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 (0.5-1.5 MeV) with 2 Compton Sources (similar to ELI-NP), then we collide the 2 counter-prop. gamma photon beams, focused to mm spot size

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)

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

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)

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

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

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

Energy-angular Spectral distribution

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

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]

Enlarged view (zoomed out over 1 cm in z and +-200 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]

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

Inverse Compton (Thomson) Scattering lL 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

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

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

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

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

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

Coming back to luminosity: now we collide a fresh 1 GeV electron bunch carrying Qb=320 pC, with Dg/g = 0.001 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…

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).

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

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

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 Source @ 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