ɺ૬खϏʔϜͷిՙͱిྲྀ͔Βੜ͡Δి࣓৔ʹΑΔऩଋྗΛड͚ɺЌؔ਺΍Τϛολϯε ϵ ͕มԽ͢ΔɻͦͷӨ‫ڹ‬ΛϕʔλτϩϯνϡʔϯͷมԽྔͰද‫ͨ͠ݱ‬ϏʔϜϏʔϜύϥϝʔλ ξ ͸ɺઢ‫ࣅۙܗ‬ͷൣғͰҎԼͷΑ͏ʹۙࣅ͞ΕΔɻ
∗
βx,y
re N∓
∗ (σ ∗ + σ ∗ )2πγ± σx,y
x
y

∗
βx,y
re N∓
=
2πγ± (σx∗ + σy∗ ) ϵx,y

ξx,y± ∼

(2)(3)

͜͜Ͱɺre ͸ՙిཻࢠͷ‫ݹ‬య൒‫ܘ‬ɺγ± ͸૬ର࿦ύϥ∗͸িಥ఺Ќؔ਺ɺϵx,y ͸ϏʔϜΤϛολ
ϝʔλɺβx,yϯεͰ͋Δɻ‫ݧܦ‬తʹɺϏʔϜϏʔϜύϥϝʔλ ξ Λେ͖͘͠Α͏ͱ͢Δͱඇઢ‫ͳܗ‬ϏʔϜϏʔϜ૬‫༻࡞ޓ‬ͷ݁ՌϏʔϜαΠζ͕ංେԽ͠ ξ ੍͕‫͞ݶ‬ΕΔ‫ݱ‬৅͕

８－ 2ද 1: KEKB B-Factory Ճ଎‫ ͱث‬SuperKEKB Ճ଎‫ث‬ͷओཁͳϚγϯύϥϝʔλParameter

KEKB B-Factory

SuperKEKB (2004)

SuperKEKB

LER

HER

LER

HER

LER

HER

E[GeV]

3.5

8.0

3.5

8.0

4.000

7.007

I[A]

1.64

1.19

9.4

4.1

3.6

2.6

Radiation Loss[MeV/turn]nb
Corssing Angle[mrad]
ϵx [nmrad]
ϵy [pmrad]
βx∗ [mm]βy∗ [µm]
σz [mm]ξx
ξyLuminosity[cm−2 s−1 ]

1.6

3.5

1.23

3.48
5018

1.76

2.43

1585
22 / 0(crab)
18
24
150
150
1200
1200
5900
5900
7
7
0.127
0.102
0.129
0.090
2.108 × 1034

30 / 0(crab)
24
24
240
240
200
200
3000
3000
3
3
0.79
0.137
0.051
0.218
2.5 ∼ 5.0 × 1035

2500
83(nano-beam)
3.2
4.6
8.64
12.9
32
25
270
300
6
5
0.0028 0.0012
0.0881 0.0807
8 × 1035஌ΒΕ͓ͯΓɺయ‫ܕ‬తͳ‫ݶ‬ք஋͸ 0.1 ∼ 0.2 ෇ۙͱ͞ྗͷόϯν಺ҐஔґଘੑΛ௨ͯ͡ϏʔϜϏʔϜ૬‫࡞ޓ‬ፏฏͳిࢠɾཅిࢠϏʔϜিಥ (σy∗ << σx∗ ) ͷ৔߹ɺʹ΋ͳΔɻ͜ͷޮՌ͸ɺ࠭࣌‫ޮܭ‬Ռ (hourglass effect)Ε͍ͯΔɻϏʔϜϏʔϜύϥϝʔλΛ༻͍ͯࣜ 1 Λॻ͖௚͢ͱ࣍

༻ͷඇઢ‫ܗ‬ੑ͕૿͢͜ͱͰϏʔϜෆ҆ఆੑͷѱԽཁҼͱ‫ݺ‬͹Ε͍ͯΔɻ

͕ࣜಘΒΕΔɻ

γ±
L∼
2ere



σy∗
1+ ∗
σx



I± ξy±βy∗(4)ϏʔϜϏʔϜύϥϝʔλ ξy ͷ্‫ݶ‬஋ͷଘࡏΛલఏͱ
͢ΔͱɺLuminosity ΛߴΊΔʹ͸ ξy ҰఆͱͳΔ৚݅
Λຬͨ͠ͳ͕Β I± /βy∗ ൺΛେ͖͘͢Δ͜ͱʹͳΔɻࣜ

3 ʹిྲྀ (N∓ ) ͕‫·ؚ‬ΕΔ͜ͱΛߟྀ͢Δͱɺ্‫ه‬ͷํ਑͸ ϵy /βy∗ ൺΛҰఆʹอͪͳ͕Β βy∗ ΛߜΔ͜ͱʹ૬౰͢Δɻ͜͜·Ͱͷٞ࿦Ͱ͸ɺিಥ఺ۙ๣Ͱਐߦํ
޲ʹ‫ͳ࣭ۉ‬ϏʔϜߏ଄ΛԾఆ͍ͯ͠Δ͕ɺβy∗ ͕े෼ʹখ͍͞ঢ়‫Ͱگ‬͸͜ͷԾఆ͕੒ཱ͠ͳ͍ɻࣗ༝ۭؒͱͳ͍ͬͯΔিಥ఺ۙ๣ͷЌؔ਺͸ɺিಥ఺͔Βͷ‫཭ڑ‬s ʹର࣍ࣜ͠ͷΑ͏ͳґଘੑΛࣔ͢ɻ 2 s∗β(s) = β 1 +(5)β∗ैͬͯɺόϯν௕ σz ʹରͯ͠িಥ఺Ќؔ਺ βy∗ ͕খ͞ͳྖҬͰ͸ɺ࠭࣌‫ܭ‬ͷΑ͏ʹόϯνͷઌ಄ͱ຤ඌ͕๲
ΒΜͩ‫ܗ‬ঢ়Ͱিಥ͢Δ͜ͱʹͳΔɻ͜ͷ݁Ռɺόϯν௕શମ͕૬‫͢༻࡞ޓ‬ΔিಥͰ͸ βy∗ < σz ͳྖҬͰͷฏ‫ۉ‬িಥஅ໘ੵ͸িಥ఺Ͱͷ‫ز‬Կֶతͳ໘ੵΑΓ޿͘ͳΓ Luminosity ͕௿Լ͢Δͱ‫ʹڞ‬ɺϏʔϜʹΑΔऩଋ

2.1

Ϛγϯύϥϝʔλͷίϯηϓτ

ද 1 ʹ·ͱΊͨͷ͸ɺKEKB B-Factory Ճ଎‫ ͱث‬Su-

perKEKB Ճ଎‫ث‬ͷओཁͳϚγϯύϥϝʔλͰ͋Δɻ
2004 ೥ʹ·ͱΊΒΕͨ‫چ‬ઃ‫ܭ‬ҊͰ͸ɺ࠭࣌‫ޮܭ‬ՌΛආ͚ΔͨΊόϯν௕ͱিಥ఺Ќؔ਺ͷൺ཰Λҡ࣋͠ɺ୹όϯνԽʹ͓͚Δٕज़త੍໿͔ΒЌؔ਺ͷѹॖ཰͸߇͑Ίʹઃఆ͠ɺβy∗ ʹΑΔ Luminosity ͷ૿‫ڧ‬͸໿ 2ഒͰɺ࢒Γ͸ओʹిྲྀ (໿ 4 ഒ) ͱϏʔϜϏʔϜύϥϝʔλ (໿ 2 ഒ) Ͱ·͔ͳ͏ߏ੒Ͱ͋ΔɻҰํɺ‫ߦݱ‬SuperKEKB Ճ଎‫ث‬ͷઃ‫ܭ‬ҊͰ͸ɺόϯν௕Λվ଄લͷ KEKB B-Factory Ճ଎‫ͱث‬ಉ౳ʹઃఆ͢ΔҰํͰɺЌؔ਺͸ 20 ෼ͷ 1 ʹઃఆ͠ɺLuminosity ૿‫ڧ‬ͷେ൒Λ βy∗ ͰՔ͙ߏ੒5 Ͱ͋Δɻ͜ͷઃఆͷΈͰ͸࠭࣌‫ޮܭ‬ՌͷൃੜΛආ͚ΒΕͳ͍ͷͰɺLarge Piwinski Angle িಥͱ‫ݺ‬͹ΕΔख๏Ͱճආ͍ͯ͠Δɻ࠭࣌‫ޮܭ‬ՌʹΑΔ໰୊ͷຊ࣭͸ɺෆద੾ͳϏʔϜαΠζͷϏʔϜ͕িಥ
͢Δ͜ͱͰ͋ΓɺຊํࣜͰ͸ਫฏํ޲ʹࡉ͍ϏʔϜͱେ͖ͳަࠩ֯Λ૊Έ߹ΘͤΔ͜ͱͰϏʔϜਐߦํ޲ͷিಥྖҬΛ βy∗ εέʔϧ·Ͱѹॖ͢Δ͜ͱͰ࠭࣌‫ޮܭ‬
5 ϏʔϜϏʔϜύϥϝʔλ ξ ͸ਾ͑ஔ͖ɺిྲྀ૿‫ڧ‬͸ 2 ഒఔ౓yʹ཈͍͑ͯΔ８－ 3

ՌΛճආ͍ͯ͠Δɻ‫͑׵͍ݴ‬Ε͹ɺ෯޿ͷϏʔϜΛਖ਼‫࣓ۃ‬৔ͷΞϥΠϝϯτิਖ਼༻ͷਫฏɾਨ௚εςΞϦϯ

໘িಥͤ͞Δ୅ΘΓʹɺਫฏ໘಺΁ͷ౤Өஅ໘ੵ͕౳

άίΠϧͱ skew ࢛ॏ‫ۃ‬ίΠϧΛඪ४૷උ͢Δ΄͔ʹɺ͍͠܏ࣼͨ͠਑ۚͷΑ͏ͳϏʔϜಉ࢜Λিಥͤ͞Δ͜Ґ૬ۭؒΛ࿪Ίͯ QC2 Ͱͷ෺ཧ‫ݶ੍ܘޱ‬Λ؇࿨͢Δ

ͱͰɺ࣮ޮతͳόϯν௕Λѹॖ͠ɺβy∗ ͷॖখΛՄೳʹീॏ‫ۃ‬ίΠϧ΍ྗֶ‫ʹܘޱ‬༗֐ͳ࿡ॏ‫ۃ‬ϞʔυΛิਖ਼͍ͯ͠Δɻܽ఺ͱͯ͠͸ɺਫฏํ޲ͷϏʔϜαΠζͷ

͢Δ normal ‫ ͼٴ‬skew ࿡ॏ‫ۃ‬ίΠϧͳͲ͕ಋೖ͞Εͯѹॖ͕௚઀ʹ͸ Luminosity ੑೳʹ‫د‬༩͠ͳ͍఺ͱ྆

͍ΔɻϏʔϜͷয఺͕ଗ͏ͷ͸த৺্࣠ͷΈͰਫฏํ޲ͷৼิঈιϨϊΠυʹΑΓ‫ݕ‬ग़‫ث‬ιϨϊΠυ࣓৔ͷେҬ෯ʹैͬͯয఺Ґஔ͕ͣΕΔ͜ͱͰ͋ΔɻSuperKEKBతͳӨ‫ڹ‬͸ิঈ͞Ε͍ͯΔ͕ɺιϨϊΠυ࣓৔ʹΑΔ

Ճ଎‫Ͱث‬͸ɺ͜ͷিಥํࣜΛઃ‫্ܭ‬ͷԖ௚ํ޲ϏʔϜ‫ॴہ‬తͳ‫ي‬ಓ໘ͷճసʹରԠ͢ΔͨΊʹɺLER ଆͷ௒αΠζ͕ nm εέʔϧ6 ͱͳΔ͜ͱ͔Β “nano-beam ํ఻ಋ࢛ॏ‫࣓ిۃ‬ੴʹ͸ 10mrad Φʔμʔͷճస͕֯ઃࣜ” ͱ‫ݺ‬ΜͰ͍Δɻ͜ΕΛ੒ཱͤ͞ΔͨΊʹɺিಥ఺ਫฏϏʔϜαΠζ σx∗ ∼ ϵx βx∗ ΋ 1 ܻҎ্ߜ͍ͬͯΔ

ఆ͞Ε͍ͯΔɻϏʔϜ‫ي‬ಓ͕࠷ऴऩଋ‫ܥ‬Λߏ੒͢Δ௒
఻ಋ࢛ॏ‫࣓ిۃ‬ੴͷத৺෇ۙΛ௨ΔΑ͏ʹɺ‫ݕ‬ग़‫ث‬ιͨΊɺিಥ఺෦Ͱͷਫฏํ޲ͷ৭ऩࠩิਖ਼΋ඞཁʹͳϨϊΠυͱิঈιϨϊΠυʹΑͬͯਨ௚ํ޲ͷ‫ي‬ಓ͕Γিಥ఺ޫֶ‫͕ܥ‬ෳࡶԽ͍ͯ͠Δɻ

େ͖͘ऄߦ͢Δ LER Ͱ͸ɺিಥ఺Λ௨Δ‫ي‬ಓͷ઀ઢʹରͯ͠ QC1P ‫ ͼٴ‬QC2P ʹ 1mm Φʔμʔͷਨ௚Ξ

2.2ϥΠϝϯτ͕ઃఆ͞ΕɺQC1P ͔Βͷ࿙Ε࣓৔Ͱਫฏ

িಥ఺ޫֶ‫ܥ‬ͷίϯηϓτ

ํ޲ͷ‫ي‬ಓมߋΛड͚Δ HER Ͱ͸ɺিಥ఺Λ௨Δ‫ي‬িಥ఺ΛऔΓғΉ‫ݕ‬ग़‫ث‬ιϨϊΠυ࣓৔ʹΑΔਨಓͷ઀ઢʹରͯ͠ QC1E ‫ ͼٴ‬QC2E ʹ ±700µm ͷਫ௚Τϛολϯε΁ͷӨ‫ڹ‬Λ࠷খԽ͢ΔͨΊʹɺిࢠɾฏΞϥΠϝϯτ͕ઃఆ͞Ε͍ͯΔɻ͜ΕΒͷ௒఻ಋ࢛ཅిࢠϏʔϜϥΠϯ͸‫ݕ‬ग़‫ث‬ιϨϊΠυ࣠ʹରͯ͠ॏ‫࣓ిۃ‬ੴ‫܈‬͸அ೤ਅۭ༰‫ͱ·ʹ಺ث‬Ίͯ૷ண͞Εɺ

41.5mrad ͷަࠩ֯Ͱઃஔ͞ΕΔɻ·ͨɺ‫ݕ‬ग़‫ث‬ιϨϊΠυ࣓৔ʹΑΔϏʔϜ΁ͷӨ‫ڹ‬Λิঈ͢ΔͨΊͷิঈιϨϊΠυΛ྆ϏʔϜϥΠϯʹඃ͏Α͏ʹઃஔͯ͠
͍Δɻਫฏɾਨ௚ํ޲ͷিಥ఺Ќؔ਺ΛߜΔͨΊͷ࠷ऴऩଋ‫ܥ‬͸ɺϏʔϜϥΠϯຖʹಠཱͨ͠௒఻ಋ࢛ॏ‫ిۃ‬࣓ੴμϒϨοτΛ྆ϏʔϜϥΠϯؒͷ‫ׯ‬বΛආ͚ΔΑ
͏িಥ఺͔Β LER ਨ௚ํ޲ऩଋి࣓ੴ (QC1P)ɺHERਨ௚ํ޲ऩଋి࣓ੴ (QC1E)ɺLER ਫฏํ޲ऩଋి࣓ੴ (QC2P)ɺHER ਫฏํ޲ऩଋి࣓ੴ (QC2E) ͷॱʹ‫͍ޓ‬ҧ͍ʹ഑ஔ͠ɺ൓ରଆͷϏʔϜϥΠϯ΁ͷ࣓৔ͷ࿙ӮΛආ͚ΔͨΊ QC1P Ҏ֎ʹ͸࣓‫ؾ‬γʔϧυ͕૷උ͞Ε͍ͯΔɻQC1P ʹؔͯ͠͸ɺηύϨʔγϣϯෆ଍ʹΑΓ࣓‫ؾ‬γʔϧυͷ୅ΘΓʹ HER ϏʔϜϥΠϯ্ʹ࿡ॏ‫ۃ‬Ҏ্ͷଟॏ‫࣓ۃ‬৔Λ૬ࡴ͢Δ௒఻ಋ࿙Ε࣓৔ΩϟϯηϥʔίΠϧ͕༻ҙ͞Ε͍ͯΔɻHER ͷ QC1P
࿙Ε࣓৔Ωϟϯηϥʔ͸ɺྗֶ‫ʹܘޱ‬༗֐ͳ࿡ॏ‫͔ۃ‬
Β 12 ॏ‫Ͱ·ۃ‬ͷ‫ ܭ‬4 छͷଟॏ‫ۃ‬ΩϟϯηϥʔίΠϧΛूੵͨ͠΋ͷͰɺͦΕͧΕͷଟॏ‫ۃ‬ΩϟϯηϥʔίΠϧ͸ϏʔϜަࠩ֯ͱ QC1P ͷճస‫ͼٴ‬Ԗ௚ΞϥΠϝϯτΦϑηοτʹΑͬͯ‫ʹ޲ํ͕͖࣠޲ͱ౓ڧ‬มԽ͢Δ࿙Ε࣓৔ʹରԠ͠ɺ࣠ํ޲ʹίΠϧີ౓΍޲͖͕ม
Խ͢ΔΑ͏ઃ‫͞ܭ‬Ε͍ͯΔɻ7 ิਖ਼ίΠϧͱͯ͠ɺ࢛ॏ

૊ཱͯ‫ʹޙ‬ϝΧχΧϧΞϥΠϝϯτΛ‫ݸ‬ผௐ੔͢Δ͜

6 ਖ਼֬ʹ͸਺े nm εέʔϧ

7 ੡࡞࣌ͷ࿈བྷͷෆඋ͔Βɺ‫ڸ‬ରশʹՃ޻͞Ε͍ͯΔ͜ͱ͕ɺΠϯετʔϧ௚લʹ൑໌͓ͯ͠Γɺskew ࣓৔͸ิਖ਼ग़དྷͳ͍ঢ়ଶʹ
ͳ͍ͬͯΔͱ͕ग़དྷͳ͍ͨΊɺ૊Έࠐ·ΕΔεςΞϦϯάίΠϧ
ͷఆ֨͸গͳ͘ͱ΋ ±500µm ૬౰ͷΞϥΠϝϯτิਖ਼͕ՄೳͱͳΔΑ͏ʹઃ‫͞ܭ‬Εͨ8 ɻ࠷ऴऩଋ‫Ͱܥ‬ੜ͡Δ‫ۃ‬Ίͯେ͖ͳ৭ऩࠩΛิਖ਼͢Δ
ͨΊɺিಥ఺Λ‫ڬ‬Ή࠷ऴऩଋ‫ܥ‬ͷ֎ଆʹ͸ਫฏɾਨ௚
ํ޲ͷ৭ऩࠩิਖ਼෦Λઃஔ͍ͯ͠Δɻ৭ऩࠩิਖ਼෦Ͱ
͸ɺิਖ਼ʹඞཁͳେ͖ͳ෼ࢄؔ਺ΛಘΔͨΊͷγέΠ
ϯ಺ʹ −I′ సૹߦྻͰ݁͹Εͨ࿡ॏ‫࣓ిۃ‬ੴϖΞΛઃஔ͠ɺͦΕͧΕͷิਖ਼ର৅ͷ QC1ɾQC2 ʹϕʔλτϩϯҐ૬Λ߹Θ͍ͤͯΔɻ

3 িಥ఺ޫֶ‫ܥ‬ͷϞσϦϯά
SuperKEKB Ճ଎‫ث‬ͷઃ‫Ͱܭ‬͸ɺྗֶ‫( ܘޱ‬ϏʔϜण໋) ΍ਨ௚Τϛολϯεʹର͢Δ࠷ऴऩଋ‫ܥ‬ͷ࣓৔෼෍ͷӨ‫ۃ͕ڹ‬Ίͯେ͖͘ͳΔͨΊɺՃ଎‫ث‬ϞσϧʹΑ
ΔੑೳධՁʹ͸ਫ਼ີͳ࣓৔ϞσϦϯά [3] ͕ඞཁͱ͞
ΕΔɻSuperKEKB Ճ଎‫ث‬ͷ࠷ऴऩଋ‫ܥ‬͸ɺ௒఻ಋιϨϊΠυͱΞϥΠϝϯτΦϑηοτ෇͖ͷ௒఻ಋଟॏ
‫࣓ిۃ‬ੴ‫ؾ࣓ʹ܈‬γʔϧυΛ૊Έ߹Θͤͨ΋ͷͰɺ࣓‫ؾ‬γʔϧυ΍ϦλʔϯϤʔΫ౳ͷߏ଄෺͕௒఻ಋి࣓
ੴͱҟͳΔରশੑΛ࣋ͭͨΊʹγεςϜશମͱͯ͠ͷ
8 ૊ཱͯɾઃஔਫ਼౓͕ 500µm Λେ͖͘ӽ͑Δ৔߹͸ɺ෼ղͯ͠
ͷௐ੔ɾ࠶૊ཱͯΛ૝ఆ͍ͯ͠Δ８－ 4

ରশੑ͸ࣦΘΕ͍ͯΔɻߴਫ਼౓ͳՃ଎‫ث‬Ϟσϧ࡞੒ʹ‫ܗ‬ঢ়Ҽࢠ d†n (z) ͷ࣮෦ͱ‫ڏ‬෦͸ɺ࣓৔ͷ skew Ϟʔυ͸ɺ࣓‫ؾ‬γʔϧυ΍ϦλʔϯϤʔΫ౳ͷ࣓ੑࡐྉͷ഑ͱ normal ϞʔυʹରԠ͍ͯ͠Δɻ͞Βʹɺz ํ޲ͷஔΛऔΓࠐΜͩ 3 ࣍‫ݩ‬੩࣓৔‫ࢉܭ‬ͷ݁ՌΛ༻͍͍ͯΔɻ

Fourier ม‫׵‬Λద༻͢Δͱɺ‫ܗ‬ঢ়Ҽࢠͷ z ඍ෼͸೾਺kz Λ༻͍ͯҎԼͷΑ͏ʹॻ͖௚ͤΔɻ

3.1

∞

n!(n + 2m) (kz r)2m
B̃r (n, kz )
˜
=
d
(k
)
n
z
rn−1
(n + m)! 4m m!
m=0࣓৔ͷ‫ج‬ఈల։ͱ‫ܗ‬ঢ়Ҽࢠ੩࣓৔ΛϏʔϜ࣠Λத৺࣠ͱͨ͠ԁப࠲ඪ‫Ͱܥ‬ϞσϦϯά͢Δͱ͖ɺ࣠ۙ๣ʹిՙɾిྲྀ͸ଘࡏ͠ͳ͍ͷͰɺ࣓‫ؾ‬εΧϥϙςϯγϟϧ͸্࣠Ͱ‫׈‬Β͔ͳ Poissonදࣔ (r, θ) ͷத৺Ͱ‫׈‬Β͔ͳղ ϕ(r, θ) ͸ɺ࣍ͷΑ͏ʹҰൠԽ͞ΕΔ͜ͱ͕Α͘஌ΒΕ͍ͯΔɻ

ϕ(r, θ) =∞dn rn sin (nθ + χn )

(6)

n=0

͜͜Ͱɺdn ‫ ͼٴ‬χn ͸ 2n ॏ‫ۃ‬Ϟʔυͷৼ෯ͱҐ૬Ͱ
͋Δɻಉ༷ʹɺ࣠ํ޲ͷ෼෍͕ଘࡏ͢Δ৔߹ʹ͸ɺࣜ

6 ʹ r ґଘੑͷमਖ਼͕ՃΘͬͨҎԼͷ‫ج‬ఈల։͕੒ཱ
͢Δɻ

ϕ(r, θ, z) =∞

rn sin (nθ + χn )

n=0


 ∞
 (−1)m n!r2m d2m dn (z)4m m!(n + m)! dz 2m
m=0

(7)

੩࣓৔Λ࣓‫ؾ‬εΧϥϙςϯγϟϧ͔Β B = ∇ϕ Ͱ༩͑ͨ৔߹ɺԁப࠲ඪ‫Ͱܥ‬ͷ੒෼දࣔ͸ҎԼͰ༩͑ΒΕΔɻ

Br =

1 ∂ϕ
∂ϕ
∂ϕ
, Bθ =, Bz =
∂r
r ∂θ
∂z

(8)

࣓৔ͷ 2n ॏ‫ۃ‬੒෼͸ɺ࣓৔෼෍͔Β θ ํ޲ͷ FourierʹΑΓ࣍ͷΑ͏ʹநग़Ͱ͖Δɻ 
 1 2π B dθ·0B̂· (n) ≡ 2π 2π1B e−inθ dθ
π

0

·

2m

i

n!n (kz r)
B̃θ (n, kz )= d˜n (kz )n−1r(n + m)! 4m m!
m=0

−i

∞

n!
B̃z (n, kz )(kz r)2m
˜n (kz )=dnkz r(n + m)! 4m m!
m=0ํఔࣜͷղͰ͋Δɻಛʹɺ࣠ํ޲ͷฒਐରশੑ͕ଘࡏ
͢Δ৔߹ɺ2 ࣍‫ ݩ‬Poisson ํఔࣜʹؐ‫͞ݩ‬Εɺ‫࠲ۃ‬ඪ

∞


(13)
(14)
(15)

͜ ͜ Ͱ ɺd˜n (kz ) ͸ ෳ ૉ ‫ ܗ‬ঢ় Ҽ ࢠ ͷ Fourier ม ‫׵‬∞ †d (z)e−ikz z dz Ͱ͋Δɻࣜ 13-15 ͷࠨล͸ԁப࠲−∞ n∞ඪ‫Ͱܥ‬ͷ࣓৔෼෍ͷ Fourier ม‫͋Ͱ׵‬Γɺӈลͷ m=0
߲͸ kz r ͷΈͷؔ਺Ͱ͋ΔɻैͬͯɺFourier ม‫׵‬Λ௨ͯ͡೾਺ྖҬͰඍ෼ԋࢉࢠʹΑΔ৞ΈࠐΈΛղ͘͜ͱͰɺ࣓৔෼෍͔Β‫ܗ‬ঢ়ҼࢠͷεϖΫτϧදࣔ d˜n (kz )ΛಘΔ͜ͱͰ͖Δɻ

SuperKEKB Ճ଎‫ث‬ͷઃ‫͢༻࢖ʹܭ‬ΔՃ଎‫ث‬ίʔυ
SAD [4] ͷଟॏ‫࣓ۃ‬৔ͷϞσϦϯάύϥϝʔλ͸ɺσόΠε͕ଘࡏ͢Δ۠ؒ (z0 , z1 ) ্ͷ࣓৔ͷੵ෼Λ༻͍ͯҎԼͷΑ͏ʹఆٛ͞Ε͍ͯΔɻ z1 n ∂ By 
1
Kn ≡
dz
(16)
Bρ z0 ∂xn x=y=0
 z1 n ∂ Bx 
1
SKn ≡
dz
(17)
Bρ z0 ∂xn x=y=0
͜͜ͰɺKn ‫ ͼٴ‬SKn ͸ 2(n + 1) ॏ‫࣓ۃ‬৔ͷ normalϞʔυͱ skew ϞʔυͷϞσϦϯάύϥϝʔλͰɺBρ͸ϏʔϜͷ magnetic rigidity Ͱ͋Δɻ͕ͨͬͯ͠ɺෳ
ૉ‫ܗ‬ঢ়Ҽࢠ d†n (z) Λ༻͍ͯࣜ 16-17 ͸ҎԼͷΑ͏ʹॻn=0
n ̸= 0(9)

SKn + iKn =͜͜Ͱɺ· ͸ r, θ, z Λ୅ද͍ͯ͠ΔɻෳૉԽͨ͠‫ܗ‬ঢ়Ҽࢠ d†n (z) ≡ (sin χn + i cos χn )dn (z) Λಋೖ͢Δͱࣜ

7 ΑΓ࣍ͷҰൠղ͕ಘΒΕΔɻ∞(−1)m n!(n + 2m)r2m d2m d†n (z)B̂r (n)
=
(10)
n−1
r
4m m!(n + m)!
dz 2m
m=0

∞

(−1)m n!nr2md2m d†n (z)B̂θ (n)(−i)=
rn−1
4m m!(n + m)!
dz 2m
m=0

∞

(−1)m n!r2m+1 d2m+1 d†n (z)B̂z (n)=rn−1
4m m!(n + m)! dz 2m+1
m=0

͖௚ͤΔɻ

(n + 1)!
Bρ

 z1
z0

d†n+1 (z)dz(18)ಉ༷ʹɺσόΠε۠ؒ (z0 , z1 ) Ͱͷਐߦํ޲࣓৔ͷฏ‫ۉ‬஋Ͱఆٛ͞ΕΔ SAD ͷιϨϊΠυϞσϦϯάύϥ
ϝʔλ BZ ͸ɺෳૉ‫ܗ‬ঢ়Ҽࢠ d†0 (z) ͔Β࣍ͷΑ͏ʹ༩
͑ΒΕΔɻ

1
BZ ≡
z1 − z0

(11)

 z1
z0



d†0 (z)Bz (z)dz =z1 − z0

z 1

(19)

z0

ࣜ 13-15 ʹΑΔෳૉ‫ܗ‬ঢ়Ҽࢠͷநग़Ͱ͸ɺਅۭதͷ(12)

Maxwell ํఔࣜΛຬ଍͢Δແ‫ݶ‬ਫ਼౓͔ͭ࿈ଓͳ࣓৔෼

８－ 5෍͕खʹೖΔ৔߹͸ɺn > 0 Ͱ͸ 3 ࣜͱ΋ಉҰͷෳૉ‫ܗ‬ঢ়Ҽࢠ d˜n (kz ) Λ༩͑ΔɻιϨϊΠυϞʔυ (n = 0)‫ث‬Ϟσϧ΁ͷ࣮૷ʹࡍͯ͠Ճ଎‫ث‬ίʔυ͕࣓৔ͷॏͶʹؔͯ͠͸ɺରশੑ͔Βࣜ 14 ͸‫౓ײ‬Λ࣋ͨͳ͍ɻҰύϥϝʔλΛ༻ҙ͢Δඞཁ͕͋ΔɻಛʹɺSuperKEKB

ํɺ3 ࣍‫࣓ݩ‬৔‫͔ࢉܭ‬ΒಘΒΕΔ࣓৔෼෍ͷ֨ࢠִؒՃ଎‫ث‬ͷ࠷ऴऩଋ‫Ͱܥ‬͸࢛ॏ‫࣓ిۃ‬ੴ͕࣠֎ʹஔ͔Ε͕༗‫͋Ͱݶ‬Δ͜ͱ͔Β z ඍ෼ͷগͳ͍ํ͕ਫ਼౓ྑ͘ɺ

͓ͯΓɺઃ‫ܭ‬ͷࡍʹ͸Ϛονϯάม਺ʹ͢Δඞཁ΋͋߹ΘͤΛαϙʔτ͠ͳ͍৔߹12 ɺ߹੒ͨ͠ϞσϦϯά

ιϨϊΠυϞʔυ (n = 0) ʹ͍ͭͯ͸ࣜ 15 ͕ɺҰൠͷ

Δ͜ͱ͔Βɺ࢛ॏ‫࣓ిۃ‬ੴͷεϥΠεʹΦϑηοτΛଟॏ‫ۃ‬Ϟʔυ (n > 0) ʹ͍ͭͯ͸ࣜ 13 ͱࣜ 14 Λ༻͍෇͚ͯ࣠֎ʹઃஔ͠ɺྖҬ͕ॏͳΔιϨϊΠυ࣓৔౳

Δ͜ͱ͕๬·͍͠ɻ·ͨɺ‫݁ࢉܭ‬Ռͷ༗ޮ਺ࣈ͕༗‫ݶ‬ͷଟॏ‫ۃ‬੒෼͸ thin Ϩϯζͱ࢛ͯ͠ॏ‫࣓ిۃ‬ੴͷεϥ

Ͱ͋ΔͨΊɺओϞʔυҎ֎ͷ‫د‬ੜϞʔυͷ‫ܗ‬ঢ়Ҽࢠ͸Πεલ‫ʹޙ‬షΓ෇͚ͯϞσϦϯά͍ͯ͠Δɻ

ܻམͪ౳Ͱ༗ޮ਺ࣈ͕গͳ͘ͳΔɻ͜ͷͨΊɺϞσϦ‫ي‬ಓ‫਺ֶؔޫͼٴ‬ͷԠ౴͸࣓৔ͷॏͶ߹Θͤʹରϯάύϥϝʔλͱͯ͠࠾༻͢Δࡍ͸Ϟʔυల։࣍਺ͷͯ͠ઢ‫ͳܗ‬ͷͰɺthin ϨϯζΛ૊Έ߹Θͤͨۙࣅ͸εଧͪ੾Γ౳Λ‫ݕ‬౼͢Δඞཁ͕͋Δɻ·ͨɺ༗‫ݶ‬ཁૉ๏ϥΠε͕े෼ബ͍ྖҬͰ͸্ख͘ߦ͘ɻҰํɺΤϛοͳͲʹΑΔ 3 ࣍‫࣓ݩ‬৔‫Ͱࢉܭ‬͸ɺ‫݁ࢉܭ‬Ռ͕࣓ੑମɾ

λϯεධՁʹ‫د‬༩͢Δ์ࣹੵ෼͸࣓৔ʹରͯ͠ඇઢ

ίΠϧ‫ܗ‬ঢ়ͷରশੑΛ‫ʹີݫ‬ຬ଍͠ͳ͍͜ͱ΍ɺϝο‫߲ͳܗ‬Λ‫ؚ‬ΉͨΊʹɺॏͳΓ߹࣓ͬͨ৔Λ࣠ํ޲ʹ෼γϡߏ଄ͷෆ‫ྖͳ࣭ۉ‬ҬͰ࣓৔෼෍͕ Maxwell ํఔࣜ཭ͯ͠ද‫͢ݱ‬ΔۙࣅͰ͸ਖ਼֬͞Λଛͳ͏͜ͱʹͳΔɻ

Λຬ଍͠ͳ͍͜ͱ͕༗ΔͷͰ‫ܗ‬ঢ়Ҽࢠͷநग़લʹ࣓৔SuperKEKB Ճ଎‫ث‬ͷিಥ఺Ͱ͸ɺ্‫ه‬ͷϞσϦϯά
ख๏Ͱ thin ϨϯζԽ͞ΕͨιϨϊΠυ࣓৔ͷࣹӨ੒෼
SK0 ͕ਨ௚ΤϛολϯεͷධՁ͔Β࿙ΕաখධՁͱ
ͳΔͨΊɺthin Ϩϯζ্ͷ K0 ‫ ͼٴ‬SK0 ੒෼ΛΦϑηοτ࢛ͨ͠ॏ‫࣓ిۃ‬ੴεϥΠεʹҠ͠ସ͍͑ͯΔɻ͜ͷࡍɺ࢛ॏ‫࣓ిۃ‬ੴ͕ճస͍ͯ͠Δࡍʹ͸ɺճస֯ʹԠͯ͡ (K0 , SK0 ) ϕΫτϧΛճస͢Δॲཧ΋ඞཁ
Ͱ͋Δɻ์ࣹੵ෼ͷධՁʹؔͯ͠͸ɺೋॏ‫࣓ۃ‬৔੒෼
(K0 , SK0 ) ͷϑϦϯδಉ࢜ͷுΓ߹Θͤʹࡍͯ͠ɺಉ
ූ߸ͷுΓ߹ΘͤͰ͸աখධՁɺҟූ߸Ͱ͸աେධՁ
͕ൃੜ͢Δɻਖ਼͍͠ධՁΛಘΔʹ͸ɺՃ଎‫ث‬ίʔυଆͰॲཧ಺༰ʹԠͯ͡ϑϦϯδύϥϝʔλͷऔѻ͍Λมߋ͢Δ΋͘͠͸ɺϋʔυΤοδϞσϧʹ thin ϨϯζͰޫֶؔ਺΁ͷϑϦϯδޮՌΛ௥Ճ͢Δ౳ͷॲஔ͕ඞཁ
ͱͳΔɻ·ͨɺ࢛ॏ‫࣓ۃ‬৔΍͞Βʹߴ࣍ͷଟॏ‫࣓ۃ‬৔ʹΑΔ์ࣹޫͷ‫د‬༩͕ແࢹͰ͖ͳ͍৔߹ɺ์ࣹੵ෼ͷऔѻ͍ʹ͍ͭͯҰൠͷ Kn , SKn ʹؔͯ͠ಉ༷ͷ໰୊͕ൃੜ͢ΔɻϞσϦϯάύϥϝʔλͷ߹੒࣌ʹҰൠͷଟॏ‫ۃ‬੒෼ͷฒਐม‫׵‬ΛऔΓѻ͏ͷ͸‫ۃ‬Ίͯ൥ࡶͳͷͰɺ͜͏ͨ͠৔߹Ͱ͸Ճ଎‫ث‬ίʔυଆͰ࣓৔߹੒ͷ௚઀తͳαϙʔτΛߦͳ͏͜ͱ͕๬·͍͠ɻ9෼෍ͷ݈શੑΛ֬ೝ͢Δඞཁ͕͋Δ ɻ

3.2

িಥ఺σόΠεϞσϦϯάͱͦͷ߹੒িಥ఺σόΠεϞσϦϯάͰ͸ɺਐߦํ޲ͷ෼෍ΛऔΓࠐΉͨΊϞσϦϯά࣠ํ޲ʹ͋Δఔ౓ͷ෯ͰσόΠεΛྠ੾Γ (εϥΠε) ʹͯ͠ɺεϥΠεຖʹϞσϦϯάύϥϝʔλΛׂΓ෇͚ΔɻSuperKEKB Ճ଎‫ث‬ͷিಥ఺Ͱ͸ɺ±4m ͷ۠ؒΛ 10mm ࠁΈͰεϥΠε͠

͍ͯΔɻՃ଎‫ث‬ϞσϦϯάίʔυͰ͸ɺ࣓৔ͷϒϩοΫΛϞσϦϯάͨ͠ࡍʹ‫ڥ‬քͰੜ͡ΔϑϦϯδޮՌΛऔΓࠐΉͨΊʹɺઢ‫ܗ‬ϑϦϯδΛϞσϦϯά͢ΔύϥϝʔλΛઃ͚͍ͯΔ΋ͷ͕ଟ͘ɺεϥΠεϞσϦϯά
ʹ͓͍ͯ͸ઢ‫ܗ‬ϑϦϯδͷ௕͞10 ΛεϥΠε௕ʹઃఆ͢Δ͜ͱͰɺਐߦํ޲ͷ෼෍ΛંΕઢۙࣅ͢ΔɻϞσϦϯάύϥϝʔλͷநग़ʹඞཁͳ 3 ࣍‫ݩ‬੩࣓৔෼෍͸ɺιϨϊΠυ࣓৔ʹؔͯ͠͸িಥ఺ͰͷϏʔϜ઀ϕΫτϧΛ࣠ͱͨ͠ԁப࠲ඪ‫ܥ‬ɺଟॏ‫ۃ‬ίΠϧʹؔͯ͠͸ίΠϧ࣠Λத৺ͱͨ͠ԁப࠲ඪ‫ܥ‬ͷ֨ࢠ఺্ͷ੩࣓৔Λ

3 ࣍‫࣓ݩ‬৔‫ࢉܭ‬ίʔυ͔Βͷग़ྗͱͯ͠ड͚औΔɻ3 ࣍‫࣓ݩ‬৔෼෍͔ΒϞσϦϯάύϥϝʔλͱͯ͠ɺιϨϊΠυ࣓৔ʹؔͯ͠͸Ծ૝తͳϏʔϜ࣠11 ্ͷ BZ ‫ͼٴ‬ਫฏ໘಺ͷιϨϊΠυ࣓৔ͷ܏ࣼʹΑΔࣹӨ੒෼ SK0‫ͼٴ‬ιϨϊΠυ࣓৔ͷϑϦϯδͰੜ͡Δ SKn (n > 0)Ͱ͋Γɺଟॏ‫ۃ‬ίΠϧʹؔͯ͠͸ίΠϧ࣠Λத৺ͱͨ͠ଟॏ‫ۃ‬ల։ύϥϝʔλ Kn , SKn ͕ಘΒΕΔɻՃ଎ࢀߟจ‫ݙ‬[1] “Letter of Intent for KEK Super B Factory”, SuperKEKB Task Force, KEK Report 2004-4, Jun 20049 ಺෦తʹ࣓‫ؾ‬εΧϥʔϙςϯγϟϧΛ࢖͍ͬͯΔίʔυͷ৔߹͸ɺ‫ిཱݽ‬ՙ͕ੜ͡ΔҎ֎ͷ໰୊͸‫͜ى‬Γʹ͍͘ɻ
10 SAD Ͱ͸ F 1 ύϥϝʔλ͕૬౰͢Δ
11 িಥ఺‫ي‬ಓͷ઀ઢ

８－ 6

12 SAD ΋‫ؚ‬Ίɺී௨͸ͦΜͳ໘౗ͳ‫ػ‬ೳ͸αϙʔτ͞Εͳ͍[2] Y. Ohnishi, “Accelerator design at SuperKEKB”,
Prog.

Theor.

Exp.

Phys.

(2013)

03A011,

10.1093/ptep/pts083, March 2013
[3] “SuperKEKB

Interaction

RegionModeling”,

A. Morita, Proc. of IPAC2011, San Sebastián, Spain,
September 2011, THPZ006, p. 3690 (2011)[4] K. Oide, Nucl. Inst. Meth. A276, 427(1989),
http://acc-physics.kek.jp/SAD/

８－ 7