Electron cloud in the Fermilab Booster Page: 2 of 4
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ELECTRON CLOUD IN THE FERMILAB BOOSTER
K.Y. Ng,* Fermilab,f Batavia, IL 60510, USA
Simulations of the Fermilab Booster reveal a sub-
stantial electron-cloud buildup both inside the unshielded
combined-function magnets and the beam pipes joining the
magnets, when the second-emission yield (SEY) is larger
than ~ 1.6. The implication of the electron-cloud effects
on space charge and collective instabilities of the beam is
Following the analytic solution of Metral and Rug-
giero,  we computed the stability contour of the Fermi-
lab Booster beam near injection including space charge and
octupole tune spread. The dashed curve in Fig. 1 is the
stability contour in the complex coherent-tune-shift plane
having an octupole tune spread +0.05 with space charge
turned off. The region under/above the contour implies sta-
bility/instability. As space charge is turned on, the stability
contour becomes the solid curve. The Booster has a cir-
cumference of 2irR=474.2 m, composing of 84 rf buckets.
The Booster bunch is of intensity Nb = 6x1010 at 1.40 GeV
(near injection), betatron tunes v ,y = 6.7/6.8, normalized
rms emittance 2.0 irmm-mr, and rms length a- = 0.70 m,
with maximum space charge tune shift Auv1 ~0.60. In
the derivation, coasting beam is assumed, but the peak cur-
rent has been used. Now the stability region becomes much
wider as a result of the large space-charge tune spread. Un-
fortunately, this wide stable area has been shifted far far
away from center of the plot as a result of the large incoher-
ent tune shift. The inductive part of the vacuum chamber
impedance, which is usually small, must be extraordinary
large to be under the contour in order to stabilize the beam.
SPACE-CHARGE TUNE SHIFT
The code POSINST  is employed to study electron
cloud buildup near injection. The Booster is made up of
24 combined function F-magnets and 24 combined func-
tion D-magnets. In the simulations, the inside volume of
the F-magnet where the beam resides is represented by a
13.0" x 1.64" rectangular pipe with uniform magnetic field
0.084102 Tesla, while that of the D-magnet is represented
t Operated by the U.S. Department of Energy, under contract with the
Fermi Research Alliance, LLC.
Figure 1: Stability contour from octupole with (solid) and with-
out (dashes) space charge.
by a 12.0" x 2.25" rectangular pipe with 0.071480 Tesla.
According to the observed initial loss rate of ~1.5% for the
first 500 turns, beam loss to the surrounding per beam par-
ticle per meter is 6.49x10-8, and each of these strayed par-
ticles is assumed to generate 100 electrons. They dominate
over the electrons generated by collision with ions at the
vacuum pressure of 1x 10-- Torr. Figure 2 shows the elec-
tron density around one transverse o-,y of the beam inside
the F- and D-magnets for various SEY's. The bunch pat-
tern has been taken to be 81 bunches plus 3 empty buckets.
Thus the density dips in the plots correspond to the ends
of revolution turns. We see that saturation is reached in the
D-magnet when SEY> 1.5, while it requires a SEY> 1.9 to
have saturation in the F-magnet. This may be due to the fact
that the vertical gap of the D-magnet is much bigger and
can therefore trap more electrons. The same simulations
were performed for the 168 m of 2.25" and 28.8 m of 4.25"
circular stainless steel pipes joining the magnets. The re-
Bucket Number soo soo o
seY-20 Long St Secti n
SEYt s 2 25in pipe
o oo zoBucket Number so so s
I Booster Dqua
o 1oo 2oo aoo Bucket Number
Short St Section
4 25in Pipe
o oo zoBucket Numberso so so
Figure 2: (Color) Electron cloud linear density inside an F-
magnet (top left), a D-magnet (top right), the 2.25" pipe in the
long straight sections (bottom left), and the 4.25" pipe in the short
straight sections (bottom right) for various values of SEY. The
beam's average linear density is shown in dashes as a reference.
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Ng, K. Y. Electron cloud in the Fermilab Booster, article, June 1, 2007; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc888827/m1/2/: accessed February 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.