Cerenkov Free Electron Laser ( CFEL )

AndHybrid FEL Devices

Vivek B. Asgekar

Physics DepartmentUniversity of Pune

Pune 411 007, INDIA

(asgekar@physics.unipune.ernet.in)

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

COUPLING DEVICE+

COUPLING DEVICE ---- UNDULATOR UFEL

SLOW WAVE STRUCTURE(Cerenkov effect) CFEL

(metal grating) S P FEL

e bunch

em radiation

iγif γγ

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)

-- BUNCHING

Undulator Free Electron Laser (UFEL)

Iε,,γ

Δγγ,

-- Electron beam

, temporal structure

-- Undulator

UU λ,B )]λ

z2Sin(B[B

UU

--

---- ----

-- electron trajectory

c

λ

βc

λ

c

λ uu 2u

2γ

λλ 1β ………

for the sinusoidal trajectory

; )K2

1(1

2γ

λλ 2

2u (cm)(T).λ0.9BK uu

-- amplitude ukK

a

-- undulator induces a transverse component of velocity

10MeV 1;K4cm,[λu

75μλ

SYNCHRONIZATION

-- electrons from the and the second bunch subsequent bunches

em radiation field x)tkz(ESinE r

2

k

rB

zvv zinj

+

undulator field y)zk(SinBB uu

uu

2k

-- beating of rad. field & und. field gives

tzkk uc

)k(k

ωv

uph

ωtzkk u

c)k(k

ωv

uph

)k(k

ωvv

uphz )K

2

1(1

2γ

λλ 2

2u

conductor

dielectric film

Cerenkov condition

βn(λ)

1)Cos(

-- Cerenkov Free Electron Laser ( CFEL)

Fundamentals of Microwave Engineering -- R.E.Collins

Beam velocity = phase velocity of the mode

for mode01TM

)1

1(tan

1c

d2

21

2

ε

επdγλ

12

-- Synchronization

1~

]752,4.11,1.2[ mmd

m]7510MeV 1;K4cm,[λu

-- BUNCHING in CFEL

Advantages : 1) Low energy accelerator

i) pulse modulators [ 50 – 250 keV] ii) Marx Generators [ 500 keV – 1 Mev]

iii) rf accelerators [ up to ~ 5MeV]

Make the device compact

2) Short interaction region ( ~ 10 to 30 cm) II

+

--------------------------

A Table Top Device

Dispersion : Free Space

Limitations : i) wavelength range limited by beam size ii) power limited by dielectric breakdown

ε

επdγλ

12

1) single slab configuration

3) cylindrical slab configuration

2) double slab configuration

Different Dispersion Relations for

Different Configurations

Dielectric loaded film waveguide

(100 micron CFEL at Frascati) NIM A272,1988,132

film thickness – 92.5 microns film thickness – 48 microns

-- double slab geometry

-- dielectric constant : 2.12 ( TPX )

NIM A259,1987,125

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

- X-band Cerenkov FEM amplifier

A MM-WAVE, TABLE-TOP CERENKOV FREE ELECTRON LASER*I. de la Fuente, P.J.M. van der Slot, K. J. BollerUniversity of Twente, Laser Physics & Non-Linear Optics Group, PO Box 217, 7500 AE Enschede, The Netherlands

Nominal operational frequency 50 GHzAccelerating voltage From 65 to 100 kVLiner Material fused quartzDielectric constant : 5.8Thickness 1.3 mmInner diameter 3 mmLength 250 mmMagnetic field on axis 0.15 TBeam diameter 2 mmBeam current 800 mA

Table 1.1. characteristics of the CFEL

[2004 FEL Conf]

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

Hybrid FEL Devices

-- electron motion in an Undulator

even hormonic oscillations along the undulator axis and odd harmonic perpendicular to the axis

Dattoli et. al.

J Appl Phys 97 , 113102, 2005

SASE - FEL

SEGMENTED UNDULATOR

SASE - FEL

Pierce parameter ρ

* growth rate )N32exp(EE u0

1N s

u* undulator length

to reach saturation

* power transfer beamL PP at saturation

* limit on beam

energy spread

32

02

0 ])(4

K[ρ

R

P

u

c

0

0

2ω ;

dz

d

dz

d

),(f ),(

d),(fe)(

distribution function of particles in space

dv),(fe)(J z,yz,y

yv

d),(f

][)(J y

Substituting the expression for

Expanding the integral in Fourier series and keeping the terms in synchronism with the radiation field

-- Eqs of motion in ),( space

t

J

c

Z

t

E

c

1

z

E y02

y2

22

y2

sin

dz

dEs

cos

dz

d

[ V.B.Asgekar & G.DattoliOptics Communications 206 , p 373,2002 and 255 , p309, 2005]

c J 1

4

32 2

1.7 104

3 2

J

1

3

u u K J 8.36103

u

2J K fb K 1( ) 2

1

3

0 2.33 4.67 7 9.33 11.67 141 10

6

1 105

1 104

1 103

0.01

0.1

1

10

100

1 103

1 104

1 105

1 106

F z( ) H z( )

T z( )

Q3 z( )

F2 z( ) H2 z( )

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 )

0 1 2 3 4 5 61 10

51 10

41 10

30.01

0.1

110

100

1 103

1 104

1 105

1 106

F z( ) H z( )

T z( )

z

F(z)+H(z) ---- CFEL (300 micron)+UFEL(100 micron)

T(z) ---- UFEL(100 micron)

] 1.42K cm, 1 1.8, m, 10.8d 10,[ u

-- FEL Oscillators ( ?? )

( gain > losses)

-- integrate other types