Multipactor threshold sensitivity to Total Electron

Multipactor threshold sensitivity to Total Electron Emission Yield in parallel-plate waveguide and TEEY models accuracy. N. Fil (1), M. Belhaj (2), J. Hillairet (1), J. Puech (3) (1)

CEA, the French Alternative Energies and Atomic Energy Commission, DRF//IFRM/SI2P/GSCP, CEA Cadarache, 13108 Saint Paul-Lez-Durance, France (2) (3)

ONERA, the French Aerospace Laboratory, DESP, 31000 Toulouse, France

CNES, the French National Centre for Space Studies, DCT/RF/HT, 31000 Toulouse, France

Abstract — Multipactor effect can lead to RF components deterioration which could be fatal to RF systems in space communication payloads or in experimental fusion devices. To avoid such risk, oversized margins are used. Multipactor simulations are used to get voltage threshold predictions. Since the power breakdown depends on the Total Electron Emission Yield (TEEY) curve a sensitivity study has been made to determine which parameters of the TEEY properties are critical. An evaluation of multipactor threshold sensitivity to TEEY curve variations is realized and two critical parameters are found for parallel-plate geometry: first cross-over energy and the curve definition for incident electron energy between the first crossover and the maximum curve energies. Six TEEY models and their accuracy to predict voltage threshold are compared. Electron emission experimental measurements have to be accurate on the first cross-over energy and TEEY model must respect this value to obtain coherent multipactor voltage threshold. Index Terms — Multipactor, Parallel-plate waveguide, Electron emission, power breakdown simulations, spatial and fusion reactor microwave components, TEEY model.

I. INTRODUCTION Multipactor effect can lead to radio-frequency (RF) discharges which can occur within microwave antennas and components. These kinds of components are commonly used in telecommunication satellite [1] as well as in fusion experimental reactors such as Tokamak [2], where components are under vacuum conditions. Multipactor is initiated by free electrons provided by the harsh space weather for spatial matters or by the plasma inside the reactor chamber. These electrons are accelerated by the RF electric field and then impact the walls of the microwave components. There, electrons interact with the material and its structure. The incident electron (IE) impacting the material surface can have interactions with atomic nucleus, free electron, valence electron, surface plasmon, bulk plasmon [3]. Interaction can be associated with energy loss which can lead the incident electron to excite inner material electron to escape the surface: this emitted electron is called secondary electron (SE). The incident electron can also transfer a part of its energy through inelastic interactions or diffuse with elastic interactions and escape the material surface: those electrons

are respectively called inelastic and elastic backscattered electrons. The number of electrons emitted by the surface divided by the number of incident electrons is the Total Electron Emission Yield (TEEY, σ). We can also find this same ratio referred as Secondary-Electron Yield (SEY). In this paper, TEEY means the ratio of all electrons emitted by the surface on incident electrons while SEY refers to the ratio between the number of secondary electrons and the number of incident electrons. TEEY being higher than unity is one of the conditions for the development of Multipactor discharge. TEEY varies with incident electron energy and the incident angle [4]. Multipactor development also needs a synchronism between the motion of the electrons and the RF signal. In the case of parallel-plate, the electrons flight time from their emission to the opposite plate has to be an odd number of half periods of the RF signal. If the two previous conditions are satisfied at the same time, the electron density inside the waveguide will grow. This electron cloud can increase the system noise level and the return loss as well as arise locally the temperature [5]. Multipactor can also lead to ionization process and then corona discharge or electrical breakdowns. At last, space RF components can be damaged or destroyed leading to unavailable RF payload for communication. In microwave antenna for fusion reactor application, multipactor breakdowns can damage the antenna waveguides or RF ceramic feedthrough. These RF feedthroughs are used to make pressure transition between the atmospheric pressure outside the reactor and the vacuum vessel pressure (typically 10-5 Pa). These components are safety relevant, since any damage in this vacuum barrier leading to a vacuum leak will stop immediately the reactor. For both space and fusion domains, accurate predictions of multipactor power thresholds would enable to lower the analysis margins without taking any risks. In order to measure microwave components power threshold, experimental methods have been proposed in the literature such as the third harmonic detection technique or the phase nulling [5]. Multipactor simulations codes can also be used to calculate the voltage threshold that would trigger the electron density growth [6]-[7]. A multi-laboratory project has

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made a benchmark of different multipactor simulations codes and has shown uniformity of the power predictions for small gap waveguide structures [8]. These similar power threshold results have been obtained when all simulations used the same TEEY curve. On the other hand, when TEEY model employed to fit experimental TEEY data are used in simulations, the power threshold results are not uniform anymore. Though an evaluation of multipactor threshold sensitivity to TEEY curve variations was considered in order to get a better understanding of the influence of electron emission on multipactor breakdown, then we are able to determine which TEEY models are the most suited to be used to predict multipactor threshold. In this paper, we use a parallel-plate waveguide which is a good model to study small gap structures where the RF wave electric field is essentially homogeneous [9]. A capacitive waveguide geometry with silver material has been chosen in order to use results from [8]. In Sec. II, we have extracted from literature two TEEY curves which respectively represent clean silver samples (evaporated or ion cleaned under UHV conditions) and technical silver samples (exposed to atmosphere). In Sec. III, to evaluate the multipactor threshold sensitivity to TEEY curve variations, we have divided the TEEY curve into seven parameters. For each parameter, several variations have been made based on the dispersion extracted from many TEEY curves found in the literature and our own experimental measurements. In Sec. IV, each variation has been used in multipactor simulations in order to determine multipactor voltage threshold sensitivity to TEEY curve parameters. In Sec. V, these results enabled us to identify which TEEY models are the most suited to be used to predict multipactor power threshold. II. CLEAN AND TECHNICAL TEEY CURVES In this section we establish two reference TEEY curves. To do so we have collected electron-emission silver measurements from the Joy&Joy Database [10], data from [8] and our own data [1]. With this whole literature we got six TEEY data series for clean samples and five for technical samples. We make the distinction between clean and technical samples in light of the dispersion of experimental measurements between both types of samples. The difference between clean and technical samples lies on the presence of layers of hydrocarbon compounds at the surface and the near surface region for technical samples while clean samples are free of these layers. The emitted secondary-electron are generated within the first nanometers under the surface material [1] which explains why these layers have such an influence on SEY. To obtain both the reference TEEY curves presented on the Fig.1, we have calculated the average TEEY at each incident energy available and then smooth the whole TEEY curve.

Fig. 1. Technical (square) and clean (triangle) samples reference TEEY curves obtained from literature. The error bars correspond to the dispersion of the data extracted from literature.

III. MULTIPACTOR THRESHOLD SENSITIVITY TO TEEY CURVE VARIATIONS

Our aim is to determine which part of the TEEY curve most influences the simulated multipactor power threshold. We choose to divide both clean and technical TEEY curves with the following seven parameters (reported in the left column in Table I): behavior of the TEEY curve for energies under 𝐸𝑐1 , energy of the first cross-over 𝐸𝑐1 , behavior of the TEEY curve for energies between 𝐸𝑐1 and 𝐸𝑚𝑎𝑥 , energy of the maximum (𝐸𝑚𝑎𝑥 ), TEEY of the maximum ( 𝜎𝑚𝑎𝑥 ), behavior of the SEY curve for energies above 𝐸𝑚𝑎𝑥 and energy of the second cross-over 𝐸𝑐2 . For each of the seven parameters we determine their variations from literature experimental measurements dispersions. It’s important to tune only one parameter at the time to get coherent results. Hereafter we take the example of the first cross-over energy (𝐸𝑐1 ) in the technical samples reference TEEY curve.

TABLE I SUMMARY OF TEEY DISPERSION EXTRACTED FROM LITERATURE - ENERGY EXPRESS IN EV TEEY parameter dispersion

TEEY parameters

Clean samples

Technical samples

𝐸 < 𝐸𝑐1

± 0.08

± 0.095

𝐸𝑐1

[54 - 74 - 125]

[19 - 24 - 30]

𝐸𝑐1 < 𝐸 < 𝐸𝑚𝑎𝑥

± 0.19

± 0.13

𝐸𝑚𝑎𝑥

[500-800-1000]

[200-250-450]

𝜎𝑚𝑎𝑥

[1.57-1.78-1.94]

[2.06-2.17-2.30]

𝐸𝑚𝑎𝑥 < 𝐸

± 0.20

± 0.13

𝐸𝑐2

[2800-3600-4600]

[3200-3600-4100]

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Clean and technical reference TEEY curves give respectively an average power threshold of 5333±45W and 217±3W. All the simulations use the exact same Spark3D simulation parameters such as the initial number of electrons (10,000 was used), no force uniform DC magnetic field and power loop precision, initial power and maximum power. To evaluate the multipactor threshold sensitivity to TEEY curve variations we compared the relative difference between the average power thresholds for one TEEY curve variation with the average power threshold obtained from simulations with reference TEEY curve (clean or technical depending of the case). Table II synthesis bound power threshold results, we now compare relative difference with simulation precision. Fig. 2. Representation of variations of first cross-over energy for the technical samples reference TEEY curve obtained from literature dispersion. 𝐸𝑐1 ∈ [19 − 𝟐𝟒 − 30]

First is determined the 𝐸𝑐1 for a reference TEEY curve, then we extract the dispersion of all experimental measurements from literature. For this case we have 𝐸𝑐1 ∈ [19 − 𝟐𝟒 − 30] with 24eV the first cross-over energy of the technical samples reference TEEY curve, 19 eV the lower limit and 30 eV the higher limit. From here we create new TEEY curves representing that same dispersion, all other parameters being constant. These curves have to vary only around 𝐸𝑐1 to get coherent results. Fig. 2 shows the created TEEY curves in that case. The same procedure is done for the seven parameters and for both clean and technical TEEY curves which make seventy-three new TEEY curves ready to be used in multipactor simulations codes. IV. POWER THRESHOLD SIMULATIONS From [8], different multipactor simulation codes have been benchmarked and have demonstrated the uniformity of the power predictions for small gap waveguide structures. The benchmark model is a Ku-Band parallel-plate sample with a gap of 0.10 mm, this broadband type sample has been simulated at 12 GHz. The choice of using Spark3D software [11] for our multipactor simulations comes from its speed simulation time (more than four hundreds simulations have been performed). This code has been cross-validated with measurements and other software [8]. We also cross checked some parallel-plate waveguide cases with two other codes, CST Particle (CST PS) [6] and with an internal multipactor 2D code. Spark3D allows importing a TEEY curve; we use this functionality to simulate all our seventy-five different TEEY curves. For each TEEY curve, five identical simulations have been done from which we extract an average power threshold value and simulations precision: between 0.80 % and 2.19 %.

TABLE II SUMMARY OF MULTIPACTOR POWER THRESHOLD SIMULATIONS RESULTS. TEEY parameters

Power threshold variation compared to references Technical Clean samples samples

𝐸 < 𝐸𝑐1

1.56%

1.72%

𝑬𝒄𝟏

8.44%

4.24%

𝑬𝒄𝟏 < 𝑬 < 𝑬𝒎𝒂𝒙

13.75%

8.16%

𝐸𝑚𝑎𝑥

0.31%

0.76%

𝜎𝑚𝑎𝑥

1.56%

1.24%

𝐸𝑚𝑎𝑥 < 𝐸

0.31%

1.24%

𝐸𝑐2

0.98%

0.28%

Therefore we determine two critical parameters, the ones which have relative difference above 2.19 %: first cross-over energy and the curve definition for incident electron energy between the first cross-over and the maximum curve energies. Experimental measurements need to be accurate at those energies in order to get coherent multipactor voltage threshold predictions. V. TEEY MODELS FOR MULTIPACTOR ACCURATE PREDICTIONS We study six TEEY models [12]-[17] to determine which ones are the most suited to be used to predict accurate multipactor power threshold. A suitable TEEY model has to respect certain precision for 𝐸𝑐1 and 𝐸𝑐1 < 𝐸 < 𝐸𝑚𝑎𝑥 . The tolerance ranges for both parameters have been calculated from experimental measurements (precision of ±1𝑒𝑉) and simulations precision (between 0.80% and 2.19%); we work with the worst case. Table III synthesis the main results which show TEEY models capabilities to predict multipactor voltage threshold by being or not under tolerance ranges. TEEY model [14] works for both clean and technical TEEY curves and is the only one between the six TEEY models compared which take into account the first cross-over energy. TEEY model [17] works only for technical TEEY curve.

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TABLE III

EVALUATION OF TEEY MODELS FOR MULTIPACTOR ACCURATE SIMULATION PREDICTIONS

Dispersion from REF TEEY TEEY models

Clean samples

Technical samples

𝐸𝑐1

𝐸𝐶1 < 𝐸 < 𝐸𝑚𝑎𝑥

𝐸𝑐1

𝐸𝐶1 < 𝐸 < 𝐸𝑚𝑎𝑥

Tolerance range

13.5% (±10eV)

1.8 %

8.3% (±2eV)

5.1 %

[Dionne, 12]

27%

6.5%

37.5%

14.3%

[Dekker, 13]

23%

2.7%

2.2%

7.4%

[Sombrin, 14]

4.1%

1.6%

0%

4.9%

[Agarwal, 15]

258%

33%

167%

29.6%

[Seiler, 16]

189%

24%

117%

19.2%

[Vaughan, 17]

84%

12%

2.3%

2.8%

VI. CONCLUSION Multipactor predictions in parallel-plate waveguide need accurate description of the TEEY curve between the first cross-over and the maximum point energies. TEEY models for multipactor simulations must respect these parameters to get coherent voltage threshold like TEEY model [14] does. REFERENCES [1] N. Balcon et al, “Secondary electron emission on space materials: evaluation of the total secondary electron yield from surface potential measurements,” IEEE Trans. Plasma Sci., vol.40, no. 2, pp.282-290, February 2012. [2] M. Preynas et al, “Coupling characteristics of the ITER-relevant lower hybrid antenna in Tore Supra: experiments and modelling,” Nucl. Fusion, vol.51, 16pp, January 2011. [3] J. Roupie et al, "The study of electron emission from aluminum in the very low primary energy range using Monte Carlo simulations," J. Phys. D: Appl. Phys. Vol. 46, 2013. [4] Gineste et al, “A novel experimental setup for the measurement electron backscattering yield,” Meas. Sci. Technol. Vol.25, 7pp, May 2014. [5] R. Udiljak et al, “New Method for Detection of Multipaction,” IEEE Trans. Plasma Sci. vol.31, no.3, pp.396-404, June 2003. [6] G. Romanov, “Update on Multipactors in Coaxial Waveguides using CST Particle Studio,” Proceedings of 2011 Particle Accelerator Conference, 3pp, 2011 [7] V. E. Semenov et al, “Multipactor in rectangular waveguides,” Physics of Plasmas, vol.4, no.3, 2007. [8] J. Puech et al, “Synthesis of the results of the EVEREST project,” MULCOPIM Workshop, 2014. [9] E. Sorolla and M. Mattes, “Multipactor saturation in parallelplate waveguides,” Physics of Plasmas, vol.19, 10pp, July 2012. [10] D. C. Joy, “web.utk.edu/~srcutk/database.doc,” University of Tennessee, latest update on April 2008 [11] J. Perez et al, “High Power Analysis in Coaxial Combline Resonator Filters,” available on fest3d.com/papers.php

[12] G. F. Dionne, “Origin of secondary electron emission yield curve parameters,” Journal of Applied Physics, vol. 46, pp.3347-3351, 1975. [13] R.G. Lye and A.J. Dekker, “Theory of secondary emission”, Phys. Rev. vol.107, pp.977-981, 1957. [14] J. Sombrin, “Claquage hyperfréquence et effet multipactor dans les satellites,” OHD 93, published results have been obtained with the Sombrin TEEY model. Its development is explained on a CNES internal report. [15] B.K. Agarwal, “Variation of secondary emission with primary electron energy,” Proc. Phys. Soc. vol.71, pp.851-852, 1958. [16] H. Seiler, “Secondary electron emission in the scanning electron microscope,” J. Appl. Phys. vol.54, no.11, November 1983. [17] J. Rodney and M. Vaughan, “A New Formula for Secondary Emission Yield,” IEEE Transactions on electronic devices, vol.36, no.9, pp.1963-1967, 1989.

APPENDIX - SOMBRIN TEEY FORMULA J. Sombrin has developed the following TEEY model in the 90s from which he obtained the power threshold results published in [14]. The formula is meant to be accurate on the first cross-over energy. Its value is directly considered in the formula (2) used to calculate the total electron emission yield, σ, with (1):

𝜎=

𝐄𝒊 ) 𝑬𝒎𝒂𝒙 2𝐸 𝐄 1+( 𝒊 ) 𝑬𝒎𝒂𝒙

2.𝜎𝑚𝑎𝑥 .(

𝐸

.

(1)

With,

𝐸=

2 𝑙𝑛 (𝜎𝑚𝑎𝑥 − √𝜎𝑚𝑎𝑥 −1)

𝑙𝑛(

𝐸𝐶1 ) 𝐸𝑚𝑎𝑥

.

𝐸𝑖 is the incident electron energy. Formulas (1) and (2) make Sombrin TEEY model.

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(2)