AHF Synchrotron Lattices
P. Schwandt*, D.L. Friesel* and F. Neri*
Indiana University Cyclotron Facility
#
Los Alamos National Laboratory
Abstract. Lattice designs for a high-energy, moderate-intensity proton synchrotron complex under study for an Advanced
Hydrotest Facility are presented.
INTRODUCTION
607i) and momentum acceptance (at least ± 0.4%), and
must accommodate at least 25 200-ns beam bunches of
up to 2xl012 protons per bunch. The ring should
incorporate at least 3 long (100m), dispersionless
straight sections for fast kick-injection, 0.2 MV of RF
and single-bunch fast extraction (with option for future
slow-spill extraction).
The conceptual design of an accelerator complex to
provide 50 GeV proton beam pulses for an Advanced
Hydrotest Facility (AHF) is underway at the Los
Alamos National Laboratory [1]. This complex
consists of a 4 GeV, 5 Hz Booster synchrotron,
injected from a 157 MeV H" linac, feeding a 50 GeV
slow-cycling (3.3 sec acceleration ramp) Main ring
synchrotron. This paper presents design criteria and
general properties of the 50 GeV Main ring and 4 GeV
Booster ring lattices. Two possible Main ring lattices
presently being evaluated are described: a
conventional, regular FODO lattice in which the beam
crosses transition (real yt < ymax) and a transitionless
(imaginary-yt) lattice.
Two lattice designs are presently under study. The
principal feature separating these two lattices is the
transition energy. In the conventional, regular FODO
lattice option (A), the beam is expected to pass
through transition (at about 13 GeV) with acceptably
small beam loss and emittance growth using only the
requisite fast RF phase jump, as in the Fermilab Main
Injector (FMI). The acceleration rate dy/dt for the AHF
ring is an order of magnitude lower than for the FMI
and may set an intensity limit. The fall-back option for
high-intensity operation is the addition of a bipolar yt jump capability at transition using local dispersion
inserts of fast, pulsed jump quad triplets [2].
50 GEV MAIN RING LATTICES.
The intended application of this proton synchrotron
in the AHF context demands robust, stable and highly
reliable operation but also operational flexibility.
Principal design criteria thus call for a simple lattice of
conventional and conservative design. Operational
simplicity mean few "knobs" and low installation cost
The second lattice option (B) being explored is a
transitionless lattice tuned to imaginary yt to avoid
transition crossing altogether, as in the proposed
16 GeV Fermilab Proton Driver [3] or the 50 GeV
Main ring of the Japan Hadron Facility [4]. Note,
however, that in contrast to these machines the AHF
ring is a very-slow-cycling machine for lowerintensity beams (by an order of magnitude) of smaller
emittance and momentum spread.
The ring layout for these two 50 GeV AHF lattice
options is presented in Fig. 1.
Option A: Conventional FODO Lattice
This 4-sided ring geometry employs a regular
FODO cell structure repeated throughout the ring, in
both arc and straight sections, using identical 927 92°
cells. This produces a very simple, straightforward
lattice with perfectly smooth lattice functions around
the ring (no beta-modulation) but places yt = 15 within
the operating range. The design allows for the later
addition of pulsed yt -jump quad insertions mentioned
-aae -m* -ago -ass
FIGURE 1. Layout of two 50 GeV main ring lattices (m)
requires repetitive cell structures involving few types
of identical, room-temperature magnets. The lattice
must have moderately large dynamic aperture (at least
CP642, High Intensity and High Brightness Hadron Beams: 20th ICFA Advanced Beam Dynamics Workshop on
High Intensity and High Brightness Hadron Beams, edited by W. Chou, Y. Mori, D. Neuffer, and J.-F. Ostiguy
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150
above if needed for improved transition crossing.
Dispersion-suppressing sections at the ends of arcs
require half-length dipoles in addition to full-length
(6.8m, 1.64T) arc dipoles. A single family of identical
quads (1.3m, 18.5T/m) is employed.
The present choice of operating point in betatron
tune space is shown in Fig. 2. These tunes were chosen
such that they are not close to integer multiples of the
ring periodicity (4) and lie in a region free of
systematic and structural sum resonances. Because of
negative tune shifts from beam space charge, the
working point is located below the octupole coupling
resonance 2vx - 2vy = 0, but since the horiz. & vert,
tunes are essentially unsplit, some emittance growth in
the presence of strong space-charge forces may occur.
M+0.5
(m)
FIGURE 3. Transitionless lattice functions in one arc
module.
The fractional tunes result in the same nominal
working point location in betatron tune space (see
Fig. 2) as for the conventional FODO lattice (A), but
now the horiz. & vert, tunes per superperiod, Qx?y =
8.47, 7.46, are separated by one unit, hopefully
rendering harmless any effects of the nearby octupole
coupling resonance 2vx - 2vy = 6.
Betatron Tune Space
(4 orders, periodicity 1)
————— normal sextupole
————- skew Bestupole
——— — octupole
Although proposed as a transitionless ring lattice
for fixed operation at imaginary yt, this same lattice
can also be retuned for operation at either (a) real yt >
ymax (by simply switching quad polarities from DOFO
to FODO, without any change in cell phase advances),
or (b) real yt < ymax with horiz. cell phase advance
adjusted to 90 deg which is optimum for addition of an
effective yt - jump system (if needed) producing only
minor, localized perturbation of lattice functions.
Lattice:
Conventional FODO: N=M=19
Transitionless: N=25, M=22
N+0.5
FIGURE 2. Nominal working point in tune space for main
ring lattices and low-order resonances.
Option B: Transitionless Lattice.
This 3-sided ring geometry (cf. Fig. 1) uses an arc
structure incorporating missing-dipole cells to reduce
the value or change the sign of the momentum
compaction factor a = l/(yt)2, leading to large real or
imaginary yt. Each arc module consists of 3 DOFO
cells, with bend dipoles removed from the center cell.
Such a module, as illustrated in Fig. 3, exhibits fairly
smooth horizontal and vertical beta-function
amplitudes but a bipolar dispersion function D which
is either very small (on the average) or negative in the
regions occupied by bend dipoles, hence resulting in
either very small or negative a, i.e., imaginary yt in the
latter case. Eight such modules per arc, each tuned to a
horiz. phase advance of 7/8 x 2n, produce an
achromatic arc (i.e., with integer phase advance, here
Qx = 7) which results in essentially zero horiz.
dispersion in each of the 3 long straight sections.
Fig. 4 shows 1/3 of a complete ring (straight + arc)
with its bipolar dispersion wave through the arc which,
for the particular ring betatron tunes of Qx = 25.42, Qy
= 22.38, results in a transition yt = i26.
FIGURE 4. Transitionless lattice functions
superperiod (1/3 ring.).
in one
This single, versatile lattice design can thus provide
a flexible choice for as yet unidentified future needs or
as yet unforeseen problems or limitations with
imaginary yt operation (while imag. yt has been
adopted in several recent high-energy, high-intensity
lattice designs, there is as yet no operating experience
with such a lattice).
151
This lattice design (B) is based on a single length
of each magnet type (dipole, quadrupole, sextupole).
The resulting economy of scale (many identical
magnets, few types) reduces the total cost of both
magnets and associated power supplies. In comparison
to the conventional FODO lattice A, however, lattice
B has about 10% greater circumference and requires
about 10% more quadrupoles (each 20% stronger)
because of the missing-dipole arc cells. Lattice B also
has 3 times larger maximum dispersion in the arcs and
40% larger natural chromaticity than lattice A. Two
families of chromaticity-correcting sextupoles can
reduce ring chromaticity to zero, but the ring will more
likely be operated at a chromaticity of around -6; at
this level the chromatic tune spread for a beam
momentum spread of ±0.2% is only ±0.015.
m
-20'
-30'
261 m
mm m
36
45
m
-40-
--90 •
~7d
Particle tracking calculations through both lattices
A,B (described in detail in ref. 5) have shown both
lattices capable of meeting the dynamic aperture and
momentum acceptance criteria quoted earlier.
Longitudinal dynamics calculations with space charge
[6] have verified the desired evolution of beam bunch
time structure during acceleration in both lattices and
have shown longitudinal emittance growth and beam
loss at transition crossing in lattice A to be manageable
at half the design beam intensity in the ring (5xl013
protons). The final choice of Main ring lattice will be
made after further comparative studies (of collective
effects and coherent instabilities in particular).
~§0
-20
m
"i
FIGURE 5. Layout of the 4 GeV booster ring lattice (m)
followed by a DOFO straight cell with central F-quad
split and separated to create a straight of max. magnetfree length. This structure is equivalent to a 2-cell
module with half the dipoles missing, i.e., a missingmagnet configuration which lowers the momentum
compaction a and thus raises yt. Here, depending on
the setting of the central F-quad in the bend cell, yt can
be adjusted to any desired value above 9 (at fixed
sector phase advances).
Figure 6 shows the lattice functions over one sector
(center-to-center of adjacent straights) corresponding
to yt = 9.4. Again, the horizontal dispersion D is a
(positive) minimum in the region of the bend dipoles,
resulting in a high real yt. Positive aspects of this
lattice design are a sector horizontal phase advance of
nearly 260° (odd multiple of nearly 90°) and a large
4 GEV BOOSTER LATTICE
This Booster ring shares many of the general
design criteria of the Main ring lattice: robust
conventional and conservative design, operational
simplicity (few "knobs"), low cost (compact ring, few
magnet types) and avoidance of transition crossing.
The latter is readily achieved in this small, "lowenergy" ring by simply raising the lattice yt above ymax.
Other design features include H" strip injection from a
linac at either 157 or 800 MeV, and acceleration of a
single bunch of 3-4 xlO12 protons at a 5 Hz cycle rate,
a rate low enough to moderate RF power requirements
but high enough to fill the main ring with 25 bunches
in a reasonable time (5 sec).
Fig. 5 shows the layout of the Booster ring: a
symmetric 9-sided ring, 261m in circumference, with
nine 8.4m long straight sections. Each sector or
superperiod (1/9 ring) consists of a DOFO bend cell
-r————r————r
1.0
15
s
20
r
25
(m)
FIGURE 6. Booster lattice functions for one superperiod.
152
horizontal beta function in the straights. This
combination allows (1) convenient placement of
injection bumpers to locally a bump the circulating
beam on/off the stripping foil, and (2) efficient kickextraction of the beam where small-angle (2mrad) fast
kicker in one straight produces a sizeable (4cm) beam
displacement at a septum magnet in the next straight.
Negative aspects of this lattice arrangement are (1) the
dispersion is a maximum (about 2.2m) in the straights
which contain all beam injection/extraction and beam
manipulation insertions including RF cavities, and (2)
the large vertical beta-function at the entrance of
dipoles nearest each straight require a large dipole
vertical gap (10cm). Quadrupole apertures are 15 cm
diameter.
Again, the fractional ring tune chosen for the
Booster lattice places the working point in the same
region of betatron tune space, largely free of
systematic and structural sum resonances, as for the
50 GeV Main ring lattices. The Booster tune diagram
is shown in Fig. 7. Horizontal and vertical tune
integers are widely split. Laslett coherent and
incoherent space-charge tune shifts of order -0.15 at
injection result in a bow-tie shaped tune spread region
below this working point which encompasses several
sextupole sum resonances, but preliminary beam
simulations [7] using the space-charge code
SIMPSONS show no dramatic ill-effects at full
intensity with high-quality quadrupoles.
FIGURE 7. Booster tune diagram. Low-order resonances
and nominal working point with space-charge tune shift tail
at injection.
REFERENCES
Two families of chromaticity-correcting short
sextupoles (4 per sector) easily reduce the ring natural
chromaticity from -10 to zero, if desired, with modest
(0. IT) pole tip fields.
153
1.
A. Thiessen, "The AHF Project", these proceedings.
2.
V. Visnjic, Phys. Rev. Lett. 73, 2860 (1994).
3.
Proton Driver Design Study, Fermilab Report TM2136, Dec. 2000.
4.
K Shigaki, "JHF Lattice", these proceedings.
5.
F. Neri, "Tracking AHF Lattices", these proceedings.
6.
T.-S. Wang, LANL, private communication.
7.
D.E. Johnson, Dallas, TX and LANL, private
communication.