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Required Energy Flexibility

Required Energy Flexibility. Zafer Nergiz Nigde University, Science Faculty, Physics Department Ankara University, Institute of Accelerator Technologies. Outline. I t is studied on theoretical equations and simulation codes to calculate FEL properties. The studies are at preliminary stage.

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Required Energy Flexibility

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  1. Required Energy Flexibility ZaferNergiz Nigde University, Science Faculty, Physics Department Ankara University, Institute of Accelerator Technologies

  2. Outline • It is studied on theoretical equations and simulation codes to calculate FEL properties. • The studies are at preliminary stage. • This studies below are good exercises and should be developed with beam dynamic studies. • Theoretical equations and related graphs • Simulation Results • Future Plans FEL parameter working group meeting

  3. Theoratical Studies • The wavelength of the radiation is calculated by the basic and well known formula The relationbetweenthe radiation wavelength, the electron beam energy and Krmsundulator parameter. FEL parameter working group meeting

  4. FEL Parameters • Basic characteristics of the SASE FEL are simply estimated by the FEL parameter which is given by • Where j0 is the beam current density, IA=17000 A,Ajjis the coupling factor and it is equal to 1 for helical magnet fields. For linear fields Ajj=[J0(Q)-J1(Q)]. Jn is the bessel function of FEL parameter working group meeting

  5. The formulas To Calculate Gain and Power related parameters: FEL parameter working group meeting

  6. Gain formula for optimum beta value and fundamental wavelength FEL parameter working group meeting

  7. Gain length versus radiation wavelength lu=0.015m, ku=1, I=5 kA and Energy is tuned between 4-8 GeV Gain length versus radiation wavelength lu=0.015m, ku=2, I=5 kA and Energy is tuned between 4-8 GeV FEL parameter working group meeting

  8. Gain length versus Krmsundulator parameter, lu=0.015m, Ee=5 Gev, I=5 kA • Krms: 1 • lr: 1.56 A • GainLength: 4.7 m • SaturationLength: 47 m • Gain length versus Krmsundulator parameter, lu=0.015m, Ee=8Gev, I=5 kA • Krms: 1 • lr: 0.61 A • GainLength: 8.88 m • SaturationLength: 88 m FEL parameter working group meeting

  9. Gain length for differentelectron beam energy and undulator parameter. Optimum beta values for different electron beam energy end K values. FEL parameter working group meeting

  10. Simulation studies • First stage a symmetric lattice composed to put 4.2 m undulator. • The quadrupol strengths are 2.4 m-2 and -2.4 m-2. FEL parameter working group meeting

  11. The simulation is performed by Genesis simulation code. • For 5 GeV electron beam energy, 15 mm undulator period and ku=2 the saturation occur around 90 m and 8 GW power can be produced. FEL parameter working group meeting

  12. Future Studies • Work on optimum beta parameter and a new lattice design according to this results. • Decrease the saturation length with appropriate undulator and e beam parameters • Time dependent simulation study • Simulation by the bunch distribution gotten from beam dynamic group. FEL parameter working group meeting

  13. References • E.L. Saldin, E. A. Schneidmiller, and M.V. Yurkov, Design formulas for shortwavelength FELs, Opt. Commun. 235 (2004) 415. • The European X-ray Fel Technical Designe Report, 2007 • http://genesis.web.psi.ch/index.html FEL parameter working group meeting

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