Eirini Koukovini-Platia EPFL, CERN

Effect of impedance and coatings in the CLIC damping rings EiriniKoukovini-PlatiaEPFL, CERN 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Introduction Damping Rings CLIC DR parameters • Small emittance, short bunch length and high current • Rise to collective effects which can degrade the beam quality • Their study and control will be crucial 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Impedance budget and coating • Focus on single bunch instabilities driven by impedance • Define an impedance budget • To suppress some of the collective effects, coating will be used • Positron Damping Ring (PDR): electron-cloud effects  amorphous carbon (aC) • Electron Damping Ring (EDR): fast ion instabilities  need for ultra-low vacuum pressure  Non-Evaporable Getter (NEG) • Techniques to fight electron cloud or have good vacuum do not come for free and can be serious impedance sources 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Resistive Wall Impedance: Various options for the pipe • Vertical impedance in the wigglers (3 TeV option) for different materials Resonance peak of ≈1MW/m at almost 1THz for C- coated Cu • Coating is “transparent” up to ~10GHz • But at higher frequencies some narrow peaks appear • Above10 GHz the impact of coating is quite significant N. Mounet, LER Workshop, January 2010

Single bunch simulations without space charge to define the instability thresholds • HEADTAIL code • Simulates single/multi bunch collective phenomena associated with impedances • Computes the evolution of the bunch by bunch centroid as a function of time • ImpedanceWake2D • Computes the longitudinal and transverse wake functions of multilayer structures, cylindrical or flat • Goal • Estimate the available impedance budget for the various elements to be installed after known impedance sources such us the broad-band resonator, the resistive wall and the kickers are considered 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Estimating the impedance budget with a 4-kick approximation Straight section: 13 FODO FODO cell 9mm radius round 6mm radius, flat ARC (9mm round): DS1- 47 TME cells - DS2 wiggler wiggler QF QD • A uniform coating of NEG, 2μm thickness, on stainless steel pipe • The contributions from the resistive wall of the beam chamber were singled out for both the arc dipoles and the wigglers 1st kick broadband resonator 2nd kick  resistive wall from the arcs 4th kick  rest of the FODO 3rd kick wigglers 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Estimating the machine impedance budget with a 4-kick approximation – single bunch simulations Mode spectrum of the horizontal and vertical coherent motion as a function of impedance (applying an FFT to the HEADTAIL output) TMCI 15 MΩ/m TMCI 4 MΩ/m For zero chromaticity, the (remaining) impedance budget is estimated at 4 MΩ/m • No mode coupling • Higher TMCI thresholds Head-tail instability For positive chromaticity, the impedance budget is estimated now at 1 MΩ/m 3rd Low Emittance Ring workshop - 8th-10th July Oxford

6-kick study- adding stripline kickers • 2 kickers in the DR (injection&extraction) • Calculate the wake function, and add this wake as a kick in our impedance model • Idea: Use the shortest bunch length possible in the CST simulation so that the wake function (input for HEADTAIL) could be approximated with the wake potential (output of CST) CST simulation R=25mm, Aperture=12mm/20mm, h=20mm, Thickness=4mm • Bunch of 0.2 mm • 3 lines per wavelength • ~150 million meshcells • time consuming simulation • Untrustworthy results • Use at least 10 lines per wavelength • 1 billion meshcells! • Limit for CST Design from Carolina Belver-Aguilar, IFIC

Next steps on the stripline kickers study • Convergence study with numerical parameters showed that the wake potential from CST in this frequency range (requires a very dense meshing and very long computational times) can not be just used as the wake function (for HEADTAIL simulations) • Further work needs to be done to understand and possibly overcome this problem. Benchmark of CST with other codes (such as the ImpedanceWake2D for resistive wall problems and GDfidl for geometric impedances) has also begun • Try ABCI (Azimuthal Beam Cavity Interaction) • Calculations of wake fields, wake potentials, loss factors and impedance 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Motivation for the material EM properties characterization Code calculating wake fields/ impedances EM properties of NEG and aC Instabilities studies for the CLIC DR • Need to characterize the properties of the coating materials at high frequencies (CLIC), i.e. 500 GHz • Characterize the electrical conductivity of NEG • Unknown values of the conductivity in this frequency range 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Material EM properties characterization • Establishing and testing a method to measure the properties of NEG • Combine experimental results with CST simulations to characterize the electrical conductivity of NEG • Powerful tool for this kind of measurements Experimental method CST MWS simulation Intersection Study of instabilities with HEADTAIL Material properties σ, ε, μ Calculation of the wake fields 50 cm Cu wg 9-12 GHz 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Experimental Method (I) • Waveguide Method • First tested at low frequencies, from 9-12 GHz • Use of a standard X-band waveguide, 50 cm length • Network analyzer • Measurement of the transmission coefficient S21 Experimental setup 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Experimental Method (II) • Copper waveguide • First test: a pure copper (Cu) X band waveguide • Measure the S21from 9-12 GHz |S21| for a Cu waveguide • Signals traveling in the waveguide experience loss due to the conductor resistance • S21 is related to the loss suffered in the transmission from one port to the other • Cu is a very good conductor and the losses are small • S21 is related to the material conductivity 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Conductivity of Cu • Result from the intersection of measurements with CST MWS simulations • Cu conductivity was estimated within the same order of magnitude with the known value • Average is 5.91x107 S/m • Good agreement with the known value of 5.8x107 S/m • The attenuation is very sensitive to the errors because of the small losses (high conductivity of Cu) • Despite this, the results were encouraging to continue with a coated waveguide 3rd Low Emittance Ring workshop - 8th-10th July Oxford

NEG coating of the Cu waveguide • NEG coated Cu waveguide • Same Cu waveguide used before is now coated with NEG • Coating procedure • Elemental wires intertwisted together produce a thin Ti-Zr-V film by magnetron sputtering • Coating was targeted to be as thick as possible (9 µm from first x-rays results) 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Comparison of Cu and NEG coated one • NEG coated Cu waveguide • Measure the S21from 9-12 GHz • S21 results indicate that the skin depth is small enough compared to the coating thickness • Allows the EM interaction with the NEG 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Conductivity of NEG • Upper limit for the conductivity of NEG in this frequency range (assume 100 μm thickness) • Is this frequency dependent behavior physical? • Repeat measurements with a spare Cu waveguide to check reproducibility • The non uniformity of the coating might impose uncertainties in the characterization X-Ray Fluorescence

Second Cu waveguide • Small difference observed in the S21 measurement between the 2 waveguides • How much does this affect the conductivity estimation? • 20% difference • Observing the same frequency dependence behavior • Waiting to coat at max thickness this waveguide to check 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Why all this trouble?Effect of NEG conductivity on the budget The characterization of NEG properties is important in the high frequency regime and affects the instability thresholds predictions 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Measurements with the stainless steel waveguide- accuracy of the method X band stainless steel (ss) waveguide of 50 cm length • Define the accuracy of the experimental method 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Results with the stainless steel waveguide Measurements and CST Intersection with CST • Average σ=0.75 106 S/m while expected DC value is 1.3 106 S/m (40% error) • Problem in the measurement or the model? 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Further checks for errors during the measurements or the waveguide itself Results are in very good agreement, repeated the procedure 3 times Repeat 3 times Measurements output 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Problem of the waveguide? • Add aluminum foil along the connection to ensure good contact and any extra losses (the material is not welded there but two different pieces hold together with screws)  Results are in very good agreement • Seems the experimental results can be trusted • Need to work on the model (try another code? Analytical calculation of S21?) • Further checks on this method • Work on the model • Think of other possible methods? • Before going up to 700 GHz, should be fun…  3rd Low Emittance Ring workshop - 8th-10th July Oxford

Other tasks ongoing… Summary Coating and material properties characterization are important in this frequency regime Stripline kickers and RF cavities to be added to complete further the impedance budget study Properties at 750 GHz? (EPFL Network Analyzer) • Longitudinal radiation damping being implemented. Tests to be done in the near future. Next step, transverse damping • Implementation of space charge in HEADTAIL. Modifying the code to give multiple kicks for space charge along the lattice of the ring. Tests to be done. • Study the effect of space charge with impedance in the TMCI threshold (moving to higher thresholds?) • Study the tolerable space charge tune spread in combination with the newly implemented radiation damping modules 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Acknowledgements • C. Zannini • N. Biancacci • K. Li • G. De Michele • N. Mounet • P. Costa Pinto • G.Rumolo • M. Taborelli Thank you for your attention! 3rd Low Emittance Ring workshop - 8th-10th July Oxford

Backup slides • BROADBAND MODEL • Chromaticity make the modes move less, therefore it helps to avoidcoupling (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 goal is to operate at 0 chromaticity which allows for a larger impedance budget (7 MΩ/m) • But since chromaticity will be slightly positive, a lower impedance budget has to be considered, 4 ΜΩ/m • SPS, 7 km, 20 MΩ/m

3D EM Simulations and measurements (I) • X band Cu waveguide,εr=µr=1, σ is the (unknown) scanned parameter • For each frequency from 9-12 GHz, the output result is the S21 coefficient as a function of conductivity • Combine with the measurement results  σ as a function of frequency Example at 10 GHz Intersection of the simulation results with the measurement  point of intersection defines the conductivity Value of conductivity

The 2 integration methods in Gdfidl give different results between them • Not in agreement with CST either

Try a simple structure for resistive wall compare CST, Gdfidl, ImpedanceWake2D, analytical Conductivity: 1.3e6 S/m 0.2mm bunch length

Factor of 4-4.5 difference between CST and ImpedanceWake2D. Gdfidl is in even worse agreement. Analytical and ImpedanceWake2D are in very good agreement

Eirini Koukovini-Platia EPFL, CERN