State of art and RD plans on multipacting

State of art and R&D plans on multipacting

Yolanda GOMEZ MARTINEZ, Jean Marie DE CONTO, Frederic BOULYLPSC, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France

Many thanks to Jean Luc BIARROTTE and Jean LESRELIPNO, CNRS/IN2P3, Orsay, France

EuCARD-2 / MAX21 mars 2014

• Multipacting state of art for MAX• Multipacting• Physical models

• Coaxial lines• Locally flat surfaces • RF cavities

• Codes• Some results for MAX

• Some open questions• Possible future programs• Summary

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Outline


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

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Outline


Multipacting in a coaxial line(1994) E. Somersalo et al gives some scaling laws restrict to a coaxial line with a standing wave

ZfDP po4

int1 24

int2 ZfDP po

Max E for finding a MP

1

2

max ndfE

f : frequency d : parameter of the size of the linen : order of the MP D : diameter of the external conductorZ : impedance characteristic of the line f frequency

P favorable to have a MP

244

1ndfPinput

Power for MP

2fDEkin

Impact energy of electrons

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Multipacting in a coaxial lineal(1997) Pasi Yla-Oijala gives some scaling laws restrict to a coaxial line with a traveling or mixed wave

ZfDP po4

int1 24

int2 ZfDP po

f : frequency D : diameter of the external conductorZ : impedance of the line R Reflection coefficient

Power for MP in TW

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𝑃𝑇𝑊=4∗𝑃𝑆𝑊

Power for EMP in MW

EMP: Electric multipactingMMP: Magnetic multipacting

Multipacting on locally flat surface(1998) J. Tuckmantel gives a criterion restricted to the case of a 1-point multipacting on locally flat surfaces ( )

No relativistic

Only need the magnetic induction B z,o, and the partial derivative of electric field

yE x

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Tuckmantel intended to complete to the cases of stronger curvature, two point multipacting around an electric field and in edges

e-

MP occurs for (A,B) et (A,-B)!

Multipacting in RF cavities

meB

nf

2

f : frequency n : order of the MPf: frequency e : electron chargem : electron massB: Induction magnetic field

(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)

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meB

nf

2122

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/GHzHe extrapolate for a potential one point MP

Multipacting in RF cavitiesf : frequency B: Induction magnetic fieldE: Electric fielde : electron chargem : electron mass

(2013) V. Shemelin. In the case of 2 point multipacting near the equator cavity, he defines two parameters p ( ‘geometrical’) and M (‘magnetical’):

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𝑝=

𝜕𝐸𝑥

𝜕 𝑦2𝜋 𝑓 ∗𝐵0

𝐵0 [𝑚𝑇 ]=35.7∗𝑀∗ 𝑓Author (year) Formula Value of MParodi (1995) (static B)

(correction rms B) (experiment)

2.181.541.6

Saito (2001) 1.68Geng (2003) 1,54 + 0,14/f

Multipacting maps

𝑀=𝑒 𝐵0

2𝜋 𝑓 𝑚

p

MFor the same frequency, different cavities shapes ( ≠p) have different M





Outline


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

vEvc

BxvEcv

me

dtvd

2

21

2 11

E

B

v

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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 …)• …

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Outline


what Eacc ( MV/m) for MP in the cavity βg 0,47 Pinc (kW) for MP in the couplerMeasurements ~ 6 MV/m & ~ 8 MV/m (PhD F.Bouly) In workR. 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

Some results for MAX 1 2

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Cavity βg = 0.47 Coupler





Outline


Open questions - Exemple 1: Electron initial velocity

2eV 4eV

8 10-3

10-1

MULTIPAC simulations of the cavity by F. Bouly

Ef: Final impact energy e20/C0 : Number of new electrons after 20 impacts / Number of initial electrons11

• 2 eV – 4 eV?

104

102

1 1

104

102Ef

e20/C0 e 20/C 0

Ef

range where the taken secondary yield function exceeds unity

• 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]

Thickness R measured ρ mes ( cm) Rsq (M/sq )30 nm 30 k 0,5 ~ 0,11 nm 200 M 120 ~ 1000

Material ρth ( cm)TiN 25 10-6

TiO 1012 - 25 °C 25 104 - 600 ° C

Open questions - Exemple 2: our experience of coating

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50 mm

16,4 mm

All values are not coherent!





Outline


Possible future programs• Developments of new models to identify when and where 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 )• 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!)

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Outline


• 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.

Summary

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Yolanda GOMEZ MARTINEZ, Jean Marie DE CONTO, Frederic BOULYLPSC, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France

Jean Luc BIARROTTE, Jean LESRELIPNO, CNRS/IN2P3, Orsay, France

Thank you very muchEuCARD-2 / MAX21 mars 2014

State of art and RD plans on multipacting

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