Coherent X-Rays from PEP* Simon Bairdt, Heinz-Dieter Nuhn, Roman Tatchyn, Herman Winick Stanford Synchrotron Radiation Laboratory, SLAC, Bin 69, P.O. Box 4349, Stanford, CA 94309-0210 Alan S. Fisher, Juan C. Gallardo Brookhaven National Laboratory, Upton, NY 11973 Claudio Pellegrini Department of Physics, University of California, Los Angeles, CA 90024-1547 Abstract This paper explores the use of a large-circumference, high-energy, electron-positron collider such as PEP to drive a free-electron laser (FEL), p ro d u&g high levels of coherent power at short wavelengths. We consider Self-Amplified Spontaneous Emission (SASE), in which electron bunches with low emittance, high peak current and small energy spread radiate coherently in a single pass through a long undulator. As the electron beam passes down the undulator, its interaction with the increasingly intense spontaneous radiation causes a bunch density modulation at the optical wavelength, resulting in stimulated emission and exponential growth of coherent power in a single pass. The need for optical-cavity mirrors, which place a lower limit on the wavelength of a conventional FEL oscillator, is avoided. We explore various combinations of electron-beam and undulator parameters, as well as special undulator designs and optical klystrons (OK), to reach high average or peak coherent power at wavelengths around 40 A by achieving significant exponential gain or full saturation. Examples are presented for devices that achieve high peak coherent power (up to about 400 MW) with lower average coherent power (about 20 mW) and other devices which produce a few watts of average coherent power. I. INTRODUCTION The relevant features of PEP are the long straight sections (117 m) in its 2.2km circumference, the large RF voltage (up to 40 MV), and the low bending-magnet field (0.07 T at 3.5 GeV). The electron-beam emittance required for an FEL is given by tx < X/ (27r). At 40 A, the requirement of 0.64 nm.rad can be reached by operating PEP at 3 - 4 GeV, a fraction of its 16GeV maximum energy, with low-emittance optics, and with extra emittance reduction from damping wigglers and/or the long FEL undulator itself. Radiation produced by damping wigglers and the FEL undulator reduces the damping time, facilitating operation of PEP at low energy. II. CHARACTERISTICS OF PEP Instead of the 14.5 GeV typically used in collider exper- iments, the FEL requires energies as low as 3 GeV, taking advantage of the fact that the transverse emittance scales quadratically with energy in a storage ring. Successful beam storage has been achieved at 4.5 GeV [l], but lower-energy operation has not yet been tried. Low-emittance optics [2] have been tested, giving ex = 5.3 nm .rad [3] at 7.1 GeV (compared to 30 nm . rad with colliding-beam optics). Scaling this value down to 3 GeV gives an emittance only a factor of 1.5 above the FEL requirement. The measured vertical emit- tance was 4% of the horizontal. Thus the horizontal emittance could be cut in half by coupling the two dimensions. The frac- tional rms energy spread (me in a storage ring, determined by synchrotron-radiation losses in the bending magnets, is pro- portional to beam energy and so favors low energy for the FEL. Without damping wigglers [4], oe = 6.6. 10e5 . E [GeV], giving an energy spread of 2 x 10e4 at 3 GeV. Synchrotron ra- diation from a wiggler increases the beam’s energy spread and changes its emittance [5]. Damping wigglers, in low or ze- ro dispersion locations, reduce emittance but increase energy spread. FEL gain requires a high peak current, I,. The peak single-bunch current in a storage ring is limited by the microwave instability. Add’ rng charge results in lengthening of the bunch, with no increase in I,. Transversely, there is a similar fast blow-up. The instability growth rates are short compared with the period of synchrotron oscillation. The threshold for the longitudinal instability in PEP will be reached long before the transverse. To estimate this limit, we use the ZAP code [6] and an extrapolation of bunch-length measurements made on the SPEAR ring and scaled to fit PEP data [7-81. For PEP’s low-emittance mode and an energy of 3 GeV, this gives a maximum peak current of 17.6 A. To increase this peak current, we considered compressing the circulating bunch over a half turn [2,4], in order to reach a high peak current only when the beam passes through the FEL, thereby avoiding bunch-lengthening instabilities. However, the phase-space rotation that compresses the bunch longitudinally and so increases the peak current, is accompanied by an increase in energy spread by the same factor. If the FEL gain is not close to the energy-spread limit (see below), then the half-turn compression would be helpful. However, this tolerance for extra energy spread would be put to better use by arranging an equilibrium state with a higher energy spread, since the peak-current limit scales with o:. Reasonable damping-wiggler parameters (B, = 1.26 T, Xw = 12 cm, K = 14.1, and Lw = 9 m at 3 GeV, or Lw = 18 m at 3.5 and 4 GeV) can increase the energy spread by a factor of three, increasing the peak current attainable by nine. For the same increase in energy spread, bunch compression would gain only a factor of three in peak current. The radiation damping time and the beam lifetime are of concern at the very low energy necessary for the FEL. Lifetimes of over 30 hours have been observed in PEP at 8 GeV and low current with low-emittance optics [9]. Assuming that the beam lifetime is determined by Coulomb scattering, which scales with the inverse square of the beam energy, we expect lifetimes of more than 5.7 and 4.2 hours for 3.5 and 3 GeV, respectively. These lifetimes are sufficient for FEL operation. The radiation damping times for PEP at 3 GeV, without damping wigglers and in the low emittance mode, are rXx,r = 1.02 s and rs = 0.51 s. With the damping 0-7803-0135-8/!X$O1.00 @IEEE 2748 © 1991 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. PAC 1991