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B. Azadegan , S. A. Mahdipour , W. Wagner 26.09.2013, Sevan

Simulation of positron energy spectra generated by channeling radiation of GeV electrons in a tungsten single crystal. B. Azadegan , S. A. Mahdipour , W. Wagner 26.09.2013, Sevan. Outline Introduction Theory of channeling radiation in thick crystal Numerical results

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B. Azadegan , S. A. Mahdipour , W. Wagner 26.09.2013, Sevan

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  1. Simulation of positron energy spectra generated by channeling radiation of GeV electrons in a tungsten single crystal B. Azadegan, S. A. Mahdipour, W. Wagner 26.09.2013,Sevan • Outline • Introduction • Theory of channeling radiation in thick crystal • Numerical results • Solution of Fokker-Plank equation • Positron production in a hybrid schame • Summary

  2. Channeling radiation 1. Introduction - Lorentz factor - observation angle • CR properties • quasi-monochromatic • directed • intense • tunable

  3. 2. Theory of planar channeling radiation • Planar Continuum potential: • Axial Continuum potential: • Axial continuum potential of <100> axis of W single crystal • Planar continuum potential of (110) plane of C, Si, Ge and W single crystal

  4. 2. Theory of planar channeling radiation (classical) • Classical model Planar : Axial : Angular energy distribution: Total radiated energy in thick crystal:

  5. (a) Θ0=0.0 (b) Θ0=0.25 mrad 3. Numerical results Trajectories and CR spectra for one incident point with a) zero b) 0.25 mrad incidence angles for 2 GeV electron channeled along the (110) plane of a tungsten single crystal. Planar: Trajectory (rosette motion) and CR spectra for one incident point for 1 GeV electron channeled along the <100> axis of W single crystal. Axial:

  6. 4. Solution of Fokker-plank equation Fokker-Plank equation: Boundary conditions: Drift coefficient: Diffusion coefficient: Es=13.6 MeV Time parameter:

  7. 4. Solution of Fokker-plank equation For the numerical solution of the Fokker-Plank equation, a uniform distribution of the electron across the transverse x coordinate, and a Gaussian scattering distribution tilted by an angle θ0, and with standard deviation y for the angular divergence were assumed. • Time parameter c.T • Drift coefficient D1, • Diffusion coefficient D2 • Initial probability density distribution • F0 at z=0 • calculated with standard deviation • y=100 µradand θ0=0all as function of transverse • energy for 2 GeV electrons.

  8. 4. Solution of Fokker-plank equation probability density for 2 GeV electrons channeled along (110) plane

  9. 4. Solution of Fokker-plank equation . Electron dechanneling function: Dechanneling length:

  10. 4. Solution of Fokker-plank equation Dechanneling lengths for (110)-planar channeling of electrons as function of the electron energy

  11. 4. Solution of Fokker-plank equation Radiation intensity in thick crystals: (b) W (a) C Thickness dependence of radiation spectrum for 2 GeV electrons channeled along (110) plane of a) diamond b) Tungsten

  12. 4. Solution of Fokker-plank equation Red θ=0.0 Blue θ=45.35 µradYellow θ=90.69 µrad Orange θ=136.04 µradPink θ=181.39 µrad Green θ=272.0 µrad Intensity Photon energy (MeV) Dependence of radiation spectrum on incidence angle of electrons for 2 GeV electrons channeled along (110) plane of Ge

  13. (b) (a) e+ e+ e+ e- γ e- e- e- e- Amorphous convertor Crystal Crystalline radiator • 5. Positron production in a hybrid schame • Schemes of non-conventional positron sources. • One single crystal. • Crystalline target combined with an amorphous convertor. Positron spectra are simulated by means of GEANT4 Monte Carlo code taking the CR/CB spectra as input data

  14. 5. Positron production in a hybrid schame Number of positrons Comparison of positron energy distributions between C, Si, Ge, W radiator crystals

  15. 5. Positron production in a hybrid schame Number of positrons Dependence of positron energy distribution on thickness of radiator crystal for 2 GeV electrons channeled along (110) plane of W radiator crystal

  16. 5. Positron production in a hybrid schame rad Number of positrons Dependence of positron energy distributions on incidence angle of electrons for 2 GeV electrons channeled along (110) plane of Ge

  17. 6. Summary • Planar CR emitted by electrons channeled in thick crystals has been investigated theoretically on the base of the solution of Fokker-Plank equation. • Dependence of CR spectrum on the incidence angle of electron has been investigated. • Dependence of positron energy distribution on the thickness of radiator crystal and the incidence angle of electron has been investigated in a hybrid positron production scheme. • Positron energy distributions of C, Si, Ge and W radiator crystals have been compared. • W radiator crystal with small channeling length produce more positron in comparison with C, Si and Ge. • Comparison of positron energy distribution in planar and axial CR needs the solution of Fokker-Plank equation for axial CR in two dimentions.

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