Free Electron Laser

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Free Electron Laser and Accelerator Physics
A.M. Kondratenko GOO Zaryad, Novosibirsk
The development of coherent
radiation sources on a principle of the electron
laser (FEL) is based on the accelerator
technique. On the one hand FEL stimulates
development of accelerator technique, makes
special requirement to parameters of an electron
bunch, and on the other hand opens new
possibilities in the high-energy physics.
The usage of FEL for obtaining of the
high-energy polarized beams, for acceleration of
particles with high rate, for obtaining of high
energy ?-? colliding beams with high luminosity
are discussed here. Special instability Coulomb
interaction of particles in the beam can be used
for fast coherent electron cooling.
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Overview is based on works Yaroslav Derbenev,
Anatoliy Kondratenko and Evgeny Saldin published
in 1979-1985 years.
1) Generation of Coherent Radiation by a
Relativistic Electron Beam in an Undulator.
Dokl.Akad.Nauk. SSSR v.249 p 843(1979) Part.
Accel. v.10, p.207 (1980)Zhurnal Tech. Fiz.
v.51 p. 1633 (1981). 2) On the Linear Theory of
Free Electron Lasers with Fabry-Perot Cavities.
Zhurnal Tech. Fiz. v.52 p. 309 (1982). 3)
Polarization of the electron beam in a storage
ring by circularly -polarized electromagnetic
wave. Nucl.Instr. and Methods. v.165, p.201
(1979). 4) Polarization of the electron beam by
hard circular-polarization photons.Nucl.Instr.
and Methods. v.165, p.15 (1979). 5) Laser methods
of polarized electrons and positrons obtaining in
storage rings.Proc. of Intern. Symposium on
Polarization Phenomena in High Energy Phisics,
Dubna, USSR, p.281 (1982). 6) On the
Possibilities of Electron Polarization in Storage
Rings by Free Electron Laser. Nucl.Instr. and
Methods. v.193, p.415 (1982). 7) Coherent
Electron Cooling Proceedings of 7th Conference
on Charged Particle Accelerators, 1980, Dubna,
USSR, p. 269 AIP Conf. Proc. No. 253, p.103
(1992). 8) The electron acceleration by
electromagnetic wave in ondulator. Zh.Tech.Fiz.
v.53. p.1317 (1983). 9) The use of the Free
Electron Laser for generation of high energy
Photon colliding beams. Dokl.Akadem.Nauk. SSSR
v.264, p.849. Zh.Tech Phiz v.53 p.492 (1983).
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The basic principle of FEL operation
The single-flight regime
At a sufficient length of the undulator entrance
radiation is not necessary. The resonant
harmonics of density fluctuations become large
and the bunch can radiate a powerful wave.
The cavity FEL
If the gain per one path through the undulator is
small the undulator is installed in the cavity
where the radiation is stored.
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Particle motion in undulator
Lets pass electrons through the undulator, whose
magnetic field is repeated periodically in a
period ?0
In such fields the induced velocity of electron
motion may be written in the from
Where the velocity components V and transverse
components are the functions of electron
energy E and are periodic with period ?0 . To
define the parameter of longitudinal motion mass
The deviation of velocity from induced velocity
isand to define the important chromatically
parameters as
where I and ? is the act-phase variables of
transverse motion.If I0 we have ?V0. In
helical undulators ? and ? are follows
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Here is undulator
parameter.
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Radiative instabilities of electron beam in
undulators
For ultrarelativistic electrons (? gtgt 1)
resonance wavelength of radiation is to follows
and is much less then undulator period ?0.
Radiative increments essentially depend on the
cross size of the beam. There are characteristic
quantity
which distinguishes the narrow and wide beam. Let
us write the radiative increment for the case of
a continuous beam (r0 ? ?) . In the case of wide
beam (r0 gtgt rtr ) the increment
Coulomb interaction can be neglected for enough
large angle , when
. Here is ? ?2? c/?. In the case of narrow beam
radiative increment is
under condition . Coulomb
interaction can be neglected.
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Coherent radiation characteristics
Let's estimate a fraction of the beam energy,
converting into radiation for homogeneous
undulator. The particles must shift in
longitudinal direction under the influence of
radiation field by a value of the order
wavelength
where lg is growth length. Thus, the fraction
of the beam energy, transformed to radiation is
The coherent radiation power for uniform
undulator is
Let's notice, that in a non-uniform undultor, the
fraction of the energy transformed to radiation,
can be considerably increased using the capture
of particles in the wave field in an autophasing
mode.
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Usage of FEL for fast polarization of electrons
in storage rings
Effect is based on the dependence at the Compton
scattering cross section on the initial electron
(positron) polarization. In the case of hard
photons the spin dependence is used to knock out
mainly certain helicity from an electron beam in
a single scattering. This method enables one to
achieve very short polarization times (of the
order of a few seconds). In the case of fairly
soft quanta alternative method without particle
escape from the beam may be used to polarize the
beam. This effect is based on the dependence of
the energy losses in the multiple scattering on
the spin direction together with a spin- orbital
coupling in the field of a storage ring. This
coupling is necessary for the beam polarization
by soft quanta.
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Polarization of electrons in storage rings by
soft circularly polarized photons
e
undulater
accelerator
FEL
e
e
e
Parameters of FEL
Parameters of beam in accelerator
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Polarization of electrons in storage rings by
hard circularly polarized photons
e
undulater
accelerator
FEL
e
e
Parameters of FEL
Parameters of beam in accelerator
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Method of particle acceleration by
electromagnetic wave in undulator
undulater
This method is based on autophasing well-known in
the theory of accelerators. Effective Hamiltonian
describing autophasing, is similar to Hamiltonian
describing synchrotron oscillation in
accelerators
Inversed FEL
e
e
here p E - Es is energy deviation of
equilibrium particle energy,
is amplitude of effective potential. This
amplitude is proportional to transverse component
of velocity and wave field. At linear increase of
a field undulator we have particle acceleration
with constant rate
The effective potential dependence on the phase.
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Usage of FEL for particle acceleration
(transformer of energy )
undulater
undulater
Accelerator
FEL
Electron energy is decrease
Proton energy is increase
p
e
p
e
The numerical example of proton acceleration
(case of cylindrical resonator D4mm)
Parameters of FEL
Parameters of proton accelerated beam
Acceleration rate
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Usage of the FEL for generation of high energy
photon colliding beams
FELs open practical possibility of obtaining of
colliding photon beams (?-? quanta) with energy
of about 10x10 GeV and luminosity of about
existing colliding electron beams.
Interaction points of ?-? beams
Focusing lens
e
undulater
undulater
e
e
e
Interaction points of electron beams and FEL
radiations
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Numerical example of ?-? colliding beams (see
slide 12)
Parameters of beam in linear accelerator
Parameters of FEL
Spectral luminosity of ?-? beams
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