Impedance of SPS travelling wave cavities (200 MHz)

A. Grudiev, E. Métral, B. Salvant, E. Shaposhnikova, B. Spataro

Acknowledgments:

Erk Jensen, Eric Montesinos, Rolf Wegner

Impedance meeting – March 3rd 2010

This is a work in progress…

Agenda

• Context

• EM Simulations to get the transverse wakes– Particle Studio– Try with ABCI

• Effect of these transverse wakes on beam dynamics

• Future plans

Context: SPS impedance model• A potential way to improve the LHC performance is to increase the intensity in the SPS

• Fast vertical instability is one of the limitations to increase the intensity in the SPS

many arguments point towards a Transverse Mode Coupling Instability

• Need to identify the sources of transverse impedance in the SPS to be able to find more solutions to increase the threshold of this instability

current impedance model (kickers, beam pipe, BPHs, BPVs)explains ~60% of the tune shift with intensity and instability thresholds when used in HEADTAIL beam dynamics simulations.

(direct space charge is not included in these simulations).

Other potential sources? RF cavities septa pumping ports

Context: SPS 200 MHz TW cavities

• 4 cavities– ACTA: 4*11 cells (x~ 31m, y ~ 76 m)

– ACTB: 4*11 cells (x ~84 m, y~27 m)

– ACTC: 5*11 cells (x ~25 m, y~91 m)

– ACTD: 5*11 cells (x ~85 m, y~27 m)

Example: ACTB

4 m 18.4 m

For HEADTAIL,to lump all these impedances in the same point with x = y =40 m, need to apply a factor 24to the wake of a single cell

Context: previous studies

• Resonant impedances in the SPS (T. Linnecar and E. Shaposhnikova) SL-Note 96-49 RF and G. Dome (CERN-SPS/ARF/77-11)

Longitudinal and transverse parameters of known impedances in the SPS

SW and TW cavities, kickers, septa, pumping ports included

Longitudinal

Transverse(dipolar most likely)

From SL-Note 96-49 RF

From SL-Note 96-49 RF

Context: previous studies

• Mafia Electromagnetic simulations by Bruno Spataro– Simulations of 9 cells instead of 11 (very large structure) and checked linearity with cells

of the low frequency part

-1000

-500

0

500

1000

1500

2000

0 0.5 1 1.5 2 2.5 3 3.5 4

Vertical transverse real part of the coupling impedance as function of the frequency estimated at 1.5 cm off

set along the vertical coordinate ( 9stems)

Re[Z](Ohm)

Freq[GHz]

Vertical

-1500

-1000

-500

0

500

1000

0 0.5 1 1.5 2 2.5 3 3.5 4

Vertical imaginary part of the couplingimpedance estimated at 1.5 cm off seton the vertical coordinate (9 stems)

Im[Z](Ohm)

Freq[GHz]

Vertical

Im[Z(f=0)] / m = 15 K/ m @ 1.5 cm on the vertical coordinate

Simulations with CST Particle Studio

(1) input file of Bruno was translated.(2) Sharp edges were Blended (small impact)(3) the couplers on each side were added(4) cavity was rotated by 90 degrees around z (to be checked with Bruno)(5) bunch length=2 cm rms (~6 million mesh cells)

Transverse wakes (displacement=1 cm)

s (cm)

Wy

(V/p

C)

Wx

(V/p

C)

s (cm)

s (cm)

Wdi

p (V

/pC

)

Wqu

ad (

V/p

C)

Transverse impedance (displacement=1 cm)

s (cm)

Re(

Zy)

(O

hm)

f (GHz)

Im(Z

y) (

Ohm

)

Re(

Zx)

(O

hm)

Im(Z

x) (

Ohm

)

f (GHz)

f (GHz) f (GHz)

Remarks• Very similar results than Bruno for the vertical dipolar impedance.

• Quadrupolar peaks are located at the same frequencies as the longitudinal resonances (200 MHz and 630 MHz)

noise or true signal?

• Im(Zx)=Im(Zy)~200 at 1 cm

Im(Ztransdipolar) ~ 0.5 M/m for all the cavities

• Source bunch length is large

DFT/iDFT to get wake function is more tricky than for kickers

use of wake potential directly

widens artificially the wake imported into HEADTAIL

need to think of other solutions: 2D codes or GdfidL first try with ABCI (2D code)

First try with ABCI

Rotational symmetry implies that the rods cannot be accounted for

First try with ABCI

200 MHz???

Bunch length=10 cm (rms)

Back to Particle Studio…

Same structure as ABCIOriginal structure from Bruno

Back to Particle Studio…

s (cm)

Wz

(V/p

C)

s (cm)

Zlo

ng (

Ohm

)

Longitudinal wake Longitudinal impedance

(1) CST PS and ABCI are giving very similar results (hopefully!!!)(2) Maybe we should stick to 3D simulations in this case…

Effect on beam dynamics• Wakes to be input into Headtail

s (m)

s (m)

s (m)

s (m)

Wx

dipo

lar

(V/p

Cm

m)

Wy

dipo

lar

(V/p

Cm

m)

Wx

quad

(V

/pC

mm

)

Wx

quad

(V

/pC

mm

)

Without cavities

With cavities

2 cm rms bunch length is probably too large need to find tricks or change code

Mode spectrum with HEADTAIL accounting for the current model

Threshold seen at 1.1 1011 p/b

Seems to be between modes -1 and -2

More to be done…

Future plans• Get the low currents to obtain the tune shift

• Reduce the bunch length to obtain a better wake over 1 m– Try with GdfidL

• Include other RF cavities, septa and pumping ports in the model

• Refine existing models (in particular the kickers)