1. CALIFES Workshop 2016, CERN, October, 10-12
Multipactor effect induced
by very high-energy electrons
Benito Gimeno Martínez(1,2), Daniel González-Iglesias(2)
(1) Department of Applied Physics and Electromagnetics – Institute of Material Sciences (ICMUV), University of Valencia, Spain
(2) VAL SPACE CONSORTIUM, Valencia, Spain
CALIFES Workshop 2016, CERN, October, 10-12

2. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

3. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

4. Can very high-energy electrons induce a multipactor discharge ?
Introduction
Can very high-energy electrons induce a multipactor discharge ?
This is the question that we will try to analyze in this talk…
First of all let us explain what is multipactor effect and its importance in space communications systems.
Space weather is a very hostile environment
Solar activity causes a continuous flux of high energy elemental particles towards the spaceships
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5. In a satellite there are three main electrons sources:
Introduction
In a satellite there are three main electrons sources:
Cosmic radiation
Solar radiation: Photons of Sun generate photo-electrons
Van Allen rings ( km)
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6. DESY (Hamburg, Germany)
Introduction
Multipactor effect: electrons avalanche generated by the synchronization between an intense RF electric field and the secondary electron emission phenomenon (SEY) under ultra high-vacuum conditions.
e- density
Multipactor simulation in a parallel-plate waveguide region driven by a time-harmonic electric field
Background density t
waveguide wall e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e-
Wall collisions
vacuum conditions e-
RF cycles e- d
5 TRF/2
DESY (Hamburg, Germany) e- e-
Primary (free) electron
Secondary electron e- e- e- e- e- e- e- e- e- e- e- e- e-
waveguide wall

7. Effects of a multipactor discharge on a microwave component:
Introduction
Effects of a multipactor discharge on a microwave component:
Increase of signal noise
Increase of reflected power
Heating up of device walls
Detuning of resonant cavities
Physical damages
Degradation of the device performance
Limitation of the managed RF power
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Kapton window
Low-pass filter

8. Introduction
In this undesired scenario the space agencies (in particular the European Space Agency) have to control and predict the possible existence of a multipactor discharge occurring within on-board microwave sub-systems: replacement of equipments is NOT POSSIBLE in a satellite …
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9. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

10. Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
The multipactor algorithm is based on the Monte-Carlo method, which is a statistical procedure to simulate complex problems in the areas of engineering, physics, biology, chemistry, etc.
There are a lot of versions of Monte-Carlo method implementations. For instance, to compute multi-dimensional deterministic integrals.
Monte-Carlo method has been applied for multipactor simulations, as reported in:
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11. Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
The algorithm is based on the tracking of a set of individual electrons governed by the electromagnetic fields within a microwave component:
Initially, a set of individual electrons are launched from several specific points with a random initial velocity vector each one.
The trajectories of these individual electrons are computed as a function of time.
When each individual electron impacts on a metallic/dielectric wall of the component, the SEY coefficient is computed. Its value determines if this electron is absorbed or it might generate more electrons.
If the electron is absorbed then is eliminated in the simulation. In other case the new electrons are launched.
The algorithm is stopped if a certain value of the electrons population is being reached, or when all electrons are absorbed.
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12. Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
The electrons dynamics (3D) within the waveguide is described by the relativistic Lorentz force :
where m0 is the electron mass at rest, q=-e is the electron charge, v is the magnitude of the electron velocity, g is the relativistic factor, and
are the total electric and magnetic fields, including RF and DC contributions.
The typical electron velocities values reached in space communication systems are much lower than the speed of light in vacuum: the relativistic formulation can be approached considering that g ≈ 1,
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13. Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
Finally the problem can be expressed as a coupled differential equations system of second order:
which has to be numerically solved.
A Velocity-Verlet algorithm has been used for the numerical solution of the 3D differential equations system (≈ 300 time steps per RF period):
accurate
efficient
stable
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L. Verlet, “Computer ‘experiments’ on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules,” Phys. Rev., vol. 159, no. 1, pp. 98–103, Jul

14. The total Secondary Electron Yield (SEY) coefficient d is defined as
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
Physically when each electron strikes on a surface such electron can be:
Elastically or inelastically backscattered
Absorbed
Generate one or more true secondaries
The total Secondary Electron Yield (SEY) coefficient d is defined as
The SEY coefficient depends on:
Kinetic energy of the primary electron (W)
Incidence angle of primary electron (ξ)
Surface roughness
Despite the concrete values of the SEY coefficient are different for each material, the shape of the SEY curve is universal for all of them (metal, dielectrics, ferrite).
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Experimental SEY curve measured at the ESA-VSC High Power Space Materials Laboratory

15. SEY model1,2 (Furman and Pivi)
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
SEY model1,2 (Furman and Pivi)
When an electron collides with a surface it can be:
Elastically backscattered
Inelastically backscattered
Absorbed
Generate true secondaries
Different components of the secondary electron emission
Contribution of elastically backscattered electrons 𝑎∈
Contribution of true secondaries
Contribution of inelastically backscattered electrons
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1 M. A. Furman and M. T. Pivi, “Probabilistic model for the simulation of secondary electron emission”, Physical Review Special Topics- Accelerators and Beams, vol. 5, (2002).
2 J. de Lara, F. Perez, M. Alfonseca, L. Galan, I. Montero, E. Roman, D.R. Garcia-Baquero, "Multipactor prediction for on-board spacecraft RF equipment with the MEST software tool", IEEE Transactions on Plasma Science, vol. 34, no. 2, pp , April 2006.

16. SEY model (Furman and Pivi)
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
SEY model (Furman and Pivi)
Angular dependence for the different contributions:
Z= atomic number
The probability for each kind of emission is given by:
Elastic
Inelastic
True Secondaries
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Different contributions to the SEY coefficient

17. Normalization condition
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
After the collision, if the electron is not absorbed, electron is launched back from the impact point. The velocity vector (magnitude and direction) of the released electron is controlled by the type of collision:
Elastic collision: specular reflection; velocity vector magnitude does not change.
Inelastic collision: specular reflection; velocity vector magnitude of the released electron is lower than the initial one.
Secondary electron:
- The magnitude of the velocity vector of the effective electron is calculated by means of a Rayleigh probability distribution density:
Normalization condition
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Ws = Departure energy of the secondary electron
(Ws) = Probability of release a secondary
electron with a departure energy of Ws
Wg = Standard deviation value

18. the elevation angle q has to be computed by means of the cosine law:
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
In order to implement this concept in the Monte-Carlo method, the algorithm generates a random real number r  [0,1], and the departure energy is calculated:
Note the Energy Conservation Principle has to be satisfied. It is checked that Ws<W, if not a new value of Ws is calculated until the condition is satisfied.
- The direction of the velocity vector of the individual electron is calculated in a local spherical coordinate system centred at the impact point:
the azimuthal angle j  [0,2p[ is easily calculated by means of a uniform probability density:
the elevation angle q has to be
computed by means of
the cosine law:
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J. Greenwood, “The correct and incorrect generation of a cosine distribution of scattered particles for Monte-Carlo modelling of vacuum systems” , Vacuum, vol. 67, pp. 217–222, 2002

19. Multipactor analysis on ridge and multiridge rectangular waveguides
Multipactor analysis based on Monte-Carlo
algorithm: individual electron model
With this Monte-Carlo algorithm we have solved in last ten years several RF Breakdown research activities:
Multipactor analysis on ridge and multiridge rectangular waveguides
Multipactor analysis in coaxial transmission lines considering the effect of the linear superposition of incident and reflected waves
Multipactor analysis in circular and elliptical waveguides: study of the polarization ellipse with the first two orthogonal modes
Mitigation of multipaction with external static magnetic fields: solenoid and permanent magnets (cooperation with Dr. Fritz Caspers, CERN)
Multipactor phenomenon in the presence of dielectrics: partial mitigation due to the charge of the dielectric
Multipactor effect in the presence of magnetized ferrites: magnetization in the parallel and perpendicular directions to the ferrite
Multipactor effect with short pulses
Multipactor effect with RF digital modulated signals: application to ESA Galileo project.
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20. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

21. Description of an experimental multipactor test-bed
Standard multipactor test-bed:
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22. 90Sr RADIOACTIVE SOURCE: 37 MBq
Description of an experimental multipactor test-bed
Three different primary electrons seeding are used in the experimental tests-bed of the VAL SPACE CONSORTIUM Lab:
90Sr RADIOACTIVE SOURCE: 37 MBq
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Maximum spectrum energy:
Emax=2.28 MeV

23. Description of an experimental multipactor test-bed
PHOTOELECTRIC EFFECT
Fowler’s Law:
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Ultra-Violet spectrum lamp

24. Description of an experimental multipactor test-bed
In our case the kinetic energy of photoelectrons is very low:
T = h n – F = 5.3 – 4.5 = 0.8 eV
The flux of photo-electrons generated is:
photons/s x ~ photoelectrons/s
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25. REGULATED ELECTRON GUN
Description of an experimental multipactor test-bed
To the knowledge of the Authors, an accurate and complete theory for the study of the influence of the primary electrons sources in a conventional multipactor experiment has not still been developed.
REGULATED ELECTRON GUN
It generates an electrons beam:
kinetic energy = 20 to 1000 eV
electrons current = 9 nA
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26. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

27. Multipactor induced by high-energy electrons: simulations
We might conclude that the effect of the velocities of the primary electrons in the RF power threshold has not been studied in detail.
In this scenario, we have performed numerical simulations in a Ku-band waveguide transformer:
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Electric magnetic field distribution in the rectangular waveguide transformer

28. Multipactor induced by high-energy electrons: simulations
A collimated electron beam is emitted by CALIFES LINAC crossing the rectangular waveguide transformer if RF fields are zero:
CALIFES
ELECTRONS
BEAM
L=2 cm
d=100 mm
When RF fields are present, the electron trajectories of free electrons are bent by the presence of the RF electric field (fundamental TE10 mode):
If in this gap region the multipactor conditions exist (synchronism + emission of secondary electrons), a discharge is initiated…
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29. Multipactor induced by high-energy electrons: simulations
This problem has been simulated with our home-made code at 12.5 GHz.
The Ku-band rectangular waveguide transformed has been silver coated in order to increase the electrical conductivity.
First of all, we have analysed the electrons population evolution as a function of time when electrons initial velocity is:
v0 = 200 eV
RF multipactor voltage threshold defined in the gap region as:
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for this case is 57 V
(In this case the stationary electrons population within transformer is 30 electrons).

30. Multipactor induced by high-energy electrons: simulations
Secondly, we have repeated the simulation with v0 = 1 MeV
(In this case the stationary electrons population within transformer is 50 electrons).
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Simulations have been repeated up to v0 = 200 MeV , obtaining similar results.

31. Multipactor induced by high-energy electrons: simulations
We have also analyzed the convergence of the algorithm as a function of the number of stationary electrons within transformer for different v0:
observing that the RF voltage threshold does not depend on v0 and the number of electrons.
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32. Multipactor induced by high-energy electrons: simulations
statistically
Multipactor induced by high-energy electrons: simulations
statistically
Secondary Emission Yield coefficient has been represented for silver (Furman and Pivi model):
Electrons impacting with high-energy have a SEY < 1. However, statistically any of them might extract true secondary electrons. For instance:
v0 = 1 MeV → SEY=0.27 → If 100 electrons impact, 27 secondary electrons are released. If multipactor resonant conditions exist, the discharge is generated…
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33. INDEX
Introduction
Multipactor analysis based on Monte-Carlo algorithm: individual electron model
Description of an experimental multipactor test-bed
Multipactor induced by high-energy electrons: simulations
Conclusions

34. Conclusions
The effect of the number of primary electrons and their kinetic energy in the multipactor RF voltage threshold has been analyzed in a Ku-band rectangular waveguide transformer.
Numerical simulations performed predict no variation of the multipactor RF voltage threshold within the parameter range covered.
Despite the initial electron velocity is oriented along the axial co-ordinate, the RF electric field (parallel to the gap between the plates) has been found to be enough to force the electrons collide with the waveguide walls, allowing in this way the starting point of the multipactor phenomenon.
In addition, the case of a relativistic high-energy electron beam with a kinetic energy within has been considered, finding the same multipactor RF voltage thresholds that for the previous situations.
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35. Thanks a lot for your attention.
We are open to cooperate with all of you: