Electron Cloud Simulations
Using ORBIT Code
- Cold Proton Bunch model
April 11, 2007
ECLOUD07
Yoichi Sato, Nishina Center, RIKEN
Y. Sato
ECLOUD07
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Outline
ECloud Properties to Cold Proton Bunch in ORBIT
 Proton Bunch Slope Dependence of ECloud Growth and Energy
Distribution of Electrons Hitting Surface (triangular longitudinal line
density profiles)
Proton bunches of same head triangles and the effect of bunch slope
Proton bunches of same tail triangles and the effect of primary electron amount
 Prompt-Swept Electron Simulation and Discussion of Physics
Parameters with Comparing PSR Data
Constant proton loss rate to beam intensity
Assumption of proton loss rate function of beam intensity
 ECloud Recovery Simulation After Swept
Proton loss rate estimation
Inconsistency between the recovery estimation and prompt-swept slope fit
 Conclusions
Y. Sato
ECLOUD07
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PBunch Triangular Profiles
120ns 110ns
PB tail PB tail
100ns
PB tail
90ns
PB tail
Energy band
250eV-300eV
corresponds to
SEY peak
•The longer tail of pBunch causes
the larger eCloud and its higher
growth rate. The steeper tail pBunch
gives the higher energy of hitting
The energy distribution of
electrons (E_0 > 250eV) and the
lower SEY that may lead the lower
surface hitting electrons
growth rate.
of off-peak-band reduces
ECloud growth
Y. Sato
ECLOUD07
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PBunch Triangular Profiles
•The carry-over and primary
electrons before the peak of
pBunch slightly change eCloud
peak and growth rate.
However, the slight differences
imply that the pBunch effect to
drive electrons may be
mitigated by the existence of
inside electrons during the
beginning of pBunch tail slope.
And effect of carry •To have long head in pBunch
Effect of primary
electrons stored in the over electrons
profile is a possible way to
head of proton bunch surviving beam gap accumulate more protons in a
Y. Sato
ECLOUD07
bunch.
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Future Study for Artificial PBunch
 Comparison of ep instability between Long head
profile (short gap) and isosceles triangular profile
(large gap) using ORBIT capability of simulating
proton bunch dynamics. Even a short gap can remove
the ep oscillation of carry-over eCloud in front of the
next bunch.
 Simulation of ECloud development to proton bunches
of triangular + saw profile. We can expect to mitigate
trailing edge multipaction. The saw ratio and
frequency should be optimized. Certainly, the biggest
problem: how to realize them, is remaining.
Y. Sato
ECLOUD07
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Prompt-Swept Electron Data
from Electron Sweeper at PSR
Beam Pulse
HV pulse
 The prompt electrons come out at the tail of
the beam pulse. The Electron Sweeper (ES)
functions as a large area Electron Detector
(ED) until the HV pulse arrives.
 The swept electron signal is narrow during
HV at the end of the gap.
Swept electron signal
Electron Signal (prompt electron)
The two experimental features:
(1) swept electron slope is flatter than
prompt electron slope,
(2) swept electron slope has saturation
in high intensity beam.
Y. Sato
ECLOUD07
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Prompt-Swept Electrons
constant proton loss rate to beam intensity in ORBIT
SEY_max = 1.5 ~ 2.0 & proton loss rate = 4E-6/turn
The ORBIT simulations are
performed for field free section,
where ED/ES locates in PSR.
Prompt e in ORBIT means peak of
surface current after recovery.
Swept e in ORBIT means EC line
density at PB head after recovery.
SEY_max = 2.0 & proton loss rate = 1E-8/turn ~ 4E-6/turn
PSR features are reproduced
qualitatively but not quantitatively.
In ORBIT, if both SEY_max &
proton loss rate are constant
to beam intensity, promptswept slopes are much flatter
than experimental data.
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Prompt-Swept Electrons: Assumption of
Proton Loss Rate Function of Beam Intensity
Now, we assume proton loss rate in drift space, where
ED/ES locates, is an increase function of beam intensity
(reasonable from space charge).
Starting from the prompt-swept values of
(7uC beam, 4e-6/turn proton loss rate), we performed
simultaneous fitting on both prompt swept slopes with
varying a single parameter “proton loss rate” to different
beam intensity, 4uC ~ 8uC beam.
The searched proton loss rate to fit simultaneously
experimental prompt-swept slopes becomes an almost
exponential function of beam intensity. This is another
possible way to estimate proton loss rate.
Y. Sato
ECLOUD07
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Prompt-Swept Electrons: Profile Dependence
Actual proton pulse profiles
measured in PSR.
Now, they seek to have square one.
All my simulations for prompt-swept and recovery
adopt nonotched profile except for below one.
~6uC/pulse, prompt e
and swept e slopes
are flipped in different
pulse profiles.
ORBIT suggests that
a desirable proton
profile depends on
beam intensity.
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Recovery of ECloud: PSR and ORBIT
7.5 uC proton pulse measured in PSR shows 5
turn recovery of EC peak after clearing electrons
in beam gap by HV-applied electron sweeper.
In ORBIT simulation, a set of parameters
[SEY_max=2.0, Proton loss rate ~1E-8/turn, eyield per lost proton=100] provides 5 turn recovery
of EC to 7.5uC proton beam in field free section.
Both surface current and line density of EC show the
same number of recovery turns
Same carry-over electrons in PB head of [2nd turn,
p_loss=2E-8/turn] and [3rd turn, p_loss=1E-8].
Difference of EC peaks comes from new primary
electrons (Trailing Edge Multipaction).
Energy range of electrons hitting surface keeps almost same
in recovery turns. The amount of carry-over electrons has
little effect on the energy range.
The carry over electrons before PB peak
have weaker effect on EC than the new
primary electrons after PB peak.
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Inconsistency of proton loss rate
between recovery estimation and
prompt-swept slope fit
 To perform the simultaneous fit on prompt-swept
slopes, we start from the case of [SEY_max=1.7, 7uC
beam, p_loss=4e-6/turn]. However, if we try to start
from the case of [SEY_max=1.7, 7.5uC beam,
p_loss=1e-7/turn], which matches the recovery
estimation, we cannot reproduce prompt-swept slopes.
 [SEY_max=2.0, 6.3uC beam] has minimum of eCloud
(both prompt and swept) in lowering p_loss < 1e-8/turn.
 The recovery process may be dominated by other
eCloud sources. Now, in our simulation, only primary
electrons from lost proton and secondary emitted
electrons are considered as eCloud source.
 If electrons traveled from quadrupole area to drift
space are dominant, the number of recovery turns
depends on the traveling time.
Y. Sato
ECLOUD07
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Conclusions
 Longer head beam profile is a possible way to
accumulate more protons without making electron cloud
larger. Proton bunch ep dynamics should be examined.
 Simulated prompt-swept e of constant p_loss and
SEY_max reproduces qualitative features, but not
quantitative.
 Introducing p_loss function to beam intensity is a
possible way for quantitative discussion. A possible
p_loss function that fits prompt-swept slopes
simultaneously is exponential.
 Comparing the number of turns of recovery process
between experimental data and simulations, proton loss
rate of 7.5uC beam is ~ 1E-8/turn for SEY_max=2.0 and
~1E-7/turn for SEY_max=1.7.
Y. Sato
ECLOUD07
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Conclusions, cont.
 Both of recovery estimation and p_loss function assumption indicates
quite low proton loss rate for low beam intensity in field free straight
section, and it would hard to cause ep-instability. ECloud kick on
proton beam could be mostly non-straight section.
 There is inconsistency between the recovery estimation of proton loss
rate and the assumption of proton loss rate function of beam intensity
is needed. We cannot perform the simultaneous fitting of promptswept electron slopes including the point of the parameters estimated
by recovery process. We may need additional model of ECloud
source.
 The actual PSR proton bunch profiles depend on beam intensity.
However, this effect does not change prompt-swept electron slopes so
much.
 Therefore, we need to have other model of ECloud source as shoot
electrons from quadrupole area.
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ECLOUD07
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Main Concern of ORBIT Electron
Cloud Module: e-p problem
Lost proton
Secondary
electrons
e- born at wall
from proton loss
released e-
Tertiary
electrons
energy
Secondary gain
electrons
Captured ebefore bunch
Proton beam bunch
PSR: ~60 m in 90 m ring
SNS: ~200 m in 248 m ring
Vacuum Chamber Wall
Using Electron Cloud Module in ORBIT, we can simulate
Two stream instability to captured electrons inside beam bunch (serious source of ECE)
Trailing edge multipactor (big source of electrons)
multipaction = increase of electrons from secondary e- emission
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