Updated electron-cloud simulation results for the Large Hadron Collider (LHC) Page: 2 of 3
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As a variant to the full-fit model, we have also switched
off the contributions of the rediffused and the elastically re-
flected electrons, thereby keeping only the true-secondary
component. The value of the SEY at incident electron ener-
gies $ 10 eV is an important parameter since it determines
the accumulation rate and the electron cloud intensity itself.
With this motivation we have repeated our simulations un-
der the assumption 8(0) 0.6, as an additional variant of
the full-fit model.
50 100 150 200 250 300 350
Secondary electron energy (eV)
Figure 1: Secondary electron energy spectrum dS/dE for
Eo -300 eV (measured data and our model). The energy
spectrum consists of the true secondary electrons (roughly
the portion below 40 eV), the inelastic or re-diffused elec-
trons (broad flat portion), and the elastically reflected elec-
trons (peak at E ~ Eo). The contributions to 6(Eo) are
44%, 48%, and 8% respectively. The peak of the true-
secondary component is at ~ 5 eV with a FWHM=12 eV.
0 200 400 600 800 1000
Primary electron energy (eV)
Figure 2: Our model SEY vs. primary electron energy, for
Smax=1.9 and Emax=240 eV. The case with 3(0) 0.6 is
2.2 Simulation Model
In our simulation we assume the LHC proton beam to
be composed of identical, evenly-spaced, proton bunches
with population N = 1.05 x 1011 separated by Tg. We
- measured spectrum
--- full-fit model
--- --- --- --- --- --.-- -----
assume that the bunch density is a 3D Gaussian distribu-
tion with rms sizes o,, as, az. We simulate the passage of
the beam either in a dipole or in a field-free (FF) section
in the arcs. We make the approximation that the vacuum
chamber is made of a perfectly-conducting copper pipe of
elliptical cross-section with semi-axes (a, b). The electron
generation by photons hitting the wall is represented by the
product of two parameters, Y' x Ny, where Y' is the ef-
fective photoelectric yield per penetrated photon, and Ny
is the number of photons hitting the wall of the chamber
whose energy is above 4 eV, per bunch passage. We assume
that the time distribution of the generated photoelectrons is
proportional to the instantaneous bunch intensity.
The scrubbing of the surface due to continued photon
and/or electron bombardment leads to a conditioning ef-
fect [8-10] that is responsible for a decrease of 6max. We
assume the initial value to be 6max 1.9, while 6max 1.1
represents the value after conditioning. Other electron
emission parameters have been shown to be affected by
the conditioning process. In our calculations we assume
that both Y' and Emax decrease under the combined effect
of particle and radiation bombardment  concomittantly
with 6max, as specified in Table 1.
The photoelectrons are simulated by macroparticles.
The secondary electron mechanism adds to these a variable
number of macroparticles, generated stochastically accord-
ing to the SEY model described above. The bunch is di-
vided into slices, so that the macroparticles experience Nk
kicks during the bunch passage. We typically choose the
full separation between the head kick and the tail kick to
be 5-2. We also divide the empty buckets into Ng inter-
mediate steps. The space-charge force is calculated and
applied at each slice during the bunch passage, and each
step in the empty gap. The image forces of both protons
and electrons are taken into account, assuming a perfectly
conducting wall. In all results presented here, the proton
beam is assumed to be a static distribution of given charge
and shape moving on its nominal closed orbit, while the
electrons are treated fully dynamically. Typical parameter
values used in the simulations are shown in Table 1.
3 RESULTS AND DISCUSSION
The build-up of the electron cloud in a dipole section
during the passage of the beam is shown in Fig. 3. The
electrons gradually increase in number during successive
bunch passages until, owing to the space-charge forces, a
balance is reached between emitted and absorbed electrons.
The estimated average number of electrons in a dipole vac-
uum chamber is 7 x 1010 in the case of 6max 1.9.
The power deposited by the electrons hitting the wall on
the beam screen in an LHC arc is shown in Table 2, both
for a field-free region (FF) and for a dipole magnet section.
The simulated heat load computed with the half-
Gaussian model is in very good agreement with the CERN
results . With the full-fit model, the estimated heat load
increases by a factor ~ 4 relative to the half-Gaussian
----high electron reflectivity at low energy
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Furman, M. A. & Pivi, M. Updated electron-cloud simulation results for the Large Hadron Collider (LHC), article, June 26, 2001; California. (digital.library.unt.edu/ark:/67531/metadc717162/m1/2/: accessed June 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.