RF parameter curves for a proton driver synchrotron Page: 2 of 3
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with self-excited focusing voltage. However, the induc-
tance will have a real impedance component which dissi-
pates rf power and could furthermore cause self-trapping
instability. Careful studies of the tradeoffs are required to
establish net benefit.
The slip factor is so high at injection that the cap-
tured beam has energy-phase correlation (bunch tilt) which
wastes precious bucket area and causes beam loss. Divid-
ing the rf into two parts on opposite sides of the ring reduces
the tilt and resulting loss. Dividing the rf into three equally
spaced groups would make a small additional improvement.
The planned configuration of the injection, extraction, and
collimation systems looks inconsistent with a three-way di-
Table 2 shows the injection-to-extraction transmission
efficiency and emittance at extraction for different depar-
tures from the optimum modeling result. The top entry
is the best result obtained, and each entry following gives
the transmission when one condition is changed without at-
tempting to reoptimize the other parameters. Possibly some
of the apparently lost efficiency could be recovered in such
a reoptimization, but the intention is only to suggest the
importance of various conditions to the optimum obtained.
The lower final emittance for the more closely grouped cav-
ities reflects directly the removal of bunch halo by having
the bunch tilted in the early part of the cycle.
3 SECOND STAGE (7.5 MHZ RF)
In stage 2 the PD is used to produce p's for a v fac-
tory storage ring. The extraction energy is raised to 16
GeV and the rf system is replaced with an h 18 sys-
tem to provide the desired bunch spacing. A factor four
larger extracted longitudinal emittance is allowed for each
of the 18 bunches, so the design brightness is raised by
only 65 %. The larger inter-bunch gap permits chopping
the linac beam, allowing synchronous injection. The linac
beam spans 252' of an approximately stationary bucket.
There is an additional requirement for < 3 ns rms bunch
length at extraction. It can be met by keeping the voltage at
1.4 MV as E drops toward the end of the acceleration cycle.
The rms bunch length is 0.64 ns with a bunch rotation and
1.55 ns without. The final 95 % emittances are 0.43 eVs and
0.39 eVs respectively. The rf parameters of PD stage 2 are
collected in Table 1.
3.1 Stage 2 RF Curves
Because the beam is chopped and there is more adequate
rf focusing in stage 2, an inductive insert is not used. There
are practically no losses, not only at injection, but through-
out the acceleration cycle. The voltage and magnetic ramp
curves are similar to those found for stage 1, but the buckets
are less full and there is no need for fine tuning of the curves
to control losses.
For the narrowest bunches a bunch rotation is intended.
However, merely keeping the voltage at its maximum per-
missable value of 1.4 MV until the end of the cycle gives al-
0010 0020 0030 0040
Figure 1: RF parameters durning the cycle of the Stage 1
proton driver scaled to the range 0 to 1: Vrf (fine dots), p
(dash-dot), p (solid), vs (short dash), and bucket area (long
ready an rms bunch length of 1.55 ns, somewhat better than
had been anticipated in the initial design. For injection into
the Main Injector the final voltage can be set at any con-
venient value between there and 100 kV or so. Even nar-
rower bunches can be obtained by a quarter period bunch
rotation in a mis-matched bucket. The momentum spread
becomes wide enough that the contribution of the second
and perhaps the third order dependence of path length on
momentum are important. These contributions are included
in the macroparticle model. Considered but not included
here is the effect of path length difference depending on be-
tatron amplitude. Figure 1 shows the phase space distribu-
tion of a 0.39 eVs bunch at extraction without rotation in a
bucket produced by the maximum 1.4 MV of rf. If a rotation
is made, it starts at 37.6 ms when the sychronous phase is
0s 70' and 1Vr is 145 kV. Fig. 3 shows the phase space
distribution; it has an rms emittance of 0.43 eVs and rms
length of 0.64 ns.
 "The Proton Driver Design Study", Fermilab TM-2136 (De-
 M. Champion, T. Berenc, M. May, and J. Reid, "Design and
Prototype Tests of a Large Aperture 37-53 MHz Ferrite Tuned
Booster Cavity", this conf.
 J. Dey, I Kourbanis, Z. Qian and D. Wildman, "A Prototype
7.5 MHz Finemet Loaded RF Cavity and 200 MW Amplifier
for the Fermilab Proton Driver", this conf.
 A. M. Sessler and V. G. Vaccaro, "Passive Compensation of
Longitudinal Space Charge Effects in Circular Accelerators
The Helical Insert", CERN 68-1, ISR Div. (1968)
 K. Koba et al., "Longitudinal Impedance Tuner Using High
Permiability Material", KEK Preprint 99-96 (1999), also
PAC99, New York
 M. A. Plum et al., "Experimental Study of Passive Compen-
sation of Space Charge at the LANL Proton Storage Ring",
Phys. Rev. ST Acc. and Beams, v. 2, 064201 (1999)
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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/m1/2/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.