Quantum-FEL Project

The main interest of our research relies presently on the feasibility of building  an X-ray FEL [1] source based on the quantum SASE regime [2] (research funded by INFN), which should have important and widespread experimental applications. The quantum regime in FELs occurs when the electron momentum spread mcdg (either the initial and the induced by the interaction with the radiation) is less than the momentum ћk of the emitted photon. It has been shown [3,4] that in this limit the probability of emission of a photon is much larger than those of absorption, and each electron emits coherently a single photon, recoiling by ћk. The particle ensemble behaves as a two-state system with only two possible average momenta, p=mcg₀ and p=mcg₀-ћk. In this sense, an FEL in the quantum regime is more similar to a laser where (instead of the electronic transitions between internal energy levels, as normally it occurs in a laser) the electrons back-scatter the photons of the pump field (i.e. the static or laser wiggler) into the forward radiation mode, making recoil transitions between discrete momentum levels, separated by ћk. For these reasons, the intensity profile (fig.1b) of the SASE radiation is almost coherent and the power spectrum, shown in fig.1d, is composed by narrow lines separated by ћk, corresponding to a sequential scattering of single photons. On the contrary, in a classical FEL the electron has comparable probabilities to emit or absorb a photon, so that the net gain is given by the difference between the emission and absorption probabilities. It has been shown [3] that in the classical regime each electron emits in average many photons, with a decrement of the coherence of the produced radiation. As a consequence the intensity profile of the classical SASE radiation is very spiky (see fig.1a) and the power spectrum, shown in fig.1c, is much more broad. The quantum limit set a severe condition on the quality of the electron beam, i.e. dg < l_c/l (where l_c = 0.024Ǻ is the Compton wavelength). This condition suggests the use of a laser wiggler with a wavelength of about l_w~1mm, and a low energy beam (~ 10 MeV), to generate X-rays in Angstrom region. On the other hand, the same quantum condition set also a limit of the coupling strength between beam and radiation. In fact, in the classical regime the maximum induced energy spread is dg/g₀~r (where r is the collective FEL parameter [5], proportional to J^1/3B_w^2/3 g₀^-1, where J the density current and B_w is the wiggler strength). Hence, the condition mcdg ≤ ћk implies that the parameter r’=(mcg₀/ћk)r must be less than unity, whereas an FEL behaves classically when r’>>1. This condition has been proved analytically  and numerically [6,7]. Similar results have been demonstrated for CARL [8] and in the experiments of Superradiant Rayleigh scattering [9].

References:
[1] See for instance the web site: http://sbfel3.ucsb.edu/www/vl_fel.html.

[2] R. Bonifacio, N. Piovella and G.R.M. Robb, Nucl. Instrum. Meth. A 543 (2005) 645.

[3] N. Piovella, M. Gatelli and R. Bonifacio, Optics Comm. 194 (2001) 167.

[4]. R. Bonifacio, M.M. Cola, N. Piovella, and G.R.M. Robb, Europhys. Lett. 69 (2005) 55.

[5] R. Bonifacio, C. Pellegrini and L. Narducci, Opt. Commun. 50 (1984) 373.

[6] N. Piovella, M. Cola, R. Bonifacio, Phys. Rev.A 67 (2003) 013817.

[7] R. Bonifacio, N. Piovella, G.R.M. Robb and A. Schiavi, Phys. Rev. STAccel. Beams 9  (2006)  090701..

[8] R. Bonifacio, L. De Salvo Souza, Nucl. Instrum. and Meth. in Phys. Res. A 341 (1994) 360; R. Bonifacio, L. De Salvo Souza, L. Narducci and E.J. D'Angelo, Phys. Rev.A 50 (1994) 1716.

[9] S. Inouye et al., Science 285 (1999) 571; S. Inouye et al., Nature 40 (1999) 641.