esrf impedance simulation challenges simon white, vincent serrière

ESRF impedance simulation challenges

Simon White, Vincent Serrière

OBJECTIVES

Design, procurement, preassembly, construction and commissioning of a new low emittance storage ring to reduce the horizontal equilibrium emittance

from 4 nm down to 150 pm

• Re-use the same tunnel and infrastructure• Maintain the existing insertion device and bending magnets

beamlines• Preserve the time structure operation

and a multibunch current of 200 mA• Keep the present injector complex• Reuse, as much as possible, existing hardware• Minimize the energy lost in synchrotron radiation • Minimize operation costs and maintain operation reliability• Minimize the impact on User Operations due to the downtime

for installation and commissioning [courtesy J.L. Revol]

MAIN PARAMETERS

Lattice parameters Present New

Lattice type DBA HMBA

Circumference [m] 844.390 843.979

Beam energy [GeV] 6.04 6.00

Natural emittance [pm•rad] 4000 147

Vertical emittance [pm•rad] 4 5

Energy spread [%] 0.106 0.095

Damping times H/V/L[ms] 7/7/3.5 8.5/13/8.8

Energy loss /turn [MeV] 4.88 2.60

Tunes (H/V) 36.44/13.39 75.58/27.62

Chromaticity (H/V) -130/-58 -100/-84

Momentum compaction 1.78 10-4 0.87 10-4

Qs 5.23 10-3 3.49 10-3

MAGNETS (IN HOUSE DEVELOPMENT – ID GROUP)

128 Permanent magnet dipoleslongitudinal gradient 0.16 0.65 T, magnetic gap 26 mm1.8 meters long, 5 modulesHybrid Sm2Co17 / Strontium Ferrite

96 Combined Dipole-Quadrupoles0.54 T / 34 Tm-1 & 0.43 T / 34 Tm-1

64 Octupoles 51.2 103 T/m3

192 SextupolesLength 200mm900-2200 Tm-2

Also used as dipole and skew quad correctors

128 High gradient Quadrupoles

384 Moderate gradient quadrupoles

• Gradient: 85 T/m• Bore radius: 12.5 mm • Length: 390/490 mm• Power: 1-2 kW

• Gradient: 51 T/m• Bore radius: 15.5 mm • Length: 160/300 mm• Power: 0.7-1 kW

96 Correctors (H/V)Length 120mm

0.08 T

All magnets individually

powered

VACUUM CHAMBER

CentreUpstream & downstream

ID

50*20 mm30*13 mm

(50*13 under design)

(reuse of existing ID chambers)

TE TM4.48 9.335.97 13.147.70 16.358.29 17.159.86 19.7311.57 20.7611.89 21.3613.86 23.5515.67 23.8915.86 24.07

Fcutoff [GHz]

TE TM6.08 13.767.06 18.298.06 21.369.06 22.6310.32 24.7212.87 24.9113.69 25.7016.15 26.7017.27 28.1618.42 29.30

Fcutoff [GHz]

HARMONIC CAVITY FOR LIFETIME ENHANCEMENT

Touscheck dominated lifetime: proportional to bunch length

Harmonic RF system for bunch lengthening:

• 3rd harmonic system: good compromise between size and lengthening factor

• Achievable bunch lengthening factor: 2.5 to 3

• Superconducting passive cavity: easy to tune and to operate down to low driving currents

Filling Lifetime

200 mA - 7/8 20 hours

90 mA – 16 bunches 2 hours

40 mA – 4 bunches 1.4 hours

forhor = 150 pm vert = 5 pm

IMPACT OF THE NEW DESIGN ON STABILITY

• Reduced beam pipe aperture- increased geometric and resistive wall wake fields:

• Stronger single bunch instabilities: TMCI, head-tail, microwave

• Stronger resistive wall multi-bunch instabilities

• Beam / lattice parameters:

• Smaller synchrotron tune: mode coupling instability at lower currents?

• Higher charge density (smaller beam size): enhanced ion instability?

• IBS, Touschek: lifetime, losses

• Lower b-functions: improved single and multi-bunch impedance effects

• Geometric impedance requires (in most cases) EM simulations, resistive wall wake fields can be derived analytically

• We are using CST particle studio for 3d simulations

LAYOUT OF THE NEW MACHINE

Current machine: 2 apertures New machine: 3 apertures

32mm

8mm 20mm 8mm 13mm

• The vertical aperture is reduced while keeping the same material for the vacuum chamber• There are twice the number of transitions• b-functions are smaller • How do these combine into overall impedance effects?

SINGLE BUNCH EFFECTS: TUNE SHIFT – RESISTIVE WALL ONLY

Horizontal Horizontal

VerticalVertical

New machineCurrent machine

• Tune shift from resistive wall only:• Reduced threshold in the vertical plane: lower Qs• Increased threshold in the horizontal: weaker

wake field• Challenging operation with high bunch intensity? • All dipole chambers are now Aluminium:

calculations need update (50% fill factor)

Vertical

Al in high-b regions (Al in dipoles should be even better)

MULTI-BUNCH EFFECTS: RESISTIVE WALL ONLY

• Rise time of the last bunch in the train:• Simulations done with HEADTAIL including

radiation damping• 7/8 filling pattern, 868 bunches, 200mA total

current• Well below TMCI threshold

• The chromaticity thresholds for the current machine are consistent with operational data Q’~4-6

• In all cases a chromaticity of about 4-6 is sufficient to provide stability – feedback is another alternative

RECENT MEASUREMENTS

Threshold ~0.5mA

Threshold ~0.6mA

Coupled bunch Instability (resistive wall):- Very useful bunch-by-bunchdiagnostic developed byE. Plouviez- Validation with model ongoing

Measured coupled bunch modes

Vertical single bunch instability threshold:- Full impedance budget: TMCI (Q’=0.0)- New machine, resistive wall only ~ factor 3 higher(assuming Al in dipoles): there is still some margin but geometrical impedance needs to be carefully optimized

RF FINGERS – ORIGINAL DESIGN

Top view Side view

Cavity

Transition(0.2mm step:not realistic)

• 3 fingers on the top and bottom – weak shielding in the horizontal plane?

• Beam going off-center in the cavity: horizontal wake on beam axis

• There are approximately 250 bellows in the machine, cumulated effects could be important if the design is not well optimized

OPTIMIZED DESIGN (T. BROCHARD)

taper: q=5o, h=0.7mm0.3mm step

Side view, X=0

steeper transitioncavitywell shielded

• 5 fingers on the top and bottom: better horizontal shielding – symmetry restored

• Done for larger beam pipe: frequency shift of the modes

• More realistic mechanical constraints: steeper transition (1mm instead of 0.2mm)

SMOOTHER TRANSITION

factor ~6 factor ~2

• Ongoing effort with the drafting office to find best compromise between impedance and mechanical constraints

• Reducing the taper angle to 2o significantly reduces the impedance of the structure:

kloss(5o) ≈ 2.0e-2 V/pCkloss(2o) ≈ 5.0e-3 V/pC

• A prototype will be installed during the next shutdown in May: we hope to be able to measure heating

FLANGES

Design 1 Design 2

strong trapped modes for design 1

~beam pipe cut-off

• Two designs initially proposed by the drafting office

• About 500 flanges in the new machine

• Design 2 (similar to present design performs much better than design 1

• Again, the structure is not axisymmetric: significant horizontal wake on beam axis

X1Z1X2Z2

COMPARISON WITH PRESENT MACHINE

X 2015Z 2015X2Z2

• Inserted the present beam pipe profile into the design 2 for comparison:• In both cases stainless steel was used as the material• Present design almost axisymmetric: very little horizontal wake on beam axis• Larger number of modes below cut-off for the new machine• Loss factors (3mm bunch length):

kloss(2015) ≈ 2.1e-2 V/pCkloss(Upgrade) ≈ 3.3e-2 V/pC

• Drafting office is considering the possibility of “shielding” these flanges (electrical contacts or conductor joint)

~cut-off present machine

~cut-off new machine

CURRENT STATUS

• Resistive wall:

• Lower synchrotron tune and smaller beam pipe almost fully compensated by smaller b-functions and change of material (SS->Al) in dipoles

• So far used analytical expression for elliptical beam pipes: design of the chambers now well advanced, check validity of approximation (from first tests it looks ok)

• Model validation ongoing with measurements on the running machine

• Geometrical impedance:

• ESRF upgrade is a brand new machine, model need to be completely updated• For most elements we still don’t have a final design: iterations ongoing with drafting office• Main elements we looked at so far:

• RF cavities: full calculations available, no issues there

• Button BPMs: preliminary optimization done, detailed calculations ongoing

• RF fingers: initial design not optimal, significant improvement with increased horizontal shielding, need to optimize transitions

• Flanges: preliminary estimates indicate small degradation with respect to the present machine, drafting office is considering eventual “shielding” of these flanges

• To de done: tapers, pumping holes (located in the extrusion: should not be an issue), striplines, collimators, absorbers, etc…

OPEN QUESTIONS

• The new machine will have an equilibrium bunch length of 3mm:

• We need to look at high frequencies: large number of mesh• Is it ok in some case to simulate longer bunches? For instance to look only at the low frequency components or some

information will be lost?

• In lots of cases not axisymmetric in the horizontal plane:• Strong ‘constant’ horizontal wake on beam axis: we try as much as possible to minimize it• Impact on stability? Closed orbit? Is it really detrimental?

• We currently model 3mm rms bunch length:

• Seems good enough for quick estimates, geometry optimization, relative comparisons• Already a lot of meshes: at some point we will need the wake function and first trials with deconvolution not very convincing: any

alternatives other than having shorter source, i.e finer mesh?

• Lots of geometries contain very small features (sub-millimeter): Fingers, transitions, etc..:• CST does not seem to like non-uniform mesh• Sometimes simulations becomes unstable when grid not is not uniform at open boundaries: so far to could be overcome by

adding additional material with fine mesh at the boundaries

OPEN QUESTIONS

• Simulation of Tapers / direct or indirect method: which one is the more accurate ?

• No bench measurements at ESRF: is it important to validate simulations ?

Length of beam tube ?

esrf impedance simulation challenges simon white, vincent serrière

Documents

beam energy gev6

resistive wall wake

new low emittance storage

smaller synchrotron

harmonic system

energy loss

tall magnets

magnets beamlinespreserve