Channeling Studies at LNF
Sultan B. Dabagov on behalf of CUP & X collaboration: LNF + Mainz + Aarhus About radiation features: for e+ BTF and for 150 MeV e-; Simulations by Babaev & Tomsk group; @ Free Electron Laser Self-Amplified-Spontaneous-Emission
(No Mirrors - Tunability Harmonics) SEEDING FEL project at Frascati Channeling @ FEL activity at LNF MAMBO
Channeling FEL project at Frascati Source Pulsed SelfAmplified Radiation Coherent SEEDING @ SPARC & Applications Plasmon 14.5 m 1.5m 10.0 m 5.4 m 11
quadrupoles dipoles Diagnostic 1-6 Undulator modules Photoinjector solenoid RF sections Plasmon Thomson RF deflector collimator 25 FEL Application Bunch charge (nC) Energy (MeV) Bunch length rms (ps) Norm. rms emittance (mm) Energy Spread (%) PlasmonX 0.025 0.1 0.2 Thomson 1-3 28-200 3 2-5 @ 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 Moliers 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 @ 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 MeV positrons e+ g Crysral undulator High background/noise @ Positron Channeling in Si-Ge Undulator @ Positron Channeling in Si-Ge Undulator @ Dechanneling of positrons @ Theoretical estimations: need for small divergence @ Theoretical estimations: feasibility of observation @ Experimental Setup at BTF @ Crystal characterization: MAMI 855 MeV e- @ Radiation record at BTF 600 MeV e+
No evidence for channeling / channeling radiation X-ray channeling: flux peaking @ down to bulk x-ray channeling
mm l : grazing incidence optics : from nm to mm : surface channeling nm l : diffraction angle approaches Fresnel angle : bulk channeling As is well known from quantum mechanics, any well is able to support at least one quantum bound state (channeling state); the number of bound states can be estimated from the expression for the potential (4). Equation (3) for radiation propagation in a medium with the potential (4) can be solved for the case of -guides as well as for the n-guides. The basic dierence of radiationpropagation in - and n-channels is dened by the ratio between the eective guide-channel size and the transverse wavelength of radiation (Fig. 1). The guiding channel is dened by its shape in -channels (collimation prole or surface curvature) whereas for n-channels - by the transverse channel size. Multiple reflections:
@ Simulations for x channeling (straight & bent) Angular distributions Spatial Coherent scattering: 0-L0 Multiple reflections: L0-20L0-103L0 Angle of incidence 0.5 critical angle of channeling @ Simulations for x channeling: bending of radiation
Evolution of angular distribution rcurv ~ 2 m : Strong bending effect @ wave field formation in a planar waveguide
Diffraction from Si corner (gap 30 nm; =0.1 nm): (a) analytical solution; (b) computer simulation @ planar n-guide :: quantum states of channeling
:: character of radiation transmission :: :: the ray optics approach for describing radiation propagation = 2a/ = 2a/c [c = /c ]:: the number of bound modes N. >> 2 N 1 :: the geometric optics approximation >> 2 a >> c [glassc= 40 nm] Thus for a wide waveguide a 40 nm there are many bound modesand multiple reflection of rays can be used. In the other limit