1. 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

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 1

3. 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

4. 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

5. 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

6. 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 ~ 𝑅 𝑃 𝑇𝑊 = 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

7. 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

8. 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

9. 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

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

11. 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

12. 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

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

14. Some results for MAX what Eacc ( MV/m) for MP in the cavity βg 0,471 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

15. 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

16. 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

17. 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
TiO °C
° C 12

18. 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

19. 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 (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

20. 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

21. 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