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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 10 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 11 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 12 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 14 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 15 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 16 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 17 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 18 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 21 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 22 Description of an experimental multipactor test-bed PHOTOELECTRIC EFFECT Fowler’s Law: Ultra-Violet spectrum lamp CALIFES Workshop 2016, CERN, October 10-12 23 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 24 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 27 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 28 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 29 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 30 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 31 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 34 Thanks a lot for your attention. We are open to cooperate with all of you: [email protected]