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Applicable Notes 1 IMS 2007 Workshop WMH High Power Issues of Microwave Filter Design and Realization Prediction Tools of Multipactor Breakdown in Passive Components for Space Applications V.E. Boria , B. Gimeno, C. Vicente, A.M. Pérez, G. Torregrosa, A. Coves, A. Álvarez, F. Quesada (E-mail: [email protected]) UPVA-UVEG-UMH-UPCT-AURORASAT 2 June 2007 Outline Introduction and Motivation Multipactor in Rectangular Waveguides EM-based Software Tools (complex geometries) Novel Topologies with Reduced Multipactor Risk Multipactor in Coaxial Waveguides Accurate Prediction (experimental results) Parallel-Plate Dielectric-Loaded Waveguides Future Directions and Conclusions Selected References

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Applicable Notes 1

IMS 2007 Workshop WMH

High Power Issues of Microwave Filter Design and Realization

Prediction Tools of MultipactorBreakdown in Passive Components

for Space ApplicationsV.E. Boria, B. Gimeno, C. Vicente, A.M. Pérez,

G. Torregrosa, A. Coves, A. Álvarez, F. Quesada (E-mail: [email protected])

UPVA-UVEG-UMH-UPCT-AURORASAT 2June 2007

Outline

• Introduction and Motivation

• Multipactor in Rectangular Waveguides– EM-based Software Tools (complex geometries)

– Novel Topologies with Reduced Multipactor Risk

• Multipactor in Coaxial Waveguides– Accurate Prediction (experimental results)

• Parallel-Plate Dielectric-Loaded Waveguides

• Future Directions and Conclusions

• Selected References

Applicable Notes 2

UPVA-UVEG-UMH-UPCT-AURORASAT 3June 2007

Introduction

• Multipactor Basics [1,2] :– RF & Microwave Breakdown Discharge (high power)

– High-vacuum conditions (satellites, accelerators)

– Electron avalanche (secondary emission):• Reduced output power, increased return losses

• Heating up of metal walls (losses), outgassing (corona)

Er

Er

Er

[1] A. Hatch and H. Williams, IEEE Journal of Applied Physics, April 1954

[2] J. Vaughan, IEEE Trans. Electron Devices, July 1988

UPVA-UVEG-UMH-UPCT-AURORASAT 4June 2007

Motivation

• Passive Components for Space Applications [1]:– Higher frequencies and power levels (output stage)

– Higher component integration: Intense EM field levels

– Higher risk of breakdown effects (multipactor)

[1] J. Uher et al., Waveguide Components for Antenna Feed Systems, 1993

RECEIVERRECEIVER IMUXIMUX OMUXOMUX

AMPLIF.AMPLIF.

ffaa

ffdd

RECEIVERRECEIVERRECEIVERRECEIVER IMUXIMUXIMUXIMUX OMUXOMUXOMUXOMUX

AMPLIF.AMPLIF.AMPLIF.AMPLIF.

ffaa

ffdd

Input FilterInput Filter

MultiplexersMultiplexers

Channel FiltersChannel Filters Output FilterOutput FilterSatellite RepeaterSatellite Repeater

Applicable Notes 3

UPVA-UVEG-UMH-UPCT-AURORASAT 5June 2007

Motivation

• Technologies for Space Passive Components:– Waveguide Technology (High Q, Low Losses).-

• Rectangular, circular and coaxial guides (Al, Invar, Ag-plated)

• Inclusion of dielectrics (thermal stability) for reducing mass/volume

– Planar Technology (Integration with SSPAs, MMICs)

UPVA-UVEG-UMH-UPCT-AURORASAT 6June 2007

Motivation

• Novel Software Tools for Predicting Multipactor:– Space Agencies requirements are very restrictive [1]

– Present tools are based on simple parallel-plate models [2]

– Reduction of extensive test campaigns and design cycles

[1] ESA-ESTEC, Requirements and Standards, ECSS-E-20-01A, May 2003

[2] S. Strijk (ESTEC-ESA), Multipactor Calculator (issue 1.5), Aug. 2005

Comb-line FilterWaveguide Filter

Courtesy of

Applicable Notes 4

UPVA-UVEG-UMH-UPCT-AURORASAT 7June 2007

Rectangular Waveguides

• Field-Based Multipaction Prediction Tool [1,2]:– Efficient modal and integral equation analysis techniques

• H-plane structures with arbitrary geometry and dielectrics

– Accurate computation of Voltage Magnification Factor (VMF)

• VMF and multipactor analysis plane solved for each frequency

[1] H. Esteban et al., IEEE AP-S Digest, June 2004

[2] F. Quesada et al., IEEE MTT-S Digest, June 2006

( )? 2yV b E x a= = Equivalent Voltage

( )( )( )

t

in

VVMF

V

ωω

ω=

( ) 0

2

2

0

2

2

1

2 Z

V

VMFZ

VP tin ==

UPVA-UVEG-UMH-UPCT-AURORASAT 8June 2007

Rectangular Waveguides

• Susceptibility Voltage Limit (Vdis) Calculation [1,2]:

[1] S. Strijk (ESTEC-ESA), Multipactor Calculator (issue 1.5), Aug. 2005

[2] A. Woode and J. Petit, ESTEC Working Paper No. 1556, Nov. 1989

dist VV ≤

Maximum Power Level without multipactor:- Minimum value of Pin the whole frequency band

( )

2

max 2

0

1

2

disVP P

ZVMF≤ =

Applicable Notes 5

UPVA-UVEG-UMH-UPCT-AURORASAT 9June 2007

Rectangular Waveguides• Mechanization Effects (Rounded Corners) [1,2]:

Power Level (kW)

[1] H. Esteban et al., ESA Workshop MULCOPIM, Sept. 2003

[2] F. Quesada et al., ESA Workshop MULCOPIM, Sept. 2005

13.7 13.75 13.8 13.85 13.9 13.95 14 14.050.5

1

1.5

2

f (GHz)

Rc = 0mm, Rw = 0mmRc = 3mm, Rw = 0mmRc = 0mm, Rw = 1mm

Maximum Power Levelwithout multipactor

Mechanization effects DO NOT affect the multipactor free power threshold

UPVA-UVEG-UMH-UPCT-AURORASAT 10June 2007

Rectangular Waveguides• Bandwidth and Order of Band-Pass Filters [1]:

2-pole filters of 3.6% and 6% BW

[1] F. Quesada et al., IEEE MTT-S Digest, June 2006

Narrow band-pass filters DO HAVE a reduced power threshold

Higher-order filters DO HAVE a lower multipaction threshold

5-pole filter of 7.5% BW

Applicable Notes 6

UPVA-UVEG-UMH-UPCT-AURORASAT 11June 2007

Rectangular Waveguides• Reduction of Multipaction with Dielectrics [1]:

[1] F. Quesada et al., IEEE MTT-S Digest, June 2006

Off-centered dielectric posts Triangular dielectric posts

Dielectrics posts DO HAVE a pulling effect on the E-field (25% reduced risk)

Triangular-shaped posts DO SMOOTH the pulling effect (30% reduced risk)

UPVA-UVEG-UMH-UPCT-AURORASAT 12June 2007

Rectangular Waveguides• Wedge-Shape Waveguide Filter [1,2]:

[1] J. Hueso et al., ESA Workshop MULCOPIM, Sept. 2005

[2] F. Quesada et al., IEEE-MTT-S Digest, June 2006

f0 = 9.5 GHz

BW = 100 MHz

Non-parallel plates pull the electrons out of high E-field region

Improvement of 1 dB (w.r.t. parallel-plate case) in the power threshold

Applicable Notes 7

UPVA-UVEG-UMH-UPCT-AURORASAT 13June 2007

Rectangular Waveguides

• Electromagnetic Field-based Multipactor Tool [1,2]:– Accurate computation of spatial electromagnetic field distribution

• More complex geometries, Complete waveguide devices

• Efficient full-wave methods: modal methods, integral equation technique

– Precise calculation of the resonant trajectories of the electrons

• 3D Lorentz force differential equation: Velocity-Verlet algorithm

– Generation of secondary electrons in waveguide walls

• Secondary Electron Emission Coefficient (SEEC), real secondaries

• Multipaction discharge when population of electrons grow

[1] C. Vicente et al., IEEE MTT-S Digest, June 2005

[2] C. Vicente et al., ESA Workshop MULCOPIM, Sept. 2005

UPVA-UVEG-UMH-UPCT-AURORASAT 14June 2007

Rectangular Waveguides

• Computation of EM Fields with FEST3D [1]:

[1] M. Mattes et al., ESA-ESTEC Contract Ref. 16827/02/NL/EC, March 2006

Cascaded connection of rect. wg.:• Integral Equation Technique

• Generalized Impedance Matrices (Z)

AxialComponents

Ez

, Hz

+

Applicable Notes 8

UPVA-UVEG-UMH-UPCT-AURORASAT 15June 2007

Rectangular Waveguides

• :Multipactor Prediction Tool for Space Industry [1]

[1] ESA-ESTEC Contract Ref. 16827/02/NL/EC, March 2006

Funded by::

UPVA-UVEG-UMH-UPCT-AURORASAT 16June 2007

Rectangular Waveguides

• Waveguide Gap Transformer [1] using

[1] C. Vicente et al., IEEE MTT-S Digest, June 2005

4 alodine X-band samples:different heights for critical gap

Electric Field Density:Critical element: inner gap

Applicable Notes 9

UPVA-UVEG-UMH-UPCT-AURORASAT 17June 2007

Rectangular Waveguides

• Comparison of with experiments [1]

[1] C. Vicente et al., IEEE Power Modulator Symposium Digest , May 2006

Courtesy of:

ESTEC/ESA

TESAT

UPVA-UVEG-UMH-UPCT-AURORASAT 18June 2007

Coaxial Waveguides

• MULTICOAX: Multipactor Prediction Tool [1,2]:– Accurate prediction of multipactor threshold in coaxial waveguides

under TEM mode excitation (traveling and standing waves):

– Individual effective electron model: one electron tracked

[1] A.M. Pérez et al., ESA Workshop MULCOPIM, Sept. 2005

[2] A.M. Pérez et al., IEEE MTT-S Digest, June 2006

ϕϕ ˆθc

ztωcos

a

bLnr

Vˆθ

c

ztωcos

a

bLnr

Vt),(

r

a

bLnr

Vrθ

c

ztωcos

a

bLnr

Vrθ

c

ztωcos

a

bLnr

Vt),(

2

2

1

1

DC2

2

1

1

+

+

+

=

+

+

+

+

+

=

cc

rB

rE

Applicable Notes 10

UPVA-UVEG-UMH-UPCT-AURORASAT 19June 2007

Coaxial Waveguides

• Algorithm of MULTICOAX Tool [1]:– Computation of individual effective electron trajectory:

• Initial angle and energy (velocity) are taken randomly

• Numerical integration (velocity Verlet) of the Lorentz equation:

• Checking of collision with the metallic surface:

– Secondary true (SEEC).- random output energy and angle

– Elastic collision.- Linear moment and energy conservation principles

• A multiplicity function is generated for indicating multipaction:

)BvE(FL ×+=q q = - e : electron charge

[1] A.M. Pérez et al., IEEE MTT-S Digest, June 2006

0m=L

F a

uur r

∏=

=N

i

iNe1

δ If eN > 1 Multipaction occurs

UPVA-UVEG-UMH-UPCT-AURORASAT 20June 2007

Coaxial Waveguides

• Secondary Electrons Emission Model [1,2]:

[1] J. Vaughan, IEEE Trans. Electron Devices, Sept. 1989

[2] C. Vicente et al., IEEE MTT-S Digest, June 2005

E0 varied until SEEC=1 @ E1

SEEC ≤ 1 for E<E0 according to experimental data

Applicable Notes 11

UPVA-UVEG-UMH-UPCT-AURORASAT 21June 2007

Coaxial Waveguides

• Coaxial Gap Transformer using MULTICOAX [1]:

Critical element (inner gap):b=5.65 mm a=4.65 mm

Z0=11.67 Ω f0=1.35 GHz

2a

2b

λλλλg/4

λλλλg/4

λλλλg/4

Return Losses (dB)

Experimental results:

19 dB (≈20 dB) @ f0=1.35 GHz

[1] A.M. Pérez et al., IEEE MTT-S Digest, June 2006

Copper sample

UPVA-UVEG-UMH-UPCT-AURORASAT 22June 2007

Coaxial Waveguides• Predicted Results for Coaxial Gap Transformer [1]:

[1] A.M. Pérez et al., IEEE MTT-S Digest, June 2006

After 30 impacts

360 electrons with different phases launched

Multipactionoccurs if eN > 1

Multipactor Threshold: VVTT=72 V (P = =72 V (P = 209.9 W)209.9 W)

Applicable Notes 12

UPVA-UVEG-UMH-UPCT-AURORASAT 23June 2007

Coaxial Waveguides• Experimental Results of Coaxial Gap Transformer [1]:

[1] A.M. Pérez et al., Proc. IEEE MELECON, May 2006

204.6 WExperimentat ESTEC-ESA

209.94 WPrediction threshold MULTICOAX

(In-Home)

311.23 WPrediction threshold “Multipactor Calculator”(ESTEC-ESA)

204.6 WExperimentat ESTEC-ESA

209.94 WPrediction threshold MULTICOAX

(In-Home)

311.23 WPrediction threshold “Multipactor Calculator”(ESTEC-ESA)

Sample

ElectronProbe

Radioactive Source

Performed @ ESTEC-ESA

Copper sample

UPVA-UVEG-UMH-UPCT-AURORASAT 24June 2007

Coaxial Waveguides• Comparative Study of MULTICOAX [1,2]:

[1] R. Woo, IEEE Journal of Applied Physics, Feb. 1968

[2] W. Arter et al., Tech. Rep. AEA/TYKB/28046/RP/1, May 1997

Theoretical results (Arter)

Experimental data from NASA (Woo)

Applicable Notes 13

UPVA-UVEG-UMH-UPCT-AURORASAT 25June 2007

Dielectric-Loaded Waveguides

• Parallel Plate Dielectric-Loaded Waveguide [1]:– Trajectory of an individual effective electron is computed

[1] G. Torregrosa et al., IEEE Electron Device Letters, July 2006

h

Metal

V(t)

Metal

y

zx

ε0

E EDC d

Dielectric

A

εr⋅ε0

( )hdh

VE

r

r

−+=

ε

ε00

( ) ( )xtEt ˆcos0 αω +=E

( ) ( )αω += tVtV cos0

( ) ( ) ( ) ( ) ( )[ ] ( )2

002

000

000

2coscossin tt

m

Eett

m

Eettt

m

Eevxtx dc −−+−++−

+++= αωαω

ωαω

ω

( )0

1

1,,2

1

ε

δ

A

eNEEE

jj

jdcjdcdc

−+==

DC field

considered

UPVA-UVEG-UMH-UPCT-AURORASAT 26June 2007

Dielectric-Loaded Waveguides

• Alumina-loaded Silver-Plate Waveguide [1]:

After each impact:

First Order Multipactor

0 50 1000

0.5

1

1.5

2

2.5

SE

Y

Primary electron impact energy (eV)

AluminaSilver

0 20 40 600

1

2

3

Pos

ition

(m

m)

RF cycles

Different SEY values

1−= iii NN δ

[1] G. Torregrosa et al., IEEE Electron Device Letters, July 2006

V0=110 V

f=0.5 GHz

d=3.0 mm

h=0.3 µm

A=10 cm2

Single surface multipactor

Applicable Notes 14

UPVA-UVEG-UMH-UPCT-AURORASAT 27June 2007

Dielectric-Loaded Waveguides

• Time evolution of the electron discharge [1]:

[1] G. Torregrosa et al., IEEE Electron Device Letters, July 2006

0 20 40 60

-10-4

-10-2

-100

-102

-104

ED

C (

V)

RF cycles

0 20 40 6010

0

102

104

106

108

1010

Pop

ulat

ion

of e

lect

rons

RF cycles

0 20 40 600

0.5

1

1.5

2

2.5

δRF cycles

DC field

A negative DC field is generated:

Electrons are absorbed at dielectric layer

Electron discharge is finally shut down

UPVA-UVEG-UMH-UPCT-AURORASAT 28June 2007

Future Directions

• Multipactor in Multicarrier Systems [1]:

[1] ESA-ESTEC Contract Ref. AO/14978/05/NL/GLC, 2006-2008

Investigation of the 20-gap crossing rule

Funded by:

Performed by:

Applicable Notes 15

UPVA-UVEG-UMH-UPCT-AURORASAT 29June 2007

Future Directions• Multipactor in Planar Transmission Lines [1]:

[1] ESA-ESTEC Contract Ref. AO/1-5086/06/NL/GLC, 2007-2009

Coaxial to MicrostripTransition

Funded by:

EncapsulatedMicrostrip Line

Performed by:

RibbonConnection

UPVA-UVEG-UMH-UPCT-AURORASAT 30June 2007

Future Directions

• Experimental Facility for Multipactor:

Measurements at:

L, S, C, X, Ku, K bands

Clean room:

100,000 class

vacuum system

power amplifiers

detection systems

Cooperation between:

UPVA, UVEG & AURORASAT

Expected operation: 2008

Applicable Notes 16

UPVA-UVEG-UMH-UPCT-AURORASAT 31June 2007

Conclusions

• Software tools for predicting multipactor in:– Rectangular waveguide passive devices

– Coaxial waveguide technology components

– Parallel-plate dielectric loaded waveguides

• A prediction tool for space industry applications– FEST3D: passive waveguide components

• Validation with experimental results:– Rectangular waveguide gaps and filters

– Coaxial waveguide gaps and transformers

UPVA-UVEG-UMH-UPCT-AURORASAT 32June 2007

Selected References (I)W. Arter, M. Hook, Multipaction Threshold Curves for Coaxial Geometries, Technical Report No. AEA/TYKB/28046/RP/1, May 1997.

E. Chojnacki, “Simulations of a multipactor-inhibited waveguide geometry”, Physical Review (Special Topics “Accelerators and beams”), vol. 3, pp. 032001-(1-5), 2000.

ECSS Secretariat, ESA-ESTEC, Space Engineering: Multipaction Design and Test, ECSS-E-20-01A, May 2003.

ESA-ESTEC, RF Breakdown in Multicarrier Systems, Contract No. AO/14978/05/NL/GLC, 2006-2008.

ESA-ESTEC, New investigations in RF Breakdown in Microwave Transmission Lines, Contract No. AO/1-5086/06/NL/GLC, 2007-2009.

H. Esteban, J.V. Morro, V.E. Boria, C. Bachiller, B. Gimeno, L. Conde, “Hybrid full-wave simulator for the multipactionmodelling of low-cost H-plane filters”, Proc. MULCOPIM 2003, ESTEC-ESA, Noordwijk, The Netherlands, 2003, 8 pp.

H. Esteban, J.V. Morro, V.E. Boria, C. Bachiller, A.A. San Blas, J. Gil, “Multipaction modeling of low-cost H-plane filters using an electromagnetic field analysis tool”, IEEE AP-S Digest, Monterey, CA, 2004, pp. 2155-2158.

G. Gerini, M. Guglielmi, G. Lastoria, “Efficient integral equation formulations for admittance or impedance representation of planar waveguide junctions”, IEEE MTT-S Digest, Baltimore, MD, 1998, pp. 1747-1750.

A. Hatch, H. Williams, “The secondary electron resonance mechanism of low-pressure high-frequency gas breakdown”, IEEE Journal of Applied Physics, vol. 25, pp. 417-423, April 1954.

Applicable Notes 17

UPVA-UVEG-UMH-UPCT-AURORASAT 33June 2007

Selected References (II)A. Hatch, H. Williams, “Multipacting modes of high-frequency gaseous breakdown”, Physical Review, vol. 112, pp. 681-685, Nov. 1958.

J. Hueso, D. Schmitt, D. Raboso, I. Hidalgo, V.E. Boria, B. Gimeno, “Design of a novel inductive band-pass waveguide filter to reduce the risk of multipactor breakdown”, Proc. MULCOPIM 2005, ESTEC-ESA, Noordwijk, The Netherlands, 2005, pp. 67-78.

R.A. Kishek, Y.Y. Lau, L.K. Ang, A. Valfells, R.M. Gilgenbach, “Multipactor discharge on metals and dielectrics: Historical review and recent theories”, Physics of Plasmas, vol. 5, pp. 2120-2126, May 1998.

M. Ludovico, G. Zarba, L. Accatino, “Multipaction analysis and power handling evaluation in waveguide components for satellite antenna applications”, IEEE AP-S Digest, Boston, MA, 2001, pp. 266-269.

M. Mattes, J.R. Mosig, Integrated CAD Tool for Waveguide Components, Final Report of ESA-ESTEC Contract No. 12465/97/NL/NB, Dec. 2001.

A.M. Pérez, C. Tienda, C.P. Vicente, J.F. Sánchez, A. Coves, G. Torregrosa, A.A. San Blas, B. Gimeno, V.E. Boria, “MULTICOAX: A software tool for predicting multipactor RF breakdown threshold in coaxial and circular waveguides”, Proc. MULCOPIM 2005, ESTEC-ESA, Noordwijk, The Netherlands, 2005, pp. 35-41.

A.M. Pérez, C. Tienda, C. Vicente, A. Coves, G. Torregrosa, B. Gimeno, R. Barco, V.E. Boria, D. Raboso, “Multipactoranalysis in coaxial waveguides for satellite applications using frequency-domain methods”, IEEE MTT-S Digest, San Francisco, CA, 2006, pp. 1045-1048.

UPVA-UVEG-UMH-UPCT-AURORASAT 34June 2007

Selected References (III)F. Quesada, V.E. Boria, B. Gimeno, D. Cañete, J. Pascual, A. Álvarez, J. Hueso, D. Schmitt, D. Raboso, C. Ernst, I. Hidalgo, “Investigation of multipactor phenomena in inductively coupled passive waveguide components for space applications”, IEEE MTT-S Digest, San Francisco, CA, 2006, pp. 246-249.

F. Quesada, J. Pascual, D. Cañete, J.L. Gómez, B. Gimeno, J. Pérez, A. Vidal, V.E. Boria, A. Álvarez, “Investigation of multipaction phenomena in cavity filters loaded with dielectric posts and tuning elements”, Proc. MULCOPIM 2005, ESTEC-ESA, Noordwijk, The Netherlands, 2005, pp. 109-118.

E. Somersalo, P. Ylä-Oijala, D. Porch, J. Sarvas, “Computational methods for analyzing electron multipacting in RF structures”, Particle Accelerators, vol. 61, pp. 107-141, 1998.

S. Strijk, ESA/ESTEC Multipactor Calculator (issue 1.5) Manual, http://www.estec.esa.nl/multipac/, Aug. 2005.

C. Tienda, A.M. Pérez, C. Vicente, A. Coves, G. Torregrosa, J.F. Sánchez, R. Barco, B. Gimeno, V.E. Boria, “Multipactor analysis in coaxial waveguides”, Proc. 13th IEEE MELECON, Málaga, Spain, 2006, pp. 195-198.

G. Torregrosa, A. Coves, A.A. San Blas, A.M. Pérez, C.P. Vicente, B. Gimeno, V.E. Boria, “Analysis of multipactoreffect in dielectric-loaded waveguides”, Proc. MULCOPIM 2005, ESTEC-ESA, Noordwijk, The Netherlands, 2005, pp. 27-34.

G. Torregrosa, A. Coves, C.P. Vicente, A.M. Pérez, B. Gimeno, V.E. Boria, “Time evolution of an electron discharge in a parallel-plate dielectric-loaded waveguide”, IEEE Electron Device Letters, vol. 27, pp. 619-621, July 2006.

J. Uher, J. Bornemann, U. Rosenberg, Waveguide Components for Antenna Feed Systems: Theory and CAD, Norwood, USA: Artech House, 1993.

Applicable Notes 18

UPVA-UVEG-UMH-UPCT-AURORASAT 35June 2007

Selected References (IV)J. Vaughan, “Multipactor”, IEEE Trans. Electron Devices, vol. 35, pp. 1172-1180, July 1988.

J. Vaughan, “A new formula for secondary emission yield”, IEEE Trans. Electron Devices, vol. 36, pp. 1963-1967, Sept. 1989.

C. Vicente, M. Mattes, D. Wolk, B. Mottet, H. Hartnagel, J.R. Mosig, D. Raboso, “Multipactor breakdown prediction in rectangular waveguide based components”, IEEE MTT-S Digest, Long Beach, CA, 2005, pp. 1055-1058.

C. Vicente, M. Mattes, D. Wolk, H. Hartnagel, J.R. Mosig, D. Raboso, “FEST 3D - A simulation tool for multipactionprocedure”, Proc. MULCOPIM 2005, ESTEC-ESA, Noordwijk, The Netherlands, 2005, pp. 11-17.

C. Vicente, H. Hartnagel, Multipactor and Corona Discharge: Simulation and Design in Microwave Components, Final Report of ESA-ESTEC Contract No. 16827/02/NL/EC, March 2006.

C. Vicente, M. Mattes, D. Wolk, H. Hartnagel, J.R. Mosig, D. Raboso, “Contribution to the RF breakdown in microwave devices and its prediction”, IEEE Power Modulator Symp. Digest, Washington D.C., 2006, 6 pp.

R. Woo, “Multipacting discharge between coaxial electrodes”, IEEE Journal of Applied Physics, vol. 39, pp. 1528-1533, Feb. 1968.

A. Woode, J. Petit, “Diagnostic investigation into the multipactor effect, susceptibility zone measurements and parameters affecting a discharge”, ESA Working Paper , no. 1556, Nov. 1989.