Free Electron Laser and Accelerator Physics

1. 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.

2. 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). 2

3. 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. 3

4. Particle motion in undulator Let’s 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 Eand 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 I=0 we have V=0. In helical undulators  and  are follows: 4 Here is undulator parameter.

5. Radiative instabilities of electron beam in undulators For ultrarelativistic electrons ( >> 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 >> 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. 5

6. 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. 6

7. 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. 7

8. 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 8

9. 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 9

10. 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. 10

11. Usage of FEL for particle acceleration (transformer of energy) undulater undulater FEL Accelerator Electron energy is decrease Proton energy is increase e p e p The numerical example of proton acceleration (case of cylindrical resonator D=4mm) Parameters of FEL Parameters of proton accelerated beam Acceleration rate 11

12. 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. Focusing lens Interaction points of - beams e undulater undulater e e e Interaction points of electron beams and FEL radiations 12

13. Numerical example of - colliding beams (see slide12) Parameters of beam in linear accelerator Parameters of FEL Spectral luminosity of - beams 13