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


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



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


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

4


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


Secondary Emission Surface Spectrum, cont.

The low E0 response of the stainless steel also matches Furman and Pivi’s results(Courtesy of M. Pivi)


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)


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


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


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.


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.


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.

electron cloud feedback workshop indiana university, bloomington 03/15-19/2004

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