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3

2

˸p_nn^z ͢Ƚg̧ͬ^V(z)̒ͮɶ^v(z) z flͮƕ̾ǀ^ J SCʒʩȆĴͮɛƟǀb^ǂ  ^  ^v

q~  g v(z)ρ(z)ɝŗs2

2=  120.4 [A / cm K ]   

 z flͮč^ρ(z) z flͮˮƟǀ^ε 0

Ĵƛȋ A 4π em0 kėƖ^̀˒ǟg

ðe_nn^A ɮͮƕȆĴƛȋ^kÔã¿Öçƛȋ^T ɮ¨ºéÃȒʤǂ^¥Æã«é  

ðe_nn^ͮƕ ͯɇ̢͐
m0 = 0.511MeV / c 2 ^˅ͮˮ e = 1.602 ×10 −19 C ^Ôã¿Öçƛȋ k = 8.617 ×10 −5 eV / K ^Ðáç¬ƛȋ
h = 4.135 ×10 −21 MeV s qx_ȆĴͮɛ ƊƏ x

d 2V (z) J SC
=
ε0
dz 2

m0 −1/2V (z)2e  

ǒ_ò̴ 2 dV (z) gl~^z ʧĵsdzĂû͜ȋφhƧpk^˳ɫh΀cɯ̢h͊

2

4J SC
⎛ dV (z) ⎞
⎜⎝
⎟ =
ε0
dz ⎠

m0 1/2V (z) + C 
2e  

_ʧĵƛȋ C ͢Ƚ˸ͱͮƇ¹å_
 ɮͮƕ͕ɼǩqxͮƕɮ͢ȽèͣȽ͛ͯćƛs^ C = 0 x^Ć͟nɬ̂̈́ʤź  ʜsdʩ͛ͮˮ

s_ǂ   ü÷ȵ^ı z |c~ʧĵq^ z = 0  V (z) = 0 ȪĈɾcĽ͠Ͷƃǂ hðeɮ͢Ƚɢǀƣʩ͛ͮˮĽͮ͠ɛɆǂ_ͮƇǃiĴsh^ȆĴͮɛͯͮƇǇǀƊńsͽŭǟʜsɢǀĽ͠Ͷƃ|_ʩ͛ͮˮĽ͠ͶƃflȆĴͮɛͯͮƇǇǀɆ|J SC =

͜ĖŕɹǂgƦĴp_4ε 0
92e V 3/2 (z)m0 z 2  

nn^͢Ƚͱʧ S^͢ȽèͣȽ͛ͣȽ̧ͬ dca ^ͮč Va s^ǂ  J SC =  GVa3/2 G=  2.33 × 10 −6  
S

2

dca



 



^  ÷Ŀhǒ_nn^ÊéÌ






ź  

ç¶ G ͢Ƚͱʧ S ɌĒq^g|͢ȽèͣȽ̧͛ͬ dca ü÷ŚɌĒs_ ɮͮƕ͕gǒÌéØͮɛțȆĴɰǟ_ìȽʸ ²ÏÈéÚÄ¾¬Éç½Ûé^xÐâÉçɰǟ Ĩ̸xd^Ɯͦͮƕ˖ǉń̾ųđɾpɮͮƕ͕ɼǩÌéØț͛ȿ̿Ê

½Ûéļ͆sÉç½͗^ń̾ũɘȋ+čʐ  Rg  Rb^Éç½ÛéĴŞRg  R͆s_ã¶ɱsx^ɮ͢Ƚ̷Ġ­â¾ÃͮȽh̉˛p~c^cìȽʸ_nƇť^­â¾ÃͮȽhȢ͠

²ÏÈéÚÄ¾¬Éç½ÛéèÐâÉç½ÛéƏip{~cx^­â¾ÃͮȽĬͱʧőæ¢Üé

 ²ÏÈéÚÄ¾¬Éç½Ûé^ÐâÉç½Ûé

ͱʧɒŁťylɮ͢Ƚg ͮƕɇ~qd_x^ǂ   Va |c~^­â^ɮͮƕ͕gɼǩp BG Ćí¾ÃͮȽ ņȯ˟Ǩs^͢ȽèͣȽ͛ĕͮż Veq 



Veq =

Vg +
1+

1

µ

+

ʸ

dx

µ
4 d ga 

3µ dcg+ ũȤ˺˛b_ ²ÏÈéÚÄ¾¬Éç½Ûéń̾ũɘȋ
v

ŅǸ + ũɘȋ²ÏÈéÚÄ¾¬ũɘȋ^g|Ŏɘ͗hɮͮƕ͕ɼǩpÌéØÊã

¶Ƹhōĵś͗p + ũɘȋh͊ǳp
ͮż Vg ^ìȽƊƸƛȋµ、­â¾ÃèͣȽ̧͛ͬ dga ^͢Ƚè­â¾ÃͮȽ̧͛ͬ dcg s_nƊƸƛȋµ

_ɮͮƕ͕gʈɼqxͮƕÌéØh²ÏÈéÚÄ¾¬Éç½Ûé̽̈́s»¢×ç­^ÌéØÊã¶Ĩͷh²ÏÈéÚÄ¾¬Éç½Û
éɠ̾čʐ^ȡǏƩhń̾čʐbun^¥Æã«éƌ̖΄̾ǀƌ̖΅hgl

⎛ 2π rg ⎞ ⎤⎥dw⎝ dw ⎟⎠ ⎦ ⎣⎡⎛ 2π rg ⎞ ⎤ln ⎢ coth ⎜⎥⎝ dw ⎟⎠ ⎦⎣2π d gaµ=ǏȒbÉç½ÛéŎɘ͗ĆįdÉç½ż˚fnʰVa_nn^­â¾ÃͮȽã¶Ƹ^vÌéØÊ⎡− ln ⎢ cosh ⎜_²ÏÈéÚÄ¾¬Éç½Ûé̽̈́Ǐ^ͮƕ
 



̾ǀ

͇cg^ˤɿʩ͛ʣŇs͛ń̾pxͮƕĨͷͮƕ̹c|kn^cͪ˜΄Éç½ç­΅hfn_²ÏÈéÚÄ¾¬Éç½Ûéɮͮƕ͕gÌéØ˸p_nn^­â¾ÃͮȽ æ¢Üé͛ͥ dw ^­â¾ÃͮȽ æ¢ÜéŎǍ rg s



Ŏɘ͗

_

 nn^Ď¥Æã«éͮƕń̾èɠ̾s

2.3.2. RF ʩˡͮƕͪ˜èĸɊń̾x^īłp + ͮłèčʐ̷kv

ǏɊbÉç½ÛéĆîƦknhi_~͎˾b_x^+ ʩˡƙƛŊȽ

«Û¾ÐĄ̷^ ɮͮƕ͕gʈɼqxͰʐƣ̘ʊ¥Æã«étgͰƣʢͮʚƇĵƵhb^̽̈́sͶƃbÊã¶ɱͮƕÌéØʸͮƕÌéØƣq~^ń̾ȡƏͮƇ + čʐƎkɃȒŧǩĵǋͳs

^+

ͮƕņɶ

ʩˡġ + ͮłīłɾˋťų΄¨¾Ðá΅^kń̾sx^Éç½Ûé´¶ÀØ+ ÚÄ»éɾˋťų^+ ũɘȋ̖ȌɾÐáçµͮƕÛé + ʩˡͪ˜^fĩ̾ǀĸɊń̾fnd_«Û¾Ð͌ĵgͬxʶǬġe_²ÏÈéÚÄ¾¬Éç½Ûé^ź ê˪Éç½Ûé´¶ÀØ^ͮƕͪ˜
fndŏ¸ãƛŽɘƂ + ʩˡ²ÏÈéÚÄ   ʜsd«Û¾ÐĄ̷nhƎc_˜ĩ̾ƃ

ãƛŽɘƂ + ʩˡ^bc́˴ɘƂ + ʩˡ
Éç½Ûégȿǩp~c_ƣʢǟĤxâ¥çÂáçÂƂ + ʩˡɾc

¾¬Éç½Ûé^ÐâÉç½Ûé^pͪÌéØń̾fndƎȋ¸

ͮʚƇ








ź    ƛŽɘƂ + ʩˡɾcxͮƕͪ˜_ź    ²ÏÈéÚÄ¾¬Éç½Ûé΄â¥çÂáçÂƂ + ʩˡ΅ ωt < 0į͌ȿ̿_

i^«Û¾Ðļ͆qxͮƕɠ̾p^ ω t > 0 ń̾p_«Û¾Ð̽̈́qx ÐâÉç½Ûéń̾ũɘȋŦɀŇĐs + ʩˡđɾs_n

ũɘȋ

x^ɮͮ

ƕ͕gʈɼqxÌéØÊã¶Ƹh^+ ũɘȋũȤ͗cx^ÐâÉç½Ûé̽̈́ͮƕ^b̣˴̧ͬ́ θ = 0 ôǙͪ˜p_ź    n

ͮƕͪ˜

Ⱦǜźʜ

s_


s̀˒ʊÌéØ^ͪ˜^xǴȊp+ čʐͮƕhƖŽsn_nx^ÐâÉç½ÛéīƥpͮƕÌéØÊã¶ƸǛr~ƎȋÉç½hǉǩp_ ²ÏÈéÚÄ¾¬Éç½Ûé^xÐâÉç½Ûéͮƕͪ˜|c~^ʩ͛ͮˮņȯhɬ̂iĎͮɛÌéØćƛqxƇť^̄ȮʊƦĴsnhi3  4_ź    ʜsd^̀˒qxÌéØhƛŽɘƂ + ʩˡ«Û¾Ð̽̈́si^-&ŅǸp~c«Û¾Ðͮż{~^ț͛ĔƖqxɈǅʊź    ÐâÉç½Ûé̽̈́Ǐ¥Æã«é

Ɗɠŝl_«Û¾ÐͮżʤŊͮƕ

¥Æã«éƸƌ

Δγ m0 c 2=(−eEPB sinθ 0 ) Δzgap

 





Δγ (θ ) =

−α sin θ 0ξ gap 

 



θ 0 = −ω t  + ʩˡ čʐ θ = −ω t ^țľ t ylˊ̈́qxi^«Û¾ÐĆ͟^ˤɿʩ͛ʣŇsƅɦʾƕ

ͮƇǇǀ

ǸƸ^

«Û¾Ð͗^ α = eEPB2λ ́ȶŊqxθ (z) = θ 0 +Δz«Û¾Ðͮż^ ξgap = gap ́ȶŊqx«Û¾Ðλ

2π z " 1 1 % $ − 'λ # β0 βe &˸p_ǂ 

m0 c͗^λˤɿʩ͛fl + ɘ͗s_̣˴̧ͬ z si^čʐθ(z)

čʐ^̃ǸŇȋωŅǸs + ʩˡflțľ t = 0 ˸s_x^ Δzgap
 + ʩˡ˙Ȓŧčʐʩ͛_˸p_ EPB  + ʩˡ

ͮƕͪ˜̈́



 



ǖĵǉǂ˸s

Δθ
Δz

=

2π " 1 1 %$ − 'λ # β0 βe &

 



Δθ
Δξ

=

⎛ 1
1⎞
2π ⎜ − ⎟ ⎝ β0 βe ⎠

 



_nn^ ξ = z ^ β 0  + ʩˡīƥpλͮƕ̾ǀb_ + ʩˡ«Û¾ÐgÌéØh ξ yḷ˴qxi^čʐθƣsčʐȟ˖^ǂ ɾcź   d˸p_xnčʐȟ˖Ƀ̮ƣq~^ƥǋqxĵƵʜs_ n ̆ʷ^+ ʩˡīƥpÌéØ¥Æã«é  ?9/΄ β e = 0.7 ΅^«Û¾Ðͮż ȡƏĝ αξgap = 0.06 qx_êɀ̀˒ÌéØ^+ ʩˡīƥsʏz¥Æã«éƌ̖hgl΄ ξ = 0 ΅_ȡƏń̾ŝl   Rbͮƕb^ˤɿʩ͛i^  Rļ͆sn_x^+
ʩˡ

ξ = 0

̣˴̧ͬh ξ = 1.6 «Û¾ÐɃĶ̀˒ÌéØfc~^«Û¾ÐͮżŝlxʏǏ˂  RőȢq~cxͮƕh^ ξ = 1.6 yĺyi  RĆį

ξ = 0.8ͪ˜p_ ĵƵǉɱ|c~^Éç½Ûéξ = 1.2ǹɵʺŹ΄ R΅ī^g|ȡƎȋ ͮƕͪ˜i ξ = 1.6 bnhg_êȒ^ȡƧ É
ç½͗ ξ = 1.2ib_ξ = 1.6

Éç½Ûé
 ²ÏÈéÚÄ¾¬Éç½Ûé^xÐâÉç½Ûéfc~ + čʐ Rg  RʺŹƖŽsͮƕƎȋ¸ãȿ̿|Éç½Ûé
ξ = 2.0^pͪ˜ĩ̾ǀ̷kń̾hfn_ź    ́˴ɘƂÉç½Ûéį͌ȿ̿ʜs_ξ = 2.4


1.5
1-sin θ

0.5
0Injected beam

-0.5
-1


2.4 2.0 1.6 1.2 0.8-1.5-180 -120 -60



ξ = 0

ź    ́˴ɘƂÉç½Ûé
0

60

120

180

θ [deg]ź    

?9/é̽̈́qxiį͌ȿ̿_ ź    Éç½Ûéįͪ˜èń̾p
ͮƕ

čʐƌŊ

̀˒ÌéØhÐâÉç½Ûɀƕʜs_ͮƕhīƥpĸɊȋ¸ã^īƥț

ͮƕ̾ǀ + čʐ̾˙Ȓŧčʐʩ͛_ǀhťu^+ čʐ

¹åɫôǙqx

(d mc 2čʐǸŇqhͪ˜s_vq~Éç½ÛéǏɊ¸ã|~ + čʐ̾ǀƊńpuĩ̾ɨ̷sds_xÉç½ÛéīŞgȡĸȋ¸ã^ń̾ͮƇǇǀɆʮƊńpu~fi^Éç½Ûéį̽̈́sͮƕ^+ čʐͮƕȒhĨ́dq~fk^

čʐǸŇ

̾ͮƇ

ôǙ + čʐ

¹åɫgń

ȒʣŇq~ck_nͮƕń̾hfn^ĩ̾̷}c~ckn_ń̾¥Æã«éƊńqxh{~^ͮƕ̢͐Ɗńsx^ͮƕ

v

čʐǸŇ

ǸƸ

ǸŇȋɠƨq~ci^ɆʮɳcčʐƸͪ_dz) = −eE sinθ

 

B



˸p_nn^ m = γ m0 ˛i^z Ȓŧˤɿʩ͛ɘ͗ λ0 ƣq~ ξ = z Ʀīsǂ
λ0

 





dγ

 =  − eEB λ2 sin θ =  −α sin θ 

dξ



m0 c

 



_nn^ α = eEB λ2 ́ȶŊqx«Û¾Ð
m0 cͮż_ x^Éç½Ûé + ̃ǸŇȋω^čʐ̾
ǀ v p gͮƕh÷{~c + čʐ˸s͜Ė



θ=



ωz ωz
 
−
v p ve   ^ǖĵǉǂq~



dθ
dz

=

1⎞
2π ⎛ 1−λ ⎜⎝ β w β e ⎟⎠   

dθ
dξ

=

⎛ 1
1⎞

2π ⎜
−
⎝ β w β e ⎟⎠  

˸p_nn^+ čʐ̾ǀ β w =
ǂ 

vp
s_
c

ǂ  Ŧț̄l^z ̮

ɕ{xčʐƌŊ θ ͮƕ¥Æã«é γɀƕ̨̹i_nn^êĒq~^Éç½ÛéŤʩˡń̾ͮƇǇǀčʐ̾ǀź   ^  dðexiź    ́˴ɘƂÉç½Ûéͮƕͪ˜˙Ȓŧčʐʩ͛_ nd́˴ɘƂÉç½Ûéį͜sčʐͮƕ¥Æã«éͮƕ̓Ň͜Ė̄Ȯʊ

ðe3  4_nn^ʩ͛ͮˮņȯhɬ̂iĎͮɛÌéØćƛqxƇť˟e
_Éç½Ûéį ͮƇǇǀ ǸƸ EB ^+čʐθs^ͮƕ¥Æã«é

Éç½Ûéį

ÌéØčʐ̬ͅÌéØ¥Æã«éƊń̈́ʤź
 

^ 

vwʜs_ Éç½Ûé ń̾ͮƇǇǀα^ǐ`ím~ci^x ξ = 5 Ć͟ + čʐ̾ǀ β w ĩ̾q~c_ź  ʜsd^ĸȤÌéØčʐ΄
F58^ F58^ F58^ F58^ F58΅Ťɫ ξ = 5 Ą̷ǸŇhfp^v ƸF58 Ćįśȩq~ck_n«éƸź  ¥ÆãʜsdĸȤĝɌ~Ƽh|n_


i







ź    Éç½Ûéį

ń̾ͮƇǇǀ_ź   Éç½Ûéį

ń̈́ʤ_ĸȤÌéØčʐ΄
F58^

ͮƕ
F58^

¥Æã«éƊ
F58^ F58^

F58΅_

2.3.3. Éç½Ûé´¶ÀØflɃȒŧÌéØʈȊ
 Éç½Ûé΄İʳƂ + ʩˡ΅į~ǸŇs+ ͮʚƇ

Ⱦǜźź   ʜs_ͪ˜čʐbÌéØÉç½ż˚h́Ŧțĩ̾ǀ̷k¥Æã«éhƊńq~ckh^nź    Éç½ÛéįĊȃs +

čʐ̾

ǀ_

ɃȒŧʈȊsłhģk_n^ÌéØȢ͠

ÌéØ²¢·z^xͪ˜čʐťunÉç½Ûéį + ͮʚƇ
Ȓŧǩĵ



éØ

łŝl_nɃ+ ͮʚƇÌ

ǋͳ|c~˟e_





ź  

 Éç½Ûéįͮƕčʐ̬ͅ΄˙̮ŏ č  3F584 b  ΅_ ĸ Ȥ Ì é Ø č ʐ 

΄

F58^



F58^ F58^

F58^

F58΅_ź   Éç½Ûéįflͮƕ

ŧèɃȒŧ


śȩèʈȊĐɾɀƕ_˙Ȓ İʳƂ + ʩˡʈɼs + ͮƇ
Ez = iE0 (z)J 0 (kr r)exp ⎡⎣i (ω t − kz z )⎤⎦    ˸p_nn^ˤɿʩ͛ɘ͗λɾc~
⎛ 2π ⎞
kr2 + kz2 = k 2 = ⎜ ⎟⎝ λ ⎠s_©£¶
Er = −

2  ǂ  ^ͪ˜čʐͮƇhȡƏ_
 n



Fr =

dpr
= e ( Er − βe Bφ ) dt  

d 2r
eE0 J 1 (kr r)=
2
dz γ m0 βec 2 kr*, #1 & 1 1 ∂E0 .,× +k %1−i/ exp (iθ )(+,- $ β w βe ' E0 βe ∂z ,0  1ω
E0 J1 (kr r)exp ⎡⎣i (ω t − kz z )⎤⎦
kr c









  

_nn^ k = 2π ^ λ = 2π ω ^ β w = k ^c
λkz  
_ÌéØŎǍ r hƧpcĝ|i^Ɇθ = ω t − kz z ɾc_r hƧpcĝ|i^ǂ  



d 2r
eE0 r
=
2
dz γ m0 βec 2 2*, #1 & 1 1 ∂E0 .,× +k %1−i/ exp (iθ )(+,- $ β w βe ' E0 βe ∂z ,0̷Čɾc_
J 0 (kr r)≈

1

  

J1 (kr r)

≈

1
kr r
2

    

i^ǂ  ^  ^  
Ez≅

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33
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 % ÉçÃ ), ń̾ʸ=BDIH:=@9 Ćîʜs_ŏ¸ãƛŽɘƂ + ʩˡŦɀ”cell”ɾc~ÊáÙé»̉ƛs_ń̾ʸ¸ãȋĵ”cell”̸̈s_ͧťd¸ã͛+ čʐƳ

 180deg ̉ƛs_ń̾ʸīŞèĴŞ¸ã

΄ L-END01.T7 ΅^     ä « Ý á é ¸ ãnɾc_cell 14.8516 1.2 1 327.5 9.41 17 1 -1 1428
cfield 17
cell 10.4968 1.2 1 147.5 13.32 16 1 -1 1428

cfield 21

cfield 16

238MHZ01.T7

L-CENT01.T7

 ŏ¸ãƛŽɘƂ + ʩˡ̸̈”cell”đɾs̉ƛįƝ|c~^˸ _

cell 10.4968 1.2 1 327.5 13.32 16 1 -1 1428
cell 10.4968 1.2 1 147.5 13.32 16 1 -1 1428
[

 
˸

ƹſͮƇ

L-END01.T7

cell 51 2 1 138 0.39 21 1 -1 238

_nÐå­áØ΄,΅^+ ʩˡį΄L-CENT01.T7΅ƣq~ T7 Î¢ãĐǩq^ŏ¸ãƛŽɘƂ + ʩˡɘƂ + ʩˡÖ¾Íç­)+&%=BDIH:=@9”cell”įƝ΄&!N²ÏÈéÚÄ¾¬Éç½Ûé΅_L+ ʩˡ͗

51

cm

Ra

ȢņŎǍ

2

cm

Output FlagÎ¢ãĴł

1

φ0 

+ čʐ

138

deg

E0 

+ ͮƇǇǀ

0.39

1MV/m
*0.51*0.39= 200kV

CellType	 + ʩˡʄţ

21

ΔΦmax

ʩˡį̆ʷ

1

deg

ǖƧčʐƸ
Config

ʩˡÚÁã

-1

fcell

ŅǸũɘȋ

238

cell 10.4968 1.2 1 327.5 13.32 16 1 -1 1428
cell 10.4968 1.2 1 147.5 13.32 16 1 -1 1428
cell 14.8516 1.2 1 327.5 9.41 17 1 1 1428

́˴ɘƂń̾ʸ  ÉçÃ˻Ɉń̾ʸs_́˴ɘƂń̾ʸīŞèĴŞ”cell”^ä«Ýáé¸ã|c~”trwave”ɾc_ń̾ʸīŞèĴŞ͌ĵ^fͧťd”trwave”ť̆q~¸ã˸s_x^ń̾ʸīŞ͌ĵ”cell”^ ”trwave”

ĵ
MHz=BDIH:=@9 Ćîʜ”trwave”^ ”cell”+ čʐƳ-90deg^ĴŞ͌čʐƳ+180deg s_ä«Ýáé¸ã|c~^¸ãȋyl”trwave”̸̈q^ŦrÊáÙé»̉ƛs_, ǒͮʂĵƵƉʂȪĈʅ  |

T7 Î  ¢ ã  đ ɾ s  ΄ C-COS-01.T7 ^ʚɎäç· )+&% =BDIH :=@9  ś ȩ ʚ Ƈ  ˸ s 

C-SIN-01.T7΅_ń̾ʸīŞèĴŞ

T7 Î¢ã^”coil””poisson”ɾc_”coil”ÌéØ̮^C-END01.T7 b_”trwave”

̉ƛįɾíƼkĵƵsºäÇ¢ÃʚƇ˸s_êȒ^˸   _ƪǬʊʚƇĵƵʈɼsʚɎäç·|c~ )(",,(' ̆ʷqxˋȯɾc_=BDIH

cell 3.1 0.77425 1 140 4.0 15 1 -1 5712:=@9 ^”poisson”^v

ʚƇǇǀ^fcfield 15ĵƵ̉ƛs_, ǒx T7 Î¢

C-END01.T7

ã΄SINGLE07.T7΅ɾcx^=BDIH:=@9 Ćtrwave 0.9841 0.77425 1 50 11.4 10 1 5712 14 -5 5 0.75 19îʜs_

trwcfield 14



C-COS-01.T7

poisson 1.75 -1.0952648

C-SIN-01.T7

SINGLE07.T7

trwave 1.9682 0.77425 1 50 11.4 10 1 5712 14

poisson 72.25 -0.69692

trwave 1.9682 0.77425 1 50 11.4 10 1 5712 14

SINGLE07.T7[

poisson 163.1 -0.6000848

trwave 1.9682 0.77425 1 50 11.4 10 1 5712.0 14

SINGLE07.T7

trwave 1.9682 0.77425 1 50 11.4 10 1 5712.0 14[trwave 0.9841 0.77425 1 50 11.4 10 1 5712 14 -5 5 0.75 19
cell 3.1 0.77425 1 230 4.0 15 1.0 1 5712

000001000002000003



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ĸȤ̉ƛ

 ćǣ͢ȽgȆĴpͮƕÌéØ˸  )+&%=BDIH:=@9ÉçÃ́˴ɘƂń̾ʸ”trwave”įƝ΄Ùé»^Ćî

9@9A9BH ́ƛp_ä«Ýáé¸ã΅_”scheff”L+ ʩˡ͗

1.9682cmè ÌéØͮɛ

Ra

ȢņŎǍ

0.77425cmè ĸȤ¥Æã«é”run”

Output FlagÎ¢ãĴł

1

φ0 

+ čʐ

50

E0T

+ ͮƇǇǀ

11.4

è ĸȤÌéØčʐ”run”è ͮƕĵƵdegè ʾƕȋ 

10

ʩˡį̆ʷ

1

deg

 ͮƕÌéØ

MHz



ǖƧčʐƸ
fTR

ŅǸũɘȋ

5712

TRWcellType+ ʩˡʄţ

14

NL

΀̖ɘ

ȡƧ

-5

ȡƏ

5

Ɇȋ
NU

΀̖ɘ
Ɇȋ

PhaseLength
TRWcells

1 ¸ãǈ

0.75

čʐ´ÎÂ͐

(3π/4)

Ĭ¸ãȋ

19”input”

”input”TRWtankNumber	  ń̾ʸʄţΔΦmaxŤÊáɗ^ĵƵʾƕĵƵ|c~^Ćî̉ƛȒʥͻɾǥq~c_΅čʐʩ͛í́ƛpxȻİį

øȋĵƵ


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 ΄input 1 NA αx βx εx αy βy εy Δφ ΔW ...΅èinput type 2 or 20 ΄input 2 NA αx βx εx αy βy εy αz βz εz ...΅
 ΄input 2 NA αx βx εx αy βy εy Δφ ΔW ...΅èinput type 5 or 50

x^Éç½͗Ǜr~^Ͷƃ  |ĵl~Ù ΄input 5 NA αx βx εx αy βy εy αz βz εz ...΅¾´Ý²¢·ɒƛs_ ΄input 5 NA αx βx εx αy βy εy Δφ ΔW ...΅ źèinput type 6 or 60

̾ʩˡīŞ΄ͮƕ͕g̧ͬ  A΅^˙Ȓŧ ΄input 6 NA αx βx εx αy βy εy αz βz εz ...΅Ù¾´Ý²¢·ƣs &!N Ïé¶»éń̾ ΄input 6 NA αx βx εx αy βy εy Δφ ΔW ...΅ʩˡīŞèinput type 8΄LX΅ ΄input 8 NA αx βx εx αy βy εy Δφ ΔW ...΅Ïé¶»éń̾ʩˡg), ń̾ʸǭŀ΅fl˙ȒŧÙ¾´Ý²¢·΅ .'

ĴłÁé»^ͮƕ͕g &!N Ïé¶»éń

ÌéØ²¢·΄L΅^̓Ň͐ǋͳʜs_xź    &!NAžɫ΄% ÉçÃ

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èinput type 3


2

0.16
x

΅ʾƕɋč˛̃ǀ́ƛ
x [cm]

΄input 4 x x' y y’ φ W ...΅


0.15

1.5

0.14

1

0.13

0.5

΅$D57<=BG?=M /@58=A=FG?=M ĵƵx' [mrad]èinput type 4x'èinput type 7
 ΄input 7 NA αx βx εx αy βy εy Δφ ΔW ...΅

0.12
0.01

΅Ɉ́ĵƵèſêĵƵ

0.1

1

10

0
100

zmesh size [cm]èinput type 9ź΄input 9 NA σr rmax σ φmax ...΅ ͮƕ͕g &!N Ïé¶»éń̾ʩˡ

īŞ

φ

˙ȒŧÙ¾´Ý²¢·ÌéØ²¢·^̓Ň͐Ù¾´Ý²¢·^ʾƕȋ ʩ͛ͮˮņȯ
_v

̉ƛ



̉ƛ”scheff”fn̆ʷʿǀ^ʾƕȋÙ¾´Ý²¢·́ƛp_ɃȒŧ΄ΔRSC^NR΅^f˙Ȓŧ΄ΔZSC^Nz΅Ù¾´Ý²¢·̉ƛsh^Éç½įͮˮƟǀ

ƌŊƣq~^ȡ͈Ŋsǚ˾hb_
 nn^,% ͮƕīƥųͰʐƣ̘ʊ¥Æã«éͶƃbͮƕ͕g &!N Ïé¶»éń̾ʩˡǏȒ΄ͮƕ͕g A΅

˙ȒŧÙ¾´Ý²¢·ĔƖǟʜs_̉ƛqxʾƕȋę^ɃȒŧÙ¾´Ý²¢·AA qx_

ǋͳ_



0.16

2.8

x'

0.14

2.4

0.12

2

0.1

1.6

0.08

1.2

0.06
0.001

0.01

0.1




x' [mrad]x [cm]

x

0.8
10

1











zmesh size [cm]ź   &!N Ïé¶»éń̾ʩˡīŞgA ǏȒ

˙ȒŧÙ¾´Ý²¢·Ì

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ǋͳ_


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Éç½͗

¥Æã«é

BGW DGAAW AA DGW

ͮƕ͕g

DG

 AAWAA

&9/W

&9/

&9/W &9/ȡ͈˙ȒŧÙ¾´Ý²¢·̧ͬ΄ΔZSC / Nz΅ 7AAA





7A

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付録 B
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"
0
$
$
r
Sh = $$ i 1− r$0#

i 1− r







#
%
Sp = %%$

ri 1− r

0

0

0



0

&
2
1− Γ 6 e−iφ (
(
(
Γ6
'

2

1− Γ 5 e−iφ 

Γ5



r

%
'
i 1− r ' 
'
r '
'
0
&
0



 ź Ćî  ͚Şŵ̩ÚÁã_ȪĈćƛs_x3 = Γ 7 y3,

x4 = 0,x6 = Γ 8 y6  

 8 ͮłĵ͍ų|c~

y1 = r x2 + i 1− r x3  

y2 = r x1 + i 1− r x4 = r x1  

y3 = i 1− r x1 + r x4 = i 1− r x1  



y4 = i 1− r x2 + r x3  

_x^ʣʐų|c~ź   % ÉçÃƏͮłʫďŵ̩´¶ÀØ

ÚÁ

ã_

 ͚Şŵ̩y5  =

Γ 5 x5 + 1− Γ 6 e−iφ x6 2
Γ 5 y2 + 1− Γ 6 e−iφ Γ 8 y6   y6  =  1− Γ 5 e−iφ x5 + Γ 6 x6 





=

2

2

Ȋø˴ķ

! y $ ! S
# 1 & = # 11#" y2 &% #" S21

S12 $! x1 $&#&S22 &%#" x2 &%





2

=

1− Γ 5 e−iφ y2 + Γ 6 Γ 8 y6  

_ǂ

ǂ ąīq~
1− Γ 52

˸s_nn x^y ˽˅ȋs_ΓŤ˅ƕŚƥĖȋčʐ´ÎÂŨ˽˅ȋs_s
z Γ = Γ eiθ s_ʫďŵ̩đɾsȒŧǒ_pǂ ǂǟˋťųg Śƥ + ͮłɬ̂is
_x^ʣʐų Ť͚Ş͌ ŚƥĖȋ Γ 5 ^Γ 6q^Ťń̾ʸŚƥĖȋ Γ 7 ^ Γ 8 s_ 8 ͮłĵ͍ų΄ Sh ΅ʣʐų΄ S p ΅ Ȋø˴ķĆîʜs_nn^ʣʐų

ʣʐ͐φ





y6 =

re−iφ x1 







2
2
#
&
1− Γ 5 1− Γ 6
x2 = x1 % Γ 5 r +Γ 8 re−2iφ (%(1− Γ 6 Γ 8
$
'





΄şƌʺŹO R΅s__ǂ

1− Γ 6 Γ 8









ǂ ąīq~





=

Γ1

y1 
x1
1− Γ 5=

21− Γ 61− Γ 6 Γ 82

Γ 8 re−2iφ− (1− r ) Γ 7 + rΓ 5













ǒ_ǂ



ʮ

ʹ



ĵȋ͌ĵ|c~̷Čs


Γ1 = Γ 8re−2iφ − (1− r ) Γ 7 + rΓ 5ǒ_ǂʮ+ ͮł^ʮ  ʹʮʹʮ  ń̾ʸg
ń̾ʸg


Śƥ

Śƥ + ͮłb^φ͈Ķĝs^òˠªÛç¸ãi_Ř ˟ ȍ ɴ[1] D. W. Duopn, “The Story of Stanford’s
Two-mile-long Accelerator”, SLAC-62 (1966).
[2] E. L. Ginzton, W. W. Hansen and W. R.
Kennedy, “A Linear Electron Accelerator”, The
Review of Scientific Instruments, Vol.19, Num.
2, pp. 89-108 (1948).
[3] E. L. Ginzton΄ƏɓƤê ̋΅, “ͮƕń̾u”, ƮɘȠƿ 1997.
[4] R. B. Neal, “The Stanford Two-mile
Accelerator”, W. A. Benjamin, Inc. (1968).
[5] G. Mavrogenes, et al., “Subnanosecond
High-intensity Beam Pulse”, 1973 Particle
Accelerator Conference, San Francisco, CA, pp.
919-922 (1973).
[6] N. J. Norris and R. K. Hanst, “Velocity
Modulation System for Enhancement of 50
picosecond Radiation Pulse”, 1969 Particle
Accelerator Conference, Washington, DC, pp.
323-328 (1969).
[7] S. Takeda, et al., “High-current Single Bunch
Electron Linear Accelerator”, 1985 Particle
Accelerator Conference, Vancouver, BC, pp.
3219-3221 (1985).

[8] Y. Tabata, et al., “A 35 MeV Electron Linear
Accelerator Project at Nuclear Engineering
Research Laboratory, University of Tokyo”,
Journal of the Facility of Engineering, The
University of Tokyo (B) Vol. XXXIV, No. 4.
(1978).
[9] J. S. Fraser, et al., “Photocathodes in Accelerator
Applications”, 1987 IEEE Particle Accelerator
Conference, Washington, DC, pp. 1705-1709(1987).
[10] K. Togawa, et al., “CeB6 Electron Gun for
Low-emittance Injector”, PRST-AB, 10, 020703(2007).
[11] Əɓů, “ͮƕ͕”, OHO 1990 Àª¶Â.
[12] ȳȥͩƐ, “ͮƕɥ”, OHO 2002 Àª¶Â.
[13] ȳȥͩƐ, “ʾƕɥÀª¶Â.

̉̆ɷɱ”, OHO 2006[14] K. R. Spangenberg, “Vacuum Tubes”,
McGRAW-HILL Book Company, Inc. (1948).
[15] J. M. Ponce de Leon, “Design of the Bunching
Section of the Stanford Mark IV Linear
Accelerator”, Stanford M. L. Report, No. 265(1957).
[16] M. B. James, “Production of High Intensity
Electron Bunches for the SLAC Linear Collider”,
SLAC-319, (1987).

[17] L. M. Young, “PARMELA”, Los Alamos
National Laboratory report LA-UR-96-1835(Revised April 22, 2003).
[18] H. Tanaka et al., “XFEL/SPring-8 Éç½ż˚ǟˢřs RF ɄųƌŇ ǋͳ̎ĕ”, ʮ 4ŵń̾ųƗĉƺĉ, ŭĩ, pp.613-615 (2007).
[19] Y. Otake, et al., “Timing and LLRF System ofJapanese XFEL to Realize Femto-second
Stability”, 2007 International Conference on
Accelerator and Large Experimental Physics
Control Systems, Knoxville, Tennessee, pp.
706-710 (2007).
[20] T. Shintake et al., “΀ƙƛºâ¾Ã¶ÀéÂ΀ũɘ çÐ ͚ʈ”, ʮ 2 ŵȕȦń̾ųƗĉèʮ 30 ŵâÄ ¾¬ǰ˵ʘʨĉ, ΁Ȳƴ, pp.
314-316 (2005).
[21] T. Asaka et al., “XFEL/SPring-8 īƥ͌˛l΀ũɘ´¶ÀØ ͚ʈ”, ʮ 6 ŵȕȦń̾ųƗĉèʮ 30 ŵâÄ ¾¬ǰ˵ʘʨĉ, ȬɜȨ,
pp. 906-910 (2009).
[22] T. Yamamoto et al., “XFEL īƥų x
476MHz ΀ũɘƊƸų”, ʮ 6 ŵȕȦń̾ųƗĉèʮ 30 ŵâÄ ¾¬ǰ˵ʘʨĉ, ȬɜȨ,
pp. 1181-1183 (2009).
[23] T. Hashirano, et al., “SASE-FEL ɾ 238MHz ʩˡ͚ʈ”, ʮ 2 ŵȕȦń̾ųƗĉèʮ 30 ŵâ
Ä ¾ ¬ ǰ ˵ ʘ ʨ ĉ , ΁ Ȳ ƴ , pp. 340-342(2005).
[24] S. Matsui, et al., “XFEL ń̾ųÂçÆãį žɸʚƇ͔ʱ ɝʚ”, ʮ 7 ŵȕȦń̾ųƗĉƔ̩ƴ, pp. 268-272 (2010).