Beam intensity limits in the Main Injector through transition with a normal phase jump scheme Page: 4 of 5
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impedance special designs were developed to shield vac-
uum pump connections, bellows and any undesirable steps
in the ring. Plans have also been made to reduce the
impedance arising due to special structures of Lambertson
magnets at extraction and injection regions. A conservative
estimate of the Z I /n = 1.6 Q [3]. However for simulation,
we take Zi /n = 3 Q which gives some safety margin.
Table I. The Main Injector parameters.
Mean radius of FMI 528.3019 m
ryt (nominal) 21.838
1c 267 sec-
,1 0.002091
Maximum RF 4 MV for 53 MHz
Frequency and
RF Voltage 15 kV for 106 MHz
60 kV for 2.5 MHz
15 kV for 5 MHz
Protons
el at 8 GeV Injection 0.1-0.35 eVs
IBwnch at 8 GeV 6-15 x 1010
Anti-protons
el at 150 GeV Injection 3-4 eVs
'Bwnch at 150 GeV 5-7 x 1010
Coup. imp. Zi1/n 3 Q
Beam pipe wave guide 1.5-2.2 GHz cutoff
cutoff frequency
Transverse Beam size(a) 2.2 - 5 mm
Beam pipe Radius (b) 5.8 cm (m)
a 1 is the second order term in the expansion of path length.an
40
0 3
U-
20
U-
1005
Negative Mass Instability Limit in the Main Injector
gamma dot = 267/sec
SEt 5ppb
tasE ppb
15Etppb
Ave Beam pipe radius=58 mm
Ave Beam size radius = 5 mm
Unstable
Steble Re n00
01 020 0 30 0 40 0 50
Bunch Area (eV-sec)Figure 1: Negative mass instability limits [7] for beam in-
tensity and emittance in the Main Injector. All ESME simu-
lation results presented here pertain to beam properties cor-
responding to the stable region.
ESME simulations have been carried out using 106
macro particles per bunch and ignoring the beam current
components above 14 GHz. We avoid negative mass in-
stability by observing the stability limits calculated byW. Hardt [7]. Figure 1 illustrates the negative mass instabil-
ity limits for three beam intensities as a function of bunch
area. The frequency range used in the ESME simulations
does display the qualitative features of negative mass insta-
bility for low emittance beam.200
0
-2000)
0
WI200
0
-200-0.075 0 0.075
I I-I
-0.075 0 0.075
Theta (deg)2.0
0
-2.0 o
4.0 j
2.0
0
-2.0Figure 2: Phase space distribution (i.e., AE vs 0 = AO)
of 0.25 eV-sec proton bunch in an accelerating rf bucket in
the Main Injector with 53 MHz rf system. The closed con-
tours represent the buckets for the case at 20 msec (A) be-
fore (B) after transition. The rf wave form is also shown.
The cases shown are for 15 x 1010 ppb.
Figure 2 shows phase space distribution for the highest
beam intensity bunch discussed here. We find that the phase
space density is almost unchanged across transition.
From these simulations we found that with the normal
phase jump scheme in the Main Injector the beam bunches
with 15 x 1010 ppb and emittance 0.25 - .35 eV-sec can be
accelerated through transition without any noticeable emit-
tance growth and with no beam loss. If the beam longitudi-
nal emittance is less than about 0.20 eV-sec then one might
expect considerable emittance growth due to negative mass
instability.
3 DECELERATION OF P BEAMS
For deceleration of p-, we have investigated two different
types of accelerator cycle. In the first method the 3 eV-s
beam bunch is captured at 150 GeV using 53 MHz rf buck-
ets (h = 588, Vrf = 0.5 MV). Then the bunch is rotated with
a 2.5 MHz system (h = 28, Vrf = 35 kV) and is matched.
The typical matching voltage was about 400 V. Then the
bunch is divided in to several bunches by raising the h =
588 rf voltage adiabatically. This takes less than 300 ms at
150 GeV. Thus a 3 eV-s beam bunch is distributed among 11(A) -
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Bhat, C.M., MacLachlan, J.A. Beam intensity limits in the Main Injector through transition with a normal phase jump scheme, article, May 1, 1997; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc694919/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.