headtail simulations for the impedance in the clic-drs

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HEADTAIL simulations for the impedance in the CLIC-DRs

Damping Rings

E.Koukovini-PlatiaTS CERN, NTUA

G. Rumolo, B.Salvant, K. Shing Bruce Li, N.Mounet CERN

CLIC meeting, 27/05/2011

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• Theory• Simulation• Analysis results• Summary- conclusion• Next steps

Damping Rings

Outlook

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Theory

• Particle beam in a metallic vacuum chamber

• The beam is a collection of particles multiparticle approach needed

• A charged particle generates harmful EM fields at any cross-section variation of the vacuum chamber

• As the intensity increases, the beam self-generated EM fields will perturb the external fields (needed to guide the beam)

2b

G.RumoloCAS, Varna, September 27 2010

G.Rumolo

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CAS, Varna, September 27 2010

• Wake field is the EM field generated by the beam interaction with its surroundings

• Influence the motion of trailing particles in longitudinal and transverse directions

• The wake fields act back on the beam, causing perturbation, possibly leading to energy loss, beam instabilities, excessive heating

• The instabilities occur above a threshold current

• Determine the ultimate performance of the accelerator

• Each accelerator has an intensity limit

Why study multiparticle(collective) interactions?

W0(z)

Model:A particle q going through a device of length L, s (0,L), leaves behind an oscillating field and a probe charge e at distance z feels a force as a result. The integral of this force over the device defines the wake field and its Fourier transform is called the impedance of the device of length L.

q

z

e s

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Wake fields (impedances)

L

CAS, Varna, September 27 2010G.Rumolo

The full ring is usually modeled with a so called total impedance made of three main components:

• Resistive wall impedance

• Several narrow-band resonators at lower frequencies than the pipe cutoff frequency c/b (b beam pipe radius) long-range wake

fields, act back on subsequent bunches, • One broad band resonator modeling the rest of the ring (pipe

discontinuities, tapers, other non-resonant structures like pick-ups, kickers bellows, etc.)last a short time, responsible for single bunch instabilities

Þ Total impedance designed such that the nominal intensity is stable6

Wake fields (impedances)

G.Rumolo

A perfect vacuum chamber would have a superconducting surface and be uniform around the ring. Not possible since rf systems, which by nature are not smooth, injection/ejection components , BPM, etc are needed.The loss characteristics of a particular piece or of the vacuum chamber for the whole ring is expressed in terms of an impedance Z important to estimate the impedance budget

multibunch instabilities

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1. Broadband Model (DR’s): - First approximation-Used to model the damping rings (DR’s)-Scan over impedance to define an instability threshold (estimate the impedance budget)

2. Thick wall in wigglers (Resistive wall model)- Copper-Stainless steel

Check if is possible to perform at the nominal intensity

3. Wall with coating in the wigglers• aC-ss (0.001mm )• NeG-ss (0.001mm )• aC-copper (0.001mm )• NeG-copper (0.001mm)

Simulation

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Resistive wall in the CLIC-DR regime

Pipe cross- section:

• Layers of coating materials can significantly increase the resistive wall impedance at high frequency – Coating especially needed in the low gap wigglers– Low conductivity, thin layer coatings (NEG, a-C)– Rough surfaces (not taken into account so far)

N. Mounet, LER Workshop, January 2010

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General Resistive Wall Impedance: Different Regimes• Vertical impedance in the wigglers (3 TeV option, pipe made of copper without

coating)

Note: all the impedances and wakes presented have been multiplied by the beta functions of the elements over the mean beta, and the Yokoya factors for the wigglers

Low frequency or “inductive-bypass” regime

“Classic thick-wall” regime

High frequency regime

N. Mounet, LER Workshop, January 2010

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Resistive Wall Impedance: Various options for the pipe

• Vertical impedance in the wigglers (3 TeV option) for different materials

Þ Coating is “transparent” up to ~10 GHzÞ But at higher frequencies some narrow peaks appear!!Þ So we zoom for frequencies above 10 GHz

N. Mounet, LER Workshop, January 2010

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Resistive Wall Impedance: Various options for the pipe

• Vertical impedance in the wigglers (3 TeV option) for different materials: zoom at high frequency

Þ Above 10 GHz the impact of coating is quite significant.

Resonance peak of ≈1MW/m at almost 1THz

N. Mounet, LER Workshop, January 2010

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. . .

Bunch length Bunch to bunchBunch train

In terms of wake field, we find

• The presence of coatings strongly enhances the wake field on the scale of a bunch length (and even bunch-to-bunch)

• The single bunch instability threshold should be evaluated, as well as the impact on the coupled bunch instability

• This will lower the transverse impedance budget for the DRs N. Mounet, LER Workshop, January 2010

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• Single bunch collective phenomena associated with impedances (or electron cloud) can be simulated with the HEADTAIL code

• Beam and machine parameters required in the input file

• HEADTAIL computes the evolution of the bunch centroid as function of number of turns simulated

Simulation

Methods : What to do with HEADTAIL outputs ?

1. Extract the position of the centroid of the bunch (vertical or horizontal) turn after turn simulated BPM signal

2. Apply a classical FFT to this simulated BPM signal (x)3. Apply SUSSIX* to this same simulated BPM signal (actually x – j x x’ )4. Translate the tune spectrum by Qx0=0 and normalize it to Qs

B.Salvant

Another visualization of the tune spectrum

for Nb = 3 109 p/b (Ib = 0.02 mA)

Displaying the Sussix spectrum on one line per bunch intensity

The dots are brighter and bigger if the amplitude is larger

B.Salvant

New update of the lattice design at 3 TeV

from Y. Papaphilippou, F.Antoniou

Simulation Parameters

• 20000 turns• <βx> = 3.475 m (DRs)

• < βx > = 4.200 m (wigglers)

• < βy> = 9.233 m (DRs)

• < βy> = 9.839 m (wigglers)• Bunch length = 0.0018m• Qx = 48.35

• Qy = 10.40

• Qs = 0.0029

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• Model all the DR • Round geometry• Average beta functions used• < βx > = 3.475 m

• < βy>= 9.233 m• Scan over values of impedance in order to define the

instability threshold estimate the impedance budget

Broadband Model

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Horizontal and vertical motion in a round geometry

Hor.chrom. Q’x 0Vert. chrom. Q’y 0

•Centroid evolution in x and y over the number of turns, for different values in impedance

•As the impedance increases an instability occurs

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Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of impedance•Mode spectrum represents the natural coherent oscillation modes of the bunch•The movement of the modes due to impedance can cause them to merge and lead to an instability

The mode 0 is observed to couple with mode -1 in both planesCausing a TMCI instability

TMCI 8MΩ/m

TMCI 4MΩ/m

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1 1 1157.6 10

trca x

5597rel

rel tr

Above transition

Run with positive chromaticity

damping

Broadband Model

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Horizontal and vertical motion in a round geometry

Horiz.chrom.Q’x 8

Vert. chrom. Q’y 1.7

Instability growth in both planes

Give positive steps in chromaticityGradually increasing chromaticityTill the value of the tunes in x,y

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Mode spectrum of the horizontal and vertical coherent

motion as a function of impedance

•no mode coupling•mode -1 gets unstable

•no mode coupling observed, no TMCI•Mode 0 should be damped, and higher order modes get excited •Mode 0 getting unstable?

Presence of chromaticity makes the modes move less, no couplingAnother type of instability occuring, head-tail instability

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•If the rise time < damping time, means that the instability is faster than the damping mechanism•Damping time τx=2ms

Threshold ~10 MΩ/m

Broadband Model No TMCI instability (fast), therefore no direct observation from the mode spectrum of the impedance thresholdNeed to calculate the rise time (=1/growth rate) of the instabilities (damping is not implemented in HEADTAIL)The instability growth rate is calculated from the exponential growth of the amplitude of the bunch centroid oscillations

Rise time– x plane

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Rise time– y plane

•Damping time τy=2 ms

Threshold ~2 MΩ/m

Broadband Model

X y

ChromaticityQ’x/ Q’y

Impedance threshold MΩ/m

0/0 8 4

8/1.7 10 2

16/3.4 19 2-3

24/5.1 stable 4

32/6.8 stable 4

40/11.5 stable 4

48/13.3 Stable 725

•For zero chromaticity , the TMCI threshold is at 8 and 4 ΜΩ/m for x,y respectively

•For positive chromaticity, there is no TMCI but another instability occurs (head tail).

•As the chromaticity is increased, higher order modes get excited, less effect, move to higher instability thresholds

Broadband Model

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• Impedance cause bunch modes to move and merge, leading to a strong TMCI instability

• Chromaticity make the modes move less, therefore it helps to avoid the coupling (move to a higher threshold)

• Still some modes can get unstable due to impedance

• As the chromaticity is increased, higher order modes are excited (less effect on the bunch). The behavior of mode 0 needs to be checked.

• Conclusion Either we correct the

chromaticity and operate below the TMCI threshold or sufficient high positive chromaticity must be given

Further check needed to see if we reach any resonances by increasing the chromaticity

Broadband Model

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• Radius 6.5mm (checked first, 9mm radius the rest of the machine)• Copper thickness: infinity• Conductivity: 5.9 107 Ohm-1m-1 • Length of the wigglers: 104m (Number of wigglers:52, wiggler

length:2 m )• Average beta for the wigglers

Thick wall in wigglersi) Copper

Beam Physics meeting 28

DR layout

20 April 2011

Racetrack shape with 96 TME arc cells (4 half cells for dispersion suppression) 26 Damping wiggler FODO cells in the long straight sections (LSS)

Y.Papaphilippou, F.Antoniou

Wigglers occupy ~ ¼ of the total ring…

C = 427.5 m, Lwigglers = 104 m

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Horizontal and vertical motion in a flat chamber

•Centroid evolution in x and y over the number of turns, for different values of intensity

•Scan over intensity [1.0-30.0]109

•Nominal Intensity: 4.1 109

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: The mode 0 is stableVertical: The mode 0 is shifting down, as well as mode -1.

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

x plane

y plane

No instability observed from the mode spectrum and the centroid evolution

For the case of copper, there is no instability in this intensity range

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Compare B.Zotter’s model with Yokoya factors with the resistive wall model of HEADTAIL

Thick wall in wigglersi) Copper

Is the effect on the bunch the same for both cases?

Can we use this model of HEADTAIL with safety for the case of no coating?

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Horizontal and vertical motion (Resistive Wall HD)

•Centroid evolution in x and y over the number of turns, for different values in intensity

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: Modes are stableVertical: Mode 0 is shifting down, as well as mode -1

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

y plane

x plane

No instability observed from the mode spectrum and the centroid evolution

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CompareInput wake table- Resistive Wall model HD

• The two ways to simulate the wakes have the same effect on the beam• Therefore, the resistive wall model from HEADTAIL can be used to simulate the

simple case of no coating

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• Radius 6.5mm• Stainless steel thickness: infinity• Conductivity: 1.3 106 Ohm-1m-1 • Length of the wigglers: 104 m (Number of wigglers: 52, wiggler

length:2 m 104 m total• Average beta for the wigglers

Thick wall in wigglersii) Stainless steel

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Horizontal and vertical motion in a flat chamber

•Centroid evolution in x and y over the number of turns, for different values of intensity

•Scan over intensity [1.0-30.0]109

•Nominal Intensity: 4.1 109

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: Stable, mode -1 is shifting upVertical: Coupling of mode 0 and mode -1 at 14 109 (~3.5*nominal intensity)

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

x plane

y plane

unstable 14 109

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CompareInput wake table- Resistive Wall model HD

Input wake table• Horizontal: Stable• Vertical: threshold 14 109

ResWall model HeadTail• Horizontal : Stable• Vertical: threshold 14 109

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• Radius 6.5mm• aC thickness: 0.001 mm• ss thickness: infinity• Length of the wigglers: 104 m• Average beta for the wigglers

Wall with coating in the wigglers 1) Carbon on stainless steel

a-Carbon important for the electron cloudPDR

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Horizontal and vertical motion

•Centroid evolution in x and y over the number of turns, for different values in intensity

Threshold ~ 12 109

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Wake field

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal:Mode 0 is stable, mode -1 is moving upVertical: Getting unstable (TMCI of mode 0 and -1) at 12 109

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

x plane

y plane

unstable 12 109

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• Radius 6.5 mm• NeG thickness: 0.001 mm• Same conductivity as stainless steel• Stainless steel thickness: infinity• Length of the wigglers: 104 m• Average beta for the wigglers

Wall with coating in the wigglers 2) NeG on stainless steel

NeG (Non Evaporated Getter)Important for good vacuumEDR

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Horizontal and vertical motion

•Centroid evolution in x and y over the number of turns, for different values in intensity

Threshold ~ 13-14 109

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Wake field

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: Modes are stableVertical: Vertical: Getting unstable (TMCI of mode 0 and -1) at 13-14 109

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

x plane

y plane

unstable 13-14 109

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• Radius 6.5mm• aC thickness: 0.001 mm• Copper thickness: infinity• Length of the wigglers: 104m• Average beta for the wigglers

Wall with coating in the wigglers 3) Carbon on copper

a-Carbon •important for the electron cloud•PDR

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Horizontal and vertical motion

•Centroid evolution in x and y over the number of turns, for different values in intensity

Threshold ~27 109

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Wake field

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: Modes are stableVertical: Mode 0 is shifting down

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

x plane

y plane

Only from the y centroid is observable that there is an instability occuring at 27 109 (~6 times higher the nominal intensity)

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• Radius 6.5mm• NeG thickness: 0.001 mm• Same conductivity as stainless steel• Copper thickness: infinity• Length of the wigglers: 104 m• Average beta for the wigglers

NeG (Non Evaporated Getter)•important for the electron cloud•EDR

Wall with coating in the wigglers 4) NeG on copper

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Horizontal and vertical motion

•Centroid evolution in x and y over the number of turns, for different values in intensity

Threshold ~29 109

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Wake field

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•Plot all the tunes (Q-Qx)/Qs and (Q-Qy)/Qs as a function of intensity

Horizontal: Modes are stableVertical: Mode 0 is shifting down

Mode spectrum of the horizontal and vertical coherent motion as a function of

impedance

•Only from the y centroid is observable that there is an instability growing ~29 109

x plane

y plane

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ResultsThreshold

Broadband Model 8, 4 MΩ/m

Stainless steel 14*109

aC on ss 12*109

NeG on ss 13-14*109

Copper (more conductive) Stable

aC-copper (0.001 mm) 27*109

NeG-copper (0.001 mm) 29*109

Wigglers

•Copper is better than ss but also more expensive!

•Coating doesn’t have a big impact for the wigglers (good since necessary)

•Need to calculate the contribution of the rest of the machine

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• Effect of – different thickness of the coating– different radius of the pipe

• 3 or more kicks – Coated wigglers– Coated rest of the machine– Broadband resonator

• High frequency effects of resistive wall calculate ε(ω), μ(ω), σ(ω) of the coating material

• Yokoya’s factors may not be valid at high frequency (wigglers are flat!) study ongoing…

• Include damping in the HEADTAIL code

• Check the broadband model with negative chromaticity

Next steps…

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Summary-conclusion1 kick, <β>

1st approximationImpedance budget(more critical in the vertical plane)

4 MΩ/m, for nominal intensity 4.1 109

2 kicks, <β>

Unstable at 12 109

1.36 MΩ/m

Add up all the different contributions

Reduce the impedance budget

Impedance database with all the components

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Backup slides…

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•This case (copper) is stable only for this intensity range•Extend the intensity [30.0-110.0]109

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Mode spectrum y

Extended the intensity scan to see if we observe the instability….

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Azimuthal modes and impedance

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Tune shift

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Resistive wall model

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Resistive wall model 2