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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
1
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
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
CALIFES Workshop 2016, CERN, October 10-12
3
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
CALIFES Workshop 2016, CERN, October 10-12
4
Introduction
• In a satellite there are three main electrons sources:
– Cosmic radiation
– Solar radiation: Photons of Sun generate photo-electrons
– Van Allen rings (1000-5000 km)
CALIFES Workshop 2016, CERN, October 10-12
5
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
ee- - e- ee-ee-e--ee-e-e-ee--e- -
ee-e- - ee--
e-
Wall collisions
ee-e-- ee-e-e
-e-- e-e- ee--
vacuum conditions
E
e-
0 1 2 3 4 5 6 7 8 9 10
e-
d
RF cycles
5 TRF/2
e-
ee-e-- ee-e--
e-
e-e-
ee-e- -
waveguide wall
CALIFES Workshop 2016, CERN, October 10-12
DESY
(Hamburg,
e- Primary (free) electron
Germany)
eSecondary electron
6
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
Low-pass filter
CALIFES Workshop 2016, CERN, October 10-12
Kapton window
7
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 …
CALIFES Workshop 2016, CERN, October 10-12
8
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
CALIFES Workshop 2016, CERN, October 10-12
9
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:
CALIFES Workshop 2016, CERN, October 10-12
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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:
1. Initially, a set of individual electrons are launched from several specific points with
a random initial velocity vector each one.
2. The trajectories of these individual electrons are computed as a function of time.
3. 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.
4. If the electron is absorbed then is eliminated in the simulation. In other case the
new electrons are launched.
5. The algorithm is stopped if a certain value of the electrons population is being
reached, or when all electrons are absorbed.
CALIFES Workshop 2016, CERN, October 10-12
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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,
CALIFES Workshop 2016, CERN, October 10-12
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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
CALIFES Workshop 2016, CERN, October 10-12
L. Verlet, “Computer ‘experiments’ on classical
fluids. I. Thermodynamical properties of Lennard–
Jones molecules,” Phys. Rev., vol. 159, no. 1, pp.
98–103, Jul. 1967.
13
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
d
number of secundary electrons released
1 impacting electron
• The SEY coefficient depends on:
 Kinetic energy of the primary electron (W)
 Incidence angle of primary electron (ξ)
 Surface roughness
Experimental SEY curve measured at the ESA-VSC High Power Space Materials Laboratory
• 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).
CALIFES Workshop 2016, CERN, October 10-12
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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
Contribution of true secondaries
∈
Contribution of inelastically backscattered
electrons
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, 124404 (2002).
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. 476-484, April 2006.
2
CALIFES Workshop 2016, CERN, October 10-12
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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
Different contributions to the SEY coefficient
CALIFES Workshop 2016, CERN, October 10-12
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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
Ws = Departure energy of the secondary electron
(Ws) = Probability of release a secondary
electron with a departure energy of Ws
Wg = Standard deviation value
CALIFES Workshop 2016, CERN, October 10-12
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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:
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
CALIFES Workshop 2016, CERN, October 10-12
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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.
CALIFES Workshop 2016, CERN, October 10-12
19
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
CALIFES Workshop 2016, CERN, October 10-12
20
Description of an experimental multipactor test-bed
• Standard multipactor test-bed:
CALIFES Workshop 2016, CERN, October 10-12
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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
Maximum spectrum energy:
Emax=2.28 MeV
CALIFES Workshop 2016, CERN, October 10-12
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Description of an experimental multipactor test-bed
PHOTOELECTRIC EFFECT
Fowler’s Law:
Ultra-Violet spectrum lamp
CALIFES Workshop 2016, CERN, October 10-12
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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:
8.1 108 photons/s x 3.55 10-4 ~ 3 105 photoelectrons/s
CALIFES Workshop 2016, CERN, October 10-12
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Description of an experimental multipactor test-bed
REGULATED ELECTRON GUN
It generates an electrons beam:
kinetic energy = 20 to 1000 eV
electrons current = 9 nA
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.
CALIFES Workshop 2016, CERN, October 10-12
25
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
CALIFES Workshop 2016, CERN, October 10-12
26
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:
Electric magnetic field distribution in the rectangular waveguide transformer
CALIFES Workshop 2016, CERN, October 10-12
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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…
CALIFES Workshop 2016, CERN, October 10-12
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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:
for this case is 57 V
(In this case the stationary
electrons
population
within
transformer is 30 electrons).
CALIFES Workshop 2016, CERN, October 10-12
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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).
•
Simulations have been repeated up to v0 = 200 MeV , obtaining similar results.
CALIFES Workshop 2016, CERN, October 10-12
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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.
CALIFES Workshop 2016, CERN, October 10-12
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statistically
statistically
•
Multipactor induced by high-energy electrons:
simulations
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…
CALIFES Workshop 2016, CERN, October 10-12
32
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
CALIFES Workshop 2016, CERN, October 10-12
33
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.
CALIFES Workshop 2016, CERN, October 10-12
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Thanks a lot for your attention.
We are open to cooperate with all of you:
[email protected]
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