
   !"#$%&&'() *+,- ./0&2"3%'() *+,12" 45 6
./01*78 9:;<=>* 2"?@ 0A
B
%&
&'()
*
E
&+,-./01C
D
FGHI3" 9JHI 
 !"%&GK
NC O
LM
P3./01FGJ QRST0U
FG* 2"9HVN& J3WX)*FG
Y"Z[\2"95   !" 
#$


] 
'()
^ M_H]`C
T0UaT0Ubc,./01
+
1

(ERL)

5GeV

100mA

rms

1mm-mrad

10mA

rms

0.1mm-mrad

1.1[1, 2]

SPring-8

8GeV

100mA

10mm-mrad

[3]

ERL

SPring-8

10

100fs

100mA

1.1:

ERL
5 GeV
10–100 mA1300 MHz CW
0.1–3 ps
7.7–77 pC
0.1–1mm-mradrms

J?@ 0AB *%&de NR DfgIDhiY"\&Q
Xj<k3%lmV )c*2"9?@0
A*%\nC 0AoD] Y"*&?@)c\2"QRpgIq"r*lZ[\<
39s!tHI& *%l%u]
0w xI !"y&  Dzvml V ] 0A{|Y"Z[\2"9J%&  }0 ~&  }0 D V j YsJY"9DFGY"%&aJ [!"P./01D~yY \Z[* 2"9s L W< JHINJ !I3 "%& 485D 
ERL

100mA

ERL

100mA

100mA

360

/

8640

/

ERL

NEA Nega-tive Electron Affinity

4 8 * 2"9 ¡ 7"¢£LM&¤¥¦§Y"\¨L©ª!
& 5«¬Hy©ª\­®¯° D±0 H JHI Iq"9G²*a 4c¢³\ ´e"bc~Jµ¶8%&·¸¹º»¼ 0¸½¾¿ÀÁÂ
8*FG!y  } ¡ 4
0* 2" 9Ã M&s DfgyJH
I N& % ~ HV* jÄ&ÅÆDÇI ÈÉ#-DÊgy M&É#-Ë DnCÌÍHIÎ qÏÐY"ÑÒÓ\Z[* 2"9 \ &ÔÕµ<DÖ ¡ {|Y"%&r×r×n qØ 1 DZ[JY"9ÙÚRÛÜÝ\n qØ 1 DZ[JHI3"ÞV*2"\&sÛ%ßNàá<âã$#D9äå &Ù æ &çè / B é &ê0w ±0ëìDfgyÙÚRíî é * 2"9s! %&ïð;ñò;óô< )õö÷3IFGã$* 2"9ø!ù!3IúHûH qüý "J&%&ÜÝËþ ÙÚR* DfgI Ù æ D`a*FGH&ÿF NÊgI3 " 9RP./01
 Hy*Q
 Dfgyçè / B é \Ó*ÜÝ!I!I3 " 9
3 "è0A 1B é ñý"J& .} 1 %  "N
&1  ± \  3 é 1D^
M_H]`C*{|* j"9¡ 1    J Dþ&ê0w ±0ëì*ÙÚRíî é   3 "D\hiH !I3 " 9øß&·¸Ø Ø 0¾¿Àç0êv * 2"
8*&   JHI \ !
GaAs

NEA

1/e

JLab FEL

500

[4]

100mA

1,2

ERL

SPring-8

FEL[5]X

FEL[6]

γ

[7]

10mA

1. JLab FEL

8mA

14kW

FEL

1.6µm

2. ERL

[5]

10mA

X

FEL

[6] SPring-8
X

FEL[8]
3

3

X

1-100MHz

3.

[9]

ERL

γ

[7]

RHIC(Relativistic Heavy Ion Col-

lider

ERL

!I3 "ß&è0A 1 J DþyA» N2"
  %
97!y33I
X)P./01Û%&D6
9
àá<* f"ã$#\2
M&¾¿ÜÝ¤%IÙ39
FEL

ERL

EUV

[10] ERL[11]

vacuum pump

4

NEA

6

cathodeinsulator tube

3

5

laser

anode

! D# Ml!y 0B } w @QAD
q911./01 J./01(C3INüý "9 >*%& 3IDE
H&F  G ./01D"9 >*%&  3ID
E H&w } ±/wÛ  ]:ïð Ø ¡ 3Iüý "9Ù2 H
3I% >*üý "9ÛV j !
y #$Iµ3I% >r J"9%&J U  DfgyX)>*-FKD )Û DLMY"9s!
%&    JHI N
NO !I3 "9 >*%  F)Û3Iüý "9P æ  Ù æÜÝ!I jyÛ 3Iüý "9ÙÚRÛ%àá</w  N\2 M&yÜÝ!y& 1Ùé2F)Û& 4Q8GØ Ø 0¸½¾¿À 4·¸8)Û\ !DR I3" 93Ä!
RP./01D QR
NQÙb*FGHI3 "9y×H& .0S
'()FG%T0U^ M_H]`C 1Ù2 D *TDÑÙqY"Z[\2"9"%ïð;<UV\2 M&Wz¨ ®XD  "%®X*FYZ[\\2 MUV * 2"9s! ]^Û 3I89*%_`Y"9e-bunch

7

RF

ERL

8

ERL

DC

FEL

high voltage circuit 1.1: DC NEA GaAs Û  i
G§ & æ  &Ù¾ & X&
2008
 X&X =Ó \  HI& 500 kV Û>Ñ
H
I3 "9øÛ  / D5 1.2 
Y9 æ *%&øw } ±/wJHI 250
Û Ñ2 M [12]& 500 kV 
kVÛy !" /#$% ½I "&µ* 2

X

FEL

SPring-8[13] DESY

1300MHz, 2856MHz
[14]

RF

1mm-mrad1nC

MHz"93Ä!ÛN&
'(* 2" 5DJHIæ Df W9 ø iDY9
  4)8 J *  4+8D,;-.* 2"/ .0 DfgI 1µbcdef ghi
2aH&Ù2 D3 Y"9  8 jk2y V< D45Y"9 Ø%D>M
ry&lmn G opqr
¡ D7Y"J&¢£*\ V nM6Hy
9
s¶N6HItjy39
6 H&  * :LM ! & JHI7)V!"989%&sÛ]:ïð3I & ! ; 2.1 1 uvwx<;< &ÜÝGK&:K=3IrJ& y &zy  &R b {|
ÛÜÝ % q} 0Qæ% *½I "sJD !;JY"9 >*% ? @QA&®bæ&./013Iüý&ø
NEA

1.1

GaAs

1300MHzRF

CW[15, 16, 17, 18]

NEA GaAs

[19]

[20]

DC NEA GaAs

E

B

v

q

2

dp
= q(E + v × B)
dt

(2.1)

5 ÛJw } ±/wÛ   /w } ±/w

2^ M_H]`C
T0Ubc'()Ø ¡  *T0Ua+,- ./01 V* 2"9{ %~ TY"9øz-% D~ HI&
1.2:

ERL
500 kV
1.3 GHz CW
7.7–77 pC
10–100 mA

250 kV
83.3 MHz CW
7.7–77 pC
0.64–6.4 mA((FWHM)

rms

B

50mA)

20 ps
0.1–1mm-mrad

20 ps
1mm-mraddt

zBr(r, z)

dr, z + dz)

θ

Ψ

rBz

z

dΨ
dt

 2.1: ?tzyDTY"b{ | qæ9²é%zyD5H&Fé%{D5Y9
 [15] D6HI3 "9?tzyþ\¦§Y"yD*2"&9Y"b{ RJø D
T"z D5Y Busch µ D q9&?tzy?ty\¦§Y "ynÜDÊ W9n Üy3I& r  1 
i r* Hy ? 7*&{ D
5Y@QADq92.1.1 Busch  2.1 Y L W<y< 3 z ?tzy &b q D{ tY"R(B , 0, B ) *@ } 0Qæ DA*5YJ
θ
r

z

1 d
Fθ = −q(ṙBz − żBr ) =(γm0 r 2 θ̇)
r dt

∂Ψ
∂Ψ
ṙ +
ż
∂r
∂zZ

=

= 2πrBz ṙ +

r

2πr

0

J<"9ss*&z(2.2)

D"Jfgy9 D
(2.4)

(2.2)

lHI&~@ Yq(Ψ − Ψ0 )
2πγm0 r 2

Ψ0

(2.6)

θ̇ = 0r,zA = (0, Aθ , 0)mc2
+ qcβ · Aγ
mc2
= −+ qr θ̇Aθ
γ

L = −*! !" 9 @"ÌTc%(2.7)[21] θ

r

0

(2.5)

J<"9 % ~zD5Y9
&zy%?t* @þ<*&B  ± 0è %
J<"9t;A0¹0%θ̇ = −Pθ =∂L= qrAθ + γm0 r 2 θ̇
∂ θ̇

(2.8)

β 2 c2 = ṙ 2 + r 2 θ̇ 2

(2.8)

(2.6)

(2.3)

(2.4)

∇·B = 0∂Bz
1 ∂(rBr ) +
= 0
r ∂r
∂z

”

(magnetic flux)Ψ
Z rΨ=
2πrBz dr

∂Bz
dr ż
∂z

= 2πr(Bz ṙ − Br ż)J<"9ss* ± %~ D
5Y9 ?D JHy  D M"& J<"9ss*&z%J DñòHI“(r +Ψ = 2πrAθ ,

Ψ0 =

Dfgy9

2πPθ
q

(2.9)

I5Ys J\* j"9& AlY"J&D
y&zy1  0è %&de Nw 1@QA
E = −∇φ,z(2.13)

 2.2: Åàzy{  9z<3õö 4Ψ = 0 8V { %ÅàzylY"9zy*R% Ω 9Fé\zæéD5H&²é%{ D5Y9 [15] D6HI
0L

B = −∇φm(2.13)(2.11) (2.12)

1 ∂∇ f (r, z) =
r ∂r
2



∂f
r
∂r



+

∂2f
=0
∂z 2

(2.14)DyY
9 " &1  0è?tyD In *ÜY"

CJH

D
9

3 "9
\$ !"9\ V R D lY"J&!"yD"98
4
Wzy\¦§Y "9~4% 8D%&
 WzyDz  w  % ~D,è ÓDfgI JHI3 "9ss*%& * 2"9ss*
9 @i %y&zy1®3yD * 7)÷3IzyD yD5Yzy&
 H&7) @Åà<zy\¦§Y "  0èD * Hyy D" 4 6789
J÷"*&
y&?y @*i5!"
9J<"\& ÷3I
sJ<"9 D} ±}0]`C& D % \ÝhY"
J<"
j
2"
! LM
&
ý
*
9s
]`CJ

J<"9 gI& LM
9r

f (r, z) =∞Xfν (z)r ν = f0 +f1 r+f2 r 2 +... (2.15)

ν=00(2.15)(θ̇ = 0)

Ψ0 6= 0 “immersed”

Ψ0 = 0“shielded”(2.14)∞

f1 X+[(ν + 2)2 fν+2 (z) + fν′′ (z)]r ν = 0 (2.16)
r
ν=0

“

0

r

Ψ0 = 0,Ψ = πr 2 Bz

2.2

ωc
qBz
=
= ΩL
2γm0
2

ωc

∂f
= f1 + 2f2 r + 3f3 r 2 + ...
∂r
f1 6= 0(2.10)ΩL
? t zy (B , 0, B ) ? t   y\¦§Y "yD"9 )(E , 0, E )\&y JñòHI* j"d  3 J
ÃµY"9J 1º @QALMy3I
2.1.2

r

z

z

J<"9zy3I Nà ∇ × E = 0,∇·E=0(2.11)J<"92"sJV &&*
y&zyD1  0è & D3∇ × B = 0,∇·B=0∇×E = 0 ∇×B = 0(2.12)

φ φm(2.17)rr =0

Er = 0 Br = 0

f1 = 0rzrzθ̇ = −”(2.16)(ν + 2)2 fν+2 (z) + fν′′ (z) = 0

J< M& &
&Ó\$ !
J<"9"\& * 2"s JVà "J 4 \ C8J<"sJV &%(2.18)

4f2 + f0′′ 9f3 + f1′′ = 0

f1 = 0f3 = 0fν = 0 ν(2.18)

1
f2 = − f0′′ when ν = 0
4
1 (4)
f4 =
f
when ν = 2
64 0

ÓJ<"9 gI&

(2.15)f (r, z) = f (0, z) −%r 2 ∂ 2 f (0, z) r 4 ∂ 4 f (0, z)
+
− ...
4
∂z 2
64 ∂z 4(2.19)

J<"9z y  n  Ü D ? z yJ<"9s %&{ \y&zyD

5Y
&
3I
iY"&z  òýI  !
VD &zy 9i % åi&½9{ \3 J3WsJ%&
M{  @R\ @òýI 
3s JN<"9Y< e& %N Y"9{ \ @ "3I@QA%
J<"9à  i %2"9 D lY"J*J<"
9s! D lY"J
Bz (0, z)−∂φm (0, z)/∂z = B(z)=Ez (r, z) = −V ′ (z),Er (r, z) =rz

(2.13)(2.19) f (r, z) = φm (r, z)z∂φm (r, z)∂z∂φm (0, z) r 2 ∂ 3 φm (0, z)
= −
+
− ...
∂z
4
∂z 3
r 2 ∂ 2 B(z)+ ...
(2.20)= B(z) −4 ∂z 2Bz (r, z) = −∂φm (r, z)
Br (r, z) = −∂rr ∂ 2 φm (0, z)
=
− ...
2
∂z 2
r ∂B(z)
= −
+ ...
2 ∂z

r

d
(γm0 ṙ) − γm0 r θ̇ 2 = q(Er + r θ̇Bz )dt(2.24)(2.21)\$ !"9(2.27)z∂φ(r, z)∂z
∂V (z) r 2 ∂ 3 V (z)
= −
− ...
(2.22)+∂z
4 ∂z 3(2.26)

J<"9à  i %−(2.27)

lH& (2.28)

βqEz
q2B 2ṙ + 2 z2 r
γm0 c
4γ m0

q 2 Ψ20 1
qEr
−
2
3
2
2
γm0
4π γ m0 r= 0(2.29)

J<"9 ~ 4±8*%< q& 
4w 8*5YJ&zṙ = βcr ′(2.23)r̈ = r ′′ ż 2 + r ′ z̈V

Bz (r, z) = B(z),(2.26)

r

2.1.3

?ty&?tzy¦§Y"y{ DÊ WÌÍ\* jy9? 4 ?8{ þ D"s JJH&y&zy
3I r  1 i r** Y"J&{ D
5Y@QA\'ô<"9(2.20)&(2.21)&(2.22)&(2.23)

Ψ0Bz − 2πr

lY"J&
r̈ +

r

D



d
(γm0 c2 ) = qEz βcdtγ̇ ≈ βqEz /m0 c

Ez (r, z) = −J<"9Ψ = πr 2 Bz

(2.3)

q
−θ̇ =
2γm0

(2.13) (2.19)∂φ(r, z)Er (r, z) = −∂rr ∂ 2 V (z)=− ...
2 ∂z 2(2.26)(2.6)

J<"9
 y  n  Ü D ?   y 0 è
3I 5Y9 & &
D
V &i%
N

f (r, z) = φ(r, z)

r′ ≪ 1ṙ ≪ żr

φ(0, z) = V (z)r ′′V (z) (2.25)
2≈ r ′′ β 2 c2 + r ′ β ′ βc2

J<"9 <* & &4 2"õ
Döfgy
9LMÇb\<38<*&(2.30)ż = βc z̈ = β̇c = β ′ βc2ż ≫ ṙ(2.11)∇·E = 0

1 ∂∂Ez
(rEr ) +
=0
r ∂r
∂z

J<"9 LM \ L <3*& & Df W
DJ %HI@W5* j"
9
L !"9(2.25)

rEz(2.31)

r(2.31)(2.28)Err
Br (r, z) = − B ′ (z)2(2.24)

1
1
Er = − rEz′ = − rγ ′′ m0 c2 /q22(2.32)

&(2.28) (2.32)

D(2.29)

lHIr J"J&

"

2 #
γ ′r′
γ ′′
qBz
+
r + 2 +
r
(2.33)β γ
2β 2 γ2βγm0 c

2
1
qΨ0
= 0
−
2πβγm0 cr3′′

J<"9 &

DfgIY"J(2.33) D(2.9) (2.10)
 ′′
 
2
′ ′
Ω2L
γ
Pθ
1
′′ γ rr + 2 +
+ 2 2 r−=0
2β γ
2β γ β c
βγm0 cr3(2.34)

./01*r"R \ MDgI3 "\& .  %./01\ } 4R\ MDy<38 ;< D5Y9
Ø    / D L Wµ¶Y"9N q2
4πε0 m0 c2

ν== N rc(2.39)& % 2y M{C& %{ss* 9 {  R\ & y&D lY"J
N

1[m]

rc

n[m−3 ]a[m]J<"9 / J % 0è C* 2
J 0è  J<" &"9T
%w J]`C99ss*
 D JY"J&w J]`C\µ¶!"% JT
<*&Y"Jq» ÷3I*2"9A \lgI3"
% R\ × 2 !I"s JD5Y9s%& o{ \ I  Ds*
J<"9ss*&JÃµHI3 "9Ø    / JY"\& º 0)J å!"
Dµ¶Y"J c &b DlY"J* 2"9J<"
J V
9
J<"9 & & D lY
<*&)%
"J&
J<"9
β

qφ

γ

0

N = nπa2

a2 nq 2
γ a2 ωp2=
4ε0 m0 c2
4 c2
q2
ωp = ε0nq
γm0

ν=

φ

m0 c2 (γ − 1)0m0 c2 (γ −1)+qφ =(2.35)

φ0 = −m0 c2 /q(2.36)γIA =φ(2φ0 + φ)
(φ + φ0 )2(2.35) (2.36) (2.37)(2.40)γqφ
φ
γ = 1−
=1+
2
m0 c
φ0

β2 =

(2.39)

4πε0 m0 c3
βγ = I0 βγq

I0 =(2.37)(2.33)

φ(2φ0 + φ) ′′r + φ′ r ′φ0 + φ
"

 
#
qBz 2
φ′′
φ20
+
+
r
2
2m0 c
φ + φ0

 

φ20
1
qΨ0 2
−
= 0
2πm0 cφ + φ0 r 3(2.38)

J<"9
2.2 
 .   J%& 2"²*{ R\
rgI3 " * & %÷ 3ÏH<39y×H&² *%&J ¹²* I \Ï Y"9F %(2.41)−17000 A(2.41)(2.39)

ν =N qc/I0

I = qβcN = I0 νβ(2.42)

  3 z ?@zy B = (0, 0, ∞)  R n(r) &R β(r)c D  D"9zyR\X<* &{ @TD< qI L39 !"#$"%&'()*+,-.!/01 N 
E =0
2.2.1

z

N=

" .$23 I I=

Z a

2πrn(r)dr(2.43)

2πrn(r)cβ(r)dr(2.44)

0Z a
0

"&'E = 0 " ! r
2  &"$

!

z

Er =
=

Z r
q
rn(r)dr,ε0 r 0Nq,r>a2πε0 rr ≤ a, (2.45)(2.46)"&'2 ! 0  &! $!/0! !"# "!"#!$ 0 "%&"$
2

qφa + (γa − 1)m0 c = 0(2.47)

23'()! * n(r)β(r) = n β $+!,- r !/0! !"# $!"#
./01
a a

(γ − 1)m0 c2 = (γa − 1)m0 c2 −Z a

qEr dr (2.48)"&'(2.45) "23'()!23  (2.48) 
45 #
q 2 na βaγ = γa −ε0 m0 c2

Z a

1
dr
r

Z r

r

r1
dr1
β(r1 )(2.49)"&'!678+ & β(r) = β"9:& *$
r

0

a



r2
γa − γ ≈ ν 1 − 2 ,a"&'2)

γa − γ ≪ γ(2.50)(γ − 1)m0 c2(2.51)qβ 2 m0 c2≈ −(N.R.) (2.52)
2q

V =φ = −"&'(N.R.) ;<=>?@A (non relativistic)!B"'CD "E "!2)F (γ − ,&'B72)GHγ )m c /q = νm c /q
8+! $
a

0

0

2

ν ≪ γ − 1,021ν ≪ β 2 (N.R.)
2(2.53)! * ,&'ν !IJ "K$LM!20!
NOP#P Q'RSTU!V QW=!2
X!Y- & 1/07/Z%& *$23
[$ +&'\]^_`abcdefgh!jklmn2op2 71q $2i2op()nr,-.i = nqβc !2373
& * smntuvwxyz&'{|
}~

2.2.2

nq
d2 φ
=−
2
dz
ε0

(2.54)

qφ
m0 c2(2.55)"&'!!"# (2.51) V .
γ =1−

 ,&'BB$23V&  %&- $E (0,0,∞)  #&'(2.55)
 z  2  #$(2.54) 45#$B! !
!~ i = nqβc  Q"
nq 2
q
d2 γ
iγ
p
=
=
2
2
3
dz
ε0 m0 cε0 m0 cγ2 − 1(2.56)"&'(2.56) ! 2(dγ/dz)dz 1qr
%&"$
dγ
=
dz

r

2qi
(γ 2 − 1)1/4
ε0 m0 c3

(2.57)"&' BB $r1 2on z = 0 "&V Q'B!23$z = 0dγ/dz = 0
 γ = 1  ,&B"#$2 71q"N$n1( 0 !207+&B"
&'(2.57)  z = 0 1r%&"ε0 m0 c3
iz =
2q
2

Z γ

dγ
(γ 2 − 1)1/4

2(2.58)

7&'(2.58)  &r7
,&'BB $ ? &- $r¡¢
1 γ sB!r¡¢ γ = 1 + ε " 
1N&) "γ 1γ sB!r¡¢ γ ≫ 1 " N&) !£i¤q&'  &"$
1

1

2

1

Z γ
1

dγ
(γ 2 − 1)1/4

≃

2
√
√
[2(γ1 − 1)]3/4 + 2( γ − γ1 )3(2.59)

7&'γ < γ ! * s;<=>@Ax$¥!¦ 1 §!97¨ P &' γ = 1 + 
45%&"$(2.58) (2.59)
1

β2
2

3

β =



9q
2ε0 m0 c3



iz 2 =

18π 2
iz
I0

(2.60)

7&'B Child’s law " Q'(2.52) !
 φ  N% "√4 2ε0 (−q)3/2 1
=
√
9q m0
z2
φ3/2
i

2

(2.61)"&'20! $2X45%& "¥ "&'m= −2.33 × 10 [AV]
n2o!nr S "%&"$mntuvwp!
23 I = iS " .$I/φ {"
'
−6

2

−3/2

3/2


2.2.3 X2/0 2 $ ! V .
#- .%&' BB $,- a !2017) N- *yz&'
2378+q $!,-.7'R
STU$ "W=!2Xi/07)
/Z%& *$p2X %&27)!" +&7,&' B f %'
45%&"$)
(2.45) n =(1 − f )C!p2XV&E N!#
N
πa2

qEr =

2

γm0 r̈ =N q2
r(1 − f )2πa2 ε0(2.62)

7&'$$  V&+ N!#&'Maxwell }~ V .
∇ × B = µ0 J=2ν
aa = 2β γ′′

 ,&'r #$J(r) =%&"$  %B(r) =
=

N
qβc
πa2

(2.64)

45#)*µ0r ′ J(r ′ )dr ′r 0µ0 N qβcr
2πa2(2.65)



1
−f
γ2



=K

(2.67)

2

2

A





2ν
2I
1
1
K =
−f = 2−fβ2γ γ 2β IA γ 2


2I
1
=
−
f
β 3 γI0 γ 2(2νwhen f=0β2 γ3=(2.68)
2ν
− γ when f=1"&'2

dR0/dZ=0.0
1
-0.5
-0.75
-1.0
-2.0

-1.5

0
1

Z

2

7 2.3: 89:;<=>?@:ABCDEFGHIEJKLMN dR /dZ < 0 OP QRSTUBCD
VLMW@O SXOYFGW@H
Z[O\Q89:;<=E]^_W @[`EBC
Dabcde@Hfghij\k[` lK > 0 mc
0Z r

(2.66)"&'BB$K %)01+-{'!2% 7l7 .$f > 1/γ %f < 1/γ% s34x%&'ν 5 I 6&"K
%

0

1 ∂
[rB(r)] = µ0 J(r)
r ∂r

N q2r
(1 − f − β 2 )2πa2 ε0


1
2νr
2
m0 c
−f
a2
γ2

2 2

′′

(2.63)

 ,& sBB $B %  x'L !23'
( J = J(r)ẑ  %& % φ & #1!
$B = B(r)φ̂ yz&''( Maxwell}~ &"

0"&'
1%&/0iyz&'r = a
r=a"r = r̈/β c 45%&"$R√
4 2ε0√(−q)3/2
9q m0"&'2X q $( βc !/0=%&V&+ N!+,-#!. N+% (2.65)  β N q r/2πa ε "&'(2.62) "/#*¤:&" r ! }~%

yz&'z = 0 st = 0 x! ,- a"#$1

0

R=
Z=

Q"$(2.67) %

√

a
a0

2K

(2.69)
za0(2.70)

& '{3 "( $!(% 1,&'& '{3!23 )!S"*#!9
+% "
ωp2
ωc2
2νc2
2
ΩL =
=
= 2
4

dZ

=
2

1
2R

"&'s2.3) $s2.6) "Ω !~ s2.10) V .

(2.71)

1? &"$ dR /dZ !
=#$R  Z !1 "# &B"7 N&'
= #1? -!7 2.3  ,R = 1&'|w1m sdR /dZ=0 x  N- "N$%p2XV .l7&B"7¤1&' +$ # z-2 sdR /dZ < 0 x$) ,-%8+&&7% p2X#l7#P QB"
7¤1&'
]^_`ag
2.2.4
BP $E yz& *% !
+jk." #N-! $% ,- 0! #-' BB% $ ! +7
k! *yz&'-#S
 #$( θ̇ 7)!;<=>?yz&'D#$p2X#$E V&+,-#7i .,$r %J+"
Q!7!  ,&'(2.71)

000(2.10)

r+nq 2 r+ qBz r θ̇ = 0(2.72)1
θ̇ 2 + ωp2 − 2θ̇ΩL = 02(2.73)

r(2.74)

2ε0"(2.40)  (2.72)  N% ""&'!!(%θ̇ = ΩL ±1Ω2L − ωp22

"&'Ω > ω /w !2$!(%#,.$Ω < ω /w !2% "#
2"!m$%%/Z #'Ω = ω /√2 ! *
2
L

2
p

2
L

2
p

L

p

θ̇ = ΩL



s

ωp2
2πPθ
=
2
q
2ΩL

Ψ0
1−
Ψ



(2.76)

7&'(2.76) "(2.74) G,%&"$

0m0(2.75)aL

d2 R

r 2 θ̇ 22

Ψ0 = ∓Ψ 1 −(2.77)"&'2 i !-.% (2.9) 6-'$20! z !(/ &',- r
!!"#  γ $r = 0 !!"#  γ"%&"$(2.50) V .γ − γ = νr /a "&';<=>?23 $|w1m7
&&"N$
0

2

0

2

1 2
r2
2
(βz + βθ2 − βz0
)=ν 2
2
a

(2.78)"&'β % r = 0 !/0! z 011($β $β % r !/0! z $θ !011(%'β = rθ̇/c "ν = a ω /4c [(2.40) V .]
45%&"$(2.78) %
z0

z

θ

2 2
p

θ

2
βz2 − βz0=r2 2
(ω − 2θ̇ 2 )
2c2 p

2

(2.79)"&'ω = 2θ̇ q $z !(2S-!7,&B"&'(2.74) "3GH &"$&
'{3!2374-+& "N$z !
(7)2S-!7 &&B"7¤1&';<=>?& '{3!23% $X2/0
1'( "KI z5q&¤q%' " Q!
s2.75 x%RSTU67$& '{3!23%18/%&! $X2/01'(I5% "R
STU67179& .(7 IJ%&'θ!(I:$z !(; "&! $<?23;%7= &B"&'X2/01!IJV&23I"$z !(!;>V&23;!2S.237P &'2
p2

!! "%& "$V .;<=>?!
(2.47) $(2.36) $(2.75)
*% $
φa

φa
φ0

=
=

"&'z

1 2
2
(β + βθa)2 z
1 2(β + 2ν)
2 z

=

1
2




a2 Ω2L2
βz + 2βz ="&'23%(2.80)

2φa
− 2ν
φ0

(2.81)(2.82)

 ,&'(2.82)  ν %&" ν = 2φ /3φ !
2237 ."&'(2.82) 45%& "$.
23aI(φa )3/2

16πε√ √0 (−qφa )3/2
3 6q m0= −25.4 × 10−6 [AV−3/2 ] ((2.86)

x(s) = ax0 + bx′0(2.87)x′ (s) = cx0 + dx′0

(2.88)

4-%'S %6 ? #! 1 6 %'!
Yo ,T & "N$x " y !
 #7 "&- $# $ . Q7 ,&7 $%%! R '&7 *$ '(>7 6 N&! $)*% x ! !9yz$κ (s) = κ(s) "%&'
+ 2 $! }~ (2.84) ! % $ 
7 P&'! $ s (x , x )
%q&%
0

′
0

0

20x

"&',~% "X(s) =x(s)x′ (s)

!

=

a b
c d

!

(2.83)

7&'


S% %1$u*
u !9F%&7 $. N+7,&";S"&'B!% $! +! 5%&! ,&; S
 Q'

2.3

2.3.1

κx,y (s + S) = κx,y (s)x

I = qβcN = I0 νβzr2p= I0 ν
φa − φ0 ν
φ0

I =

x,y

c

!(%
s

"&'BB $s % z V .)0?1 $! %' 27/Z%&J  6 N&1 ,&' B
B% $RSu% s !%'κ (s) %Courant Snyder

6 ? #! ,& iyz&'x, y! }~% $6 ? #%1 κ(s) "#
x′′ + κx (s)x = 0(2.84)y ′′ + κy (s)y = 0(2.85)= M̃ (s|s0 )X(s0 )x(s0 )x′ (s0 )!

(2.89)"&'/0 7- ,&- % $x(s) 7uR V ..8+7,&' B!2
3% $/0, [M̃ (s|s )] 7uR%12 V . 8+q4-+&' B!-!23 &- $ 3 }~0N

M̃ X = λX(2.90)

ax0 + bx′0 = λx0(2.91)

cx0 + dx′0 = λx′0(2.92)

 &'B!~%45  X !.N+qz& }~ $" .$λ2 − λ(a + d) + (ad − bc) = 0

4-%7,&'(2.93)

$$/0, M̃ ! determinant 7. 1 "&B" %- +!{ sWronskian x
yz& [17]'(2.84) ! 2 i! u(s) $v(s) "%&"$+!{%
u(s) v(s)u′ (s) v ′ (s)"&'Tr M̃ < 2 !2 σ %1$Tr M̃ > 2 !2
1 % 1 "&'σ%/0, M̃  σ 6%- $S*+ α̂ $β̂ $γ̂ $!V Q5%&'= u(s)v ′ (s) − v(s)u′ (s)a − d = 2α̂ sin σ(2.102)

+&'W (s)  s  #$(2.84) 6&"

b = β̂ sin σ(2.103)c = −γ̂ sin σ(2.104)

W (s) =

(2.94)dW (s)= u(s)v ′′ (s) − v(s)u′′ (s) = 0
ds(2.95)"&'iP .$(2.84) 74-+  & "N$81 ,&'(2.84) ! "W (s) % s
# Cu(s),Cv(s) sC %1x ,&! $W (s)! &B"7 N&'/07 s 1s  #- "N$(2.84) !
 u(s ) $v(s )  %&'u(s ) $v(s ) %B! /0, M̃ 6% "
1

1

2

1

2

u(s2 ) v(s2 )u′ (s2 ) v ′ (s2 )

!

= M̃

2

!

u(s1 ) v(s1 )u′ (s1 ) v ′ (s1 )(2.96)"&'(2.96) ! ! determinant % $¥!
!r- #! $determinant
W (s2 ) = det(M̃ )W (s1 )(2.97)"&'W (s) % )! W (s ) = W (s ) ,.$2det(M̃ ) = 1

1(2.98)"&'(2.98) 7& .i!% $(2.84) 7& .i*!9 ,&B"%&'1$(2.93) %(2.98)
λ2 − λ(a + d) + 1 = 0(2.99)"&' BB $S*+ σ $!V Q
%&'(2.99)

1
1
cos σ = (a + d) = TrM̃2
2

(2.100)λ1 = eiσ ,(2.101)!%

λ2 = e−iσ/0, M̃ %!
cos σ + α̂ sin σβ̂ sin σ−γ̂ sin σ
cos σ − α̂ sin σ(2.105)M̃ ="&'(2.105)  Nz&"M̃ = I˜ cos σ + J˜ sin σ(2.106)"&'BB $
I˜ =

1 0
0 1

!

J˜ =

,

α̂
β̂
−γ̂ −α̂-'det M̃ = 1 ! $!

β̂γ̂ − α̂2 = 1(2.107)(2.108)"&'I˜ = I˜$J˜ = −I˜!$(2.106) % e ="  ! i'! $cos σ + i sin σ '
2

M̃ N

2

iσ

= (I˜ cos σ + J˜ sin σ)N= I˜ cos N σ + J˜ sin N σ(2.109)|TrM̃ | = |a + d| < 2(2.110)"&'N 6 !   &/0 % $7 1!2!9- ,&'(2.100)  Q"σ 
7-23"&'α̂ $β̂ $γ̂ % Twiss S*+" $ β̂ %4+1 Q'!  λ [(2.101) ] =%&3
(2.90) 3
 u(s) "%&"$1 6 !)%1u(s + S) = eiσ u(s)(2.111)u(s) = eiσs/S Z(s)(2.112)"&'u(s) 6 1 Z(s+S) = Z(s) 6

"%&B"7 N&' BB $7&'(2.121) r#

Z(s) = |Z(s)|eiφ(s) = ω(s)eiφ̂(s)"%&"$(2.112) %u(s) = ω(s)eiψ(s) ,ψ(s) = σ(2.113)s+ φ̂(s) (2.114)
S"1q&'φ̂(s + S) = φ̂(s) + 2πn  ,.$1 6!)<9% ∆ψ = σ + 2πn  ,&'(2.114) !
K % 3 λ = λ ! 3 ,.$2

ω(s)2 ψ ′ (s) = C

7& .i'BB C %1 $ B"
7 N&'(2.114) 11q-!  (2.84) !
  ,&-  ,&'C = 1 "%& " (2.128) +&V Q ω(s) 74+1 "&'(2.122)
 (2.120) 45%&"∗1v(s) = ω(s)e−iψ(s)(2.115)"&'!% (2.114) "(2.115) !+<*(2.84)
V+ $x(s) = Aω(s) cos[ψ(s) + ψ0 ]

ω ′′ + κω −"&'(2.117) )*$ψ,ω,x 7 s !1 ,&B",1+P # *7,&7 $~7*& .%&!  Q-  $ B%9$ 
 N-'x  s %&"(2.117)= Aω(s) cos[ψ(s) + ψ0 ] cos σ−Aω(s) sin[ψ(s) + ψ0 ] sin σ"&'(2.124) %&"2−A(2ω ′ ψ ′ + ωψ ′′ ) sin(ψ + ψ0 )(2.118)"&'(2.116) "(2.118)  (2.84) 45%&"$(ω ′′ − ψ ′2 ω + κω) cos(ψ + ψ0 )−(2ω ′ ψ ′ + ωψ ′′ ) sin(ψ + ψ0 ) = 0(2.119)"&'(2.119) 7! ψ i& .i231$0

ω ′′ − ψ ′2 ω + κω = 0(2.120)2ω ′ ψ ′ + ωψ ′′ = 0(2.121)(2.124)x′ (s + S) = Aω ′ (s) cos[ψ(s) + ψ0 ] cos σ−Aω(s)ψ ′ (s) sin[ψ(s) + ψ0 ] cos σ−Aω ′ (s) sin[ψ(s) + ψ0 ] sin σ−Aω(s)ψ ′ (s) cos[ψ(s) + ψ0 ] sin σ′x′′ (s) = A(ω ′′ − ωψ ′ ) cos(ψ + ψ0 )(2.123)x(s + S) = Aω(s) cos[ψ(s) + σ + ψ0 ]

0x′ (s) = Aω ′ cos(ψ + ψ0 ) − Aωψ ′ sin(ψ + ψ0 )

1
=0
ω3

7&'
11 6 ! s + S %q&'(% $(2.116)
sV.

(2.116)"1q&'BB $A "ψ %1 ,&'A = 1!2$ω(s) %!4 +R%'x  s 
%&"$(2.122)(2.125)"&'(2.116) "(2.117) 7 X(s) #$(2.124)"(2.125) 7 X(s + S) %'B! 2 i!45  </0, M̂ )*%&"
M̂ =

!
ω′
sin σ
cos σ − ωψ′ sin σψ′ω′− ψ ′ + ψ1′ sin σ cos σ + ωψ′ sin σ(2.126)"&'(2.126) % (2.105) +&/0, M̃"'(! $α̂ = −

ω′= −ωω ′
ωψ ′

1
= ω2
ψ′
1
1
γ̂ = ψ ′ + ′ = ω 2 + 2
ψ
ω

β̂ =

(2.127)(2.128)(2.129)"&'BB $(2.122)  C = 1 "K-'1 1! #$"(2.116) (2.117)
6 &"(2.122)x2+ (ωx′ − ω ′ x)2 = A2
ω2

x’
x’max= γε(2.130)"&'(2.130) % (2.127) $(2.128) $(2.129) 6γ̂x2 + 2α̂xx′ + β̂x′2 = A2

(2.131)"&'(2.131) %%~ ,.$5
N% α̂ $β̂ P &'α̂ "β̂ % ω(s) "ω (s) P.$ω(s) % (2.123) ! QB"1$!/0=#K !i') $!. N+ & A %/0V" ¤
' '( A i7 "&  ψ i/0
+&'!
% $ '((2.131)
% $'( $"&. N+i!Y*¤:%&B"7 N&'.! A
 A "%& "$!/0%nr A π !+/Z%&'!nr!~ V .$(2.131) !
nr%

xmax= βεbeamcentroid

x

′

0

2
0

0

πA2 (β̂γ̂ − α̂2 ) = πA2(2.132)

+&' BB $(2.108) 6-'A = A!nr

0

A20 π = ǫx π

(2.133)" #$ǫ ! +" '(2.131) 45#$(2.133)  Q"$
A=A
x

0

2

′

′2

γ̂x + 2α̂xx + β̂x = ǫx

(2.134)"&'(2.134) +& α < 0 = #
 2.4  %'α > 0 ! *% $*L " L!
7 %&'(2.134) 1$,& x != # x%"& 2 i!$. N %′x=−α̂x′ +pγ̂γ̂ǫx − x′2(2.135)"&'¥ x %&"x = α̂ ǫ /β̂ !
2$x 7.
′xm (s) =q′ǫx β̂(s) =√ǫx ω(s)q2x(2.136)

 2.4: (2.131) +&)<p'
"&B"7¤1&'(2.136)  (2.123) 45%&"$!4 +R !~x′′m + κxm −

ǫ2x
=0
x3m

(2.137)

7&'
p2X% (2.67) "! +!
% (2.137) L }~ (2.34) J
z$!!4 +R }~ & "$
 ′′

Ω2L
γ ′ a′
γa + 2 ++aβ γ
2β 2 γ β 2 c2
2

Pθ
1
K
ǫ2n
−
−
+
κa
−
= 0
βγm0 ca3aa3 γ 2 β 2(2.138)′′"&'BB $!"#011+
-! +ǫn = βγǫ

(2.139) #-'γ = 1/p1 − β % +,- 0'" (2.115) !+ <* (2.116) % (2.114)+&! $!) s 1  s ! /0, M̃ (s |s ) % (2.96) 1 1 &'(2.96) 45#$¥!£i !,!
(2.114) $(2.115)
2

1

2

1

2

+&'x  #-/0!)<p/% (2.134) !+) "%&' ,& x√!= # √≤x ≤"&B"6 &",1q&"$M̃ !,ω2
cos ψ12 − ω2 ω1′ sin ψ12
ω1= ω1 ω2 sin ψ12
1 + ω1 ω2 ω1′ ω2′= −sin ψ12ω ω
 ′ 1 2′ 
ω1 ω2
−
−
cos ψ12ω2 ω1
ω1=
cos ψ12 + ω1 ω2′ sin ψ12
ω2

m11 =
m12
m21

m22

hx2 i =

(2.140)7&'BB $ω = ω(s ) $ω = ω(s ) $"#-'s − s = S !2$ψ = ψ(s ) − ψ(s )" .$(2.140) %ω = ω $ω = ω $ψ = σ"- #&&'(2.122) V .)<%
(2.126)
1

12

2

2

1
′
1

′
2

1

1

2

2

2

1

12

Z s

ds
ψ(s) ==
2s0 ω (s)

Z s

σ=

ds
ω 2 (s)=ds(2.142)"&' J !6* C "%&"$1 6,-.!4+ +! 1%4 "&7s

+&'

1
ν=
2π

s

Z s+C
s

β̂

(2.143)

β̂

rms

ǫ̃x =

p

hx2 ihx′2 i − hxx′ i2(2.144)6 &B"7 ' B $ǫ̃ "ǫ ! &'BB $/0/ f (x, y, x , y ) 6 &"hx i %
x

x

′

′

2

RRRR 2x f (x, y, x′ , y ′ )dxdydx′ dy ′hx i = R R R R
f (x, y, x′ , y ′ )dxdydx′ dy ′(2.145)2−(β̂ǫx

)1/2

2 1/2

x2 (β̂ǫx −x )R (β̂ǫx )1/2

β̂

(β̂ǫx

−(β̂ǫx )1/2

−x2 )1/2
β̂

dx
=

dx

"&'hx i i '$β̂ǫx −x2β̂β̂ǫx
4(2.146)′2

R (γ̂ǫ )1/2
′2 )1/2dx′
2 −(γ̂ǫx )1/2 x′2 (γ̂ǫx −x
γ̂
γ̂ǫx
x
hx′2 i ==R (γ̂ǫx )1/2 (γ̂ǫx −x2 )1/2
42 −(γ̂ǫ )1/2
dxγ̂x
(2.147)" .$hxx i %′hxx′ i =R (β̂ǫx )1/2−(β̂ǫx )1/2

= −

2

α̂ǫx
4

x

R −α̂x+(β̂ǫβ̂x −x )−α̂x−(β̂ǫx −x2 )1/2
β̂

R (β̂ǫx )1/2−(β̂ǫx )1/2

x′ dx′(β̂ǫx −x2 )1/2
dx
β̂

(2.148)"&'(2.146) $(2.147) $(2.148)  (2.144) 4
5%&"$
ǫ̃x =

ǫx
(2.149)4
ǫx = 1πmm-mrad

7&'! +
%$


"

!
+
rms
,&B"7¤1&'ǫ = 1 mm-mradxds
! Q"N$! 4 +R!! +% &$rms ! +

2.3.2

R (β̂ǫx )1/2

2

(2.141)

s0 β̂

Z s+S

2

−α̂x+

′

2 1/2

ds

"&'1 ",-.!)<!9 (phase advance)%
Z s+Sβ̂ǫx −x2β̂−α̂x− 
p2X#7&! +7?
i $ w ' p!)<p/1 2.5  %' w' p s+ x s+ x$x %./+ $x !91# &' 2.6 !V Q2024. Su # $Su% '()<p/1 %'"B7 $p2X7?&93 523i2024%7 "&'202
4!2pR +u7 7! *$ Su!23'(7 " .$)<pM"
&2p % [22]'
2.4

′

x’

r’
bunch sliceζx

initial 2.5: ! +7?! w' p s+ x s+ x!)<p/
bunch sliceζ 2.6: 2024!2pR +u  .
#-2024 Su 24 +!'( ζ 
8/ #23'(7 " '.$p2X#7 ζ 8/%&'
p2X#7?20! }~% $
45#
(2.66) r = r̈/β c $(2.42) $f = 0
2 2′′

r ′′ =2I(ζ)
r
I0 β 3 γ 3 a2

(2.150)" P &' BB $I(ζ) %2024 +!'( ζV .237"&B" % s 2.6 x'!- p2X#%20! '(( z V)"#$ '( r "I(ζ) P&"%&'(2.150) % r G%&! $+
p2X# ,&'B!% /0 C
!uT7.N&1#q & .i'P-$!-  m20 sr = 0 x
(
%&'B!!$z ! r "'( r  &"$
0

′
0

′

r ′ = λs (ζ)r0 z,

r = r0 +λs (ζ) 2
r0 z
2(2.151)r

 2.7: 2024 Su!2p'  r = 0 %&"$p2X#V .20
24%%& s 2.3 x''(24 S
u +!20%)<p + '(+ M&7 $"&Su%%%"&2p %'
p2X#!F7  ,&'"&'BB $p2X#%1
′
0

2I(ζ)
I0 β 3 γ 3 a2

(2.152)r′
λs (ζ)z=r
1 + λs (ζ) z 2(2.153)λs (ζ) = #-'(2.151) 1"&'(2.153) % r 8/ #B"1$)<pMR +%&"+ & s 2.7 )' #(IJ1 ,.$I(ζ)(2.153) % I(ζ)
7.N}$ N&'(2.151) V .I(ζ)
7 . N}$l-&' 2.6 !2
4 Suiyz& "$ 2.7 !V Q2p %'"&23'(iSu% $)<pM"&2p %'
 2.7 % $  0 " # &!
 $ ! +7 0  ,&B"%&'w ' p!)<p/7+ M
&B"% $ Su! +7 0 !PP./+ &B" %' "B7 $202
4% ! +%I z- V Q3z&')*$ k.$! +%! +!B" %'(2.150)  %+p2X#V .31qMIz- ! +20% $20 3 #- |,u w  N& s 2.8 x'r’

solenoid
E-gun

slit for emittancemeasurementrcathodee-bunch
anode
Ls

z1

0

z2

z

 2.8: 20 1!!! +'{ w3 z  #- |,u w !
 (%&B" $z )!! +7 N&'|,u w %  !Yo ,T!VQ$= # 6i B"
7  &' % !
+- [20]',T ! $'(G#- # z&B"7
N&' |,u w5!)$ r ,r"#!)$ r ,r "%&"
1

2

in

out

′
′
rout
= rin
−

"&'BB $

rin
,
f

1
1
=
f
4

′
in

′
out

rout = rin(2.154)

 2.9: |,u w6V&)<p+!24Su!W '(2.154)  %V Q  # z  )<p$+2 4 Su  5W $+:&B"7 N&'B!#%,- r G # &'"&24 Su!)<p/%+ |,u w! w ' p57%%
$%
7 Y .,Q'31qMl7-! +7&'V.
(2.151)′rin= λs (ζ)r0 z1 ,rin = r0 +"&'(2.156)  (2.154) 45 #$+|,u w! w' p C!'( z 
′

′
rout
+

r (z) =
 2e
Bs2 Lsp(2.155)

 ,& [23]'|,u w%*+ L )
( B i "#$R!  "%&'
 ! %'B! |,u w 
p % 
V .$2024%)z71%&! 5q&' 2.9  %V Q$)<
p + r G #- ! 5 z $
W %&' |,u w! w ' p $"&24 Su%%%7 Y .,QV Q
 &'
- B"V .?>%&' |,MuH){ w!
w31  z "%& "$ss1

λs (ζ)
r0 z12 (2.156)
2

r(z) = rout +

Z z
Zz1z

λs (ζ)r0 dz
r ′ (z)dz(2.157)"&B"1$! + Q) z
%
z1

2

1 + λs2(ζ) z12
λs (ζ)z2 −fr ′ (z2 ) = r0hλs (ζ) 2r(z2 ) = r0 1 +z
2 2i
1 + λs2(ζ) z12−(z2 − z1 )f!

(2.158)"&'r (z )/r(z ) 7 λ (ζ) 8)"& (|,u w z- "N$ Su! + %+ % $ ')+ M &'
′

2

2

s

! +% 8! " .$!
iP.$7
+&B"&' B $+"&23% ζ $ζ = #r (z )/r(z ) $!F)*%&"
′

2

2

1

2

r ′ (z2 , ζ2 ) r ′ (z2 , ζ1 )−r(z2 , ζ2 )r(z2 , ζ1 )=λs (ζ2 )z2 −1+2) 2
1 + λs (ζ2 z2 −−1+λs (ζ2 ) 2z1
2f

λs (ζ2 ) 2z1
2f

λs (ζ1 )z2 −1+
1) 2
1 + λs (ζ2 z2 −(z2 − z1 )λ (ζ )
1+ s 2 1 z12f

λs (ζ1 ) 2z1
2f(z2 − z1 )(2.159)"&'(2.159) !¥!07 +&23
&"(z2 − z1 )2[λs (ζ2 ) − λs (ζ1 )] z2 −2f"&'(2.160) 1
f=(z2 − z1 )22z2

= 0 (2.160)(2.161)"&V Q| ,u w !%& "$!7 ζ 8- #&.$)
r (z )/r(z )%! +7+&B"
z
&'(2.161)  (2.158) 45%&"
′

2

2

2

r ′ (z2 )2z2= 2r(z2 )
z2 − z12(2.162)".$ζ 8/ #'! +7+&)<p +!2024!N% $.
|,u w) "! +)!
1 ,&B"7¤1&'
BB% $ 2024!7 +$20
24,-7.1 #B"$ &i1!  &' V .)0? *$;+
7,& *!! +I.i%
 [22, 24] +-'Parmela -)*+
w [19]  [25, 26] !"#$%& ' RF ()*+ , "-./& '012.34 "56789 :;<=

 >?@A BC"#56DE RF F & '012.34 "GHIJK7LM
NO";PQ !" [1, 27]#RF F.R" >?
@A/*6$SM.R"@A TU VW
X1YZ F [\]^_ "C  Q`"#abcde f` \ [19]#ijghkl OHO mn o.$%pqrs ct
uvwu=x Py\ "#CyPzmno[28,/ .ERL $%|.}~ !"/z 24] {;Pz$%pq >?;P
z$%pq >?.\ . "#3.1  
zc Q !" <Q4{  ¡.&¢£¤z¥ ¦§¨y "©ª« ¬dispenser cath[z¯ V° Y[\ Pyode ­X ® FEL
\ " CeB LaB  [13] ±U²4?1³
cµ%M¶· FEL ¸A FEL ¹!" [28]#Q´º[¨y3.1
\ " dispenser cathode Q(FELI) ±
!"#
3

6

6

»¼½¾¿
´ 3.2 .9_RÀ.ÁzÂÃ$% ÄÅ.
Æ −w zÇÈ ÉÊË°{§Ì0K zÍÎÊÏÇ µ cÄÅRu/ φ Ð\ÑmÒÓÊQ !"_ " [29, 28]#$%c ÍÎÊ ÔÕ.Ö ÀzQ ×ØQcÄÅRu×\ ÉÊË° {§$%/E
Ù_ "#Cz RÀ4$%c ¡;PÄÅ.q "C  Q`“¯ V° Y” $%|.
Úy "#CCQc ØÛ T zFÜz$%pq$Ý{Þß"#
z6. ÉÊË°ÏÇ {/à%á
ε ε + ∆εâzã { D(ε)∆ε B `ε zà%zEÙäå {_ " ÉÊË° ε < E zÁ$%
f (ε)
3.1.1

0

Q !"#CCQ ε = (p + p + p )/2m#% 2
c$%.R"#(3.3) { (3.1) ._ "
2
x

N

2
y

2
z

Z ∞
Z ∞
Z ∞
Z ∞
2
=
dpx
dx
dpy
dy
h3 −∞
−∞
−∞
−∞
Z ∞
Z ∞
1
×
dpz
dz (ε−µ)/kT
(3.4)
e
+1
−∞
−∞

4 "#CCQ ε c 0 ≤ ε ≤ E { _#¡;P¨ dz z$% ∆t 56. ¡.
_ ".c  ∆t ≥ dz { _ !"# ¡._ "$%.Æ_ "dz .}_ "Ôc;P ∆t 4 "#x y HIzÔ{ 0 ;0P∆x 0 ;P∆y   Ç56 Ç¡ !
u. ¡._ "$%ã
pz
m

pz
m

´ 3.1: ©ª« ¬dispenser cathode ­#Y646B
 # Ázzc 8mm #>EIMACÒáz ¢>Y$ ¡;P0.1 mm z. È¨y\ "# ¢>Yz$ÇcÄ T #vacuumφωN
2= 3∆t∆x∆yh1pz
dpx dpy dpz(ε−µ)/kT
me
+1
(3.5)

Þ "#
¡. $%z ÀÌ Ru/×\ ÉÊË° { z HI.§$%z! " * Á.
q "#Ö# > w { _$%z! p
q$% 4 "#E → ∞ _ " Ç56 Ç¡ ! u.pq¨y "$%ã N c
p2z
2m

µ0

rad

Nrad

metal

´ 3.2: Áz ÂÃ$%zÄÅ zpq#
ãc
N=

Z Z Z

Z E

f (ε)D(ε)dε

(3.1)

1
e(ε−µ)/kT + 1(3.2)

4 "#CCQ D(ε) cáâ Û#$%c ÍÎÊ
à%4zQ EÙäåc ÍÎÊ ÔÕ0

f (ε) =

.ÖÀ#ε c$%z ÉÊË°µ cØÛ T QzÍÎÊ ÏÇ #kT ≪ µ z5c µ ≈ µ 4 "#$%z ÉÊË° ε Qzáâ Ûc
0

0

Z
Z ∞
Z ∞
2 dh ∞
D(ε) =
dpx
dx
dpy
h3 dε −∞
−∞
−∞
Z ∞
Z ∞
Z ∞ i
×
dy
dpz
dz
(3.3)
−∞

−∞

−∞

Z ∞

Z
pz ∞
2
=
dpz
dpx
h3 √2mw
m −∞
Z ∞
1
×
dpy (ε−µ)/kT
(3.6)
e
+1
−∞

4 "#p + p = p B\ (3.6) {$ `
_
2
x

Nrad

2
y

′2

Z ∞
2
pz
=
dpz
√
3
h
m
Z ∞2mw1×2πp′ dp′ p2 +p′2
(3.7)
z
( 2m −µ)/kT
0
e
+
1
Z
h
i
p2
4π ∞
z )/kT(µ− 2m
=
dp
p
ln
1
+
e
z
z
h3 √2mwZhi
4πmkT ∞(µ−εz )/kT
dε
ln
1
+
e
=
z
h3
w
(3.8)

4 "#CCQ µ(T ) ≈ µ ε = p /2m#z%ØÛc × / 3000K &Û ! ukT =Û.;4P4\#'Hz()}0.26eV &ãc eV &Û*= !"zQ w − µ = φ ≫ kT
0

2
z

z

0

uÌ eãc ln[1 + ec(3.8)

4 "#(3.7) zÔ}Q`"#]≈e(µ−εz )/kT ≪ 1(µ−εz )/kT(µ−εz )/kT

4πm(kT )2 (µ−w)/kTeh3
4πm(kT )2 −φ/kTeh3

Nrad ==

V (z) = w −Q ¨y "# Cyc

4u Ç¡ uz$%pq$Ýc
I=

4πmek2h3

T 2 e−φ/kT

4 " #CC Q 4πmek /h
10 [Am K ] #
2

6

−2

3

(3.9)

(3.10)=

1.20 ×−2


3.1.2 Shottky A$Ý ¯ V° Y$  z ØÛQ  uQ ¨y "FÜ ØÛ#Ø(3.10)
Û
Qc ¡.$ ( Ú " $Ý@( _ "# Cz{ Shottky   [28]#
A
φ
ω

φ’

EF C

1
4πε0

r

(3.12)e
πε0 F

eVmax = w −2

r(3.13)eF
πε0(3.14)

4 "#ÑmÒÓÊ , u$%pq-..4 "C {/0_ "#$%pqz1(
)}ãc
e
φ =φ−
2
′

r

eF
πε0

(3.15)

4 "#(3.14) {[\ (3.10) {$ `_ 
4πmek2 2 −φ/kT
I=
T e
exp
h3

e
2kT

4 "#

r

eF
πε0

!
(3.16)»¼½2345678$ `_ (3.7) {z

4πm
Nrad = 3
h

e2
e2 1
′
dz
=
−
(2z ′ )216πε z(3.11)

4 "#z c$% ¡ z&'ε c" *z($å# Cz5ÑmÒÓÊc´ 3.3 z ® A
4 "# ¨P.® B Q )¨y "( $.
z

QA

3.1.3

µ0

Z ∞

e2 1
− eF z16πε0 z1z=4B

´ 3.3: ( $Å.R"¡zÑmÒÓÊ
#® A c®B c >Ò®C c® #$%pq._$z{O" ß¡ zÑmÒÓÊ {O"#;Pz$%pq.Ru ¬ ­¡zÆ .!"$
S {# "#pq$% !"$S z6.c P
$°%M.R"ÑmÒÓÊc−R"ÑmÒÓÊ −eF z {*_ "+ÑmÒÓÊ C c

0

Z ∞

dεz

w

Z ∞
0

′

e−(εz +ε −µ)/kT
dε −(ε +ε′ −µ)/kT
e z+1(3.17)′

4 "#CCQε = p /2m ε = p /2m {9#:#¡.;<4HIz=ÉÊË°z;> c
′

′2

z

2
z

Z ∞
4πm
hε i =
dεz(3.18)
h3 Nrad w
Z ∞−(εz +ε′ −µ)/kT′ ′ e×dε ε −(ε +ε′ −µ)/kT
e z
+1
0
′

4 "#w − µ = φ ≫ kT ;Pε + ε − µ ≥u#Cy {9 À(3.18) c
w − µ ≫ kT
z

′

Z ∞
4πm
hε i =dεzh3 Nrad w
Z ∞′×dε′ ε′ e−(εz +ε −µ)/kT
′

0

=

4πm
(kT )3 e−(w−µ)/kT
h3 Nrad(3.19)

4 "#(3.9) {_ " (3.19) chε′ i = kT

(3.20)

kT2(3.21)

4 "#CCQ :zcGHIz=ÉÊË°z;>Q !"#x y HI.T (ε + ε )=ÉÊË° {§ _ " x HIz=ÉÊË°z;>cxyhεx i =

4 "#=>?{ ".c hx i { "!"#x9#=v /v = (2ε /m)/c β Q !"zQ(3.21) {
′2

2
x

′2

2
z

2 2

′
x

hx′2 i =kT
mc2 β 2

(3.22)

4 "# r z¯ V° Y.'U.$% ÔÕ\ " _ " x HI. :$%zãc
p._ "#2 ;> hx i {
2 r − x /πr
_ "
p
c

2

2
c

hx2 i =

Z rc

2
c

2

2 rc2 − x2 2
r2
x dx = c
2
πrc
4
−rc

(3.23)

r(3.24)´ 3.4: GaAs #¨0.35mm z£Î{1ÍQ uq  9[_ "#  8mm
znÓ>³ {; "C .Ru 9O"{ \ "#¼½¾¿
3.2.1 

4 "#(2.144) Q¨y " rms =>?c
rc
ǫ̃x =
2β

4 "#=ÉÊË°Qcǫ̃nx =

rc γ
2

kT
mc2

¨y: rms = >?

r

kT
mc2
γ ≈1

(3.25)

4zQ (3.25)
Q !"#¯ V° Y Qc
Q γ = 1 : ) \#
 14 SPring-8 Q7¨y\ "ÂÃ$% W°°[z$%| !" [13]#X®
 3mm ØÛ 1400 C z CeB {9[\=>?zc 0.4mm"# Q  rms
c 1.1mm-mrad Q ! u;4mrad !"#
u\ { \ "#$%|cØÛQ%¨y\ "#
◦

6


.c 4z GaAs Cs-Te ±z¯ V° Y [\ Py "#´¯3.4 c³ % o?
1³$%|.9Úy\ " GaAs V° Y#

3.2

photonhνhν0´ 3.5: z$%pq#.$%pqT {<À#W°°
1z=ÉÊË° {$% J_ " ÑmÒÓÊ hν Ð 4#: !4_#(3.7) z w {.È `O 
w − hν
Nrad =

Z ∞
Z
2
pz ∞
dp
2πp′ dp′zh3 √2m(w−hν)
m 0
×

1

p2 +p′2( z2m −µ)/kTe

4 "#p zÔ{< À(3.26)+1′

4πmkT
Nrad =
h3

Z ∞

w−hν

h
i
dεz ln 1 + e(µ−εz )/kT

4 "#(3.27) zÔz, { 0 ._ ":ß(3.27)Ôã{ y = [ε − µ + h(ν − ν )]/kT _ "
z

0

4πmk2 T 2
3
Zh

Nrad =

×

∞

0

h
i
dy ln 1 + e−y+h(ν−ν0 )/kT

4πmk2 T 2
f (δ)
h3

=

4 "#CCQ δ = h(ν − ν )/kT Q:ß [24] (3.32) cu9Úy (4.1) .9!"_ %å (QE)  W°° ° {9#;P Py "$Ý {Þß"z ' 1Q!"#¼½2345678
9#$ `_ (3.17) { w → w − hν {(3.28)

3.2.2(3.29)

Nrad =

0f (δ) =Z ∞hidy ln 1 + eδ−yQ !"#δ ≤ 0 (e
_ "

0

δ−y

f (δ) =

Z ∞z5δ Q f (δ) {8
< 1)

=
=

n

e

dy
(3.30)

4 "#δ ≥ 0 zFÜ.cf (δ) =
=

+

0
Z δ

Z ∞

′2

z

2
z

δ−y

dy ln[1 + e]

δdx ln(1 + e )Z ∞+dx ln(1 + e−x )0Z δ=dx[x + ln(1 + e−x )]z′hε i ==

0+[x ln(1 + e−x )]∞
0
Z ∞

x
+
dx x
e +1
0
∞
2
2
X
π
δ
(−1)n−1 −nδ
+
−
e
=
6
2
n2
n=1

4 "#
$% ° ¤z$Ý Ûc (3.28) ;P

′

z
′

′

′

z

x

4πmek2 2
T f (δ)h3

Q !"#$% ° ¤ # (3.19) Q[\: \ À 9O4\ε + ε − µ ≥ w − µ ≫ kTÆØÛ % (T = 0) z5.c P

y "#CzFÜε + ε − µ > 0 QcÔ}ã
.4uε + ε − µ < 0 QcÔ}ãzÔ
0
 1 .4 "#Ö# ε + ε − µ < 0 zFÜz! {_  (3.34) cz

0

I = eP Nrad = P

01
dε′ (ε +ε′ −µ)/kT
e z+1(3.33)Z ∞4πmhε i =
dεz(3.34)
h3 Nrad w−hνZ ∞1dε′ ε′ (ε +ε′ −µ)/kT
×
e z
+1
0

0

(−1)n−1 nδ
e
n2
n=1

Z δ

w−hν

Z ∞

′

nδ Z ∞
n−1 e
−ny

(−1)

dεz
′

dy ln[1 + eδ−y ]

n=1
∞
X

Z ∞

Q !"#CCQ ε = p /2m ε = p /2m#
¡.;<4HIz=ÉÊË°z;> c

0

∞
X

4πm
h3

Z µ
Z µ−εz4πmdεzdε′ ε′
h3 Nrad w−hν04πm (hν − φ)3(3.35)
Nrad h36

4 "#CCQ ω − µ = φ(´ 3.1 de) {9#\ "#pq$%ã /TU. (3.33) ;P
Nrad =(3.31)=Z
Z µ−εz
4πm µ
dε
dε′
z
h3 w−hν04πm (hν − φ)2(3.36)h32

4 "#(3.36) { (3.35) . (3.32)

4 "# Cyc Fowler zy\ " [28]#c$zäåQ ! uz ¡áPâ.DE_ "#-. P {Þß"zcQhε′ i =hν − φ3

4 "#(3.22) TU. hx i {Þß"(3.37)′2hx′2 i =hν − φ3mc2 β 2(3.38)

4 "#hx i c (3.23) T Q !"zQ rms =>?c
2

rc
ǫ̃x =
2β

r

I[mA] =hν − φ3mc2(3.39)

4 "#.!: u¯ V° YzÆØÛ
(3.39) {%{ :#¯ V° Y ØQ9Úy "C {* .R"GHI=ÉÊË° (3.20) {. ÜÚ  =ÉÊË°z/
(3.37)* :¯ V° Yz rms = >?
rc
ǫ̃x =
2β

Þ " [24]#rhν − φ
kT
+
2
3mc
mc2

(3.40) 
gh.º[Q`" 250kV *=z×$ DC 
ERL
$%| c JAEA ¬­ °ÉÊ A ¬¬ ­[31] T ÎÍ°­[30] ERLP ¬ ­[32] .!" JLab FEL V ¹
Q7  ß Py\ "# zz
CEBAF 5 $%|/Q !" ¢£¤ ¬GaAs ­{ [\ 3 Q:RÀ.$
.Ru()}ã*=z=ÉÊË° (hν) {$%.NO$%{ `q_#
¯ Yc ILC(International Linear ColGaAs V°z$%|./º[¨y "C .4#B
lider)u QcA×=ÉÊË°¹
4u¹7 {ß\ " ¬SP ¹­ .ÁÅ.!"< 50% {#O"
[33, 34] #1991 Û { *$ [35] AÊ°³c Åz$%|z¹{ ¢° YNEA ¡z%&.';4\ “Yo-Yo method” {()_ "± [36] $%|.}_ "X££{ * DC\ "#Qc +,$% ° ¤{[\:
Ð)$%-.! (Spin Polarizedz Low /<#Energy Elec\ "tron Microscopy; SPLEEM) ¹z RÀ4 DC $%|z$Ýc e[37] #C
 W°°z=ÉÊË° °¯ V° Yz
4%å ¬QE:Quantum Efficiency ­;Pλ[nm]· P [W] · QE(%)
124

(4.1)

Q`"# O 527nm z W°° {9#:FÜ100mA z$Ý{ ".c¯V° Y.
/_ "W°° °  QE zc 23.5W% 
4 "# 800nm zFÜc 15.5W% 4 "#a) MetalhνConduction Band
(C.B.)

hν0

Valence Band
(V.B.)DC b) Semi-conductor
C.B.

hν
Forbidden Band (F.B.)

V.B.

´ 4.1:   Áz$%-$%L0#Qc 12z_3=.4 2 !":ß$%-$
%L0 5C"#Qc12z_3=c6
2Q !":ß$%-$%L0c5C P4\# C
y %åz\zµQ !"#[14 W°° °{O"100mA 
.c QE = 10 &Ûzc71Q 
z×\ QE {§ {9 ÀC .
1–10%
4 "#Qc ¯ V° Y¯ V° Yz%åz8c9:.# "zQ !; À; #´[\O" [38]#±zzFÜ (´
4.1 {12 ¬<$%2 =valence band ­;P
4.1a) 
−4

2 ¬4 2 =conduction band ­. 5 ¨y " 5 ¨y:$%c Á{\\ #
<$%2 Ázz$% L0 z$
5%$%2¬4 2 ­. 5_ " $%z{
=ÉÊË°c. hν *,.4 u ¡;Pq
y4 4 "#zFÜ<$%2z_3=.
C
4 2 !":ß$%L0.Ru$%z %å À#Ü (´ 4.1b) <$%2;P'H¨y:$%
zFL0.Ru
z$%{ 5 R
5À /<$%2z_3=c6 2 (forbidden
Q :ßáâ.B\ . 5áâband) !"
.4 "C  Q`4\# $%-$%L0
c5 `  ¡.: z 5$% " * Á.q "C  Q`"#$%L0 B `4\:
ß.Qc×\ %å {Q`"#

p-type GaAs
Vaccum Level (V.L.)
C.B.

χs=4.1eV

F.B.

Εg=1.4eV0
[z$%|z¯V° YGaAs
ERL. ¨y\ "zc JLab FEL QzA$Ý
%z [4] .( O ¨4=>?,+{§$% °¤{# Q`"¯V° YQ !"C Ã
Q !"# yc Negative Electron Affinity (NEA)\ À¯ V° Y ¡z&.5\ "#NEA¡c GaAs . Ò£¤{ _ "C
.Ru _ "#«Y°,z GaAs  &Ê $zp¬ Ò£¤­zÜQc´ 4.2 .9_RÀ.B\zÍÎÊ ÏÇ ±  4 "RÀ.Ü_ " [39]#z&, YËÓ>³=ÉÊË° ¬4 2z
GaAs<$%2zfz8­c E = 1.4 eV Q ! u Ò£¤z$%M ¬Electron Affinity =4 2z" *ÏÇ z=ÉÊË°8 ­c χ =1.9 eV Q !"#  Ò£¤z" *ÏÇ GaAs z4
Czz
uNEA .c4P4\#
¡c&Ru/×4
Ê $ " *Qy\ ":ß&Ê$Ác 34 "#p « GaAs ¡;P¨ dQ Û N QY°,{\ "FÜnÓ ¢
Q !" ¡. ¡$% Ü_"# ¡$%z$S Ûc nÓ ¢z Y°,
4.1

NEA GaAs

g

m

a

Cs

Fermi Level (F.L.)

V.L.

φm=χm=1.9eV
F.L.

V.B.

´ 4.2: &Ê $z p « GaAs  &Ê $zÒ£¤zÜ \zÍÎÊ ÏÇ  
4 "RÀ.Ü_#"B#CzQc GaAs ±z4 
2zzÏÇc Ò£¤z" *ÏÇRu/Ð 4"zQ $%MczQ !"#ÛQ uCz ¡$%.R"Ñm,ÒÓÊcÑ V,H&{ \Þ "#$Fz I`c ¡.q "$% { v_HI4zQ  ¡zÑm,ÒÓÊ , "# Cz& , Y ,,z c N d . AQ&, YËÓ>³=
ÉÊË°zÔ&ÛQ !"#& , Y ,,
zab.\cA !z"#$
d.¨y:\#[37] {&, Y,,: GaAs ¡{ ".c " * ÁQ GaAs {%&  ¡' ¬(­{)l*&._"C Q !"[37, 40]#%&.c( RF  ' :+{[\ " [41]#C
ÀQ`:*&4 p « GaAs ¡c ÍÎÊ ÏÇ
#\ "# C. Ò£¤{  ÍÎ,Ê ÏÇ ! ÀRÀ.Ü_y ´ 4.3 z RÀ.
,z$%M ¬NEA ­ ¡  ¨y "#NEA¡z .\c -. zM 'Q'
 !"\c/u !"; /y4\#014 u
 >³° o:\zQ 9 )2z °ÊYW+.345f<y6\Q !"#¯ Y. W°° {e_ " 
NEA GaAs V°
7z<$%2;P 5¨y:$%c Í
GaAs
8 X,L0{BC4 P9L \  ¬´ 4.4 da2

p-type GaAs

Cs

p-type GaAs

Cs

V.L.

χ<0: NEA

C.B.

C.B.
V.L.

Εg=1.4eVχm=1.9eV

F.L.

F.L.

V.B.

diffusion

escapeV.L.

photoexcitation

hν
F.L.
V.B.

band beding
surface´ 4.3: *&._ "C Q &, Y,,{_ " GaAs ¡. Ò£¤{ µ%¥1.
_ Q  Ò£¤z" *ÏÇ GaAs 
7z4 "C2zzÏÇRu/Ð 4 "#_4ÚÌ$%M ,.4 u NEA ¡  ¨y "#e)#CzÍ8 X,L0.Ru$%c=ÉÊË° {\ÏÇ 4 2zzH., #\ #4°z, #:$%/ ¡z2£Q"=ÉÊËÒ ¤z *ÏÇRu×\=ÉÊË° {§:
ß" * Á.q "C  01Q !"#Ö# 
°z 5=ÉÊË° {×_ "  zÔ
WÉ°ÊË
= °z #:$% ° ¤ # ¨y "#<$%2;P4 2 z 5 850nm z
Y01 W°° {[\ " =ÉÊË° uz ¨\=>?,+z R\ ° ¤{# Q`"#Qz{§ Y01 W°°
(3.40) hν ∼ φ.$% ° ¤z= >{?e_"C,+ { = >?,+.Q,x "C  Q`
:. <" GaAs"¡[42]z#'.
.4 u  4 "#JLabQc" *Û { 10 Torr *, ._ "C Q 
FEL
;P500C . : \ À
1/e
{
100C
{§# ÁQc Í X,L0.Ru4 2
8
NEA GaAsÉ#:$%/9L
4 P
Q = ÊË°z,"*Á.q "C 01Q !"zQ %åc×4 " 56&cuR4\ [38]#−11

surface´ 4.4: NEA GaAS ¯ V° Y.=ÉÊË° hν {§ 5W°°{e_ "GaAs 7Q$%
4 2. 5 ¨y "#$%c Í8 X,L0
4 PGaAs Á{9L \ # ¡.:$%c  Ò£¤z" *ÏÇ GaAs z4 2zÏÇRu/Ð\:ß o,ÉÊQ" *.q "C  Q`"#.z56  %å {9_#NEA
4.1\c \ NEAz[56&z'..\ "C Qã
GaAs {
 [43] !"#$%& ' ()*+,-./0123456789:;
2<=>?@*+A"BCDNEA GaAs
EFGH5IJK LMEFGH'N$
OPQRS' "BC'TUVW 5XYLZ[\ 7] 7"NEA 2^_
`BCEFGH'TUVWa<=>'b=cdV
Wefg L' e2<=>?@*+'#$%& 5hYDa"ij )*k*'lmno* 5g
9pq5r2s'Z["l tuvwx 5R
S 9K  yza{|D2 NEA GaAs?@*+a"g#$%& }l tuvwx 5~
?@*+ "' 
2 NEA BC'D"//f:;

B 4.1: "<=>"NEA <=>' #$%& [38] efZ7" NEA <=> 5 LDef5 D [43]
  (s) QE


 10
10
<=>
Cs Sb 10
0.05<=>
GaAs < 10
0.1
NEA
−15

3

−4

−12

−9

vacuum pumplaser

cathodeinsulator tube

anode

e-bunchhigh voltage circuit 4.5: DC N$ '
 4.5 D DC N$ ' 5K  D DC gN!5"JKD NEA'?@*+5$wx (*n 7)*k* 5
GaAs #%&K  )*k*ijS_ZN$"?@*+
'(*+'N) J*S_ ' " )*k*'+D,-7ZN$.* H/0S_?@*+NaE1 tu23 548'(*+ND578678D9:S_ N;8<=aE
1 tu23Def>?S_' "E1 tu23'~@D"J7ZgN!?@*+'(*+D"JS_
LL a"N$'TU"NEA GaAs 'A
" "E1 tu23's_B_'CD
EFDG8HIDJK
4.2

NEA GaAs

4.2.1

LM

?@*+'a$,wN u2O w
N*+Pw( QR S_ '":S T'NU 5?G$, w"?@*+'(*+
'N)Def?@*+VWDXY7" 2?
@*+BC 5Z [[\ $, w']^_` 5'(*+NXY hYDa^8bcdX
Y a"N$.* HewfgN$.* Hhi*.* Hj$fDkl78$, w^S_ d L
' $, w'XY 5mnZ["XY.* Hj$fD
wf-pn H5qfG^Zf [4, 44] "rsNEG otu a .* Hewfvw'o wf 5x78 5y`K LzD{78|d [34]s'}"X
Y5~cdZ[D D 2kV 'N5 N$
'N!a–100kV 7"$,w5a`K
S_8|d [45]
hY ]^Kd$,wa"TUD]DdxzN$.*H'klDe48.* H'f
D48^S_ d48"5[
KdDaTU5hYdLz8 d *mnuD|8a"20 ' NEG o wf (22,000u(n/ 5?@*+vwD7"gTU
['Q548|dTUa 5×10 Torrd [46]L'TUowf' ;#a"]78|d 250kV f i (v$f N$ ' NEG owf' ;* 2,000 u(n/ ' 10 d
wfa¡D¢£ x5o wfK dZ[DNEG o¤S_"¥ xg NEG o wfBC ^K d P
vw5o wfK dZ[D$, wo wf 5¦K d:;d [47] *mnu a 400 u(n/'$,wo wf 5¤78|d
a 2004 §D'¨©D 2 G'$JLab FEL, wo wf 40 u(n/ ×2  z 3 G' NEG
u(n/ ×3 5=ª 7"TU
o wf 1300 "«
x' 99.9%¢£5[783 × 10 Torr|d [4] +1$¬ )*k*­®¯' ° zL'T
UowfxDef"1/e  5 100 2*iw]±
2 iwDy`KLzD{7ZCEBAF
500 *a 10 ' NEG o wf 5?@*+¨²D³|8|d PuF´F*n +5¤78 "NEG o wf'
NEA GaAS−12−11+DedN5m| |d?@*+¨©'TU]±' x05~ cdZ["JLab FEL a N7Z!"600 C
TU 75| "¢£ 5`78|d [4]*mnu aN$ z?@*+ ne*
dx w)xN5 400 C 100 'TU
7548|d [46]2"TU7'gaf*xN$*x d
4.2.2 NEA GaAs 
0D (Zn) 5 +*f 7Z p  GaAs G
h 5 ª 7"s'CD48$-58:;2$Df drstu' e D!"$5¤|d#$a"%k$w&''(A)GaAs:; df4ZGh'BC5*+,"-«¢".,¢£¢'/$01 23D7"$@f ij(*n D4,5/5Z01 BC' 
GH50 ] 786£78uf 5]9pd L_5:3z| 6£78ufaU;);_ dLz
DedBC'< 5mnZ[ d=D"Gh5> ¬% w?'j u2z@`_ d D'p"
DaSA$wBGH ?@*+5j u2D9
:K dj u2D9:7Z?@*+5C 2*DwE"¢£ 2*DwE7Z!"N$D FK d¢£ 2*DwEa RF G7Z¢£[44, 4, 46] 
H$548"GaAs <=>BCDvI7ZJC 2*DwE KL 2|5KLK d'D¤|d [48, 49, 41] 2*DwE5McZ?@*+5N / XYZ!"i*+i u26OaP
QR£ ST78N$ 'EFGH-I¤'DUKV*k*WXDYS_8|d CEBAF N$aMZ'j u25>? d  z248
f"['A\ ?@*+)]^ de D
248|d [50]
GhaEFGH-I¤'TU_GaAs'  C 2*D wEK dBC'
500 C `
,2a5`KZ[ d a *
xN$*x d)"}Kb dzca2#$%&)0"gKb dz GaAs BC 5Z [dLzD
2 d 2*D wE A 1 "d|a 2,3

4

◦

◦

QE (%)

◦

3

2

1

0
0

1

time (hour)23

 4.6: NEA GaAs ?@*+'BCd'e$
232 GaAs <=>BCD"EFGH'-I z,£'=ª5]fD Lz "?@*+'#$%&)h)48|9e$5 78|d
2a"g6hD` ±G )d '
01j 1 P* v* 56K:;)d Gh')N / X)4Z!"EFGHz,£ Oa
BC 5Addf iE x 5
NF  NEAd'"GhDijg )*k*5%[36] 
&72) ±NY# 5k:K d 4.6 D 250kV
f i (v$f N$ _8|dd'e$
5KEFGH'-I z,£'=ª5]fD
Lz "#$%&)h)48|9e$)S_8|dJLab FEL "CEBAF " *mnu"ERLPa,£ a2 9NF 548|d
a"i*+iu2TU 5?Z2|
JLab FEL
+D248 f"EFGHDed?@*+BC'daN$ '¡_  lma'(*+XY]±"EFGH5-IK d+ 4Z)"
EFGH)?@*+ ne*DA-IS_"nN
Y)o cdpF)4Zs L "?@*+ ne* _DEFGHgNYk:  5=ª 7" ne* _q d548|d [4]?@*+ ne*r@]±_qs'?@*+'Uta"u i*+548[78|d
"g#$%&"g*"}ltuvwx'vw 5?Gx?@*+] AZ; ydz#c`"'{fD"GaAs D'n tD GH5
GaAs/ 7Z AlGaAs <=>5¤|dV))|'33

dz|  )DefS_8|d
RNYD|8'  y f"uNY[51] zX
5 K d:;) ydA'' "a"= { ERL & ¤N$Da:'y f"?@*+s'A'aZ;2g];£ydz?@*+C]±578?@*+D )*k*%&K d".- (?@*+A ERL ¤?
@*+z78K dag|z  )w 5?@*+w 9D^ dLz]±" )*k*xo u($ N$.* H$ 5RS 9 dLz) ydzL'5¤|8 "rstu a
ef 3  Au 2IWC yZ f'
CEBAF
5[78|d [37, 52]z)*k*
1.8 × 10 C/cm)?@*+5.K dZ[D"?@*+) !K
d+1$¬ )*k*'C'pF 4.4 "#%5$P d|z Aydz
.?@*+)%D24Z'a"& 800nm)*k* 5 !K d GaAs  a2 9" 1x
D GaAs  5Sp dCD5]7Z L
zDed [53]zrstu as'CD 5S±D'
7(["800nm )*k* 5.K dNw +o8u
f lmno* 2.27eV(546nm) 5?G GaP  5)¤7Z [37]zL'LzDef"GaAs hD?
@*+5A?K d*CD 5".?@*+D
1¤K dLz)[8% z24Zz2".
?@*+2arstuN$ '!"$?@*+

arstu+g,-.gN'? A Dedz
8

4.2.3

2

anodization?@*+a$, wN u2O wN*+Pw(./f"s'~Q'Z[D!gTU) :; ydLza 4.2.1 K DJKZ z LL a" )*k*%&Ded.* Hhi*^ z"'2 p¬
2?@*+/'¨©5{dK dLz " L'.*Hhi*58D~QK danodization 'DG|8JKdz
01 12.8 mm '?@*+D]01 0.35mm'|)*k*5%&78|dDAh ±".*Hhi*)^dz| pFD CEBAF a0C

 4.7: NEA GaAs zNEA AlGaAs ?@*+'#$%& 2 &' 3'4|zAlGaAs 'V)"#$%&)g 9")|z|  )r±_8|dz
7Z [44]z?@*+z?@*+ ne*'5bq]±08 9dN$)"5bqD^dN)'6VW
aDef7 u257^".* Hj$fD9G]
dLz)H8 y4ZzsL "?@*+1'u
2 zL\ '#$%&)RS 92 de D)¤7Z')"anodization z@`_ d9: ydz
L'9:'V 5HIDJKdz100ml ';¢D+, 5 3 <Z±7 anodization ¤'01 5
Adz?@*+z78¤K dqaD O wEv
'=5]9p "=' _q 5TU/ 78?@*+/D01)ª±2| e DK dz / 5>>
7Z?@*+5+,01D?7"?@*+D 100V
'N!5]^dLz "01'?48|dqaD
34' anodic oxide )@S_ d {d
100nm[44]z{dS_ZAB'#$%&aEFGH)-IS_Z z78A"/qDCK8 10 `
 yd [46]zanodization a )*k*'DDj
8K d.* Hhi* 5mn') 8 "CEBAF
g JLab FEL 'WX 10mA lX DaEF'2|)un {dS_8|d)"100 mA WX
DW^8:7AGHzaI c2| e ydz
5¤|D"EFGH-IDJx 2
anodization
548?@*+/¨©'d5mnVA
bc±_ dzuNYN$ z7812V 5K
9:;)ydza"anodization '%5L][dCEBAF
8 "anodization '{ fD01 5mm ' 7−3

8uf 5]9p8?@*+''2 p¬ ©5.
["01 1mm ')*k*5%&78.* H54Zzs'"78uf 5 IK dz.*
H) a 9 92 dLz)]4Zz78uf')?@*+BC 'N)a 5 7".*
HD 5 cdzS_8|dz |C 'Gh*D anodization 5 KV ) e2N)
a 5Ad' DG e yd [50]z 4.8: 250kV f i (v$f N  zz1
 ! "#$%&'anodization ()*+/0, 12anodization 3
250kV ,-.
4562789:;, NEA <3%=*>?3@AB()* C 4.8 DEF+CEBAF G
HIJ3K *L2)6M anodization >?NO=*PQRS*TUBM )+W [\XY]^4.2.4 V XYZ
2_` Labcd
efgh SP iRjklNmn()* [54]+ab2 o0pqrs tuB LvcdNwNbM *x ;yzo{ b S*+ab
R 3|!L0} {R~B2 0} {RNbB( 3 =*+ab 3 ! *NB_`m2Q S*+efghGH
2N p {2N/{L) 5¡R¢ L)IJ3£+¤¥¦N§ ¨i©3A)(ª<«N®¯()*+
3¬­±nm#h2h<² C³´ 150mm F° 3A)(µ:;, w¶ 3mm N¢h 125kV 
· 3¸¹B2abº34'+Nn »¼3½2_` 33¾¯ R¿GHB()* [46]+n »¼À ÁÂ2ÃÄÅÆR)ÇL2È~ *É
3ÊËÌRÍ)ÇLÎÏÐ 3ÑÒ = S*+G
HIJT¿2ÓÅÔÕÖ×NA)*LØÙ·ÚÛÖ× CHPR:High Pressure Rinse F3Ü L_` C4V6Al /{2316LN
ÝÞ{qÝFNc5¿6 35MV/m &¸¹ß*ÇL3àáB()*+HPR 3B )/{& BTTT¿ )+ab3â¿N
20MV/m  HPR ãÁRä`l 2_` Lvcd
Cå !LU/{LÝÞ{qÝFLIæçè()* [46]+°±#h "#$ UÝÞ{qÝé S*+250kV ,-./0, ê12
efghIJ3ëN2HPR ãÁ B/{32 LB(ÀAB()*+2r0{Q ÞìíÒ S*+0} {x ;yî {xï{ .
NðtN$ ïñ3ò¯*0} {ó±#µ 100eV ôõR¢h St2 ð  ó±#µ 3ÑÒ0} {¬ 3 *n !â¿ =N2efgh [54] 2CEBAF[50] wö÷
3øçè*ÇL3ùúB()*+ûüýþÿ o;y¹ TÒ 2· °{{z NÉR!LÀ¯ ! *íÒ S*+JLab FEL 2=( Qê1
 * S'R2É
500kV 
3op# = 350kV B()*+· 2.
o;y¹NTè()* [55]+°±#h2CPI é 1 o;y¹3À'()*+NÏ ÅÆ
 3ÜBbbM 3 *ÇL 2É 3
4.2.5

N®¯*NB()*+ 7000GΩ
Ý .IJ 330kV ¹NS'R2·¸¹Þ
R)+ 3À56N2o;y
N 100GΩ Æ3Ñ¡o;yÞÝ .34 NB()* [46]+°±#h 750kV &· 3¥¦*NB()*+¹½·l Æ) SF Ý3
· =/{ yN =()*+
5
 250kV ,-./0,ê1 1 ¹3A)2SF Ý3 2 · =2250kV
·¸¹NB()*+500kV ê1 N)(¹ 3 10 ôõNB( 2w* S*+efgh
3I½·ê1 [56] 2êk FEL  250kV Ã
200kVê1 C 8.1 DEF U@AM()*>? 2abÎÈ~BêRo;y¹N *Lßó±#µ3¬ 10keV N®¯*ÇLRß22 êÉÌ3®ß*+o
;yNh ß $ ïñ3ò¯*ÉR ßN!
)L¯¿M *+efgh¹ 3ÒA)( t2 Ø!2 " L wN 200kV 3
Tè*>? S* [56]+&2o;y¹N êR  * =   { z % NÒ )( U3#$
&B !'(M () *+   { z  '(UQN *R2¢h S *+°±# hê1 ¢h  22) 11MV/m
13.6MV/m(500kV) 2 *+ wS*[46] +JLab FEL 
2¢h

4.2MV/m(350kV) S* [4]+
8.7MV/m 
6

6

4.2.6

JLab FEL

3A), õê1 3
A)(29.1mA L)hb3G-B()* JLabê1Æ. [4] 3 CEBAF ê1Æ. [44]FEL
L/Nª 4.2 N& L=*+JLab FEL  o0pqr0o ; 1o{,2 CW Ø
3 Nd:YLF qr3A)()* [57]+4Ë %I
5 LBO I5N Nd:YLF qr3EÊB22 6
NEA GaAs

m7 527nm  qr83¢h 5W &£ *ÇLRß*+ qr9#Ý: 30ps  S*+
;< 10kW FEL ANÈMê1 St2
 100kW 3=>B(ê1* ;, zq3
?B()* [58]+@AÉÊ8ØB2êC
¼DEb 100mA 3=>+s tuBF7¬2x{I3
3 10 NGH}
6 NGH}, { {L[57]
ÑÒ+H
10 6,
3
qrÈJ@AÉÊ8 L/KLMNS
t2OPQRJSTU )+qrÝV ;.W0X LNÒ)(UY
M( !+JLab FEL LCEBAF JMZM21/e
R 500C L 200C NSt JLab FEL >R[)+ BT B2qrÝV ;.W0XR\ *J27 ×= Cª 4.2 DEF2]!<²St
L
10 C/cm (JLab FEL) 2 × 10 C/cm (CEBAF)N2CEBAF >R[)+í^NqrW0XRh ß)>R J[ ! *+ 0} {x ;yî {xï{ ._`RabcNd **+=NSe  N2efghNÈ  SPLEEM Af<EÊg 20kV ê1NJ 2qrÝV ;.W
0X 3 1.3µm Nh *ÇLN 1.8 × 10 C/cm L)
CEBAF 3 3 i U¥j*Æ.3B()* [52]+&2J2qr7[NUklB( t2
m7[qr 3A)()* JLab FEL JnoN
S*ÇLUpqB( !+
3

2

5

2

8

2

rstuvrwxyÈ  250kV ,-./0, ê1 3z 4.9 N{ [12]+° ;yy-0 .·½2¹
Ý N =2DC · 3¸¹ *+
3SF
· / |#}T¿R~½( t2*+ LRß ð N *+ o0
pqrR*+bT¿NRT'( e&M2êC ¼RßM *+GaAs
J --;y N0{Ý .# M2¹Ã y  {z34)ª< 3×N *+¹Ão{Ý0-;3A)(2ãÁP2ª.<éÔ (preparation chamber)
3 NEA
4.3

250kV

6

ª 4.2: JLab FEL ê1 2CEBAF ê1 Æ.
JLab 10kW FELC- F

JLab 100kW FEL

CEBAF

350
420
10.56
9.1
0.122
8
75
6
10−11
500
527
8
1 ×103500

100

· (kV)¢h· *+w¶ (cm)¢hb (mA)
x {I (nC) rms ó ;/{Ý (mm-mrad)s tuBF7¬ (MHz) QE (%)
Ôõ (Torr)
 (C)
1/eqr7[ (nm)qrÝV ;.³´ (mm)]!<² 1/e  (C/cm )2

N Q¡ *+ L »¼Nð* Æ34'
P2 .o{Ý 0 - ;3A)(ê1 N Q ¡ *+SF Ý /{ yL° ;yy-0 . 3 t )  2ê1 N{+
3z 4.9 o0p q r  J 27[ 780nm 29 
2s tuBF7¬ 83.3MHz 29#Ý: 2ps
500mW
/{W00* qr (Tsunami) 3
FWHM
A)*NS*+QE=1% 2DEb 3mA
R3M *+
6v
ÉÊ8A o0pqrNQM
ERL*Æ. 3ª 4.3 N{+Íó ;/{Ý 3G-* =2GaAs x { µ:;, ó±µNø)7[ 800nm  NS*+7[ L
B(J/{W00* qrNS*R2
RhN *ÇL2 09 /{W00*I5 Ã !MT¿2-GlN)LM()* [1]+n"#M()*R2z
N?lN{B MOPA CMaster Oscillator
4.10
Fqr ÝÞ¼L$%M *>Power Amplifier
4.4

CF

100
0.135–1.35
5
75–750527

620.0004500
mid 10−12
200
800
0.35
2 ×105ª 4.3: ERL ÉÊ8A o0pqr NQ
M *Æ.+&' [1] ðt(Û+
Æ.
)=
DE9
15 W
s tuBF7¬
ì0y-9Ýó±µ 1.312GHznJ
ì0y-9Ý[
10-30 ps
7[
800 nm7[*¾Æ
7%,-00+Æ ,50ënm- %?N2¬ 100mW ./ } q / qr
k 3P* {, NG: *+JLab FEL NJ} q/ LNd : YVO *{,3
Nd : YVO 5¡ MOPA ÝÞ¼30B [57] 2°±hNJ0 ;.C»¼ (Yb) 31¹B00x qr} q / LYb 1¹00x*{,3A) MOPA ÝÞ¼30B()*[59]+2ä34NU200x 3A)k 200W
 MOPA ÝÞ¼35ùNB()*+00xqrNÒ)(¨6J&' [1, 24, 60] 3DE
M)+
4

4

ª 4.4: JLab FEL  o0pqr9Nc
 *GHIJ [57]+Ís tuB>R29Ý S
tó±µ U 8 õ 3 N ß*Ç
LT ¿2SHG ¾ J)+Ís t s t
k9 (W)45
45
k9 (W)
24
13
¾

54
30
sSHGtuBF7¬(%)
(MHz)
75
750
k9Ýó±µ 600 60(nJ)
9Ý: (ps)3030

z 4.9: 250kV ,-./0, ê1  °{ 1/zo0 ;yÝ C¥) LG CF
Oscillator

Amplifier

SHG (+OPA)

* ;, zq334 B()* JLab FEL qr k9 Nc *GHIJ 3ª 4.4 N& L=*+SHG ¾ Jì0y-9Ýó±µNUkl *N2ØÙ k9NS'(U2s tuBF7¬R  *Lk9Râå *+ ¿GHNð*L2750MHz F7¬N 20W 3£ *NJ 60W ôõ k9RP
Q L *+1300MHz NJ270∼80W  k9
RPQ L)ÇLNt NS*+
7[ 520nm T ¿ 800nm   ¾ NJ NonL)4Ë %I5 CBBO I5ÎF3A)*R
ùúM()*+&J&' [1] 3DEM)+
¾ 3 30% L *ÇLN2ª 4.3
NOPA qr k3£ *NJ MOPA qr kR
PQLM()*+B2Ç ð 
200W
kqr3 NOPA NA)*I5NEÊB L
N *TL) LMJ¨ %NSt2ißÈ RM()*+
w> RN%,-00 3ÑÒêC ¼
ê1T¿~*ÇLRN ßM%2êC
3¼Ý
o0ÝÔwIkJØÙN t2Ý o0Ýó ;/{Ý)R~Ù) C2.4 DEF+ó ;/{ÝGh3 N#$NJ2qr7%- % 34)2 »ÝC ¼T¿%C ¼N¾
BP2NEÊ *ÇLR"&B)+q
r w7%- %NJ2YVO I5Î§
collinear OPA(Optical Parametric Amplification)

z 4.10: o0pqrzÇM ¿k MOPA qr ÝÞ¼7[J 1.04µm ôõNSt2GaAs x {µ:;,3¯*ó± µ 3ò¯*ÇLRNr LB(À¯)+ÇN 2
ß62qo0rpq4Ë
%I5NS* LBO I5Î
MOPA   3
NEÊB2SHG(Second Harmonic Generation) 3
À'(7[ 520nm  qr9Ý3~ *+NJ2@AÉÊ8 NQM
JLab FEL* Íó ;/{Ý 3PQ LB )ÇLT¿2520nm 7[ o0pqrNNS*+
N{Bð N2520 nm 7[NÌê(4.1)
 1% NB( 100mA b3£*NJ 23W qr9RPQNS*+10mA T¿100mA4

Æ 3A)(9Ý 3ÒN÷BP2 /0{z36¿B( 5¡ *9ÝÝ / ;9{z9Ý÷J  100%NS*++
3A)*Ò I53À'( 8 9Ý9ÝÝ/;9{z3: »Ý qrC ¼
34)2:
2ps FWHM
%C ¼NBR&' [59] N
3M30ps()*+ w7%LØBNÔw7% U%N
S*ÇLR"&B 20ìp o LÄl* X¼3À'>RùúM()*+qr3 GaAs NEÊB LßN2
NM *Ã !MU¨ % *PQRS*+ qr L228%9R GaAs N
M( B& + °±hNJ2 p
{9 ;yN GaAs 3¡( 20W qr 3EÊB LÇ 2270 C &N õR ¥ *L)GHIJ3£()* [46]+ÃJ2
T¿³´ 5cm  -;3KÙ(<N *N'()*+

B 5.1: ERL 5CD Cockcroft-Walton EF
GHI JKLM
5%
250kV
500kV
5&
50 mA
100 mA
NOP=Q
kHz
40 kHzRST SUVW 20
8.4 nF16.8 nF
XQ
6
12
1.2 H
1.2 H
LC filter YL
LC filter YC
1.4 nF
1.4 nF
Z[\] ^_`a 1.3 × 10 0.7
× 10
Z[\] ^bca 1.9 × 10
f

f

−4

−4

−4

◦

5



Cockcroft-Walton 

ÉÊ8 A ERL  ê1 2Cockcroft@A·NQM*Æ.J2ª 5.1 N
Walton{ð N2·¾Q 1 × 10 N 500kV ¥· 3È~B2100mA ¥b3 *L)UNS* [1]+z 5.1 N{J2ERL 
ê1,-./0, LB(È  250kV 250mA
NS*+zí ¥
Cockcroft-WaltonR·/ |2íJM()*+
{zN0}H °{ {WR M()*+F7¾· J0o{ñ LwÔwNM()*+ÇNJ2
jÁ3&' [61] 3DN
Cockcroft-Walton
BR¿] !
−4"#
z 5.2 {$J6 %-&jN' !0 $%J()*+ ,- 0V N' !0’ . 0 $/01%2340’ $5%0 0 $5678* U $9:3;<=>1?8*@ !0 $5%A 0 
5.1

Cockcroft-Walton0′

d 5.1: 250kV 440mA Cockcroft-Walton 5e
78*4U V fgh .i40 → 1 → 0 $ji
5&A&) C Ak5 () !1 $5%0lm
nop/$56 0.6V qrs)t 0 .u563',40 $5678* −U V .f !0 $5%A
78*4−U V fgh .i40 → 1 → 1 $0
ji5&A&) C Ak5 () !1 $5%0l
mnop/$56 0.6V qrs)t 1 .u56
3' !C vw5xqy,z(f{)t41 $5
60 0 78* −U V |h)*+,40 78* −2U V .@ }~ .f !
 5%&EF qX ~ .345
 n  −nU $5% qH( ~ .A3i !
1%2 $J$ 1 Um]K0d 5.2 $} C 4C 0k5 ()*@ !$Um
′

0

′

′

1′

′

0

′

′

0

1

′

′

1′

′

0

0

0

1′

1

S1

S2

1’ [0]

12’ [-2U0]

C1

C2’

2

S1’

S2’

C1’

C2
0’>0

0’>0

S1
0’ [U0]0 [0]

1’ [0]

1 [-2U0]S1’

S1
1’ [-2U0]
0’<0
C1’

C1

0’ [-U0]0 [0]d 5.2:  5%&EF]3 0 $5%A 0 78* U V fgh .i45%&EF q 2 X 8hh $ qd 5.3 !1 $56A −2U V 41 $56A 0V 3' ~$ji5&A&)4C 0→2 →1.vw 13k
5 () ! ( w$Um] q−2U V
d 5.4 !0 ,1 ,2 ,1 $56 0 0 78*))4−U V,−2U V,−4U V,−2U V .f !g*41 → 2 → 2 $ji5&A&)42 $560
f,4C 0 −2U V 3k5() !N X
−4U V .
 . n $56A −2N U V .f !
\m\ 5CD$ Cockcroft-Walton EFq
d 5.5 !7EF . ~ .,4I $RST SUAk5 () EQA =&EF * 2 fg*@
′

0

′

0

′

2′

0

′

0

′

′

0

0

0

2

0

′

0

0

5.2 
5CDvw iz()5C!o"0 CockcroftF .g*0#x$%& 1 X$7
Walton E
 Cockcroft-Walton 5e#xAr'4lmno
p$()*+Ars3i,-04RST SU
A./k5 () .4$0 q|1&&f2
34U = −U 4U = −U 4U = −2U .f#x ^5C!o"a5& I A&) .RST S
1′

0

C1

0’ [U0]0 [0]1 [-2U0]
S1’

′

C1’

1′′

0

1

0

d 5.3:  5%&EF$ 2 X Xk54$
J$Um]
U C 055&7 Cockcroft-Walton 5e3
04d 5.6 3&} 2f $P=Q ^f 01%2
$P=Q a3k5A6 ,7()h8455/
0 1/2f 3'U $5%0k55,−2U <f
U < −2U + I/(2f C ) .
X$7 Cockcroft-Walton EF ^d 5.5) 3Nu9:; <*$ RST SU0 C 4C 4
A=8'C 3>;w),-4RST SU CC
78* 2f $P=Q3k5q6 ,7&k5/?
3' 1/2f $/45& I ,5xq5z&$5%0 −2U < U < −2U + I/(2f C) .
U
fg*4o@A]$5%0 −2N U vw
31O& [61]~$5%1−2N U + N I/(2f C)
O$ peak to peak 0 q Z[\] .BC4$ }
B()
1

1

1

0

0

1

n

n′

n

n′′

n

0

n

0

0

0

δV =

NI
2f C

(5.1)

B 5.1 &DCEFG3GHI$5e$04I =HI
4
4
4
0.05A f = 20kHz C = 8.4nF N = 6 q
8* Z[\] q_`&.4δV = 890V (δV /V =fERL 5CD3J8 w)*@
3.6 × 10 ) .
 1 × 10 K$ Z[\]bL04~$MM30
NO3'
 ~34d 5.7 & LC PQ]qR@h Z[\]ST qUg*@ Rm] .RST SU$ m
SVolSW0 i2πf L 4−i/(2πf C ) f$34I
−3

−4

f

f

LC filter

S22’ [-4U0]

output register2 [-4U0]
0’<0
S2’

N

N’

C2’

N’’

C2
UN’

S1
1’ [-2U0]

CN’

CN

UN

CN’’

UN’’
(N-1)’’

1 [-2U0](N-1)’
(N-1)

S1’
C1’

C1
n

n’

0’ [-U0]

n’’

0 [0]
Un’

Cn’

Cn

Un

Cn’’

(n-1)’

d 5.4:  5%&EF$ 2 X Xk54$
L$Um]
2E
E5% V 7&zE5% V $ 0
in

2’

U2’

2’’

2
C2’

C2

2 2

in

in

2 2

f

f

f
2 2

1’

(5.2)

 & 1 ≫ 4π f C L 78*78*.ff,4P=
V =V .
1 ≪ 4π f C L
f &3'
V = −V /(4π f C L ) .
 5% q|184Z[\]1O5%$q%
3ioWPQ]o .fg*@B 5.2 $0 qg*_`& .41/(4π f C L ) = 0.038
3'Z[\]5%0 34V ;w)250kV
78* 1.3 × 10 3',4LM0 q 8
h ~ .f

U2

C2’’

U2’’

U1’

1’’

1
C1’

C1

U1

C1’’

U1’’

out

f

f

f

f

0’

0

0’’

f

2 2

−4


 wv$35CD () q(w8h,-45% RST Q SAvf@RST Q SI55& .4]W5 Ao@A] )!" ifzE*+ qI) .4zE*+/ if56# q$4o@A] .%)&'56 /56#A()'f ~),4o@A] .u56  ()5*) .4+S p./355A+i ''f ,M ,4zE*+0553 )!"5 0 q Z@[&F- q1,()fz
E*+. .Z@[F- q1hf@h8455.3(n-1)’’
(n-1)

out

Vout
1
=
2
Vin
1 − 4π f 2 Cf Lf

out

Un’’

d 5.5: N X7 Cockcroft-Walton EF
A />0@]W/?3o@A] q1,*5e )!"~ .f
5e305 Wq2 o 84
Cockcroft-Walton
34K55 0A ) .5* 657E
Fq8 .&Z@[Wm [9F-A,@*@A4
WVop:;A<(zE*+o@A]5 A )!" .4I RST SU C /56#A()'f ,4I 560 +S p56
=> 'n 56A12 wf@ .& .4?;
t N . N − 1 / if@5*Almnop
,4ABqC'D)A<vv\   m \ 5 CD R  * 5 e 3 0
lmn o pq 2 E FG
350G40F(HVCA)
H4d 1 ElmnopqG8*@I@
5*A 40kV/E3<~ .vw480kV M3@5
n

′

′

1’

1’’

1

U 1’

C 1’

0’

C1

U1

C1’’

U1’’

0’’

0

j5%& ^dipole magnet a4!o"lS\ q'{*44 ,f+(o o qc4&~ .
8*@~~304~) wc4)*,@*4+,-.&/012345
5CDvw!o"=4S ]!o5C!o" @[SWc4R)6~7@W Z[
qR@hW8 ",@9:;& [63, 42, 13]d 6.2 &}45C!o"qW Z[=qR@9<@!o"=[>?4/5xE?
@[SW3@A)6!o"1B& !o"= [0 @[SWC"A ?q13
DE"AC"A ?qc4846FGQ
7896$/5 \ [&6td 2.4 &
6$/HIJ qJ8~7A3i ~6v
W Z[6F3 Twiss +(o o 7 @[w
SWqJ8~7A3i
MNO
6.1.1 KL5CDvw5C!o"PQ04Twiss +(o o 7 @[SW.{30RM wS4T
@/5xUV WX qY{/5xUVWX qZ[&A< 7@ }\]vw4W
Z[:qR4&5C!o" S^ o\_`0 (2.138) 3ab)6~~345C!o" ]!o1?Ac  ^γ = 0 4γ = 0 a4θ
j;dC OWAc [P = 0 Y(2.9) 8h}e opqf }%,q 0 &] 4+o2P=Qc ^Ω = 0 Y @[SWc4W8 "
g j%,Ahi8f@a4jklf8 ^κ = 0 a
qm4&(2.138) 0
6.1

d 5.6: 1 X7 Cockcroft-Walton EF
Vin

Vout
Lf
Cf

d 5.7: LC PQ]EF*I; w)1- 30 250kV/6=41.7kV
@5*Avv g*@55 ,42  K5
@5*Avv  .AB& LC PQ]o
Rm]Fy ,{hUoo q4zE*+HR .8* } qUghA4lm
nopABA @h 4RST Q S
 1MΩ 4!o"  10kΩ  zE*+qy,{*@
304RST Q S 0
JLab FEL
4!o"  500Ω *+ qg*@
140MΩ
Ro] 30 Kaiser Systems, Inc.[62] ,))h4Cockcroft-Walton 5e30f@4* 5e qR& zE*+
750kV 100mA
,@*04 ] @" q4*\W0 75MΩ *+q{*@ [46]

6 5CD78*c4&A<!o"-04 @[SW4 S904 ]!o"A ,45 3<d 6.1 &}4\m\ 5CD304 l]W Z[a4# j$ ^a4#^
double slit

deflecting cavity

′

′′

θ

L

a′′ −

K
ǫ2
− 3 n2 2 = 0
a
a γ β

(6.1)

7f~~34/5xEqB& K 0 (2.68) 34n)6\+op3f@h8 K = =7f ?4(6.1) 0
2ν
β2 γ3

a′′ =

2I
ǫ2n
+
aI0 γ 3 β 3 a3 γ 2 β 22II0 β 3 γ 3(6.2)

d 6.1: RSERL 5CD \m\3< 250keV 5CD !o"_c W8 "'_d@[SWc4q double slit W8 "3U@4S90c4q# j$ (deflecting cavity) qR@9U}
# j5%&04!o"lS\A &5CDe opq !Mf@}!o"q# j)45C!o" ]!o"A ?c4 R@
7f  1 A /5 xUV qB&  4 nated beam 7fB 6.1 5C!o"+(o 2 A @[SW qB&3<g9 4 oq?W Z[: d  qJ8S95
3<6t4 @[SWA@A x 77pC 4S9: 20ps FWHM 3<34Vo≪
>f!o" (emittance dominated beam) 7f 5 0 I = 3.85A 7fB 6.1 +~~34 @[SW ǫ 0!o" S^ o\  (oo 7 (6.3) HI&7\m\ 5@[SW3<?rms @[SW ǫ̃  4  CD3043? rms @[SW ǫ = 0.3mm0 7f [(2.149) ]5CD  @[SW0 mrad 4W Z[: 20µm 4R = 0.028 7fg
>f,- @[SW3RM  @[ hJKLM3< 500keV 5CD343? rms
SW0 rms 0 (3 ) 3B&~7A@34@[SW 0.1mm-mrad qc4&,-W Z[
:q 10µm 7&7 R = 0.041 7fgh
K rms @[SW3:;
S @[SW DC 5CD ^]W*W Z[: q d 7& 74W Z[3 gh5
C!o" 0 a = d/2 7f~6 q (6.2)  5CD  " a09Ef3)6
HI84 2  71  q
9 ?4u93 @[SWc4Af)69@HB?qB 6.2 &JLab[55] 4 
Id
4
@S6@9 4R 0 0.1 R=(6.3)[42] SCSS[13]32I γβǫ̃
74n& 74R ≪ 1 3<6t emittance domi- ?()@0 7fg9@~7A2v SCSS 
2I
aI0 γ 3 β 3

ǫ2n3a γ2 β2

n

n

2

0

2
n

n

Space charge
Dominated Beam

Emittance
Dominated Beam

x

x’
x’1b

x’1a

x’1b

x1

x’1a
x1

x

Slit

d 6.2: @[SWc4 `d5C!o"qW Z[3!o"F84!o"F!o""A ?q
To q6$\ [&~7 @[SW Twiss +(o oqJ8
~7A3c4&
 i
B 6.1: ERL 5eRCDvwC!o" @[SW@A>f!o"&h8
q
W Z[ \m\ 5eR

E [keV]γβcharge [pC]
Lb [ps]I [A]ǫ̃n [mm-mrad]d [µm]
R

250
1.49
0.741
77
20
3.85
0.3
20
0.028

500
1.98
0.863
77
20
3.85
0.1
10
0.041

@9 25,50,100 µm W Z[c48 @
? 2f@ @[SW q h. 200µm
W Z[ i' f [13]200µm  R
7f~7vwR 0 0.1 ? ()= 0.12@A<
W Z[4"Agh!o"c4 789
 aW ZoSaO`W Z[7P
+T Qe [\amoWAo=A<?\m\CD al]W Z[B 6.2: 9EfS @[SWCD @[SWc4R)6h W Z[ 
? JLab D. Engwall et al. [55]?SCSS  K. Togawa
N. Yamamoto et al. [42]?et al. [13]  SCSS
JLab
E [keV]γβcharge [pC]
Lb [ps]I [A]ǫ̃n [mm-mrad]d [µm]
R

250
1.49
0.741
10
40
0.25
0.25
50
0.017

120
1.23
0.587

500
1.98
0.863

10−8
0.1
40
4 ×10−9

1
0.6
100
0.030

W8 "qR@9 @[SWc4 qU }4< b o [7Bt6
 V  }Ah ')@h@2t
W Z[qR@hb qUg9@.
c4 X-Y  @[SWA w6]A<h m\ 789W Z[qR@h?
[42] 

< [63]~6.c4 X  Y  @[SWA w6,W Z[qR@7W Z[
qO)fA w]c4qU}A<?Avv A] <MK 1997  NEA GaAs e op DC
JLabCD  >f @[SWc4 qUg9@
d  !o"_c W8 " JLab W[55]  6.1
8 "q:89 @ =o o Nd:YLF  = (=0 527nm) q@ DC * 2 <gh =o o]W=250kV 300kV WJ  σ =20ps =o oW [AS9x 80pC 3? rms
2mm@[SW 2mm-mrad 8pC 3? rms @[SW 0.5mm-mrad q 9@~CDL
i JLab FEL R@ w69 ?=o oW [ 6mm S9x 135pC 3? rms@[SW 8mm-mrad q 9@80pC 7135pc
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S p![\ ]!o$%&=0q1, p+m =o oqR@h,-!o" @[SWeopRM @[SW=@07f 300K  26meV $%8(3.25) `]o 0A RM  @[SW =ooW [  ?& 1mm ,3? rms @[SW ǫ̃ = 0.06mm7f?H5eJ)60.1mmmrad
h& ~7A i  N. Yamrad qb =o o=0 760nm K
mamoto5 0.15mm-mrad q 9@[42]Dunham b [64] =o o=0 840nm  @[SW 34meV 514nm  103meV q 9@~b
Vvw800nm = 1mm  0.07mm = 1mm  0.12mm-mrad
mrad 500nm
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45eopqgh DC CDvwS
NEA GaAs@[SW!o"q  NO =o o=
0 q GaAs  S p![\=@ 800nm_&A  <A [42] C 
A 100ps _ 7!'5ps FWHM : [66] 52: =o o 100ps _
ps FWHM [44]8o] q$]A<= "#e op
R@~7 QVR$%&)6q
9@A [43] CS90c4CD 7g9
vf@'o] < S90c4 () P*m]!o"q&$+
5 qW Zo e (+c4&A+,<A + 5 q C!o"
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6.2

e-beam250keV
83.3MHz
77pC

deflecting cavity
499.8MHz
165W
7 mrad40ps
screend 6.3: # j$ qR@hC S90c4 W8"
d 6.3 \m\CDRS90c4
W8 " `d q& ug/# j$(g![\vv ; 7(gq0"%;

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; i) 76$C  'F8hW 
ZoSc4vwC S90 q&~7A i250keV C!o"q 1.8keV
 [&  ^ 7mrad af RF  o_`0 165W  < [67]
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 TM110 2op$ qGH 8 [69] 
1.3 GHz
C!o" S90c4 q 120kV[70] 200kV 7
K;9@X  FEL
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B=/5 Xl#2  #4  R  /L #2
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duty 25%
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klLö÷k!øY¤ù=/B|4%/[79]5i
8* 10 Torr \]|#úóBûüLýþÿ=/ A/5i8* 10 Torr (LíîG 100 ïð\ #10 Torr (G 10000 ï
ð\ B% ´µb 4%/ [78]5RF F
7.1

−10

−11

−12

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1–10
F RF (MHz)433
duty (%)
25 bbR0 (nm) 527
ç èé |QRS (MHz)27
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−11

1
2

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7.2

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2

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ELSA

−9

−10

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hijk
mn pqrs, tpuv, wxyz,“ {|}~
[1] l
ERLo, ”, KEK Report 2007-7, JAEAResearch 2008-032, Feb. 2008.

[7] R. Hajima, T. Hayakawa, N. Kikuzawa, and E.
Minehara, J. Nucl. Sci. and Tech. 45, 441 (2008).

interval (ns)

48.1
48.06
48.02
47.98

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47.94
0

2

4
6
time (min.)8

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8

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1 g £9:;n |4}+L
M' |C}"nc2 +J V pS10 -n+ LM'  1.2%+,¬S £9:;n  18ps +"n
 x0( + 13ps +,¬S ,“ {|}~ERL  ”,[2] 5(1), 13 (2008).
 |
[3] SPring-8
"#$%!
&'()*6 6 GeV
p
+, 

%./0
23

-
|
&4
5
789 -:+1; <K. 83pmrad
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