Channeling Studies at LNF: proposal for SPARC Sultan B. Dabagov About radiation features: for e+ BTF and for 150 MeV e-; Simulations by Babaev & Tomsk group;

@ Channeling of Charged Particles @ Amorphous: @ Channeling: Atomic crystal plane planar channeling e + e- Atomic crystal row (axis) axial channeling e- - the Lindhard angle is the critical angle for the channeling

@ Channeling of Charged Particles & Channeling Radiation Atomic plane of crystal e + - the Lindhard angle is the critical angle for the channeling @ Channeling Radiation: - optical frequency Doppler effect - CUP project studies the positron channeling for the development of Crystal Undulator for Positrons and represents the first step of an ambitious project that investigates the possibility to create new, powerful sources of high-frequency monochromatic electromagnetic radiation: crystalline undulator and -laser, based on crystalline undulator. The physical phenomena to investigate are essentially two: the spontaneous undulator radiation by channeling of relativistic positrons and the stimulated emission in periodically bent crystals (the lasing effect). Powerful radiation source of X-rays and -rays: polarized Tunable (keV - MeV) narrow forwarded

@ Channeling: Continuum model screening function of Thomas-Fermi type screening length Molier’s potential Lindhard potential …… Firsov, Doyle-Turner, etc. Lindhard: Continuum model – continuum atomic plane/axis potential

@ Channeling Radiation - optical frequency Doppler effect - Powerful radiation source of X-rays and -rays: polarized tunable narrow forwarded

@ Bremsstrahlung & Coherent Bremsstrahlung vs Channeling Radiation @ amorphous - electron: Radiation as sum of independent impacts with atoms Effective radius of interaction – aTF Coherent radiation length lcoh>>aTF Deviations in trajectory less than effective radiation angles: Nph Quantum energy

@ Bremsstrahlung & Coherent Bremsstrahlung vs Channeling Radiation @ interference of consequent radiation events: phase of radiation wave Radiation field as interference of radiated waves: . Coherent radiation length can be rather large even for short wavelength @ crystal: d Nph Quantum energy

@ Bremsstrahlung & Coherent Bremsstrahlung vs Channeling Radiation @ crystal: d channeling at definite conditions channeling radiation can be significantly powerful than bremsstrahlung B: CB: ChR:

@ Channeling Radiation & Thomson Scattering - radiation frequency - - number of photons per unit of time - - radiation power - @ comparison factor: Laser beam size & mutual orientation @ strength parameters – crystal & field:

@ Channeling Radiation & Thomson Scattering For X-ray frequencies: 100 MeV electrons channeled in 105 mm Si (110) emit ~ 10-3 ph/e- corresponding to a Photon Flux ~ 108 ph/sec ChR – effective source of photons in very wide frequency range: in x-ray range – higher than B, CB, and TS however, TS provides a higher degree of monochromatization and TS is not undergone incoherent background, which always takes place at ChR

@ "Quantum State" and "Classical" Dechanneling Length - i Electron Beam Energy 195 MeV “Occupation Length” 855 MeV 1500 MeV “Classical Dechanneling Length”

@ "Quantum State" and "Classical" Dechanneling Length - ii

@ Channeling in Si-Ge Undulator Planar channeling for for a beam undulating

@ Dechanneling of positrons

@ BTF Layout BTF as unique European facility to deliver positron beams in the range of the energy required for CUP strong photon peak with energy from 20 keV up to 1,5 MeV should appear according well accepted channeling and undulator theories for 400-600 MeV positrons e-/e+ g Crysral undulator High background/noise

@ Theoretical estimations: need for small divergence

@ Common Discussion of the 855 MeV and 270 MeV Measurements Ebeam = 855 MeV Strong reduction of channeling radiation No peak at 0.636 MeV observed Flat Crystal Possible explanation of both observations: Enhanced dechanneling due to centrifugal forces Undulator Crystal Nearly no reduction of channeling radiation Ebeam = 270 MeV Possible explanation: Centrifugal forces are not anymore of importance Undulator crystal Flat crystal Peak observed, but not at the predicted energy and with predicted line shape. Possible explanation: Inhomogeneities of the undulator caused by the production process. 17

@ Internal Clock by Channeling of Electrons /RICCI coll./ - i Axial electron channeling becomes promising potential candidate to check famous ideas

@ Internal Clock by Channeling of Electrons /RICCI coll./ - ii

@ Internal Clock by Channeling of Electrons /RICCI coll./ -iii

@ Nanotube simulations Nanosheet CC Base: fullerene molecule C60 sphere of d ~ 0.7 nm Roled graphite sheets: nested nanotubes

@ Potentials: Doyle-Turner approximation - form-factor for the separate fullerene dR r continuum potential as sum of row potentials r – distance from the tube I0(x) – mod. Bessel function

@ Potentials: Doyle-Turner approximation Continuum potential in C60 fullerite: [100] and [110] after averaging of the wall potential

@ Potential for neutral particles: Moliere approximation “Continuous filtration by energy” Ne Phys. Lett. A250 (1998) 360 NIM B143 (1998) 584

Multiple reflections: @ Simulations for dechanneling Angular distributions Coherent scattering: 0-L0 Multiple reflections: L0-20L0-103L0 Extremely powerful bending efficiency Angle of incidence – 0.5 critical angle of channeling

@ Coherent Diffraction Radiation Diffraction radiation appears when a charged particle moves in the vicinity of a medium. Impact parameter h – the shortest distance between a particle and a target. Incoherent radiation: Coherent radiation:

@ Parametric X-Ray Radiation DEI PXR diagnostics facility at LEBRA Nihon Univ.

Dechanneling studies  quantum ^ classical dechanneling lengths; @ Various crystal channeling studies at SPARC Channeling radiation at flat crystals (keV-MeV); Dechanneling studies  quantum ^ classical dechanneling lengths; Undulator radiation in periodically bent crystals (keV); Other solutions for X-source (imaging?): - PXR radiation - Diffraction radiation: studies for coherent  CDR; Channeling as a tool for fine experiments (“atomic clock” at SPARC); Channeling in nanostructures  nanotubes as beam guides

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