Free Electron Laser[1]

8/7/2019 Free Electron Laser[1]

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PRESENTED BYPRESENTED BY

ANANTANANTKUMAR SINHAKUMAR SINHA

M. Tech. (EP) 2010M. Tech. (EP) 2010--1111

UNDER THE GUIDANCE OFUNDER THE GUIDANCE OFMUKESH KUMARMUKESH KUMAR

USBAS , G. G. S. I. P. UNIVERSITYUSBAS , G. G. S. I. P. UNIVERSITY

DWARKA ,NEW DELHIDWARKA ,NEW DELHI--110075110075


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1. INTRODUCTION :1. INTRODUCTION : What is a FELs?

2. BASIC COMPONENTS2. BASIC COMPONENTS

3. WORKING PRINCIPLE :3. WORKING PRINCIPLE :How does an FEL work?

3.1. SPONTANEOUS EMISSION3.1. SPONTANEOUS EMISSION

3.2. STIMULATED EMISSION3.2. STIMULATED EMISSION

4. APPLICATIONS4. APPLICATIONS


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FreeFree--electron lasers (FELs) are lasers that use aelectron lasers (FELs) are lasers that use aelectron beam from an accelerator to produceelectron beam from an accelerator to produce

widely tunable , high power, ultrafast pulses ofwidely tunable , high power, ultrafast pulses of

coherent radiation .coherent radiation .

The freeThe free--electron laser ( FEL ) is a new kind ofelectron laser ( FEL ) is a new kind oflaser in which the electrons are not bound inlaser in which the electrons are not bound inatomic or molecular systems .atomic or molecular systems .


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The source of these free electrons is an electronThe source of these free electrons is an electronaccelerator, such as a linac or a synchrotron .accelerator, such as a linac or a synchrotron .

The interaction of free electrons andThe interaction of free electrons andelectromagnetic radiation , in the presence of aelectromagnetic radiation , in the presence of auniform magnetic field , can results in stimulateduniform magnetic field , can results in stimulatedemission or absorption .emission or absorption .

It is therefore a classical rather than a quantumIt is therefore a classical rather than a quantum--mechanical laser .mechanical laser .


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BASIC COMPONENTSBASIC COMPONENTS


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Schematic figure of FEL :Schematic figure of FEL :


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WORKING PRINCIPLEWORKING PRINCIPLE

The FEL mechanism involves three steps :The FEL mechanism involves three steps :

1. The electrons oscillate inside the undulator1. The electrons oscillate inside the undulator

and emit spontaneous emission.

and emit spontaneous emission.

2. This radiation acts back on the undulating2. This radiation acts back on the undulating

electrons and bunches them .electrons and bunches them .

3. The bunched electrons emit coherent3. The bunched electrons emit coherent

stimulated radiation and amplify propagatingstimulated radiation and amplify propagating

electromagnetic wave .electromagnetic wave .


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SPONTANEOUS EMISSIONSPONTANEOUS EMISSION

The heart of the FEL is the undulator whichThe heart of the FEL is the undulator which

produces a magnetic field that is static in time ,produces a magnetic field that is static in time ,but varies sinusoidally in space:but varies sinusoidally in space:

BBu = y Bu = y Buu cos( Kcos( Kuu Z );Z );where Bwhere Buu is the peak value of the magnetic field ,is the peak value of the magnetic field ,

KKuu=2/=2/u ,u , and and uu is the period of the undulator .is the period of the undulator .


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When a high energy electron beamWhen a high energy electron beam(relativistic) from an electron accelarator ,(relativistic) from an electron accelarator ,moving along the zmoving along the z--axis , is injected intoaxis , is injected into

this undulator , the electrons experience athis undulator , the electrons experience a

Lorentz force due to the transverse magneticLorentz force due to the transverse magneticfield , and starts oscillating in the xfield , and starts oscillating in the x--z plane .z plane .

Like any oscillating charge moving with aLike any oscillating charge moving with a

relativistic speed , the electron radiate in therelativistic speed , the electron radiate in the

forward direction in a narrow cone with aforward direction in a narrow cone with asemi angle of ~1/ , where is the energy ofsemi angle of ~1/ , where is the energy of

electron in units of its rest mass energy.electron in units of its rest mass energy.


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The wavelength of emitted radiation isThe wavelength of emitted radiation is

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2

2K

u

r!

K

PP


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This is called resonance equation.This is called resonance equation.where k is called the undulator parameter and is givenwhere k is called the undulator parameter and is givenby k= e Bby k= e Buu uu /2mc ./2mc .

Typically , the longitudinal distribution ofTypically , the longitudinal distribution ofthe electrons is random within a distance r .the electrons is random within a distance r .

The radiation from individual electrons thereforeThe radiation from individual electrons therefore

adds incoherently and termed as SPONTANEOUSadds incoherently and termed as SPONTANEOUSEMISSION .EMISSION .


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STIMULATED EMISSIONSTIMULATED EMISSION

As the electron beam travels down theAs the electron beam travels down the

undulator , it gets bunched as a result ofundulator , it gets bunched as a result of

interaction with the undulator magnetic fieldinteraction with the undulator magnetic field

and the coand the co--propagating radiation beam ofpropagating radiation beam offrequencyfrequency LL ( spontaneous emission ).( spontaneous emission ).


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This bunching can be explained in terms ofThis bunching can be explained in terms ofthe longitudinal Lorentz force arising due tothe longitudinal Lorentz force arising due to

the coupling between the transverse velocitythe coupling between the transverse velocityvvxxof the electron , arising from the interactionof the electron , arising from the interaction

with the undulator magnetic field , and thewith the undulator magnetic field , and the

oscillating magnetic field Boscillating magnetic field BLL of the radiationof the radiation

beam.This force is known as thebeam

.This force is known as thePONDERMOTIVE FORCE .PONDERMOTIVE FORCE .


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For a plane EM wave,For a plane EM wave,

BBLL = y B= y BLL cos (Kcos (KLL zz -- LL t +t +LL)) ..

vvxx can be shown to varry as to sin (can be shown to varry as to sin (KKuu z ).z ).

Then the magnitude of the pondermotive forceThen the magnitude of the pondermotive force

FFzz ( = e( = evvxx BBLL)) is given byis given by

FFzz [ [ -- sin (Ksin (KLL z + Kz + Kuu zz -- LL t +t +LL) + sin (K) + sin (KLL zz -- KKuu zz-- LL t +t +LL)] .)] .


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The term ( kThe term ( kLL zz +k+kUU zz-- LL t +t + LL) is known as) is known as

pondermotive phase .pondermotive phase .

Different electrons see different phases andDifferent electrons see different phases and

therefore experience the pondermotive forcetherefore experience the pondermotive force

with different magnitudes and directions , andwith different magnitudes and directions , andthis leads to bunching of electrons .this leads to bunching of electrons .

ForFor LL ~~ RR, i.e. near resonance , the z, i.e. near resonance , the z--

component of the electron velocity iscomponent of the electron velocity is LL//((kkLL++kkUU))


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The distance between successive bunchlets isThe distance between successive bunchlets is

2/2/((kkLL++kkUU)) ..

All the electron in the bunchlet radiate at theAll the electron in the bunchlet radiate at thesame phase and successive bunchlets radiatesame phase and successive bunchlets radiate

with phase difference of 2 .with phase difference of 2 .

Hence this radiation develops coherence , and isHence this radiation develops coherence , and istermed as coherent radiation .termed as coherent radiation .


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Free Electron Laser[1]