rings are listed in Tables 2 and 3. The nominal operating
energy is 2.0 GeV, although the rings are being designed
to operate between 1.8 GeV and 2.2 GeV. This will pro-
vide the operational flexibility to balance faster damping
rates against smaller equilibrium emittances. Both rings
will store multiple trains of bunches. The pre-damping
ring will store two 90 bunch trains at once while the main
damping ring will store four 90 bunch trains. The bunches
in a train are separated by 1.4 ns while the trains them-
selves are separated by 60 ns so that fast kickers can inject
and extract individual trains. In this manner, each bunch
train is stored for two machine cycles in the pre-damping
ring and four machine cycles in the main damping ring.
Finally, the maximum average current is roughly 1 A for
the NLC-III parameters; note that for NLC-III the bunch
trains are only 75 bunches long and the train separation is
roughly 80 ns.
The pre-damping ring will operate on the difference
coupling resonance. In this case, the equilibrium emit-
tances are yc,,y = 30 mm-mrad and the transverse damp-
ing time is r,y = 3.45 ms; thus, after two 180 Hz machine
cycles, the beams are stored for 3.2 damping times. In
the main damping ring, the horizontal equilibrium emit-
tance, including the intrabeam scattering for 1.5 x 1010,
is yex = 3.1 mm-mrad while the vertical equilibrium emit-
tance of ye2 = 0.02 mm-mrad is determined by the align-
ment tolerances. Finally, the vertical damping time is 4.64
ms; this corresponds to roughly 4.8 vertical damping times.
In both rings, the damping is slightly greater than that re-
quired; this provides a margin for injection transients and
mismatches.
In the next sections, we will briefly describe the op-
tical design of the--positron pre-damping ring and the
main damping rings. Then, we will discuss the injec-
tion/extraction and the RF systems. Finally, we will de-
scribe the tolerances and dynamic aperture of the rings.
II. OPTICAL DESIGNS
Both rings are designed in a race-track form with two
arcs separated by straight sections. The pre-damping ring
is roughly 110 meters in circumference while the main
damping ring is twice as large.
In the pre-damping ring, each arc consists of 14 FOOF
cells plus dispersion matching sections; the FOOF cell is a
modified FODO lattice where the defocusing quadrupole is
replaced by a combined function bending magnet. Because
the ring needs a large dynamic aperture and does not re-
quire a small equilibrium emittance, we use a weak focusing
lattice. We chose to use the FOOF structure since it con-
strains the beta functions, allowing us to design a smaller
vacuum chamber aperture and thereby less expensive mag-
nets. In the arcs, the vacuum chamber measures 3 cm by
3.2 cm. This provides physical aperture for an injected
normalized edge emittance of 0.09 m-rad (50% larger than
nominal) plus 2 mm clearance for alignment and steering.
In the main damping ring, each are consists of 19 TME
cells [4] plus dispersion matching sections. The straight
sections are roughly 30 meters in length. One side of the

ring is devoted to the damping wigglers while the other side
contains the injection and extraction components and the
RF cavities.
The TME cells consist of a single combined function
bending magnet, two focusing quadrupoles and a single
defocusing quadrupole. Each cell contains six sextupoles,
in three families, to correct the chromaticity. The vacuum
chamber is circular with a 25 mm diameter and an ante-
chamber to handle the intense synchrotron radiation; the
chamber is described further in Ref. [51. Preliminary de-
signs have been made of the bending magnets, quadrupoles
and sextupoles. The bending magnet has a central field of
15.3 kG with a gradient of 125 kG/m and a half gap of
1.6 cm. The quadrupoles have a maximum gradient of 600
kG/m with an aperture of 1.6 cm while the sextupoles have
a maximum gradient 82By/8x2 of 30,000 kG/m2 with an
aperture of 1.7 cm. In all cases, the poles are designed to
fit around the ante-chamber.
In addition, the main damping ring requires roughly 25
meters of high field wiggler to attain the desire damping
times. The two parameters that are relevant for a damp-
ing wiggler are the integral of By, which determines the
damping, and the quantum excitation, which is set by the
field and the period. In the NLC design, we have chosen to
consider a relatively short, high field device. If we assume a
sinusoidal By with a peak of 22 kG (close to the saturation
of Vanadium Permandur), then we need a length of 25.6
meters and a period of 25 cm. Simple scaling laws suggest
that such a wiggler could be build as either a permanent
magnet hybrid wiggler or an electromagnetic wiggler.
The SSRL Beam-Line 9 wiggler [6], which was recently
constructed, nearly meets our requirements. It is a hybrid
wiggler with a peak field of 20.5 kG and a 26 cm period.
Because the wiggler poles were designed to optimize the
total flux, the field is not sinusoidal and the integral of B
is within 1% of our requirements.
III. INJECTION/EXTRACTION
In both damping rings, injection and extraction are
performed using DC septum magnets and pulsed kicker
magnets. The design concept is similar to the system de-
veloped for the SLC [7]. The kickers are required to inject
or extract a single 126 ns bunch train onto or from the
closed orbit without disturbing the other stored bunches.
Thus the rise and the fall times must be less than the
train separation 60 ns. Finally, to reduce RF transients,
a new bunch train is injected on the same revolution that
a damped bunch train is extracted.
The main damping ring kickers must provide a deflec-
tion of 2.5 mrad with a stability of AO/6 < 0.5 x 10-3 for
the extraction kickers and A9/8 _ 3.5 x 10-3 for the in-
jection kickers; these tolerances limit the beam jitter due
to the kickers to 10% of the beam size. The deflection can
be provided using a 1.2 meter kicker with an impedance of
50 0 and a voltage of 17 kV. Achromatic (double) kicker
systems will be used to ease the stability requirements.
Here, an identical kicker, powered by the same pulser, is
placed in the injection/extraction line and separated from

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