Bruchon, M

ozénou, F

Visentin, B

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EU contract number RII3-CT-2003-506395 CARE-Conf-07-032-SRF  SRF       ELECTROPOLISHING ON SINGLE AND MULTI-CELL:  COMSOL MODELLING  M. Bruchon, B. Visentin, F. Eozénou  CEA-Saclay, DSM/DAPNIA/SACM - 91191 Gif/Yvette, France    Abstract  In the framework of cavity electropolishing improvement, modelling allows evaluating some parameters not easily accessible by experiments and can also help us to guide them. At CEA Saclay, COMSOL software is used to model electropolishing of cavity in two dimensions. First, single-cell electropolishing with different shapes (TESLA, ILC Low Loss (LLILC), ILC Reentrant (REILC) and the optional Half Re-entrant profile) is studied with acid inflow like in our set up. Then some improvements of both outflow and inflow of the acid are considered. This work is extended to TESLA nine-cell cavities in collaboration with KEK to understand if electropolishing process is related to some misunderstood RF performances.   Contribution to the “13th International Workshop on RF Superconductivity” Beijing (China), 15-19 October 2007      Work supported by the European Community-Research Infrastructure Activity under the FP6 “Structuring the European Research Area” programme (CARE, contract number RII3-CT-2003-506395)   ii R=i Ntc ∇+∂∂iiiiiii ucFczN ∇cD +−∇−= φω25222 O                 (1)   ELECTROPOLISHING ON SINGLE AND MULTI-CELL:  COMSOL MODELLING   Mélanie BRUCHON# - Bernard VISENTIN - Fabien EOZENOU CEA Saclay - DSM / DAPNIA / SACM - 91191 Gif / Yvette – FRANCE  Abstract  In the framework of cavity electropolishing improvement, modelling allows evaluating some parameters not easily accessible by experiments and can also help us to guide them. At CEA Saclay, COMSOL software is used to model electropolishing of cavity in two dimensions. First, single-cell electropolishing with different shapes (TESLA, ILC Low Loss (LLILC), ILC Reentrant (REILC) and the optional Half Re-entrant profile [1, 2]) is studied with acid inflow like in our set up. Then some improvements of both outflow and inflow of the acid are considered. This work is extended to TESLA nine-cell cavities in collaboration with KEK to understand if electropolishing process is related to some misunderstood RF performances [3, 4].   INTRODUCTION To build the future International Linear Collider (ILC), the “cold” technology has been selected. It is based on superconducting radiofrequency (SRF) cavities. Electropolishing is presently accepted like the most efficient surface treatment to reach high gradients (40 MV/m) with niobium RF cavities. However, this technique presents the disadvantage to be not very reproducible. Experimental researches try to improve it and modelling appears like an interesting and helpful way to better understand electropolishing. In this study, COMSOL software is used to model horizontal electropolishing on 2D for single-cell and nine-cell cavities. ELECTROPOLISHING PROCESS AND KINETICS EQUATION COMSOL allows coupling of different physical phenomena such as chemical reaction with dynamics fluid for our purpose. It is also used in other labs; however without the introduction of chemical reactions for niobium electropolishing [5]. Generally the bath used for electropolishing is composed by a mixture of hydrofluoric and sulphuric acids (1:9 in volume) [6]. Considering that the bath is mainly composed by sulphuric acid, its characteristics (viscosity and density) have been used for modelling. The general chemical equation for niobium oxidation is:  55 HONbHNb +→+Then the pentoxide layer Nb2O5 is attacked by the  hydrofluoric acid following the equation (2):   OHNbOFHHFONb 25252 3210 +→+      (2) For modelling, it is assumed that the oxide layer is continuously formed and so only equation (2) is considered. The reaction velocity v is a second order kinetics [7]; so it is equal to                         v ]][[ 52 HFONbk=                     (3) where k is a kinetic constant in l/mol.s and  concentrations (mol/m3) are noticed in square brackets. If x is considered as the production of H2NbOF5 at a time t, α the initial concentration of Nb2O5 and β the initial concentration of HF, the equation (3) can be written:              )10)((21 xxktxv −−=∂∂= βα             (4) As each concentration is directly connected to the other, results for [HF] will be privileged; however [H2NbOF5] or [Nb2O5] can help to understand results.  CONVECTION DIFFUSION AND NAVIER-STOCKES EQUATIONS Different equations are used to solve the coupling between niobium reaction and fluid dynamics: -  The mass balance equation:                                                 (5)                              Where ci is the concentration of the specie i (mol/l), Ni its flux (mol/l.s) and Ri its net creation rate (mo/l.s).  -  The Nernst-Planck equation:                                                                    (6)                                                        The first term ii cD ∇ relates the diffusion transport where Di is the diffusion coefficient and Ci the concentration of the specie i. To determine the diffusion coefficient, the time to build up a viscous layer has been compared between experimental results on electropolished samples and its modelling with different diffusion coefficients. Then it has been found that the most optimal result of modelling is obtained for a value of diffusion coefficient equal to 10-8 m2.s-1 [8].    The second term Φ∇iii Fczω expresses the transport by electromigration. zi represents the valence of the specie i, ωi its mobility and Φ the electrostatic potential. F is the Faraday constant As for electropolishing in case of high concentrated #W  ““EU contract number RII3-CT-2003-506395 CARE-Conf-07-032-SRF___________________________________________  melanie.bruchon@cea.fre acknowledge the support of the European Community-Research Infrastructure Activity under the FP6Structuring the European Research Area” program (CARE, contract number RII3-CT-2003-506395) and of the Région Ile-de-France”. iiiiiiii RucFczcDc =+∇−∇−∇+∂ )( φωt∂Gpuuutu =∇∇ (ρηelectrolyte, the transport of species is mainly due to diffusion and convection, electromigration can be neglected [9,10].  The last term represents the convection where u is the velocity of specie (m/s).  iucBy combining equations (5) and (6), the general equation to solve is:                                                                                     (7)  where Ri  is calculated thanks to the velocity of the chemical reaction in equations (3,4). - The equation (7) is coupled to Navier-Stockes equation (8) for an incompressible fluid (9), to model the fluid dynamics in the cavity:  +∇+−∂∂ ).2ρ                (8)                                     0. =∇                                 (9) a bc db d a c uη is the dynamic viscosity (10-3 kg/m.s) u the fluid velocity (m/s) p the pressure (N/m2) G (N/m3), the resultant force, only the gravity is considered here. Acid concentration [HF] (mol/m3) during time is studied. It is considered that at time t=0, the cavity is full with acid. Maximal time (20 000 s, ∼ 6 hours), corresponds to a standard electropolishing (100 µm). Acid concentration is calculated for a so long period, because a simple defect in acid attack would be easily detected. Velocity fluid (m/s) is also used to help us in the understanding of electropolishing process.  SINGLE-CELL First studies have been motivated by the optimisation of   electropolishing set up for single-cell cavities at Saclay: the acid inflow comes by a hole in the middle of the cathode and exits from the “right” beam tube. The flow rate is 2 l/mn. This type of horizontal electropolishing has been modelled on different cavities shapes. For each shape, acid rebounds on the “right” iris and the “left” beam tube is very bad renewed in acid (figures 1 and 2). For LL and half RE profiles, there is an impoverishment of acid in one side of the cell and the “left” beam tube is less renewed than for the two other shapes (TESLA and RE profiles). A modification of the acid inflow has been studied on TESLA shape to improve the electropolishing on the left beam tube: the acid arrives from the left beam tube and goes out by the right one with a flow rate of 10 l/mn (figures 3a and 3b). This new configuration is beneficial for both beam tubes; however the acid sweeps badly the cell. A protuberance cathode has been added to force the acid to sweep the bottom of the cell (figures 3c and 3d). It improves electropolishing in the cell however it creates a little dissymmetry of acid attack in the beam tubes comparing to the previous solution. The best way seems to be the one developed for the nine-cell cavities with an inflow in the middle of the cathode and the outflow on both beam tubes (figure 4). As consequence of this result, we plan to modify our electropolishing set-up in such direction. However, irises have a higher acid attack than other parts of the cavity.          Figure 1: Velocity (m/s) in single-cell for different shapes (1a: TESLA, 1b: half RE, 1c: RE and 1d: LL)          EU contract number RII3-CT-2003-506395 CARE-Conf-07-032-SRF    Figure 2: [HF] (mol/m3) in single-cell for different shapes at time = 20 000 s (2a: TESLA, 2b: half RE, 2c: RE and 2d: LL)   Fluid Velocity      ba     dc          [HF]              Figure 3: Fluid velocity (m/s) for new acid arrival (3a and 3c) and [HF] (mol/m3) at time = 20 000s (3b and 3d)  Fluid Velocity       a     b         [HF]      Figure 4: Fluid velocity (m/s) (4a) and [HF] (mol/m3) at time =20 000s (4b) for exit on both beam tubes                     Figure 5: Velocity fluid (m/s) (5a) and [HF] (mol/m3) at time 4 000s (5b) and 20 000s (5c) for TESLA nine-cell. Fluid Velocity a b c [HF] EU contract number RII3-CT-2003-506395 CARE-Conf-07-032-SRFNINE-CELL TESLA CAVITIES Then work has been extended to TESLA nine- cell cavities, with an electropolishing similar as KEK set up [4]. Acid arrives by 9 holes located in the middle of each cell and goes out from both beam tubes. Size of the hole is higher in the central cell (10 mm in cell 5) and decreases (down to 6 mm) in the direction of the beam tubes to optimise the sweeping of each cell. Modelling allows showing an asymmetric acid attack of cells. That could be an explanation to the field flatness degradation experimentally observed after electropolishing [3].  Cell 5 is well swept by the acid, arguing for a good electropolishing compared to an impoverishment for the others cells.  In our model, we noted on figure 5 a tiny right-left dissymmetry in the acid flow and attack, this can be explained by a dissymmetry of the mesh in the central part of the cell 5 (figure 6).         Figure 6: Mesh repartition of the cell for modelling  CONCLUSION      First results on modelling are promising and show that electropolishing is heterogeneous in single and nine-cell cavities. These results can give explanation to disparate RF test and degradation of field flatness after electropolishing. Further parameters have to be introduced to perform a more realistic modelling of cavity electropolishing: rotation, temperature. 3D modelling is currently under consideration too (figure 7).                    Figure 7:  3D single cell cavity  REFERENCES [1] J.Sekutowicz., “Design of a Low Loss SRF Cavity for the ILC”, Proceedings of 2005 Particle Accelerator Conference, Tennessee, USA. [2] V. Shemelin, H.Padamsee, “The Optimal Shape of Cells of a Superconducting Accelerating Section”, TESLA Report 2002-1.  [3] E.Kako et al., “Vertical Test Results on the STF Baseline 9-cell Cavities at KEK”, WEP10 in this conference. [4] Y. Morozumi, private communication. [5] C.E Reece, “Hydrodynamic Thermal Modelling in 9-cell ILC Cavity. Electropolishing and Implications for Improving the EP Process”, this conference, TUP62.  [6] K.Saito, “Superiority of Electropolishing over Chemical Polishing on High Gradients, 8th Workshop on RF Superconductivity”, Abano Terme (Padova), Italy, 1997.  [7] A. Agulyansky, “Chemistry of Tantalum and Niobium Fluoride Compounds”, Elsevier Science 2004.   [8] F.Eozenou et al.,”Electropolishing of Niobium: best EP Parameters”, CARE Report-06-010-SRF.  [9] D.Landolt, “Fundamental Aspects of Electropolishing”, Electrochimica Acta, vol 32, p.1-11, 1987.  [10]J.P. Diard et al. ”Cinétique Electrochimique”, Edition Hermman, 1996, p.41.    EU contract number RII3-CT-2003-506395 CARE-Conf-07-032-SRF

Electropolishing on single and multi-cell: COMSOL modelling

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