• R. Bonifacio, R. Bonifacio
  Universidade Federal de Alagoas, Maceio
• M. Ferrario
  INFN/LNF, Frascati (Roma)
• N. Piovella
  Universita' degli Studi di Milano, MILANO
• G.R.M. Robb
  Strathclyde University, Glasgow
• A. Schiavi
  Rome University La Sapienza, Roma
• L. Serafini
  INFN-Milano, Milano

Funding: Istituto Nazionale di Fisica Nucleare (INFN), Italy

Quantum effects in high-gain FELs become relevant when ρ'=ρ(mcγ/ ћ k)<1. The quantum FEL parameter ρ' rules the maximum number of photons emitted per electrons. It has been shown that when ρ'<1 a "quantum purification" of the SASE regime occurs: in fact, the spectrum of the emitted radiation (randomly spiky in the usual classical SASE regime) shrinks to a very narrow single line, leading to a high degree of temporal coherence. From the definition of ρ it appears that in order to achieve the quantum regime, small values of ρ, beam energy and radiation wavelength are necessary. These requirements can be met only using a laser wiggler. In this work we state the scaling laws necessary to operate a SASE FEL in the Angstrom region. All physical quantities are expressed in terms of the normalized emittance and of two parameters: the ratio between laser and electron beam spot sizes and the ratio between Rayleigh range and electron β-function. The feasibility study of a Quantum SASE FEL experiment using parameters as those foreseen in the SPARC/PLASMONX projects in construction at the INFN Frascati is explicitly discussed.

• G. Dattoli
  ENEA C.R. Frascati, Frascati (Roma)
• M.  Migliorati, A. Schiavi
  Rome University La Sapienza, Roma

The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. A code devoted to the analysis of this type of problems should be fast and reliable: conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problem in accelerators. The extension of these method to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators implemented numerically in C++. We show that the integration procedure is capable of reproducing the onset of an instability and effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, parametric studies are presented on the dependence of the effects on the e-beam energy spread and bunch length, considerations on the threshold of the instability are also developed, and future improvements of the work are presented.