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
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