SPARC is a photo-injector for production of high-brightness lowemittance electron beams to drive a FEL experiment in various configurations, including SASE-FEL radiation of 1–10nm (SPARCX project). Due to a high-brightness source, the SPARC facility can be used to study the physics of ultrashort beams, plasma-wave based acceleration, production of X-rays by means of Compton backscattering, channeling of electron beams and other experiments. The initial process of electron beam generation inside the RF gun determines the main parameters of the electron beam. Interaction of electrons with high-frequency laser beam

leads to modulation of the electron beam. In this paper we present electron beam spectral distribution for SPARC photoinjector parameters. The estimate of electron beam energy loss for such electron distribution also is given

Dabagov, S. B.

Dik, A. V.

Ferrario, M.

Podlesnaya, A. S.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2011-10964-0Colloquia: Channeling 2010IL NUOVO CIMENTO Vol. 34 C, N. 4 Luglio-Agosto 2011Spectral distribution of SPARC photoinjector electronsA. S. Podlesnaya(1)(∗), A. V. Dik(2), S. B. Dabagov(2)(3) and M. Ferrario(3)(1) National Research Nuclear University MEPhI - Kashirskoe Sh. 31115409 Moscow, Russia(2) RAS P.N. Lebedev Physical Institute - Leninsky Pr. 53, 119991 Moscow, Russia(3) INFN Laboratori Nazionali di Frascati - Via E. Fermi 40, 00044 Frascati, Rome, Italy(ricevuto il 22 Dicembre 2010; pubblicato online il 19 Settembre 2011)Summary. — SPARC is a photo-injector for production of high-brightness low-emittance electron beams to drive a FEL experiment in various configurations, in-cluding SASE-FEL radiation of 1–10 nm (SPARCX project). Due to a high-bright-ness source, the SPARC facility can be used to study the physics of ultrashortbeams, plasma-wave based acceleration, production of X-rays by means of Comptonbackscattering, channeling of electron beams and other experiments. The initialprocess of electron beam generation inside the RF gun determines the main param-eters of the electron beam. Interaction of electrons with high-frequency laser beamleads to modulation of the electron beam. In this paper we present electron beamspectral distribution for SPARC photoinjector parameters. The estimate of electronbeam energy loss for such electron distribution also is given.PACS 41.60.Cr – Free-electron lasers.PACS 41.85.Ct – Particle beam shaping, beam splitting.1. – IntroductionThe free-electron laser (FEL) is a device that uses high-brightness (low-emittance,high peak current) electron bunches crossing a transverse periodic magnetic field togenerate wavelength-tunable high-power electromagnetic radiation.The SPARC project was proposed by the collaboration among ENEA-INFN-CNR-Universita` di Roma Tor Vergata-INFM-ST, and is progressing in the area of the FrascatiNational Laboratories [1]. The common denominator of SPARC project is to investigatethe scientific and technological issues for production of high-brightness electron beamsto drive a SASE-FEL experiment in the visible range [2]. In addition, SPARC is theinjector prototype for SPARX project, a new high-brightness electron linac for generatingSASE-FEL radiation in the 1–10 nm range [3, 4].(∗) E-mail: alinapodlesnaya@mail.ruc© Societa` Italiana di Fisica 359360 A. S. PODLESNAYA, A. V. DIK, S. B. DABAGOV and M. FERRARIODue to high brightness source, the SPARC facility might be used to study the physicsof ultrashort beams, plasma-wave based acceleration, production of X-rays by means ofCompton backscattering, channeling of electron beams and other experiments [3, 5-7].Besides the physics, X-ray laser radiation can be used to research in chemistry, biology,medicine, in various applied sciences, which previously had not been possible [8].The possibility of generation undulator radiation in the range of λ ∼ 1 nm and lessgives advantage to the SASE-FEL regime over a conventional FEL. This is due to the factthat at very short wavelengths, normal-incidence mirrors with sufficient high reflectivityfor making an optical cavity resonator are unavailable [9]. Nevertheless the tuned SASE-FEL source allowing to control output radiation with high precision has not been done sofar. Intensity and spectrum of laser radiation in the SASE-FEL regime depend on micro-bunching process in the undulator. Formation of microbunches is an unstable processand mainly depends on electron beam parameters at the entry of the undulator. Thus,the realization of the stable SASE-FEL regime first of all requires quality control of theelectron beam from the moment of its generation.2. – Electron beam spectral distribution for SPARC photoinjector parametersThe SPARC photoinjector involves a standard UCLA/SLAC/BNL 1.6 cell S-bandRF gun (working at 2.856GHz), operating at a peak accelerating gradient of Eac =120MV/m. The laser system including the Ti:Sa active medium is able to generateultrashort radiation with a rise time less then 2 ps and variable pulse duration (4–10 ps).During interaction (τ ∼ 10 ps) of ultraviolet laser beam (E0 = 190MV/m) with a copperphotocathode, electrons are emitted due to photoeffect. Such system allows to extractthe electron beam with charge ∼ 1 nC [2].During the electron beam generation inside the SPARC photoinjector a high-frequencylaser field (ω0 ∼ 1015 s−1) created by incident and reflected laser beams affects on allelectrons.As you can see [10], the action of this field results in modulation of the electronbeam. Thus, in laser field the photocathode electrons experience either a deceleration oracceleration, forming a periodic structure of the electron beam in accordance with theperiod of a laser wave as shown in fig. 1.Due to acceleration in external electric field and appearance of a periodic structure,electrons radiate and this radiation depends on electron beam parameters. To tracebehavior of electrons in the SPARC photoinjector we need information about electronbeam radiation.In the present paper the radiation by electron beam is estimated taking into accountthe SPARC photoinjector parameters. Oblique laser incidence (at 70 degrees) has beentaken in this task as shown in fig. 2.As shown in [10], the dependence of the electron trajectory on the action of themagnetic component of a laser field is negligible. The nonrelativistic electron energyradiation in the frequency range dω at long range is given by the following [11]dE(ω) =2e23π c3∣∣∣∣∫ ∞−∞¨r (t)eiωtdt∣∣∣∣2dω.SPECTRAL DISTRIBUTION OF SPARC PHOTOINJECTOR ELECTRONS 361Fig. 1. – Spatial distribution of the electron beam near the SPARC photocathode under laserradiation effect. Time duration of laser beam ∼ 1 ps. Note that only a part of the electronbunch is shown. In fact the number of electrons is much larger [10].Therefore, a spectral distribution function is defined as follows:(1) f(ω) =dE(ω)dω=2e23π c3[∣∣∣∣∫ ∞−∞x¨(t)eiωtdt∣∣∣∣2+∣∣∣∣∫ ∞−∞z¨(t)eiωtdt∣∣∣∣2],where x¨(t) and z¨(t) are determined by the electron motion equation:z¨(t) =eEacm− eE0msin θ{sin(ω0t− kir ) + α sin(ω0t− krr )},x¨(t) =eE0mcos θ{sin(ω0t− kir )− α sin(ω0t− krr )}.The phase of laser fields (incident and reflected) in the point of electron position at theFig. 2. – Interaction fields scheme near the SPARC photoinjector cathode.362 A. S. PODLESNAYA, A. V. DIK, S. B. DABAGOV and M. FERRARIOtime t can be written asω0t− kir = at2 + b1t + β1 − 2αδ sin(at2 + b2t + β2),ω0t− krr = −at2 − b2t− β2 − 2δ sin(at2 + b1t + β1),where δ ∼ 10−5, a = ω0eEac cos θ/2mc, β1 + β2 = 2ω0c−1C3 cos θ, b1 and b2 depend onthe projection of initial electron velocity. For nonrelativistic velocity of electron beamwe can take b1 = −b2 ≈ ω0.Then we use the Fourier transform for computing the first and second terms in eq. (1):∫ ∞−∞x¨(t)eiωtdt = − eE02imcos θ√π2ae−iβ1[G1(ω)− αei(β1+β2)G2(ω)],∫ ∞−∞z¨(t)eiωtdt = − eE02imsin θ√π2ae−iβ1[G1(ω) + αei(β1+β2)G2(ω)].Substituting the results into eq. (1), we obtain the equation for energy spectral distribu-tion of one electron for the SPARC photoinjector parameters:f(ω) =μ0e3E20 cos θ24πmω0Eac(2)×[∣∣∣G1(ω)− αei(β1+β2)G2(ω)∣∣∣2 + tan2 θ ∣∣∣G1(ω) + αei(β1+β2)G2(ω)∣∣∣2],where G1(ω) and G2(ω) are the functions of only two variables (time and frequency):G1(ω) = ei(ω−ω0)2a [(C(z0 − z)− C(−z))− i(S(z0 − z)− S(−z))] ,G2(ω) = e−i(ω−ω0)2a [(C(z0 + z)− C(z)) + i(S(z0 + z)− S(−z))] ,and C(z), S(z) are Fresnel integrals; z0 = τ√2a/π, z = (ω − ω0)√2/aπ.Equation (2) shows that if the reflection coefficient (α) approaches zero, electrons co-herently emit the radiation. The presence of reflected laser wave leads to the dependenceof radiated energy on electron spatial distribution as shown in fig. 3.It is important to underline the difference in the radiated energy for different reflectioncoefficients. There is no contribution of a reflected wave to the energy spectrum in caseof α = 0.01 (fig. 3,a). At the α increase the radiated intensity, in part of a spectrumcorresponding to reflected wave, also increases as presented in figs. 3,b,c. For the caseof total reflection (α = 0.99) the spectrum reaches its frequency-integrated maximum byintensity, due to the electron emission in the field of both incident and reflected laserbeams (fig. 3,d).To estimate the spectral distribution of all the electrons extracted from the SPARCphotocathode for the period of τ ∼ 10 ps, let us discuss the process of electron emission.Let us assume that the concentration of electrons generated near the cathode surface(S ∼ 1mm2) is Nt ∼= I0S/2h¯ω0, where I0 = (1 − α)Ii is the intensity of transmittedwave. If Nt(t) is the number of electrons at the moment t, then the time of electronmotion is τ − t. Hence, taking into account eq. (2) we can obtain spectral distributionfor all Ne− = Ntτ ∼ 1010 electrons as shown in fig. 4.SPECTRAL DISTRIBUTION OF SPARC PHOTOINJECTOR ELECTRONS 363Fig. 3. – Spectral destribution of one electron near the SPARC photoinjector cathode for differentreflection coefficients: a) α = 0.01, b) α = 0.3, c) α = 0.6, d) α = 0.99.Fig. 4. – Spectral distribution for electron beam near the SPARC photoinjector cathode. Forany reflection coefficient α the number of electrons equals 103 (a, b, c, d), and 1010 (e).364 A. S. PODLESNAYA, A. V. DIK, S. B. DABAGOV and M. FERRARIOFor electron bunches we observe similar dependences as for a single electron (com-parison between figs. 3 and 4). When the intensity of the reflected laser beam goes up,the radiation spectrum becomes broader too. Analysis of the electron beam spectraldistribution reveals the amount of energy radiated by electrons, of about 10−8 J for thetime τ ∼ 10 ps, that is by four orders of magnitude smaller than the total energy ofelectron beam. Meanwhile, in the absence of electron beam modulation, radiated energyby the electron beam for the interval τ ∼ 10 ps might be about 10−18 J. Great differencebetween radiated energy of the electron beam with and without modulation is due tothe presence of coherent effects. In this condition we have the opportunity to trace thebehavior of electrons in high-frequency laser beam in dependence of the degree of modu-lation in real experiments. That can be useful in order to control the electron beams inthe initial stage of the beam forming.3. – ConclusionWe have considered radiation of electron beam under SPARC photoinjector param-eters. As it was shown in [10], due to high-frequency laser field the electron beammodulation occurs. Coherent effects that are due to the beam modulation lead to anenergy radiation increase in 10 orders of magnitude. It gives us advantage for testingthe process of electron beam modulation and using that for electron beam control in theinitial stage. Moreover, periodic structure of electron beam may be of interest from aperspective preliminary microbunching before an undulator stage.∗ ∗ ∗The present paper has been done within the PhD works (AP and AD). AP and ADgratefully acknowledge the support of LNF INFN. AP is grateful to the “Channeling2010” Organizing Committee for the financial support that made possible the author’sparticipation in the conference.REFERENCES[1] Alesini D. et al., Proc. of the 2003 Particle Accelerator Conference (2003).[2] Cianchi A. et al., Phys. Rev. ST Accel. Beams, 11 (2008) 032801.[3] Renieri A., Nucl. Instrum. Methods A, 507 (2003) 507.[4] Palumbo L., The SPARX-FEL project, Proc. of IPAC’10, Kyoto (2010).[5] Bacci A. et al., Nucl. Instrum. Metheds A, 608 (2009) 90.[6] Giannessi L. et al., Nucl. Instrum. Methods A, 593 (2008) 132.[7] Dabagov S. B. and Zhevago N. K., Riv. Nuovo Cimento, 31 (2008) 491.[8] Ragozin E. N. and Sobel’man I. I., Phys. Usp., 47 (2004) 195.[9] Andruszkow J. et al., Phys. Rev. Lett., 85 (2000) 18.[10] Podlesnaya A. S. et al., J. Phys.: Conf. Ser., 236 (2010) 012035.[11] Landau L. D. and Lifshitz E. M., Course of Theoretical Physics, Vol. 2 (Nauka, Moscow)1988.

Spectral distribution of SPARC photoinjector electrons

http://eprints.bice.rm.cnr.it/17357/1/ncc9948.pdf

Spectral distribution of SPARC photoinjector electrons

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository