1. Channeling Studies at LNF
Sultan B. Dabagov
on behalf of CUP & µX collaboration:
LNF + Mainz + Aarhus
About radiation features: for e+ BTF and for 150 MeV e-;
Simulations by Babaev & Tomsk group;

2. @ Free Electron Laser Self-Amplified-Spontaneous-Emission
(No Mirrors - Tunability – Harmonics)

3. SEEDING FEL project at Frascati Channeling @ FEL activity at LNF MAMBO…
Channeling
FEL project at Frascati
Source
Pulsed
Self Amplified
Radiation
Coherent
SEEDING

4. @ SPARC & Applications Plasmon 14.5 m 1.5m 10.0 m 5.4 m 11º
quadrupoles
dipoles
Diagnostic
1-6 Undulator modules
Photoinjector
solenoid
RF sections
Plasmon
Thomson
RF deflector
collimator
25º
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

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

6. @ 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

7. @ 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

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

9. @ 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

10. @ 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

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

12. @ 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:

13. @ 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

14. @ 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

15. @ Positron Channeling in Si-Ge Undulator

16. @ Positron Channeling in Si-Ge Undulator

17. @ Dechanneling of positrons

18. @ Theoretical estimations: need for small divergence

19. @ Theoretical estimations: feasibility of observation

20. @ Experimental Setup at BTF

21. @ Crystal characterization: MAMI 855 MeV e-

22. @ Radiation record at BTF 600 MeV e+
No evidence for channeling / channeling radiation

24. X-ray channeling:
flux peaking

25. @ down to bulk x-ray channelingmm 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 di°Ëerence of radiationpropagation in - and n-channels is deÖned by the ratio between the e°Ëective
guide-channel size and the transverse wavelength of radiation (Fig. 1). The guiding channel is deÖned by its shape in -channels (collimation proÖle or
surface curvature) whereas for n-channels - by the transverse channel size.

26. 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

27. @ Simulations for x channeling: bending of radiation
Evolution of angular distribution
rcurv ~ 2 m :
Strong bending effect

28. @ wave field formation in a planar waveguide
Diffraction from Si corner (gap 30 nm; =0.1 nm):
(a) analytical solution; (b) computer simulation

29. @ planar n-guide :: quantum states of channeling
:: character of radiation transmission ::
:: the ray optics approach for describing
radiation propagation
ζ = 2πθсa/λ = 2πa/λ┴c [λ┴c = λ/θc ] :: the number of bound modes N.
ζ >> 2π N 1 :: the geometric optics approximation
ζ >> 2π a >> λ┴c [glass λ┴c = 40 nm]
Thus for a wide waveguide a  40 nm there are many bound modes and multiple reflection of rays can be used.
In the other limit ζ << 1 or a  7nm one even bound mode

30. @ planar n-guide Expansion in a set of guiding modes ::
:: population of m-th mode
For an ultra narrow waveguide with aperture ::
2a = 5.2 nm (ζ = 1/sqrt(6))
the integral intensity of the bound mode ::
P = Q12 = 25a k┴in=0
Normal incidence of the incoming beam ::
Effective aperture:: about one order larger than the geometrical one
Strong dependence on the incidence angle:
Q12 = 4.5a at θin = k┴in/k = 0.5•θc
Q12 = 0.6a at θin = θc.

31. @ planar n-guide
Angular dependence for the population of a single mode propagation in ultra narrow planar waveguide.
The dependence is norma-lized to geometrical accep-tance of the waveguide.

32. @ flux peaking effect Integral within -θm ≤ θin ≤ θm
For the considered ultra narrow waveguide the intensity at the gap center
I = 3.5 I0 at θin = flux peaking effect
Attenuation with penetration due to absorption! In the glass cladding 73 % of the wave intensity (tunneling length ~3a  8 nm)
… the strong tunneling effect…
-θm ≤ θin ≤ θm

33. @ total transmitted power for a planar n-guide
Normalized value of radiation power integrated within vacuum gap vs. coordinate x calculated for step-like entrance function (bottom lines) and for total calculated field (top lines). Solid lines are the result of computer simulation and dashed lines are the result of asymptotic solution

34. @ circular n-guide wave equation in circular guide
J_{m}(y) and K_{m}(y) –
the 1st kind and the modified 2nd kind Bessel functions
Two limits:
inside the core
the cladding
dispersion equation

35. @ circular n-guide
@ effective aperture is larger than the geometric one in ~1010 times;
due to very large tunneling length, which is equal to
no absorption!
@ the average effective aperture at θm=θc only 24 times is larger than the geometric one.
@ the flux peaking is also strong – the intensity of the bound mode at the center of wave guide at θin = 0 is equal I(0) = Q012•A2 = 576.
Intensity increase is 576 times due to the logarithmic singularity of the function
K0(x)|

36. @ flux peaking effect Flux peaking effect for a circular guide.
Due to the flux peaking effect, at the guide center, the radiation intensity may overcome in 2 orders the intensity of the incoming beam

37. @ nanocapillaries - number of modes ~ 40 nm for glass
Tunneling length ~ 8 nm

38. @ Resume for x channeling
Analysis of radiation propagation through the guides of various shapes, above presented, has shown that all the observed features can be described within unified theory of X-ray channeling: - surface channeling in μ-size guides - bulk channeling in n-size guides. The main criterion defining character of radiation propagation is the ratio between the transverse wavelength of radiation and the effective size of a guide, i.e the ratio between the diffraction and Fresnel angles. @ this ratio is rather small, i.e. when the number of bound states is large, the ray optics approximation - λ⊥ ≃ d, a few modes will be formed in a quantum well; - λ⊥ ≫ d - just a single mode . @ flux peaking of X radiation, i.e. the increase of the channeling state intensity at the center of a guide - a proper channeling effect that can be explained only by the modal regime of radiation propagation, and may find an interesting application for the purposes of extreme focusing. @ all the considerations taken for X-rays should be valid for thermal neutrons.

39. …? additional information ?…
thank you