State of art and R&D plans on multipacting Yolanda GOMEZ MARTINEZ, Jean Marie DE CONTO, Frederic BOULY LPSC, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France Many thanks to Jean Luc BIARROTTE and Jean LESREL IPNO, CNRS/IN2P3, Orsay, France EuCARD-2 / MAX 21 mars 2014

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014 1

Multipacting Multipacting (MP) is a phenomenon of resonant electron multiplication encountered in electromagnetic (EM) field region in which a large number of electrons build up an electron avalanche. Order of MP: defined as the number of RF cycles that an electron takes to return to its original emission site. Classification Y-point: defined as the number of impacts sites (Y) per MP cycle This phenomenon affects the RF structures in many ways; it can lead to power losses and limit the power coupling/matching between the power source and the RF cavities. It can produce internal surfaces heating which can produce thermal breakdown in superconducting structures and it source of degradation as the breaking of the ceramic widows of the couplers 2

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Multipacting in a coaxial line (1994) E. Somersalo et al gives some scaling laws restrict to a coaxial line with a standing wave Max E for finding a MP P favorable to have a MP Power for MP Impact energy of electrons f : frequency d : parameter of the size of the line n : order of the MP D : diameter of the external conductor Z : impedance characteristic of the line f frequency 3

Multipacting in a coaxial lineal (1997) Pasi Yla-Oijala gives some scaling laws restrict to a coaxial line with a traveling or mixed wave EMP: Electric multipacting MMP: Magnetic multipacting 𝑃 𝑇𝑊 = 4∗𝑃 𝑆𝑊 Power for MP in TW 𝑃 𝑅 𝐸𝑀𝑃 ~ 1 1+𝑅 2 𝑃 𝑇𝑊 = 4 1+𝑅 2 𝑃 𝑆𝑊 Power for EMP in MW f : frequency D : diameter of the external conductor Z : impedance of the line R Reflection coefficient 4

Multipacting on locally flat surface (1998) J. Tuckmantel gives a criterion restricted to the case of a 1-point multipacting on locally flat surfaces ( 𝑒 𝐸 𝑠𝑢𝑟 𝑚 2𝜋𝑓 2 𝑅 𝑐𝑢𝑟𝑣 ≪1 ) No relativistic Only need the magnetic induction B z,o, and the partial derivative of electric field e- MP occurs for (A,B) et (A,-B)! Tuckmantel intended to complete to the cases of stronger curvature, two point multipacting around an electric field and in edges 5

Multipacting in RF cavities (1979) R. Parodi et al proved that on equator of elliptical cavities the one point MP is not possible (1995) R. Parodi et al consider the mean energy of an electron in a constant magnetic field, they suppose the electron starting with a negligible energy and perpendicularly from the conductor and they approximate the electron trajectory by half a circle. MP may occur for a trajectory duration equal to an odd times the half cyclotron period (two point MP) f : frequency n : order of the MP f: frequency e : electron charge m : electron mass B: Induction magnetic field It can be corrected by taking the RMS value of the field leading, for example, to 55 mT/GHz for n=1 instead of 78 mT/GHz He extrapolate for a potential one point MP 6

Multipacting in RF cavities (2013) V. Shemelin. In the case of 2 point multipacting near the equator cavity, he defines two parameters p ( ‘geometrical’) and M (‘magnetical’): f : frequency B: Induction magnetic field E: Electric field e : electron charge m : electron mass 𝑝= 𝜕 𝐸 𝑥 𝜕𝑦 2𝜋𝑓∗ 𝐵 0 𝑀= 𝑒 𝐵 0 2𝜋𝑓 𝑚 𝐵 0 𝑚𝑇 =35.7∗𝑀∗𝑓 Multipacting maps Author (year) Formula Value of M Parodi (1995) 𝐵 0 𝑚𝑇 =78 𝑓 𝐺𝐻𝑧 (static B) 𝐵 0 𝑚𝑇 =55 𝑓 𝐺𝐻𝑧 (correction rms B) 𝐵 0 𝑚𝑇 =𝟓𝟕 𝑓 𝐺𝐻𝑧 (experiment) 2.18 1.54 1.6 Saito (2001) 𝐵 0 𝑚𝑇 =𝟔𝟎 𝑓 𝐺𝐻𝑧 1.68 Geng (2003) 𝐵 0 𝑚𝑇 =𝟓+𝟓𝟓 𝑓 𝐺𝐻𝑧 1,54 + 0,14/f p For the same frequency, different cavities shapes ( ≠p) have different M M 7

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Codes Basic idea of codes: to design the devices, calculate the fields, integrate the dynamic equations of the electron in time varying EM fields and search for MP. CODES MUSICC 3D - MULTIPAC - SPARK 3D MUPAC - MULTP - TRAJECT TWTRAJ TRACK 3P SPARK - XING - TRAK 3D … f fréquency, electron speed, c vacuum light speed, m = mass, e: charge, electric field, magnetic induction 8

Codes Some differences between codes are: … Geometry ( 2D / 3D) EM field solver included or not Method of resolution of the dynamic equation of the electron (Runge Kutta, leapfrog, Newton…) Interaction electron - matter ( diffusion elastic, not elastic, ...) Initial conditions (initial emission angle, initial velocity, initial sites, EM phase, fields levels, reflection coefficient in coupler case, RF- phase, energy of the impacting electron , SEY - secondary emission yield…) Definition of the emission of secondary particles (SEY, curve, angle d’ émission…) Way to identified multipacting (evolution of the number of the secondary electrons, resonant trajectories with electron SEY >1, time focusing where the time between two impacts was an integral number of RF cycles…) Outputs (in real time or not, trajectories of electrons, MP order and type, evolutions of the number of electrons…) End of tracking (will continue for a specified number of RF cycles, minimum and maximum number of secondary electrons …) … 9

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Some results for MAX what Eacc ( MV/m) for MP in the cavity βg 0,47 1 2 Cavity βg = 0.47 Coupler what Eacc ( MV/m) for MP in the cavity βg 0,47 Pinc (kW) for MP in the coupler Measurements ~ 6 MV/m & ~ 8 MV/m (PhD F.Bouly) In work R. Parodi 8.6 MV/m ( 2-point order 1) MULTIPAC 8.3 MV/m < Eacc (βg) < 11.4 MV/m E. Somersalo Pos 1: 40 kW (1-point ordre 5 inner conductor) Pos 2: 70 kW ( 1-point order 8 inner conductor) P. Yla-Oijala NO MP in TW 10

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Open questions - Exemple 1: Electron initial velocity 2 eV – 4 eV? MULTIPAC simulations of the cavity by F. Bouly range where the taken secondary yield function exceeds unity 2eV 4eV 104 104 Ef Ef 102 102 1 1 10-1 8 10-3 e20/C0 e20/C0 11 Ef: Final impact energy e20/C0 : Number of new electrons after 20 impacts / Number of initial electrons

Open questions - Exemple 2: our experience of coating TiN coating of a ceramic window (see figure) Resistivity measurement Expected values Rutherfold Backscattering Spectrometry (RBS): 30 nm TiN [ 42 % Ti , 50 % N, 8 % O] 16,4 mm 50 mm Thickness R measured ρ mes ( cm) Rsq (M/sq ) 30 nm 30 k 0,5 ~ 0,1 1 nm 200 M 120 ~ 1000 All values are not coherent! Material ρth ( cm) TiN 25 10-6 TiO 1012 - 25 °C 25 104 - 600 ° C 12

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Possible future programs Developments of new models to identify when and where 𝑀𝑃 may occur Role of main parameters (ex: initial electron energy, SEY, coating…) Simulation by existing codes Experimental validation Ex: test of a structure with a variable frequency (measurement on 𝑀𝑃) Ex: study of coating and material processing (test on 1-30 nm TiN coating for example) Set up collaborations for analysis tools Coating thickness and composition. Ex: 4MeV accelerator @IPNL (RBS, NRA, ERDA, PIXE…) Electronic microscopy . Ex: CTµ Lyon (Scanning and transmission Electron Microscopy) Further collaborations with Néel Institute (Grenoble) for materials physics and characterization – Might be interesting also for IN2P3 and CERN. Agreement and support from IN2P3 (including some budget!) 13

Outline Multipacting state of art for MAX Some open questions Physical models Coaxial lines Locally flat surfaces RF cavities Codes Some results for MAX Some open questions Possible future programs Summary EuCARD-2 / MAX 21 mars 2014

Summary I did the syntheses of the state of art of multipacting on work Models Codes I showed some ideas for a future work on multipacting If you are interested too or you have a need, please contact us. Yolanda GOMEZ MARTINEZ, Jean Marie DE CONTO, Frederic BOULY LPSC, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France Jean Luc BIARROTTE, Jean LESREL IPNO, CNRS/IN2P3, Orsay, France Thank you very much EuCARD-2 / MAX 21 mars 2014 14