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FERMILAB-Conf-01/195-T July 2001
RF PARAMETER CURVES FOR A PROTON DRIVER SYNCHROTRON
J. A. MacLachlan, Z. Qian, J. E. Griffin
Fermi National Accelerator Laboratory, Box 500, Batavia IL 60510-0500*
High average beam power proton synchrotrons in the
medium energy range are under consideration at several
laboratories for intense and specialized secondary particle
sources like muon colliders and v factories. A 12- 16 GeV
machine with a 15 Hz cycle and 3 - 1013 p/pulse capabil-
ity called the Proton Driver (PD) has been studied as a re-
placement for the Fermilab Booster and as a base for fu-
ture facilities. A staged development is proposed, ini-
tially using 20 modified 53 MHz Booster cavities in 12 GeV
operation. A second stage would allow 16 GeV top en-
ergy using a 7.5 MHz rf system consisting of 100 15 kV
low-Q cavities. This paper discusses the choices of rf
system parameters made in the design study. The limited
number of existing Booster cavities has led to considera-
tion for stage 1 of an inductive insert in the ring to aid
initial beam capture by compensating longitudinal space
charge, an admittedly speculative expedient requiring fol-
lowup with further calculation and some beam experiments.
This report is one of nineteen papers at this conference by
members of the Proton Driver design team; it relies on these
others to help establish the general context.
2 FIRST STAGE (53 MHZ RF)
Stage 1 of the PD serves to replace the present Booster in
the Fermilab injector chain and perhaps directly for low en-
ergy neutrino production. The top energy is 12 GeV using a
lattice designed for 16 GeV capability. It will employ refur-
bished Booster rf cavities modified to give a 5 inch apera-
ture. The parameters defining rf requirements are collected
in Table 1.
The combination of performance demands with the man-
dated use of a 400 MeV linac injector and modified Booster
cavities calls for some unconventional measures. The space
charge impedance corresponding to the perfectly conduct-
ing wall force is ZI /n -230iK at injection energy. To
control the space charge defocusing, a tunable inductive in-
sert is proposed to cancel this impedance throughout most
of the cycle. The insert looks attractive in the modeling;
it makes the difference between 96.8 % and 99.97 % for
the particle transmission efficiency for the complete cycle.
The idea is not new; it has been tried in two different
machines.[5, 6] However, studies have not been carried out
over a wide range of beam energy, momentum spread, etc.,
and more are needed.
The magnet ramp is driven by a 15 Hz resonant sup-
ply plus an independant second harmonic supply that is ad-
justed in phase and amplitude to minimize the required peak
* Operated by the Universities Research Association under contract
number DE-AC02-76CH03000 with the U. S. Department of Energy
rf voltage. The parameter optimization is driven primarily
by the effort to minimize beam loss. Because the rf voltage
limit is so strigent, loss limitation naturally relates closely
to longitudinal emittance preservation also.
2.1 Capture and Acceleration
A macroparticle tracking model has been used for the
entire cycle from multi-turn injection through matching to
Main Injector buckets. The injected protons are taken as a
continuous coasting beam at the energy of Bmin lasting up
to 90 ps timed symmetrically about Bmin; assymetric tim-
ings and energy offsets have not proved helpful. For nom-
inal linac intensity, 70 ps is sufficient to give the required
3 - 1013 protons, but efficiency does remain good over a
longer injection time. The perfectly conducting wall term
and the inductive insert are the only sources for the collec-
tive potential in these simulations.
The rf voltage is raised linearly during injection from 0
to 65 kV. It is then raised somewhat more slowly to estab-
lish a bucket area of 0.064 eVs at 226 ps. Because the slip
factor y is large at injection, the particles near 180 of rf
phase are all captured in this simple manouver. Certainly
some are quite close to the separatrix and subject to later
loss, but these losses are practically eliminated by the in-
ductive insert. They could also be controled with a sub-
stantially higher rf voltage. After 226 ps, the voltage curve
holds the bucket area constant until 4.96 ms where the volt-
age has reached the design limit of 1.2 MV. It is held at that
value until y has dropped sufficiently at about 30 ms to per-
mit reduction. Because of decreasing y and the control of
E by a second harmonic component in the magnet current,
the bucket area scarcely changes until it is allowed to rise
at the end of the cycle. Nonetheless, in the absence of the
inductive insert there are losses at maximum p (about 0.025
s into the cycle). This indicates that the 1.2 MV peak volt-
age is marginal. B reaches zero at 37.93 ms. The voltage
required for acceleration alone is 1.09 MV at maximum p,
so there is not much rf focusing. The synchronous phase
reaches about 64g.
The curves for p(t), p(t), Vr(t), bucket area SB (t), and
synchrotron tune vs(t) are plotted together in Fig. 1. The
curves are normalized to the range between zero and one to
display their qualitative interrelation; the magnitudes are in-
dicated by the parametrs in Table 1. Fig. 2 displays the nor-
malized rms emittance, the rms bunch width, and the rms
bunch height simillarly normalized.
The apparent effectiveness of an inductive insert and its
importance for low loss with the h 126 rf has resulted in
its tentative adoption for reducing beam loss and emittance
growth. A limited amount of rf focusing is suplemented
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James A. MacLachlan, Z. Qian and J.E. Griffin. RF parameter curves for a proton driver synchrotron, article, July 12, 2001; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc722372/m1/1/: accessed December 12, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.