Electron Cloud Feedback Workshop Indiana University, Bloomington 03/15-19/2004
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Transcript of Electron Cloud Feedback Workshop Indiana University, Bloomington 03/15-19/2004
1 Y. Sato Indiana University; SNS, ORNL
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 Y. Sato Indiana University; SNS, ORNL
What we are doing
Pipe Electron Cloud Region Proton Bunch
L=248 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.
Proton beam 3D SC potential grid Electron Cloud Grids with few (may be only one) longitudinal slices
2 Y. Sato Indiana University; SNS, ORNL
3 Y. Sato Indiana University; SNS, ORNL
Surface Model
The secondary emission surface under a phenomenological model --- simplified one from Furman and Pivi’s: PRST-AB 5 124404 (2002)
Removes a macroparticle hitting the surfaceAdds a macroparticle whose macrosize is multiplied by the secondary emission yield and energy is determined by model spectrum with Monte Carlo method
(x,y)
(n_x,n_y)
MacroSize
MacroSize
(secondary current)
(incident electron beam current)
3
We can keep the same number of electron-macroparticles through the secondary emission process
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Surface Model, cont.
elrdts
elelastic backscattered currentincident currentrdrediffused currentincident currenttstrue secondary currentincident current
Elastic backscattering emission: elRediffuing emission: rdTrue secondary emission: 1nMemiss
tsPn,tsPi,tsPn,tsMemissCntsMemisstsMemi
ss i=1
Memiss n Memiss-n
Each component has particular model spectrum. With following probabilities we choose the type of emission and get emitted energy with its spectrum.
For getting energy of true secondary, we use to simplify the model
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5 Y. Sato Indiana University; SNS, ORNL
Secondary Emission Surface Spectrum
Truesecondaries
rediffused
backscattered
Gaussian distribution around E0 in the data corresponds to energy resolution of the detector
The ORBIT spectrum matches Furman and Pivi’s simulationPRST-AB 5 124404 (2002)Including the response around E0
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Secondary Emission Surface Spectrum, cont.
The low E0 response of the stainless steel also matches Furman and Pivi’s results(Courtesy of M. Pivi)
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0 200 4000.01
0.1
1
10
PSR beam line density (scaled) complete SE model (0)=0.5 (P ivi and Furman) ORBIT E-Cloud module =
ini ORBIT E-Cloud module =
ini*0.95
ele
ctr
on
's d
en
sit
y (
nC
/m)
t, nsec
Pipe Electron Cloud Region Proton Bunch
No kick on the proton bunch to compare the results with Pivi and Furman’s PRST-AB 6 034201 (2003)
EC peak height is sensitive to the low energy SEY .
E-Cloud Development (ORBIT Simulation)
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Analytic Electron Cloud Model in KV proton beam
p-bunch ap,bp
e-cloud aeap, bebp
Ref: D. Neuffer et. al. NIM A321 p1 (1992)
Centroid oscillation model of uniform line densities of proton and electronyp_c p Exp[ i( n t )] , ye_c e Exp[ i( n t )]
Dispersion relation (no frequency spread):e pnep
ep freq.
rev. freq.
betatron freq.
n longitudinal harmonic of ep mode
ep freq.
p,Verpcbeaebe
e,Vprecbpapbp
The eqs. of motion are valid for the inside of streams
9 Y. Sato Indiana University; SNS, ORNL
Analytic Electron Cloud Model in KV proton beam, cont.
e pnep
ep freq.
rev. freq.
betatron freq.
ep freq.
The dispersion relation has complex solutions (instability) near e and n, slow wave, under satisfying the threshold condition pene
For ae=be=ap=bp=30mm, 1GeV proton beam, betatron tune Qx=Qy=6.2 and revolution frequency 0=2/T=6.646[1/s],
Qe = e/0 = 172.171Qp = p/0 = 2.79616 fe ; fe = neutralization factor
and the most unstable at the longitudinal harmonic number n = 178. n = 178 has 4 roots of :
1 /0 = 172.171 |Ae/Ap| = 1.56E62 /0 = 171.961 – 0.716i |Ae/Ap| = 116.097 where Ae/Ap = Qe /(Qe (/0) )3 /0 = 171.961 + 0.716i 4 /0 = 184.250 |Ae/Ap| = 6.77964
So, if we set the initial electron cloud and proton beam are the slow waves having n=178 modulation in benchmark, we can expect EC centroid oscillation as the superposition of the last 3 eigen modes ( = 2, 3, 4).
1/2
1/2
10 Y. Sato Indiana University; SNS, ORNL
Two stream benchmark (ORBIT Simulation)
Growth rate is given by Im0
Instability threshold is found by solving Im0
y p_c A Exp[ i( n t )] , y e_c B Exp[ i( n t )]
Up to t = 35ns we can say the centroid oscillation is the superposition of the two eigen modes of .
If there is no kick on proton beam, the EC centroid does not move.
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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.
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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.Furman’s 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.