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Application of Transverse Gradient Wigglers in High Efficiency Storage Ring Fel's APPLICATION OF TRANSVERSE GRADIENT WIGGLERS IN HIGH EFFICIENCY STORAGE RING FEL’s J. Madey To cite this version: J. Madey. APPLICATION OF TRANSVERSE GRADIENT WIGGLERS IN HIGH EFFICIENCY STORAGE RING FEL’s. Journal de Physique Colloques, 1983, 44 (C1), pp.C1-169-C1-178. 10.1051/jphyscol:1983116. jpa-00222545 HAL Id: jpa-00222545 https://hal.archives-ouvertes.fr/jpa-00222545 Submitted on 1 Jan 1983 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque Cl, suppZe'ment au noZ, Tome 44, fe'vrier 1983 page CI-I69 APPLICATION OF TRANSVERSE GRADIENT WIGGLERS IN HIGH EFFICIENCY STORAGE RING FEL'S J.M.J. Madey High Energy Physics Laboratory, Stanford lhziversity, Stanford, Cazifornia 94305, U.S. A. RksumC - La puissance de sortie, lrefficacitC et le gain d'un laser B Clectrons libres sur anneau de stockage peuvent dtre nettement amCliorCs avec l'utilisation d'un onduleur prCsentant un gradient transversal, "gain-expanded wiggler". Les paramktres critiques pour la rCalisation d'un tel projet sont la dispersion en Cnergie, le courant crdte et l16mittance. Une longue r6gion d'interaction (10 metres) doit aussi Ctre pr6vue. Abstract - A significant improvement in the power output, efficiency, and gain of storage ring FEL's can be realized through the use of a gain-expanded wiggler. The design of such systems must emphasize energy acceptance, peak current, and emittance. Long (10 m) interaction lengths must also be provided. I. - INTXODUCTION Storage rings are an attractive means to generate the electron beam for free electron lasers for a variety of reasons. These include: 1. favorable electron energy and current 2. favorable electron current density 3. favorable electron bunch length 4. low ionizing radiation. Of these factors, the current density is probably the most important. The advantages of the SRFEL configuration can most readily be seen by comparing the current density requirements of the FEL with the current density available using the various accel- erator technologies. Assuming the use of the transverse wiggler with an acceptance just equal to the emittance of the electron beam, Smith and ~ade~lhave shown that under optimum conditions the gain per pass is given by: where X = optical wavelength (cm) magnet period (cm) la - EX,Ey horizontal, vertical emittance (cm-radians) ipeak = instantaneous peak current (amperes). Inverting this relation, we can solve for the current density rewired to reach a given gain at a given wavelength with given wiggler parameters K' and X . 9 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983116 CI-170 JOURNAL DE PHYSIQUE The current density requirements in the wavelength range 100A) < A < 10~are plotted in Figure 1 which shows the current density required to reach 100% gain per pass for the case K2 = 1 for the wigglers with A = 1 cm and 10 cm, respectively. As is apparent in the figure, the current densiey required to operate the FEL increases as A-1/2, and increases sharply as the magnet period is reduced. The value of = 1 was chosen as representative of the magnetic field strength at which the gain is maximized. Figure 1 also plots the current density available from storage rings and other types of accelerators. The current density available from accelerators using ther- mionic, field emission, and plasma cathodes is defined by the cathode characteristics, space chan e and wake field effects, and aberrations in the electron optics. Lawson and Penner 5 have observed that the characteristics of most existing accelerators using such cathodes can be fit by the r,elation: < i > = y2 zx E x lo3 amperes (21 Y where < i > is the time averaged current and E and z the area of the phase X Y' space ellipses in the transverse coordinates (x,xt) and (y,yl). (Since the Lawson- Penner relation defines only the average current < i > , the peak current density in RF accelerators will typically exceed this value due to the bunching of the beam by the RF accelerating field. Assuming the microscopic duty cycle of the electron beam is likely to lie within the limits 0.01 to 1.0, the peak current density attainable from accelerators using thermionic field emission and plasma cathodes will lie in the range: i 5 2 lo3 < xe2 < 10 amps/cm . (3) y2z E x Y These limits are indicated by the lower set of dotted lines on Figure 1. The arrows on the vertical scale of Figure 1 indicate the peak current densities secured in the SLAC linac injector in its normal mode, and using a 240 MHz subharmonic buncher. In its normal configuration, the SLAC linac operates at a microsc ic duty cycle of 2p 0.01, producing a peak current density equal to lo4 amperes/cm . Note that while the microscopic duty cycle of RF accelerators can be reduced be- low 0.01 through the use of sub-harmonic bunching, such measures may not result in a proportional increase in the peak current density. At high peak currents, the electron beam excites a wake-field in the accelerating structure which acts back on the electron beam to raise both the energy spread and the emittance In the case of the SLAC linac, the peak current density remained below lo5 amps/cm2 even when the duty cycle was reduced to 0.001 through the use of the subharmonic buncher. As opposed to linear accelerators, in which the electron's phase-space density is unaffected by the accelerator process, the current density in storage rings can be raised through synchrotron damping, with the final emittance determined by the balance of damping and quantum fluctuations. The upper set of dotted lines indicates the range of current densities expected from the new synchrotron radiation sources at Wisconsin and Brookhaven, and in the SLAC damping ring. (A factor of lok1 is assumed around the design objectives for these machines. Since damping and quantum fluctuations are functions of the specific design of a storage ring, the current density will also depend on the design. Thus for storage rings there can be no equivalent to the universal Lawson-Penner relation for linear accelerators. The machines cited in Figure 1 were each optimized for high current density, and are believed to be representative of what can be accomplished in the energy range around 1 GeV. Note that the design value of the peak current density in these rings exceed the current densities available from thermionic, field emission and plasma cathodes by a factor of lo3 - 10'. It is seen from Figure 1 that the current density requirements for FEL operation at long wavelength (A > 1 p) can be met using either linear accelerator or storage ring technology, but that the requirements at short wavelengths (A < 1 y) probably can not be satisfied with linear accelerator technology. As a point of reference, the circled point in Figure 1 indicates the current density required for 100%gain per pass using the existing Stanford 3.2 pm superconducting wiggler at K2 = 0.5. As can be seen in the figure, this system was designed to operate near the limits of the available current density using linear accelerator technology. Barring further improvements in the current density available from linear accelerators, the Stanford 3.2 pm FEL probably represents (within factors of 2) the practical limit for short- wavelength operation using linear accelerator technology. By comparison the current density available in the new synchrotron radiation sources should be adequate for operation throughout the visible and UV wavelength well below 1000 8, perhaps as short as 100 a. Motivated by these reasons, a number of storage-ring FEL concepts have been pro- posed. Most notably, these include: 1) devices operated in the small signal regime with linear gain in which the electrons' optical phase is assumed to vary stochastically on successive 2 passes through the wiggler; 2) devices in which the optical phase is preserved from pass to pass, thereby generating a family of closed stable orbits in which the electrons circulate in the optical potential wells created in the wiggler. In such an Isochronous FEL, the energy radiated by the electrons scales as the electric field rather than the intensity.3 3) Devices operated in the large signal regime in which the optical synchrotron frequency is high, and the electrons are tightly bound in the optical potential wells. In such systems, the radiated energy is determined by the variation in resonance energy along the interaction length, as determined by the variation in wiggler period and magnetic field. Such systems i clude the tapered wiggler and phase-displacement acceleration concepts. 8 Of these concepts, the one which has received the most attention to date has been that in which the small signal limit and non-isochronous electron optics have been assumed. In general, this choice appars to offer the best available small signal gain and minimizes the spurious ultraviolet radiation generated at the harmonics of the operating wavelength. The power output in this configuration is expected to scale in proportion to the power emitted by electrons as incoherent synchrotron radiation. For simple constant period undulators, Renieri has shown that:3 where (aE/Eo) is the fractional energy spread induced in the circulating electron beam by the laser interaction.
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