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Increase of PXR intensity due to Borrmann effect

Increase of PXR intensity due to Borrmann effect. 1) Islamic Azad University, Malayer , Iran, Physics department 2) Belarusian State University, Minsk, Belarus, Physical faculty, Department of Theoretical physics. A. Ahmadi 1),2) , I.Feranchuk 2) , A. Benediktovitch 2 ). Outline.

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Increase of PXR intensity due to Borrmann effect

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  1. Increase of PXR intensity due to Borrmann effect • 1) Islamic Azad University, Malayer, Iran, Physics department • 2) Belarusian State University, Minsk, Belarus, Physical faculty, Department of Theoretical physics A. Ahmadi1),2) , I.Feranchuk2), A. Benediktovitch2)

  2. Outline • 1917: Dynamical diffraction theory by P.Ewald • 1950:Borrmann effect – first time it was really used • General expression for spectral-angular distribution of PXR • Simplifications in thick crystal case • Reduced density effect, increased intensity • Outlook and conclusions

  3. Spectral-angular distribution In the Fraunhofer regime the Green function of Maxwell equation is The spectral –angular distribution of emitted radiation from current leads to A.Ahmadi, I. Feranchuk, NIM B 311 (2013) 78-85

  4. Spectral-angular distribution In the Fraunhofer regime the Green function of Maxwell equation is The spectral –angular distribution of emitted radiation from current leads to A.Ahmadi, I. Feranchuk, NIM B 311 (2013) 78-85

  5. Wave field calculation: “Time-reversed” wave field boundary condition at r→∞

  6. Wave field calculation: two beam dynamical diffraction Set of equations for two strong waves dispersion equation solutions near Bragg conditions

  7. Spectral-angular distribution: general case Transferred momentum and radiation coherent length in vacuum in crystal

  8. Spectral-angular distribution: general case Transferred momentum and radiation coherent length Electron scattering in the medium in vacuum in crystal

  9. Spectral-angular distribution: general case Transferred momentum and radiation coherent length Electron scattering in the medium in vacuum in crystal

  10. Spectral-angular distribution: when Under conditions we can use at we have

  11. Spectral-angular distribution: when

  12. Spectral-angular distribution: dynamical vs. kinematical (σpolarization) Dynamical theory result Kinematical Borrmann parameter

  13. Outcome: reduced density effect Lengths that bound PXR outcome in kinematical approach: Crystal thickness , absorption length , maximal vacuum coherence length For maximal outcome it should be hence Borrmann parameter

  14. Outcome: reduced density effect

  15. Outcome: increased intensity Si (220) 100 MeV, σ 400 MeV, σ 855 MeV, σ 855 MeV, π

  16. Outcome: increased intensity Si (111) 700 MeV, σ 1100 MeV, σ

  17. Outlook • Correct description of high-resolution experiments • Lower threshold for Parametric Beam Instability • More pronounced effect can be expected for • Parametric Gamma Radiation (PGR) *) • Borrmann parameter is smaller, • but assumption is wrong. atoms nuclei *)

  18. Conclusions • Expressions for PXR distributions taking into account the dynamical diffraction treatment are formulated in compact way highlighting Borrmann parameter • Dynamical treatment results in higher energies for density effect and higher PXR intensity • These effects are expected to be more pronounced in the case of PGR

  19. Thank you for your attention!

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