1. Brainstorming on photon-photon scattering experiment
Scaling Laws for Photon Fluxes, Bandwidths, Luminosity, etc, and a look at the interaction point (e-g with primary and secondary electron beams)
Can we get up to L= 1027 cm-2sec-1 ??
Nev = 1 mbarn*1027 = 1 ev/hour
L. Serafini - INFN-Milan
First we produce Gamma photons ( MeV) with 2 Compton
Sources (similar to ELI-NP), then we collide the 2 counter-prop.
gamma photon beams, focused to mm spot size

2. Small Compton Recoil in quasi-Thomson back-scattering
= electron relativistic factor
= angle of observation (q = 0 -> photon scattered on electron beam propagation axis)
= laser frequency
ng = frequency of the scatterd (X,g) photon
a0 = dimensionless amplitude of the vector potential
for the laser e.m. field , a0=eE0/(wLmc)

3. Relative deviation of Comtpon vs. Thomson
frequency/wavelength (optical incident photons)
x=0.01
ELI
Thomson (elastic)
neglig. recoil
Classical Synchr. Rad.
Intermediate zone
Quantum Effects Dominant

4. All quantities below are per shot (i.e. nRF=1 fRF=1)
g (MeV)
ELI-NP-like machine
U= 1 Joule
st = 1.5 psec
Q=480 pC (3.109 e-)
hn = 1.2 eV
hn=2.4 eV
hn=1.2 eV
total # gamma photons
over solid angle per shot
All quantities below are
per shot (i.e. nRF=1 fRF=1)
sx (mm)

5. Total Scattered Photons
UL = Laser pulse energy
Q = electron bunch charge
fRF = RF rep rate
nRF = #bunches per RF pulse
f = collision angle (<<1)
f = 0 for head-on collision
st = laser pulse length
hn = laser photon energy [eV]
sx = electron bunch spot size at collision point
N.B. all quantities are intended as rms,
all distributions are assumed as gaussians in (phase) space and time

6. Angle-frequency correlation
Collecting the radiation over the whole solid angle,
the spectrum is white. n q
CAIN results Dn Dn
The more energetic photons are emitted on or close to the axis Dn
By selecting the photons on axis with a system of collimators
one can reduce the bandwidth.
White spectrum

7. RMS bandwidth, due to collection angle, laser phase space distribution and electron beam phase space distribution
electron beam
laser

8. Energy-angular Spectral distribution

10. Luminosity in collision
Cost (Meuro): 2 x ( laser 5 + linac 15) = 40

11. Envelopes of the laser beam (dotted line), first electron beam (for Compton back-scattering, dashed) deflected after collision with laser to clear the second electron beam (solid line).
laser envelope
envelope of first
electron beam deflected
x [mm]
Laser intensity distribution
and first electron bunch at
Compton back-scattering
Collision point
collision
point
second electron beam
envelope to collision
incoming gamma
photon beam envelope
z [mm]

12. Enlarged view (zoomed out over 1 cm in z and microns in x) to show laser envelope clearance and deflecting dipole poles (0.3 T B field applied).
laser envelope
x [mm]
envelope of first
electron beam deflected
collision
point
second electron beam
envelope to collision
incoming gamma
photon beam envelope
z [mm]

14. Energy available W in the center of mass
1 GeV electron against 10 MeV gamma -> W=200 MeV
Luminosity in collision
hng = gamma photon energy [MeV] ; Te = colliding electron energy [MeV]
s0 = electron bunch (and gamma photon beam) spot size at collision point
Ne= # electron in bunch ; Ng = # gamma photons in burst
fRF = RF rep rate ; nRF = # electron bunches per RF pulse

15. Inverse Compton (Thomson) ScatteringlL
energy = Ee= g me q lX
Normal Compton Scattering the photon has higher energy than the electron
The inverse process has the Thomson cross-section when hx < Ee
The scattered photon satisfies the undulator equation with period lL/2 for head-on collisions
(1+a02/2+gq)
lX = lL
4g2
Therefore, the x-ray energy decreases substantially at an angle 1/g

16. The electron gamma collider will operate in the weak
Compton regime to generate the gamma photons:
the gamma photon energy will be approx. given by
So the center of mass energy W
becomes (for a0=0.15) g

17. Scattered photons in collision
electrons
laser
Thomson cross-section
Scattered flux
Luminosity as in HEP collisions
Many photons, electrons
Focus tightly
N.B. there are two collisions: the first is in the Compton Source, between the first electron
bunch and the laser pulse (optical photons) to produce the gamma-ray beam (spot size sx).
The second collision is between the “focused” gamma ray beam and a second independent
electron bunch (spot size s0): luminosity is calculated in this second collision

18. We have to decide what is the maximum acceptable bandwidth for the gamma photon beam: let’s assume 10%, this defines univocally the maximum collection angle Yopt
so the # gamma photons within the requested bandwidth (0.1) is function only of the laser and electron beam characteristics

19. ELI-NP extended f = 0 , T = 800 MeV Dg/g = 0.001
en = 0.5 mm Dng/ng=0.1
This is the number of gamma photons per shot to be used in the luminosity formula

20. Therefore the photon beam peak Brilliance (on single shot) becomes
We can also derive the emittance of the gamma photon beam: this is a quadratic sum of the electron beam emitt. and rms angle of scattering, i.e. Yopt /g
Therefore the photon beam peak Brilliance
(on single shot) becomes

21. Coming back to luminosity: now we collide a fresh 1 GeV electron bunch carrying Qb=320 pC, with Dg/g = en = 0.5 mm and sz = 190 mm against the gamma photons per burst
What is the minimum spot size s0 ?
We have to respect the hour-glass condition for the collision, i.e.
therefore
because
c.v.d…

22. Concerning the separation of the two counter-propagating electron beams: since the laser-electron collision (Compton Source) to produce the gamma photons occurs 4.7 mm before the final collision point (where laser and electron beam have 5.5 mm spot size), and the gamma photon beam focuses down to the collision point to 0.21 mm spot size, it is enough to deflect the first eletron beam (the one colliding with the laser) by a very small angle = 6*0.21 mm / 4.7 mm = 0.27 mrad. This small deflection angle is enough to clear the two counter-propagating electron beams (note that the gamma photon beams retains almost the same emittance as the electron beam that produces it by Compton back-scattering, with a slight degradation).

23. Spectral broadening due to ultra-focused beams:
Thomson Source classically described as a
Laser Syncrotron Light Source X e- X e-
focus
envelope
Scattering angle in Thomson limit (no recoil) is small, i.e. < 1/g

24. Spectral broadening due to ultra-focused beams:
Thomson Source classically described as a
Laser Syncrotron Light Source
focus X
Limit to focusability due to max acceptable bandwidth

25. Brilliance of X-ray radiation sources
Beam param. invariant under linear optics
12.4
1.24
0.124
l (nm)
FLAME
SASE-FELs will allow an
unprecedented upgrade in
Source Brilliance
SPARX
TTF
Covering from the VUV to
the 1 Å X-ray spectral range:
new Research Frontiers
Thomson LNF
Compact Thomson Sources
extend SR to hard X-ray range
allowing
Advanced Radiological
Imaging inside Hospitals
First Collisions and X-ray generation expected by march 2012
FDT-2011, Frascati, Nov. 30th 2011