e+e- Linear Colliders
X-Ray SASE FEL
Bn 
1/ 2
2 Iˆ
nb Ne2
Pb  E 


L  f rep
* * HD 
4 x  y
Ecm  n ,y 

 
  

2
2
 n, x n, y
2
HD
L
R
2
2
1  n  1  p ,o  1
  
 

2IA  3     3 mc   3
I
 K sol 
p ,o
mc 2
1
L

2
 n,z
1
2 6
  L3

m 
Bn  1015  2 
A
KzSC g 
 nx   ny  1 
I
> 3 kA
L  10 34 cm 2 s 1 
KzRF L
 n.x
10 

 333
 n,y
0.03
Flat Beam Production
In 1998 Y. Derbenev invented a linear optics device for
transforming a beam with high ratio of horizontal to vertical
emittance (flat beam) to one with a vortex motion (rigid rotor).
After injecting such a beam into a matched solenoid this vortex
motion can be canceled to create a magnetized beam with equal
emittances in the transverse degrees of freedom (round beam)
(UM-HE-98-04).
In 1999 R. Brinkmann, K. Flottmann and Y. Derbenev proposed to
reverse the process: obtain a flat beam from a round beam
produced from a cathode in a magnetic field: A Flat Beam Source
for Linear Colliders (TESLA-99-09)
In 2000 H. Edwards and the A0 collaboration have seen the first
flat beam from a photo-injector.
Vortex Motion
 p ,o  1
2
 3
R Ksol R  
mc  R
2
Req 
p ,o
   Ksol 
mcR2
R  4 
1
2
p ,o
 '  0
mcKsol
r 2 r2  r  rr   r2   x y
2
2
2
x  x o 
x  kyo 
y   yo 
  

y1 kxo 
x 
x 
y 
 
y2
Clockwise
rotation
Bz  0
xo 
0 
y 
 o 
0 o
D. Edwards
eBz
2mc
 x  kyo
 y  kxo
0
1
0
0
0
0
1

0

x o
0x

o

kyo 
0
kyo 
 y   kx o 
 o   1 

0 kx   y 
o
 o
  
Identity matrix in x
90o phase advance in y
Q1
k
1
0
 0

0

D1
Q2
D2
Q3
By choosing =1/k, particles end up with
equal displacement and angles in x and y
This is a flat beam 45o inclined.
 x 4k 2  c2

y
c 2
Flat Electron Beam Production from A0 Photo-injector
Round beam image on fluorescent screen
Flat beam image on fluorescent screen
Flat beam measurements
Fermilab/NICADD Photoinjector Laboratory (FNPL):
Demonstrated large emittance ratio (50:1)
with small emittance 0.9 mm-mrad @ 1 nC
Beam image through slits for emittance
measurement
Req   

p , o
mc K sol