Electron%20Cloud%20Feedback%20Workshop%20Indiana%20University,%20Bloomington%20%20%20%20%2003/15-19/2004

1
Electron Cloud Feedback WorkshopIndiana
University, Bloomington 03/15-19/2004

• Simulation of e-Cloud
• using ORBIT
• Yoichi Sato
• Indiana University, Bloomington SNS/ORNL
• J. Holmes, A. Shishlo, S. Danilov,
• S. Cousineau, S. Henderson
• SNS/ORNL

Y. Sato Indiana University SNS, ORNL
2
What we are doing
L248 m and about 1000 turns

• We have to simulate a building up an electron
  cloud, its dynamics, its effect on a proton bunch
  during the whole accumulation period or at least
  for several turns to detect the development of
  instability.

2
Y. Sato Indiana University SNS, ORNL
3
Surface Model
The secondary emission surface under a
phenomenological model --- simplified one
from Furman and Pivis PRST-AB 5 124404
(2002) Removes a macroparticle hitting the
surface Adds a macroparticle whose macrosize is
multiplied by the secondary emission yield d and
energy is determined by model spectrum with Monte
Carlo method
(secondary current) (incident electron beam
current)
d(E0)
MacroSize, E0
(n_x,n_y)
MacroSized, E
q0
q
We can keep the same number of electron-macroparti
cles through the secondary emission process
(x,y)
3
4
Surface Model, cont.

• (E0) del drd dts
• del ( elastic backscattered current )/(
  incident current )
• drd ( rediffused current )/( incident current
  )
• dts ( true secondary current )/( incident
  current )

Each component has particular model spectrum.
With following probabilities we choose the type
of emission and get emitted energy with its
spectrum.
Elastic backscattering emission (del/d)
Rediffuing emission (drd/d)
True secondary emission 1b n b Memiss (dts/d)( Pn,ts / S Pi,ts ) Pn,ts (MemissCn)(dts/Memiss) (1-dts/Memiss)
Memiss
n
Memiss-n
i1
For getting energy of true secondary, we use E0
p E to simplify the model
4
5
Secondary Emission Surface Spectrum
Gaussian distribution around E0 in the data
corresponds to energy resolution of the detector
The ORBIT spectrum matches Furman and Pivis
simulation PRST-AB 5 124404 (2002) Including the
response around E0
backscattered
True secondaries
rediffused
6
Secondary Emission Surface Spectrum, cont.
The low E0 response of the stainless steel also
matches Furman and Pivis results (Courtesy of M.
Pivi)
7
E-Cloud Development (ORBIT Simulation)
No kick on the proton bunch to compare the
results with Pivi and Furmans PRST-AB 6 034201
(2003)
EC peak height is sensitive to the low energy
SEY d(E00) .
8
Analytic Electron Cloud Model in KV proton beam
Centroid oscillation model of uniform line
densities of proton and electron yp_c Ap Exp
i( n q - w t ) , ye_c Ae Exp i( n q -
w t ) Dispersion relation (no frequency
spread) ( we - w ) wb wp - ( n w0
- w ) we wp
2
2
2
2
2
2
2
ep freq.
rev. freq.
betatron freq.
ep freq.
n longitudinal harmonic of ep mode
wp,V 4le rp c / g be (ae be)
2
2
we,V 4lp re c / bp (ap bp)
2
2
The eqs. of motion are valid for the inside of
streams
Ref D. Neuffer et. al. NIM A321 p1 (1992)
9
Analytic Electron Cloud Model in KV proton beam,
cont.
( we - w ) wb wp - ( n w0 - w )
we wp
2
2
2
2
2
2
2
ep freq.
rev. freq.
betatron freq.
ep freq.
The dispersion relation has complex solutions
(instability) near w we and w (n w0-wb), slow
wave, under satisfying the threshold condition
wp t (wb/we) nw0 - we - w For
aebeapbp30mm, 1GeV proton beam, betatron tune
QxQy6.2 and revolution frequency
w02p/T6.6461/ms, Qe we/w0 172.171 Qp
wp/w0 2.79616 fe fe
neutralization factor and the most unstable at
the longitudinal harmonic number n 178. n
178 has 4 roots of w w1 /w0
-172.171 Ae/Ap 1.56E6 w2 /w0 171.961
0.716i Ae/Ap 116.097 where Ae/Ap
Qe /(Qe - (w/w0) ) w3 /w0 171.961 0.716i
w4 /w0 184.250 Ae/Ap 6.77964 So, if
we set the initial electron cloud and proton beam
are the slow waves having n178 modulation in
benchmark, we can expect EC centroid oscillation
as the superposition of the last 3 eigen modes (w
w2, w3, w4).
1/2
1/2
2
2
2
10
Two stream benchmark (ORBIT Simulation)
Growth rate is given by Im(w)gt0 Instability
threshold is found by solving Im(w)0 y p_c
A Exp i( n q - w t ) , y e_c B Exp
i( n q - w t ) Up to t 35ns we can say
the centroid oscillation is the superposition of
the two eigen modes of w . If there is no kick
on proton beam, the EC centroid does not move.
11
Two stream benchmark (ORBIT Simulation), cont.
The solvable model is valid when the EC is
overlapping the proton beam. We can apply the
model upto t 37ns If there is no kick on
proton beam, the EC keep the same radius.
12
Conclusion

1. The whole new e-cloud module has been integrated
   in the ORBIT simulation code.
2. Secondary emission surface model based on M. Pivi
   and M.Furmans shows matching spectrum results
   with theirs. PRST-AB 5 124404 (2002), PRST-AB 6
   034201 (2003)
3. The benchmark of the code with the two stream
   instabilities example is in progress. Initial
   benchmarks with simplest models that can be
   solved analytically have been done.