E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146 143 THE FREE ELECTRON LASER KLYSTRON AMPLIFIER CONCEPT E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany Abstract as short as 10-100 µm have never been measured and are challenging to predict. We consider optical klystron with a high gain per cas- The situation is quite different for klystron amplifier cade pass. In order to achieve high gain at short wave- scheme described in our paper. A distinguishing feature of lengths, conventional FEL amplifiers require electron beam the klystron amplifier is the absence of apparent limitations peak current of a few kA. This is achieved by applying which would prevent operation without bunch compression longitudinal compression using a magnetic chicane. In in the injector linac. As we will see, the gain per cas- the case of klystron things are quite different and gain of cade pass is proportional to the peak current and inversely klystron does not depend on the bunch compression in the proportional to the energy spread of the beam. Since the injector linac. A distinguishing feature of the klystron am- bunch length and energy spread are related to each other plifier is that maximum of gain per cascade pass at high through Liouville’s theorem, the peak current and energy beam peak current is the same as at low beam peak cur- spread cannot vary independently of each other in the injec- rent without compression. Second important feature of the tor linac. To extent that local energy spead is proportional klystron configuration is that there are no requirements on to the peak current, which is usually the case for bunch the alignment of the cascade undulators and dispersion sec- compression, the gain will be independent of the actual tions. This is related to the fact that the cascades, in our peak current. We see, therefore, that klystron gain in linear (high gain) case, do not need the radiation phase matching. regime depends only on the actual photoinjector parame- There are applications, like XFELs, where unique proper- ters. This incipient proportionality between gain and ties of high gain klystron FEL amplifier are very desirable. I0/σγ ( is a current and is a local energy spread in units of Such a scheme allows one to decrease the total length of I0 σγ the rest electron energy) is a temptation, in designing an magnetic system. On the other hand, the saturation effi- XFEL, to go to very high values of and very long ciency of the klystron is the same as that of conventional I0/σγ values of bunch length. Starting with this safe scenario, one XFEL. may gradually increase compression factor getting shorter FEL pulses with higher peak power (brilliance). Note that INTRODUCTION the average power (brilliance) is almost independent of the compression factor. It is also worth mentioning that there High gain FEL amplifiers are of interest for a variety of is a possibility [8] to get short (10 fs) radiation pulses for potential applications that range from X-ray lasers [1, 2] to the pump-probe experiments, having long (10 ps) electron ultraviolet MW-scale industrial lasers [3]. There are var- bunches. To illustrate further possible advantages of the ious versions of the high gain FEL amplifier. A number klystron amplifier, we describe a multi-user facility having of high gain FEL amplifier concepts may prove useful for a ring geometry, and thus being similar to the 3rd genera- XFEL applications. Two especially noteworthy ones are tion synchrotron radiation facilities. the FEL amplifier with a single uniform undulator [1, 2] and the distributed optical klystron [4, 5, 6, 7]. The high gain cascade klystron amplifier described in this paper is THE GAIN OF A KLYSTRON AMPLIFIER an attractive alternative to other configurations for opera- tion in the X-ray wavelength range (see Fig. 1). A detailed theoretical analysis of a klystron amplifier Electron bunches with very small transverse emittance with a high gain per cascade can be found in [8]. Here and high peak current are needed for the operation of con- we present some results of that analysis. ventional XFELs. This is achieved using a two-step strat- The principle of klystron operation is simple and is very egy: first generate beams with small transverse emittance similar to that of a multi-resonator microwave klystron. A using an RF photocathode and, second, apply longitudinal modulated electron beam radiates in a first undulator, and compression at high energy using a magnetic chicane. Al- the radiation modulates the beam in energy. Then the beam though simple in first-order theory, the physics of bunch passes a dispersion section where the energy modulation compression becomes very challenging if collective effects is converted into the density modulation which is much like space charge forces and coherent synchrotron radiation higher than the original one. In the second undulator the forces (CSR) are taken into account. Self-fields of bunches beam with the enhanced density modulation radiates pro- Available online at http://www.JACoW.org Single-Pass FELs 144 E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146 Figure 1: Schematic diagram of high gain cascade klystron amplifier ducing much higher energy modulation etc. The process In the latter case the diffraction parameter is big, and can continue in several cascades up to saturation in the last the velocity spread due to emittance should be carefully (output) undulator. Since the gain per cascade is high, the taken into account. Note that in contrast with a conven- phase matching (on the scale of the radiation wavelength) tional SASE, the effects of emittance and energy spread between the beam and the radiation is obviously not re- on longitudinal dynamics are separated in a klystron am- quired. An initial signal for such a device in VUV and plifier: emittance (energy spread) is important in undula- X-ray spectral range is the shot noise in electron beam. tors (dispersion sections). The noticeable feature of the re- We present here the expressions for a gain per cascade sults (1) and (2) is that the gain depends on the ratio I0/σγ for two different regimes of the klystron amplifier opera- and is, therefore, independent of compression factor in the tion. In the first case the geometrical emittance of the elec- beam formation system. It is also interesting to note that tron beam is small as compared to λ/(2π), where λ is in the case of a small emittance the gain is defined by the the resonant wavelength. In this case the beta-function in longitudinal brightness of the electron beam, while for a the undulators can be chosen in such a way that the diffrac- large emittance - by total brightness (particles density in 2 tion parameter, 2πσ /(λLw), is small (here σ is transverse 6-D phase space). size of the beam and Lw is the length of an undulator seg- ment). At the same time the effect of velocity spread due to emittance on FEL operation can be neglected. After op- timization of the strength of the dispersion section one gets Let us present an example for the case when the emit- the amplitude gain per cascade [8]: tance is below diffraction limit and the undulator is planar. 3 With the numerical values λw =3cm, K =1, γ =10, A2 K2 N I JJ w 0 (1) the resonance value of wavelength is λ =30nm. If the G0 4 2 , (1 + K ) σγ IA number of the undulator period is Nw = 100, normalized where K is the rms undulator parameter, Nw is the number transverse emittance n =2µm, and betatron function is of undulator periods per an undulator, IA =17kA is the equal to the undulator length, the diffraction parameter is Alfven current, AJJ =1for a helical undulator and about 0.4. For a peak current of 100 A and a local energy spread of 5 keV, appropriate substitution in (1) shows that AJJ =[J0(Q) J1(Q)] 2 − the gain per cascade pass is about G0 10 (or, intensity 2 2 2 4 for a planar undulator. Here Q = K /(2 + 2K ) and gain G0 10 ). In order to reach saturation in a klystron Jn(Q) is a Bessel function of nth order. amplifier, starting up from the shot noise, the total inten- In the opposite limit, 2π/λ 1, after optimizing beta- sity gain should be of the order NλNw [8], where Nλ is function and the strength of dispersion section one gets: the number of electrons per radiation wavelength. Thus, for the considered set of parameters, one needs two cas- A2 K2 N I λ 2 cades of amplification and the output undulator as shown G 2 JJ w 0 . (2) 0 (1 + K2) σ I 2π in Fig. 1. γ A MOPOS16 E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146 145 Figure 2: Diagram of a possible fourth-generation synchrotron facility using free-electron laser klystron amplifiers Figure 3: Electron ring cell design. Using a klystron electromagnetic dispersion section as a switching element it is possible to quickly switch off (on) the cell klystron amplifier thus providing multi-user capability. This design makes it possible to make various wavelengths available in the XFEL laboratory quasi-simultaneously Single-Pass FELs 146 E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146 MULTI-USER DISTRIBUTION SYSTEM vantage that injector and electron beam transport lines in FOR XFEL LABORATORY the new scheme of multi-user facility operate at fixed pa- rameters and that an ”electron switchyard” is not required.