ILC damping ring Workshop, Dec 19, 2007, KEK, L. WANG Ecloud simulation 2007 ILC Damping Rings...

ILC damping ring Workshop, Dec 19, 2007, KEK, L. WANG

Ecloud simulation

2007 ILC Damping Rings Mini-Workshop18-20 December, 2007

Lanfa Wang, SLAC


Content

• Update of the ecloud in wiggler

• Update of Grooved Chamber

• Electrode effect

• Simulation of the ecloud experiment in PEPII

• Head-tail instability

• Summary


Ecloud in wiggler

kzykxkBk

kB

kzykxkBB

kzykxkBk

kB

yxy

z

yxy

yxy

xx

sinsin)cosh(

,coscosh)cosh(

cossinh)sinh(

0

0

0

0 50 100 150 200

-20

-10

0

10

20

Z (mm)

Y (

mm

)

3D distributions shows:

There is very low e-cloud density in the middle of the two adjacent poles!

(L. Wang, F. Zimmermann, PAC07, TUPAS067)

Ecloud in wiggler magnet

Wiggler fields

Middle of poles

SEY=1.2

Magnetic fields

beam

Grooved Chamber and clearing electrode should work in wiggler (similar as in dipole magnet!)


Ecloud build-up in wiggler

0 20 40 60 80 10010

10

1011

1012

1013

Bunch ID

e (

m-3

)

1 long train125 Bunch trains

0 20 40 60 80 100 12010

9

1010

1011

1012

1013

Bunch ID e

(m

-3)

2767 bunches, 125 bunch train5782 bunches, 118 bunch trains

Beam filling pattern effect

• A long bunch train with low bunch current (Low Q) can significantly reduce the electron density

•The short period of the wiggler magnetic field can slightly reduce the electron density (a field with a period of 0.2m reduces the electron

cloud density 30% comparing it with a period of 0.4m. )


Comparison with dipole magnet

The peak electron density in the dipole magnet is larger than that in a wiggler by a factor of 2.7 due to the variation of the field with longitudinal position and the absence of multipacting in the region between successive wiggler poles

0 50 100 15010

10

1011

1012

1013

1014

Bunch ID e

(m

-3)

DipoleWiggler

Electron build up in a dipole and in a wiggler, for a beam of 2767 bunches and 125 bunch trains.

There is a lower ecloud density in wiggler!


Content


• Update of Triangular Grooved Chamber




• Summary


60 65 70 75 801

1.1

1.2

1.3

1.4

1.5

1.6

W=4.5mm, Rtip

=0.2mmW=3mm,R

tip=0.25mm

W=2mm,Rtip

=0.25mm

Impedance enhancement of grooved chamber

-50 -40 -30 -20 -10 0 10 20 30 40 50-50

-40

-30

-20

-10

0

10

20

30

40

50

X (mm)

Y

(mm

)Impedance enhancement factor of the triangular grooved surface with round tips

Model of the beam pipe with grooved surface in a dipole magnet in CLOULAND

)

W The impedance enhancement factor increases linearly with angle in the region we are interested in and it is smaller than 2.0. The required grooved surface is only 15% of the total surface. Therefore, the overall impedance enhancement due to the grooved surface is small.

(L. WANG, et. al. NIMA, 571 (2007) 588)


Adaptive IMEPDANCE ANALYSIS of Grooved Surface

Rounded Tip

(b)

Mesh and field near the grooved surface

(L. Wang, PAC07, THPAS067)

(Thanks Karl Bane for very helpful discussions)


Roots and Tips of the grooved surface( sample) (Courtesy Frank Cooper, SLAC)


Estimation of SEY of the grooved chamber in PEPII Dipole magnet

Peak SEY 0=1.2, Width =2mm, Dipole field=0.2Tesla

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

1.2

1.4

Energy (eV)

SE

Y

0=1.20,B=0.2 Tesla,R

tip=0.08mm

Grooved SurfaceFlat Surface

Simulation Parameters

Radius of tip=0.08mm=77.1o

0 200 400 600 8000

0.2

0.4

0.6

0.8

1

1.2

1.4

Energy (eV)

SE

Y

0=1.20,B=0.2 Tesla,R

tip=0.25mm

Grooved SurfaceFlat Surface

Radius of tip=0.25mm=78o

The radius of the tips from manufacture is smaller than we expected! It can reduce the SEY from 1.2 to 0.5!

worst case, close to the Design


Content






• Summary


Accumulation of ecloud around electrode

0 100 200 300 400 500 6000

2

4

6

8

10

12

14x 10

12

Time (ns)

e (

m-3

)

AverageCenter

In most cases, Electron density near the beam is low, but more electrons can accumulate outside the electrode

electrode

Sey=1.4 v=300VoltsOne electrode at the bottom


Effects of the rectangular grooved chamber in PEPII

• Reduction of the premaries

• Reduction of the secondaries


Estimation of the reduction of primary electrons

Results (relative Photon electron number for the same amount of photons):

1. Flat 1 : 1.0

2. Flat 2: 0.8

3. Groove 1: 0.04 ( 1/14)

4. Groove 2: 0.041 (1/13)

The rectangular grooved chambers reduced the photon electrons by a factor of 13~18! (like a mini-ante-chamber)


0 0.5 1 1.5 2 2.50

0.05

0.1

0.15

0.2

0.25

Beam Current(A)

I e ( 1

0-6 A

/cm

-2)

=0.6, Cloudland=0.7, Cloudland=0.8, Cloudland=0.9, Cloudland=1.0, Cloudland=1.1, Cloudland=1.2, Cloudland

Suppression of the secondaries

reduction of secondaries

Due to the coating (SEY<1), there are no much secondaries, further reduction of the SEY by grooved chamber doesn't reduce the electron current much although the SEY is LOWER!

Electron current with the same primaries


Comments

• In the test of clearing electrode and grooved surface, our goal is to reduce the secondaries. Therefore, it would be better to let the multipacting happen (generate more secondaries), and then suppress them, make the effects more clear and easier in analysis


Content






• Summary


Electron-Beam instability (single bunch)

J.W. Flanagan, K. Ohmi, et. al., Phys.Rev.Lett.94:054801, 2005.

Vertical Tune Sideband

~y+sy

0.32 0.34 0.36 0.38 0.4 0.42 0.44

0.5

1

1.5

2

2.5

x 10-9

Frequency [q]

Pow

er Qy

Qy+Qs

Measurements KEKB Simulation

Beam size blow-upSynchro-beta sideband

two-streams instability PIC code is developed

Sideband is reproduced


Adaptive simulation of Head-tail

Drift region dipolewiggler

Advantages• High accuracy• Fast• Very Easy to use • Arbitrary boundaries• Arbitrary beam shape

and ecloud shape

Sample: Mesh of chamber & beam in field free region

Challenge in such kind of simulation: Very large ecloud vs. very small beam spot (a few m) , The pinch factor in ILC is very larger (60)(15for B-factory)

adaptive method will be applied, the ecloud from the build-up can be loaded to the instability simulation


Summary• We simulated the ecloud in various conditions with 3D program

CLOUDLAND• Electron cloud in wiggler is understood: There is a minimum ecloud density at the middle the magnet poles A low Q beam has low electron density A small period of the wiggler can low the ecloud density The ecloud in wiggler is lower than in dipole

• The radius of the round tip of the triangular grooved chamber is smaller than we expected and the grooved surface can significantly reduce SEY. A build-up simulation with the design geometry is under the way.

• The rectangular grooved chamber can reduce both primaries and secondaries. However, it is extremely difficult to distinguish them precisely due to the coating effect.

• There is a strong pinch effect in ILC, we use a adaptive code to simulate of single bunch Instability, which can model the realistic distributions of the ecloud (Very large) and Beam (VERY small)


Beam-Ion instability in PEPII HER

Time (3hrs)

Luminosity drop

Beam currentNumber of bunches increase

HER Beam Dipole oscillation + beam size blow-up

1730 bunches with 2 RF bucket spacing (total ring can fill 1746 bunches)

(LER beam size drop)

(Courtesy S. Heifets, et.al.)

1.75A


Challenge of the Strong-strong simulation for ILC

•Number of Bunches: >1000

•Number of elements along the ring (ion-stations) ~500

•Macro Number particle per bunch: 10000

•Macro number particle per element 10000

•Number of turns > 1000

Total macro particles of beam: 10E7

Total macro particles of ions: 5E7

Minimum requirements:

A. Kabel, Cho-Kuen NG from SLAC (Advanced Computation Department) are going to help.

Beam study (ATF, ALS, PEPII)

1000CPU?

ION-MAD has been used to simulate ATF, However,


Thank you all!

Merry Christmas!

&

Happy New Year!!


Backups


Application of the ecloud Mitigations

Region 1 Region 2

SEYAnte_chamber •Coating

•Grooved chamber

•electrode


Photon flux before alignment

x=-5.2mmx=-4.2mm

2.27m1.86182m 2.27m

S=17m S=21mG1 F1 G2 F2S=22.9m

_photon=2.3mrad _flat1=2.8mrad

1.86m

_photon=1.7mrad_flat2=2.3mrad

The large horizontal offset shadows the two Flat chambers!


Electron current change after the beam pipe alignment

E-current in the flat chambers increases by a factor >20/10; the shape also changed!

E-current in Grooved chamber reduced by a factor 2

E-current of the stainless steel chamber remain the same.


Particle Mesh In CLOUDLAND

Mesh of chamber

Real charge distribution Meshed Charge distribution

Three dimensional irregular mesh to better represent the general chamber geometry

handle accuracy with high order elements.

Charge assignment

0QNQ ii 1i

iN

20 node element

ILC damping ring Workshop, Dec 19, 2007, KEK, L. WANG Ecloud simulation 2007 ILC Damping Rings...

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