Cerenkov Free Electron Laser
( CFEL )
And
Hybrid FEL Devices
(asgekar@physics.unipune.ernet.in)
Vivek B. Asgekar
Physics Department
University of Pune
Pune 411 007, INDIA
Undulator
Field Profile
-- Free Electron Laser (FEL)
- idea was proposed in 1972
- first experiment
1977-78
*
*
* : Halbach PM Undulator
* :different Undulator configurations
* : new devices ( 1983
*
*
Cerenkov FEL)
-- Free Electron Laser
basic idea
to produce electron bunches < radiation wavelength
Free Electron Laser schematic
e bunch
γi
+
γf  γi
COUPLING DEVICE
em radiation
COUPLING DEVICE ---- UNDULATOR
SLOW WAVE
STRUCTURE(Cerenkov effect)
(metal grating)
UFEL
CFEL
S P FEL
-- BUNCHING
Interaction of e beam
with radiation field
(~ a few mm)
(~ a few microns)
Energy modulation
on scale length of
wavelength
+
Dispersive action of
the coupling device
Energy modulation
space modulation
(Bunches)
Undulator Free Electron Laser (UFEL)
-- Electron beam
-- Undulator
Δγ
γ,
, ε, I , temporal structure
-γ
B
,λU
----U ----
2z
[B  B U Sin(
)]
λU
-- electron trajectory
λu
λ λu


c
βc
c
λu
λ 2
2γ
………
β 1
for the sinusoidal trajectory
λ
-- amplitude
a
K
k u
λu
1 2
(1

K );
2
2γ 2
K  0.9Bu (T).λ u (cm)
[λ u  4cm,K  1; 10MeV
λ  75μ
-- undulator induces a transverse component of velocity
 SYNCHRONIZATION
-- electrons from the
second bunch
em radiation field
+
undulator field
and the
subsequent bunches

E r  ESin (kz  t  )xˆ

Br      

2
B  BuSin (k u z) yˆ k u 
k
2


vinj  v z zˆ
u
-- beating of rad. field & und. field gives
k  k u z  t  
ω
v z  v ph 
(k  k u )
ω
v ph 
c
(k  k u )
k  k u z  ωt  
λu
1 2
λ  2 (1 K )
2γ
2
ω
v ph 
c
(k  k u )
-- Cerenkov Free Electron Laser ( CFEL)
Cerenkov
condition
Cos( ) 
1
βn(λ)
dielectric film
conductor
Fundamentals of
Microwave Engineering
-- R.E.Collins
-- Synchronization
Beam velocity = phase velocity of the mode
for T M01
mode
2

1


d


tan1 (
)
2
2
c
  1
  1
 ~1
λ  2πdγ
ε 1
ε
[  2.1, d  11.4m,   2    75m]
[λ u  4cm,K  1; 10MeV   75m]
-- BUNCHING in CFEL
ε 1
λ  2πdγ
ε
Advantages : 1) Low energy accelerator
i) pulse modulators [ 50 – 250 keV]
ii) Marx Generators [ 500 keV – 1 Mev]
iii) rf accelerators [ up to ~ 5MeV]
2) Short interaction region ( ~ 10 to 30 cm)
Make the device
compact
+
II
-------------------------A Table Top Device
Dispersion : Free Space
Limitations : i) wavelength range limited by beam size
ii) power limited by dielectric breakdown
1) single slab configuration
Different Dispersion Relations
for
Different Configurations
2) double slab configuration
3) cylindrical slab configuration
Dielectric loaded film waveguide
(100 micron CFEL at Frascati)
NIM A272,1988,132
NIM A259,1987,125
-- double slab geometry
-- dielectric constant : 2.12 ( TPX )
film thickness – 92.5 microns
film thickness – 48 microns
- X-band Cerenkov FEM amplifier
Parameters of the expt :
electron energy
: 890 keV
beam current
: 500 Amp
pulse duration
: 100 nsec
interaction region : 17.8 cm
dielectric constant : 10
f = 9 GHz
100 kW
3 MW
( eff. ~ 3 %)
PRL 65,2989,1990
A MM-WAVE, TABLE-TOP CERENKOV FREE ELECTRON LASER*
I. de la Fuente, P.J.M. van der Slot, K. J. Boller
University of Twente, Laser Physics & Non-Linear Optics Group, PO Box 217,
7500 AE Enschede, The Netherlands
[2004 FEL Conf]
Nominal operational frequency
Accelerating voltage
Liner Material
Dielectric constant :
Thickness
Inner diameter
Length
Magnetic field on axis
Beam diameter
Beam current
50 GHz
From 65 to 100 kV
fused quartz
5.8
1.3 mm
3 mm
250 mm
0.15 T
2 mm
800 mA
Table 1.1. characteristics of the CFEL
Hybrid FEL Devices
Self Amplified Spontaneous Emission
( SASE ) FEL --- [ 4 GLS ]
-- a single pass device
-- very large gain, noise/seed to saturation in one pass
-- no mirrors required
-- electron beams with low energy spread & high brightness
-- electron motion in an Undulator
even hormonic oscillations along the
undulator axis and odd harmonic
perpendicular to the axis
SASE - FEL
Dattoli et. al.
J Appl Phys 97 ,
113102, 2005
SEGMENTED
UNDULATOR
SASE - FEL
Pierce parameter
ρ
K 0 P 2 3
ρ [
]
2
4( R ) 0
* growth rate
* undulator length
to reach saturation
* power transfer
at saturation
* limit on beam
energy spread
;
ω0 
2c 0
u
E  E0 exp(2 3Nu )
1
N su 

PL  Pbeam



-- Eqs of motion in (, ) space
d
 
dz
d
 
dz
f ( , )  distribution function of particles in (, ) space
(  )   e  f (  ,  ) d 
J (  ) y , z   e  f (  ,  ) v y , z d
Substituting the expression for
J y ()  []
vy
f ( , )
d

Expanding the integral in Fourier series and keeping the terms in synchronism
with the radiation field
dEs
sin
 
dz

 2E y
z 2
2
1  E y Z 0 J y
 2

c t
c t 2
d
cos
 
dz

1
 3 2 
3 2 

 c     J  

       J

4
4  
1
.7

1
0


2
1
3
1


 u   u  K J 
3
8.3610


  u  J K fb( K 1)

2

2

3
[ V.B.Asgekar & G.Dattoli
Optics Communications 206 , p 373,2002
and 255 , p309, 2005]
1 10
6
1 10
5
1 10
4
1 10
3
100
F( z )  H( z )
10
T( z)
1
Q3( z )
0.1
F2 ( z )  H2( z )
0.01
1 10
3
1 10
4
1 10
5
1 10
6
0
2.33
4.67
7
9.33
11.67
14
z
T(z) ---- UFEL (10 micron )
Q3(z) ---- 3rd harmonic of UFEL (30 micron )
F2(z)+H2(z) ---- UFEL (30 micron) + UFEL (10 micron)
F(z)+H(z) ---- CFEL (30 micron) + UFEL (10 micron )
1 10
5
1 10
4
1 10
3
1 10
100
F( z )  H( z )
10
T( z)
1
0.1
0.01
3
1 10
4
1 10
5
1 10
6
0
1
2
3
4
5
6
z
F(z)+H(z) ---- CFEL (300 micron)+UFEL(100 micron)
T(z) ---- UFEL(100 micron)
[  10,d  10.8m,   1.8,u  1 cm, K  1.42 ]
-- FEL Oscillators ( ?? )
( gain > losses)
-- integrate other types