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National Research Nuclear University MEPhI, MoscowRole of transversal size of bunches in soft X-ray Smith-Purcell radiation Daria SergeevaAlexey TishchenkoMikhail StrikhanovWorkshop THz and X-ray, March 18-19, 2013, KEK1 General of Smith-Purcell radiationA.A. Tishchenko, A.P. Potylitsyn, M.N. Strikhanov, Phys. Rev. E (2004)A.A. Tishchenko, A.P. Potylitsyn, M.N. Strikhanov, Phys. Lett. A (2006)The theory of X-ray and UV radiation from the bunch!Possibility of noninvasive submicron bunch diagnostics

2Workshop THz and X-ray, March 18-19, 2013, KEKPolarization current method

The polarization current density:

The radiation field:

A.P. Potylitsyn, M.I. Ryazanov, M.N. Strikhanov, A.A. Tishchenko, Diffraction Radiation from Relativistic Particles, Springer, 2010.3Workshop THz and X-ray, March 18-19, 2013, KEK

Spectral- angular distribution

4Workshop THz and X-ray, March 18-19, 2013, KEK

Form-Factorcylindrical cross section of the bunch rectangular cross section of the bunchD.Yu. Sergeeva, A.A. Tishchenko, M.N. Strikhanov, Nucl. Instr. and Meth.B, 2013 (in print).5Workshop THz and X-ray, March 18-19, 2013, KEK6 Transition radiation

G.M. Garibian and Y. ShiX-ray Transition Radiation, 1983

hWorkshop THz and X-ray, March 18-19, 2013, KEKDiffraction radiation: incoherent form-factor

7Workshop THz and X-ray, March 18-19, 2013, KEK

Role coherent and incoherent form-factor(energy of KEK ATF)(energy of LUCX)

8(energy of SLAC)Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.1)(Fig.2)(Fig.3)Carbon Window 5 - 4.4 nm (0.25 -0.28 keV)Water Window 4.4 - 2.3 nm (0.28 -0.53 keV)Penetration depth in water and in biological materials

Soft X-ray 1 - 4 nm (1000 300 eV)EUV4 60 nm (300 20 eV)9Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.4)

Role coherent and incoherent form-factor(energy of KEK ATF)(energy of LUCX)

10(energy of SLAC)Workshop THz and X-ray, March 18-19, 2013, KEK

(Fig.1)(Fig.2)(Fig.3)

Incoherent form-factor

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Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.5)(Fig.6)

Incoherent form-factor rectangular cross section of the bunch

12(energy of KEK ATF)Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.7)(Fig.8)

Incoherent form-factor cylindrical cross section of the bunch

13(energy of SLAC)Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.9)(Fig.10)

Role of the bunch transverse size for incoherent form-factorWorkshop THz and X-ray, March 18-19, 2013, KEK

14X-RayTHzOptics

(Fig.11)(Fig.12)(Fig.13)Possibility of noninvasive submicron bunch diagnostics

I L C

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Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.14)(Fig.15)

C L I C

16Possibility of noninvasive submicron bunch diagnostics Workshop THz and X-ray, March 18-19, 2013, KEK(Fig.16)(Fig.17) Summary - Incoherent form-factor is proved to exist; uniform distribution is explored in detail and it is shown that parameters range is rather narrow;

- Coherent form-factor depends on transversal size for .

- The theory of Smith-Purcell radiation is developed for UV and X-ray frequency ranges, which is very important for noninvasive submicron beam diagnostics.17

Workshop THz and X-ray, March 18-19, 2013, KEK Thank you for your attention!1920

Incoherent form-factor

21Workshop THz and X-ray, March 18-19, 2013, KEK Incoherent form-factor and transverse size of the bunch

22Workshop THz and X-ray, March 18-19, 2013, KEK Incoherent form-factor and transverse size of the bunch

23Workshop THz and X-ray, March 18-19, 2013, KEK Incoherent form-factor and transverse size of the bunch

24Workshop THz and X-ray, March 18-19, 2013, KEK