The idea of producing single high energy photons at the range of the TeV scale is not new. Historically it was formulated during the 60s [Aru63] inside the theory of Compton scattering. Although the physics behind the for-mulation of Compton scattering is well-known and totally understood, the experimental requirements for the realization of a photon collider seems to be not simple. Several aspects concerning the construction and functionality as well as the physics processes of central importance are specified in Ref.
[KT02].
The starting point for an adequate introduction of the principles of the photon collider is the description of the dynamics which occurs in the Comp-ton scattering. Thus one considers a single laser phoComp-ton with an energy ω0
what is scattered by an electron with energy E0 at a small collision angle α in the conversion region. The energy of the scattered photon (or “converted”
electron) ω depends on its angle θ relative to the motion of the incident electron as follows:
where x is a dimensionless parameter and ωm denotes the maximum photon energy. When the scattered photon goes through the direction of electron, the whole phenomenon is called Compton “backscattering”.
The energy spectrum of the scattered photons is defined by the Compton cross section (without non-linear corrections) the quantitiesPc and λdenote the helicity of laser and electron, respectively.
The total Compton cross section reads
σc =σnpc + 2λPcσ1, (6.4) denoting the cross section with and without polarized electrons, respectively.
These expressions does not have a strong influence on the initial polarisation configuration in contrast to the energy spectrum (6.2). It should be noted that the curve is significantly improved when the product of helicities is negative, what actually doubles the number of hard photons.
In order to see the advantage in having polarized beams, in Fig. 6.2 (left-panel) the monochromatic character of spectrum for ω/E0 ≈ 0.8 when 2λPc = -1, is displayed. Naively one can imagine that this monochromaticity grows simultaneously with the laser energy, but unfortunately the parameter x is limited to be roughly 4.8. For values x >4.8 the production of e+e− pairs takes place by producing undesired e±γ collisions. On the other hand, the resulting polarisation is expressed as follows
< λγ>= −Pc(2r−1)[(1−y)−1+ (1−y)] + 2λexr[1 + (1−y)(2r−1)2] (1−y)−1+ 1−y−4r(1−r)−2λePcxr(2−y)(2r−1) ,
(6.7) where a circularly polarized laser is assumed. The right panel shows the subsequent polarisation of the scattered photons for various scenarios of he-licity configuration. The most favorable configuration is that of 2λPc = -1
Figure 6.2: (left) Photon spectrum for different values of product 2λePc = −1, and (b) the polarization as function of ratio ω/E0
as shown that the photons would conserve their initial polarisation. This very interesting phenomenon is of enormous interest in current experiments [Beh02] in which a lowest degree of polarisation degradation is needed.
Effects by High Order Corrections
The Compton scattering in first order is not enough for a correct under-standing of the physics during the conversion. Due to the presence of a high density of photons, the electron has a non-negligible probability in absorb-ing several photons before the final state. Expressed in the Feynman graphs language, the electron propagator receives an infinite contribution of legs by modifying substantially the total amplitude [B+71]. Undoubtedly, there ex-ists a transition of linear to non-linear regime in the sense that the electron does not suffer of pure Compton scattering but also is sensitive to a more complex situation. This leads to define the intensity parameter
η2 = 2nγre2λ
α (6.8)
which tell us about the influence of non-linear effects over the observables.
Herenγ denotes the number of absorbed photons,λthe laser wavelength and
Figure 6.3: Influence on the Compton spectrum by non-linear corrections. From right to left, η2 = 0,0.1,0.2,0.3,0.5 according to [KT02].
re the electron radius. Therefore the existence of non-linear effects has the following consequences
m2 →m2(1 +η2) and ωm
E0 = x
1 +x+η2, (6.9) what is reflected in the photon spectrum essentially. These relations can also be interpretated as the necessity in including secondary quantum effects because the presence of a strong electromagnetic field. Fig. 6.3 shows in an instructive way the influence of these non-linear effects on the photon spectrum. For x= 4.8 and 2λPc = -1 the left panel displays the degradation of peak of the curve for various values of η2. Indeed, the figure indicate us that the high energy region of spectrum suffers a displacement to the left side in agreement to (6.9). Interestingly is noted the presence of high harmonics at the high energy region is response to the absorption phenomenon. Actually these secondary effects is clearly against our goals and thus the knowledge of an optimum value for η2 is crucial for a respectable performance of a photon collider. Previous works have established that η2 = 0.3 might be the best upper limit. For example, the relative shift ∆ωm/ωm is of order of 5%which is still acceptable for physics studies.
Pair Creation and Other Processes
For values ofxgreater than 4, the possibility in gettinge+e−pairs is not null anymore. In effect, the collisions between backscattered photons and laser photons happens and it is realizable above thresholdωmω0 =m2 resulting in a x≈ 4.83. The Dirac1 cross section for e−e+ creation is given by initial state helicities. To see the relevancy of e+e− pairs creation, an per-taining evaluation of 6.12 should be performed. For example, σγγ→e+e− turns out to be bigger than the Compton cross section by a factor 1.5 just for x
= 10. However the maximum conversion efficient k is reduced in up to 30%.
Thus for higher x does not necessarily means that an acceptable luminosity is guaranteed. So that one expects x≤ 4.8 which is equivalent to have ak ≈ 0.4. For these values and a beam energy of 500 GeV one gets λ of order of 1µm which is compatible with high performance lasers. Furthermore, pairs creation dynamics is affected by non-linear corrections. It means that the pairs are created by the interaction of the high energy photons and several laser photons. An immediate consequence is the displacement of x what is shifted to xef f = 4.8(1+η2) when thee+e− pair goes to superintense regime.
In addition to pair creation, the complexity of the physics at the conversion region is manifested by the presence of
• Low energy electrons; what are produced because of multiple Compton scattering. Simulations have shown the minimum energy of an electron after of leaving the conversion region is of about 2%of its initial energy.
This result partially serves for removing the disrupted electrons where in conjunction the disruption angle is also needed.
• Non-linear pair creation, which is possible because the non-negligible probability for collisions between several laser photons and the backscat-tered one below the single photon threshold x = 4.8.
1In his book, Landauet al [B+71] have pointed out that P. M. Dirac was the first one in solving the cross section.