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HEADTAIL simulations for the impedance in the CLIC-DRs

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HEADTAIL simulations for the impedancein the CLIC-DRs

Damping Rings

E.Koukovini-Platia

TS CERN, NTUA

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

CERN

CLIC meeting, 27/05/2011

2b

- 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)

G.Rumolo

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

Why study multiparticle

(collective) interactions?

- Determine the ultimate performance of the accelerator
- Each accelerator has an intensity limit

G.Rumolo

z

W0(z)

L

s

e

q

Model:

A particleq going through a device of length L, s (0,L), leaves behind an oscillating field and a probe chargee 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.

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

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 resonatormodeling 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

multibunch instabilities

- Total impedance designed such that the nominal intensity is stable

G.Rumolo

- 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)

- Thick wall in wigglers (Resistive wall model)

- Copper

-Stainless steel

Check if is possible to perform at the nominal intensity

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

Resistive wall in the CLIC-DR regime

- 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)

Pipe cross- section:

N. Mounet, LER Workshop, January 2010

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, andthe Yokoyafactors for the wigglers

Low frequency or “inductive-bypass” regime

“Classic thick-wall” regime

High frequency regime

N. Mounet, LER Workshop, January 2010

Resistive Wall Impedance: Various options for the pipe

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

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

N. Mounet, LER Workshop, January 2010

Resistive Wall Impedance: Various options for the pipe

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

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

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

N. Mounet, LER Workshop, January 2010

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

Bunch length

Bunch to bunch

Bunch train

. . .

N. Mounet, LER Workshop, January 2010

- 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

Methods :What to do with HEADTAIL outputs ?

- Extract the position of the centroid of the bunch (vertical or horizontal) turnafterturn simulated BPM signal
- Apply a classical FFT to thissimulated BPM signal (x)
- Apply SUSSIX* to thissamesimulated BPM signal (actuallyx – j xx’ )
- Translate the tune spectrum by Qx0=0 and normalizeit 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 thelatticedesign at 3 TeV

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

from Y. Papaphilippou, F.Antoniou

- 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

Horizontal and vertical motion in a round geometry

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

- As the impedance increases an instability occurs

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 planes
- Causing a TMCI instability

TMCI 8MΩ/m

TMCI 4MΩ/m

Horizontal and vertical motion in a round geometry

- Give positive steps in chromaticity
- Gradually increasing chromaticity
- Till the value of the tunes in x,y

Instability growth in both planes

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

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

- no mode coupling
- mode -1 gets unstable

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

No TMCI instability (fast), therefore no direct observation from the mode spectrum of the impedance threshold

Need to calculate the rise time (=1/growth rate) of the instabilities (damping is not implemented in HEADTAIL)

Rise time– x plane

The instability growth rate is calculated from the exponential growth of the amplitude of the bunch centroid oscillations

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

Threshold ~10MΩ/m

- 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

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

- 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.

i) Copper

- 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

C = 427.5 m, Lwigglers = 104 m

DR layoutWigglers occupy ~ ¼ of the total ring…

Y.Papaphilippou, F.Antoniou

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

Beam Physics meeting

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

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 intensity
- Horizontal: The mode 0 is stable
- Vertical: The mode 0 is shifting down, as well as mode -1.

x 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

y plane

i) Copper

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

Horizontal and vertical motion (Resistive Wall HD)

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

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 intensity
- Horizontal: Modes are stable
- Vertical: Mode 0 is shifting down, as well as mode -1

x plane

- No instability observed from the mode spectrum and the centroid evolution

y plane

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

ii) Stainless steel

- 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

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

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

x plane

unstable 14 109

y plane

CompareInput wake table- Resistive Wall model HD

Input wake table

ResWall model HeadTail

Horizontal : Stable

Vertical: threshold 14 109

- Horizontal: Stable
- Vertical: threshold 14 109

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

- a-Carbon
- important for the electron cloud
- PDR

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

Horizontal and vertical motion

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

Threshold

~ 12 109

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

y plane

unstable 12 109

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

- 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

- NeG (Non Evaporated Getter)
- Important for good vacuum
- EDR

Horizontal and vertical motion

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

Threshold

~ 13-14 109

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

y plane

unstable 13-14 109

Wall with coating in the wigglers 3) Carbon on copper

- a-Carbon
- important for the electron cloud
- PDR

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

Horizontal and vertical motion

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

Threshold

~27 109

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 intensity
- Horizontal: Modes are stable
- Vertical: Mode 0 is shifting down

x plane

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

y plane

Wall with coating in the wigglers 4) NeG on copper

- 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

Horizontal and vertical motion

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

Threshold

~29 109

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 intensity
- Horizontal: Modes are stable
- Vertical: Mode 0 is shifting down

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

y plane

- 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

Wigglers

- 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

- 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

Impedance budget

(more critical in the vertical plane)

1 kick, <β>

4 MΩ/m, for nominal intensity 4.1 109

1st approximation

2 kicks, <β>

Unstable at 12 109

- Add up all the different contributions

1.36 MΩ/m

- Reduce the impedance budget

- Impedance database with all the components

This case (copper) is stable only for this intensity range

Extend the intensity [30.0-110.0]109

Mode spectrum y

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

Azimuthal modes and

impedance

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