ISSN 1063-780X, Plasma Physics Reports, 2016, Vol. 42, No. 6, pp. 610–618. © Pleiades Publishing, Ltd., 2016. Original Russian Text © A.S. Sakharov, V.A. Ivanov, M.E. Konyzhev, 2014, published in Uspekhi Prikladnoi Fiziki, 2014, Vol. 2, No. 5, pp. 476–485.
APPLIED PHYSICS
Particle-in-Cell Simulation of Multipactor Discharge on a Dielectric in a Parallel-Plate Waveguide A. S. Sakharova, V. A. Ivanova, b, and M. E. Konyzheva a
Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia b National Research Nuclear University “MEPhI,” Kashirskoe sh. 31, Moscow, 115409 Russia e-mail:
[email protected] Received September 17, 2014
Abstract—An original 2D3V (two-dimensional in coordinate space and three-dimensional in velocity space) particle-in-cell code has been developed for simulation of multipactor discharge on a dielectric in a parallelplate metal waveguide with allowance for secondary electron emission (SEE) from the dielectric surface and waveguide walls, finite temperature of secondary electrons, electron space charge, and elastic and inelastic scattering of electrons from the dielectric and metal surfaces. The code allows one to simulate all stages of the multipactor discharge, from the onset of the electron avalanche to saturation. It is shown that the threshold for the excitation of a single-surface multipactor on a dielectric placed in a low-profile waveguide with absorbing walls increases as compared to that in the case of an unbounded dielectric surface due to escape of electrons onto the waveguide walls. It is found that, depending on the microwave field amplitude and the SEE characteristics of the waveguide walls, the multipactor may operate in two modes. In the first mode, which takes place at relatively low microwave amplitudes, a single-surface multipactor develops only on the dielectric, the surface of which acquires a positively potential with respect to the waveguide walls. In the second mode, which occurs at sufficiently high microwave intensities, a single-surface multipactor on the dielectric and a two-surface multipactor between the waveguide walls operate simultaneously. In this case, both the dielectric surface and the interwall space acquire a negative potential. It is shown that electron scattering from the dielectric surface and waveguide walls results in the appearance of high-energy tails in the electron distribution function. DOI: 10.1134/S1063780X16060064
1. INTRODUCTION Suppression of microwave discharges in the vacuum transmission lines of high-power microwave devices is a very challenging problem in various fields of science and technology, such as assurance of reliable operation of space microwave communication systems [1, 2], creation of new types of high-power microwave sources [3], and development of schemes for microwave launching into nuclear fusion magnetic confinement devices [4, 5]. Microwave discharges deteriorate the transmission properties of vacuum waveguides; lead to intermodulation and generation of microwave harmonics; and may result in damages of the elements of transmission lines, including destruction of the input and output dielectric windows [6–8]. An important stage of a microwave discharge on a dielectric or metal surface is the so-called electron multipactor—an electron avalanche caused by secondary electron emission (SEE) from the surface bombarded by electrons accelerated in the microwave field. Two main types of multipactor discharge are traditionally considered in the scientific literature: sin-
gle-surface multipactor on a dielectric and two-surface multipactor between two metal walls [9–12]. In the classical single-surface multipactor [10] (Fig. 1a), the external microwave electric field E0sinωt is directed along the dielectric surface and the emitted electrons return back to the surface under the action of the restoring force F, caused by the positive charge accumulated on the dielectric. For this type of discharge to develop, it is necessary that the electron oscillation energy in the microwave field εosc =
(eE 0 / ω) 2 /2me be higher than the first crossover energy ε1 (the energy above which the secondary emission yield (SEY) δ is larger than unity). In the simplest model of a two-surface multipactor [11, 12] (Fig. 1b), the external microwave field is directed perpendicular to the waveguide walls and the discharge develops if εosc ≥ ε1 and the electron transit time between the walls satisfies the resonance condition ttransit ≈ (2n + 1)π/ω. The development of a multipactor discharge on a dielectric surface results in the formation of an electron sheath near this surface. If the dielectric is adjacent to the waveguide walls, the properties of the
610
PARTICLE-IN-CELL SIMULATION OF MULTIPACTOR DISCHARGE
611
e
y
(а) 5
εemit
7
4
3
2
E
6 λg
E0sinωt
H10 mode e
b = 6 cm
εinc e
1
(а)
F
y
Fig. 2. (a) Scheme of the experiment (side view): (1) evacuated waveguide (p ~ 10–6 Torr), (2) microwave discharge plasma, (3) 24-mm-diameter circular below-cutoff waveguide, (4) dielectric plate, (5) diagnostic window, (6) photo camera, and (7) 10-mm-diameter circular belowcutoff waveguide; (b) waveguide cross section. The freespace wavelength is λ0 = 15.4 cm, and the waveguide wave-
(b)
e E0sinωt
εinc e e
length is λg = λ 0 (1 − (λ 0 /2a)2 )1/2 ≈ 20 cm.
e z
Fig. 1. Two types of multipactor discharge: (a) single-surface multipactor on a dielectric and (b) two-surface multipactor between two metal walls.
sheath can be affected by these walls. Moreover, at sufficiently high microwave intensities, both types of multipactor discharge can develop simultaneously. Hence, it is of interest to consider such a combined multipactor discharge and examine how the above two types of multipactor discharge affect one another. To take these effects into account in simulations, the numerical code should be at least two-dimensional in coordinate space. On the other hand, secondary electrons are emitted at different angles with respect to the surface and the SEY depends on the angle at which the primaries are incident onto the surface. This requires taking into account all three components of the electron velocity. Therefore, we have developed an original 2D3V (two-dimensional in coordinate space and threedimensional in velocity space) particle-in-cell (PIC) code for modeling the effect of the waveguide walls on a single-surface multipactor on a dielectric [13, 14]. The code is based on solving the equations of electron motion in the microwave field and the self-consistent field of the electron space charge with allowance for SEE from the dielectric surface and waveguide walls, finite temperature of secondary electrons, and elastic PLASMA PHYSICS REPORTS
E a = 12 cm
z
εemit
(b)
Vol. 42
No. 6
2016
and inelastic electron scattering from the dielectric and metal surfaces. The code makes it possible to simulate all stages of multipactor development, from the onset of the electron avalanche to saturation. 2. PHYSICAL MODEL This study was motivated by the experiments carried out at the Plasma Physics Department of the Prokhorov General Physics Institute, Russian Academy of Sciences. The experiments were performed on the BRUS device [15–18]. The scheme of the experiment is shown in Fig. 2. The dielectric target (LiF crystal, NaCl crystal, or SiO2 plate) was placed in the antinode of the H10 standing mode of a 6 × 12-cm evacuated (p ~ 10–6 Torr) rectangular waveguide. The input microwave power at the frequency 1.95 GHz (λ0 = 15.4 cm) was up to 2 MW, and the microwave pulse duration was τ < 20 μs. At high microwave powers (Pimp ≥ 1 MW), three stages of the discharge on the dielectric target were observed: (i) multipactor discharge (which lasted for several microseconds), (ii) filamentary microwave breakdown (in which up to 70% of the microwave power was absorbed), and (iii) plasma-flare microwave discharge (in which the absorption coefficient dropped to 20−30%) [18]. At microwave powers slightly above the multipactor threshold, only the first stage was observed. The onset of a multipactor discharge was detected by the appearance of a feeble glow on the dielectric surface
SAKHAROV et al.
and the current onto the electron collector installed under the dielectric plate [15]. The experiments have confirmed that single-surface multipactor on a dielectric develops at electron oscillation energies exceeding ε1. The simulation geometry was chosen to be similar to the geometry of the above experiment (see Fig. 3). The problem is solved in a rectangular box 0 < y < h, 0 < z < zmax. The z coordinate is directed along the waveguide. The metal walls are at y = 0 and y = h. Along the x axis, the problem is homogeneous. In fact, such geometry corresponds to a parallel-plate waveguide unbounded in the x direction. An infinitely thin dielectric plate is placed at z = 0. The external microwave electric field E0sinωt is directed along the y axis and is independent of z. The microwave magnetic field is disregarded. This implies that we consider a region located near the antinode of the standing wave (|z| ≤ c/ω). The system is assumed to be symmetric with respect to z = 0. The main assumptions adopted in calculating the electric field and particle motion are considered below. 2.1. Electric Field (i) The electric field is assumed to be the sum of the external microwave field and the electrostatic field produced by the electron space charge, E = E0sinωt – ∇φ, where the electrostatic potential φ satisfies Poisson’s equation,
∂ 2ϕ ∂ 2ϕ (1) + = 4π ene. ∂y 2 ∂z 2 (ii) On the metal walls, the potential is zero, and, at z = zmax, we set ∂φ/∂z = 0. The boundary condition on the dielectric is ∂ϕ (2) = − 4πσ( y), ∂ z z →0 where σ(y) is the surface charge density formed on the dielectric surface in the course of multipactor discharge. (iii) Microwave reflection from the electron cloud is ignored, which can be done if the following condition (which should be proven in the course of simulations) is satisfied:
ω n dz n = meω . (3) e cr 2 c 4π e (iv) The multipactor discharge on the dielectric is concentrated within an extremely narrow region adjacent to the dielectric surface (z ≤ 10–3 cm). On the other hand, the electric field produced by the uncompensated surface charge accumulated on the dielectric penetrates into the waveguide volume up to z ~ h. Therefore, to save computer resources, we used a nonuniform numerical mesh over z: Δzi = (1 + αzi)Δz0,
∫
2
y Metal
h
Dielectric
612
Free boundary
E0sinωt 0
zmax
Metal
z
Fig. 3. Geometry of the model.
where α = const > 0 and Δz0 is the step over z just near the dielectric surface.
2.2. Particles (i) The electrons are simulated by model particles having the same charge-to-mass ratio as the actual electrons. The model particles have all three velocity components. (ii) The particles incident on the dielectric surface and metal walls are absorbed or reflected with given probabilities. (iii) The particle’s impact is accompanied by the emission of model particles with the secondary emission yield (SEY) δ(ε, θ) depending on the primary’s energy ε and the angle of incidence θ. In this study, we used a simplified version of Vaughan’s formula for the SEY [19] with a zero cutoff energy (ε0 = 0),
δ = δ m(θ)(V exp(1 − V )) κ,
(4)
where V = ε/ ε m(θ) , κ = 0.62 for V < 1, κ = 0.25 for V > 1, δm(θ) = (1 + θ 2 /2π)δ m0 , and εm(θ) = (1 + θ 2 / π)ε m0 , with δm0 and εm0 being the peak value of the SEY at θ = 0 and the incident energy corresponding to this peak, respectively. (iv) The secondaries have thermal (Maxwellian) distributions over velocities with the temperatures Ted (dielectric) and Tem (metal). (v) The velocities of the emitted particles (both secondary and reflected ones) are distributed over directions according to the cosine law dN/dΩ ~ cosθ, where dΩ is the element of the solid angle and θ is the angle between the velocity direction and the normal to the surface. (vi) The particles crossing the right boundary z = zmax are mirror reflected. (vii) The number of model particles was varied from 105 (in test simulations) to 2 × 10 6. (viii) In order for the number of model particles N in the stage of multipactor development not to grow above a prescribed maximum value, one-half of the particles were removed if their number exceeded a certain threshold value N1 (N → N/2 if N > N1). In this PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
PARTICLE-IN-CELL SIMULATION OF MULTIPACTOR DISCHARGE
case, the charges and masses of the remaining particles were doubled [20]. (ix) The discharge was initiated by injecting seed particles from the dielectric surface at t = 0.
102 (а) 101 S/ncr z0
3. SIMULATION RESULTS 3.1. One-Dimensional Simulations
3.2. Two-Dimensional Simulations
No. 6
102 103
2016
(b)
102 n0/nc
101 100 101 102 103 102 (c)
δz/z0
101 100 101 102
3.2.1. Increase in the threshold for the excitation of a single-surface multipactor. Figure 5 presents results of 2D simulations of a multipactor discharge on a LiF crystal (δm0 = 7.5) in the presence of bounding walls with different SEYs. The interwall distance is h = 1.5 cm. At a low electron oscillation energy (εosc = 18 eV, Fig. 5a), drift of secondary electrons onto the absorbing (δm0 = 0) or low-emitting (δm0 = 0.5) walls results in the suppression of the single-surface multipactor on the dielectric, whereas in the presence of copper walls with a moderate SEY (δm0 = 2), the multipactor develops even at microwave intensities only slightly exceeding the threshold intensity in the 1D case (ε1D thr ≈ 16 eV). At a moderate oscillation energy (εosc = 50 eV, Fig. 5b), the single-surface multipactor develops for any wall material, the areal electron density in the saturated regime being practically independent of the wall material, although saturation in the case of fully absorbing walls (δm0 = 0) is reached somewhat later. Finally, at a very high oscillation energy (εosc = 450 eV, Fig. 5c), secondary electrons drift onto the walls so fast that absorbing walls again suppress the Vol. 42
100 101
Typical results obtained using a 1D3V version of the code [21] for the electron oscillation energy εosc = 450 eV, much exceeding the threshold oscillation energy (ε1D thr ≈ 16 eV) for the onset of a single-surface multipactor on a LiF crystal are presented in Fig. 4. The discharge was initiated by injecting seed electrons with an areal density of Sinj = 0.05ncrz0 = 0.8 × 107 cm2 and a Maxwellian distribution over velocities (Tseed = 1 eV) from the dielectric surface. It is seen from Fig. 4 that, after the avalanche phase, the discharge reaches a dynamic saturation, in which the surface charge density S, the maximum electron density n0, and the effective width of the electron sheath defined as δz = S/n0 oscillate with the frequency equal to 2ω. Although the electron density in the saturation stage is much higher than the critical density ncr, the electron sheath is practically transparent for microwave radiation, because condition (3) is satisfied with a large margin. As the electron density grows, the region occupied by the electron space charge shrinks to ~10–3 cm.
PLASMA PHYSICS REPORTS
613
0
2
4
ωt/2π
6
8
10
Fig. 4. Typical time evolution of the (a) surface charge density S, (b) electron density n0 at z = 0, and (c) effective width of the electron sheath δz = S/n0 in a 1D single-surface multipactor operating on the surface of a LiF crystal (δm0 = 7.5, εm0 = 1000 eV, ε1 =14.5 eV). Here, ω = 12.25 × 1010 s–1 (λ0 = 15.4 cm, ncr = 4.7 × 1010 cm–3), the electron oscillation energy is εosc = 450 V, the temperature of secondary electrons is Ted = 1 eV, the characteristic inhomogeneity scale of the electron density is z0 = vTe/ω ≈ 3.4 × 10–3 cm, and the areal density of seed electrons injected from the dielectric surface is Sinj = 0.05ncrz0 = 0.8 × 107 cm2.
development of a single-surface multipactor on a LiF crystal. Figure 6 shows the threshold oscillation energy for the development of a single-surface multipactor on a LiF crystal in the presence of bounding walls as a function of the interwall distance h. The SEE properties of the walls are the same as in Fig. 5. The domains
614
SAKHAROV et al.
εthr, eV
102 (a)
101
103
100 101 102 103
0
2
εosc = 18 eV
2
1
1
102
3
3
50
100
150
102
200
250
300
101
0
0.5
ε1D thr ≈ eV 1.0
1.5
2.0
(b)
2.5
3.0 h, cm
S/ncr z0
101 Fig. 6. Threshold oscillation energy for the development of a single-surface multipactor on a LiF crystal in the presence of bounding walls as a function of the interwall distance h for the same SEE properties of the bounding walls as in Fig. 5: (1) fully absorbing walls, (2) soot, and (3) copper. The areal density of seed electrons is Sinj = 0.05ncrz0.
100 3
2
1
101 102 103
εosc = 50 eV 0
20
40
102
60
80
100
(c)
101 100
3
101
εosc = 450 eV
2
102 103
1 0
2
4
ωt/2π
6
8
10
Fig. 5. Influence of the bounding walls on the development of a single-surface multipactor. Time evolution of the y-averaged surface charge density on a LiF surface at different electron oscillation energies for walls with different SEE properties: (1) fully absorbing walls (δ = 0), (2) soot (δm0 = 0.5, εm0 = 500 eV), and (3) copper (δm0 = 2, εm0 = 500 eV). The interwall distance is 1.5 cm; the areal density of seed electrons is Sinj = 0.05ncrz0; and the temperatures of secondary electrons emitted from the dielectric and metal surfaces are Ted = 1 eV and Tem = 3 eV, respectively.
corresponding to the onset of a multipactor lie to the right of the corresponding curves. It is seen from the figure that the threshold oscillation energy εthr depends substantially on the wall material at interwall distances of h ≤ 2 cm (i.e., in a low-profile waveguide). At h ≥ 3 cm, εthr is practically independent of the wall material and is close to ε1D thr . It should be noted, however, that the threshold also depends on the areal density of seed electrons, approaching ε1D thr with increasing Sinj.
Moreover, after the discharge has reached saturation, the influence of the walls decreases and the interwall distance can be reduced substantially without quenching the single-surface multipactor even in the case of fully absorbing walls. 3.2.2. Change in the potential of the dielectric surface. In a 1D single-surface multipactor, the total negative surface charge in the electron sheath is exactly equal to the positive surface charge accumulated on the dielectric surface; therefore, the total surface charge density is zero. In the 2D case, a fraction of emitted electrons escape onto the metal walls, so it is natural to expect that the multipactor will acquire an excess positive charge and the electric potential of the surface will grow until it reaches the maximum electron drift energy equal to 4εosc. Figure 7 shows the time evolution of the y-averaged relative (with respect to the metal walls) electric potential ϕ 0 of a LiF surface bounded by copper walls for h = 1.5 cm and two values of the electron oscillation energy. It is seen that, for εosc = 24.5 eV, the electric potential of the dielectric surface, as was expected, grows monotonically in time, whereas for εosc = 128 eV, it drops to about –170 V. Figure 8 shows the 2D distributions of the electric potential in the simulation region for εosc = 24.5 and 128 eV at different times. It is seen that, for εosc = 24.5 eV, the positive potential formed on the dielectric surface penetrates into the waveguide up to z ≈ h. For εosc = 128 eV, the electric potential in the region adjacent to the dielectric surface rapidly drops and, then, the region with the negative potential expands along the z axis until it occupies the entire simulation region. 3.2.3. Combined (single-surface + two-surface) multipactor discharge. Figure 9 shows the time-averaged z profiles of the potential near a LiF surface in the PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
PARTICLE-IN-CELL SIMULATION OF MULTIPACTOR DISCHARGE ,V ϕ 0 100
,V ϕ 0 50
εosc = 24.5 eV
80
0
60
50
40
100
20
150
0
200
400
600
800
1000 ωt/2π
200
615
εosc = 128 eV
0
50
100
150
200
250
300 ωt/2π
Fig. 7. Time evolution of the y-averaged relative (with respect to the metal walls) electric potential ϕ 0 of a LiF surface bounded by copper walls for h = 1.5 cm and two values of the electron oscillation energy.
ϕ, V 40 30 20 10 0
ϕ, V 160 120 80 40 0 40
εosc = 24.5 eV ωt/2π = 100
10 z, mm 20 30 0
15 10 5 y, mm
εosc = 128 eV ωt/2π = 20
10 z, mm 20 30 0
ϕ, V 800 600 400 200 0 200
15 10 5 y, mm
εosc = 128 eV ωt/2π = 100
y, mm 15 10 5
10 z, mm 20 30 0
Fig. 8. 2D distributions of the electric potential in the simulation region for εosc = 24.5 and 128 eV at different times (a LiF surface bounded by copper walls).
1D case (curve 1) and the difference between the yaveraged potential ϕ(z) near the LiF surface bounded by copper walls and the average potential ϕ(0) on this surface (curve 2) for εosc = 128 eV and h = 1.5 cm. It is seen that, although the potential of the dielectric surface becomes negative with respect to the metal walls, both profiles almost coincide, i.e., in the 2D case, the dielectric surface, as before, has a positive charge and the structure of the electron sheath near the dielectric remains practically unchanged.
face, which means that the two-surface multipactor begins to develop near the dielectric surface and then gradually expands along the z axis. At ωt/2π = 100, the bunches have already become almost uniform along the z axis. Here, the single-surface multipactor is seen as a very narrow dark strip adjacent to the left boundary.
Analysis of the distribution of the electron density in the simulation region shows that the drop in the electric potential in the interwall space is caused by the development of a two-surface multipactor, the negative space charge of which also leads to the drop in the electric potential on the dielectric surface. Figure 10 shows the distributions of model particles in the simulation region for εosc = 128 eV at two times. At ωt/2π = 20, one can see two electron bunches, the densities of which decrease with distance from the dielectric sur-
∫
PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
The dynamics of electron bunches in the two-surface multipactor is illustrated in Fig. 11, which shows the relief of the function S1(y, t) = z max
z1
(ne ( y, z, t )/ ncr )dz / z 0 in the (y, t) plane within the
time intervals ωt/2π = 20−24 and 100−104 (Figs. 11a and 11b, respectively). Here, zmax = 3 cm and integration over z is performed from z1 = 0.2 cm in order to exclude the contribution from the electron sheath of the single-surface multipactor on the dielectric. It is seen that, in the early stage of the two-surface multipactor (Fig. 11a), the bunches are periodically injected from both walls and then propagate into the interwall
616
SAKHAROV et al.
0
z, cm 0.010
0.005
1 2 3 4
1 2
5 ϕ(z) ϕ(0), V
Fig. 9. Time-averaged z profiles of the potential near a LiF surface in the 1D case (curve 1) and the difference between the y-averaged potential ϕ(z) near the LiF surface bounded by copper walls and the average potential ϕ(0) on this surface (curve 2) for εosc = 128 eV and h = 1.5 cm.
space, gradually spreading due to the finite electron temperature and electrostatic repulsion between the bunch electrons. In Fig 11b, the two-surface multipactor has already reached saturation and transformed into two specific single-surface multipactors operating independently on each waveguide wall. It should be noted that, although the saturated multipactors on the dielectric and metal surfaces actu-
ally operate independently of one another, the singlesurface multipactor on the dielectric accelerates the development of the two-surface multipactor, serving as a source of seed electrons for the latter. For the same number of initial electrons in the interwall space, but without a dielectric, the two-surface multipactor develops at an appreciably slower rate. 3.2.4. Influence of electron scattering on the electron distribution function. Finally, we have considered the influence of electron reflection (scattering) from the dielectric and metal surfaces on the electron energy distribution function (EEDF). The coefficients of elastic and inelastic reflections from the dielectric were assumed to be R = η = 0.05, and those on the metal walls, R = η = 0.1. Upon elastic reflection, the energy of the reflected electron εref was set equal to the energy of the incident electron εinc, whereas upon inelastic scattering, it could take any value between zero and εinc with equal probabilities. In both cases, the reflected electrons were distributed over velocity directions according to the law dN/dΩ ~ cosθ (see Section 2.2). Figure 12 shows the distribution functions of electrons incident on the dielectric surface (curves 1', 1) and bounding metal walls (curves 2', 2), calculated for two values of εosc without and with allowance for electron reflection (dashed and solid curves, respectively). It is seen that the introduction of an even small scattering that insignificantly affects the general properties of the multipactor results in the appearance of high-energy tails in the EEDF, which extend up to 30εosc. The effective temperature of S1 10 5 3 2 1.75 1.50 1.00 0.75 0
(а)
1.5 1.0
y, cm
1.5 ωt/2π = 20
0.5
1.0 0.5
y, cm
0 20
0
21
1.5
22 ωt/2π
23
24 S1 300 150 100 70 40 30 20 10 0
(b) 1.5 ωt/2π = 100 0.5 0 0
0.5
1.0
1.5 z, cm
2.0
2.5
3.0
Fig. 10. Distributions of model particles in the simulation region for εosc = 128 eV at two times (a LiF surface bounded by copper walls, h = 1.5 cm).
y, cm
1.0 1.0 0.5 0 100
101
102 ωt/2π
103
104
Fig. 11. Dynamics of electron bunches in the two-surface multipactor within the time intervals ωt/2π = (a) 20–24 and (b) 100–104 (a LiF surface bounded by copper walls, h = 1.5 cm, εosc = 128 eV). PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
PARTICLE-IN-CELL SIMULATION OF MULTIPACTOR DISCHARGE
617
100
F, arb. units
101
εosc = 24.5 eV
1
εosc = 128 eV
102 1′ 2
103 104 2 ′
2
105 106
1′ 2 ′ 0
100
200
300
400
500
600 0 ε, eV
1000
1 2000
3000
4000
Fig. 12. Distribution functions of electrons incident on the dielectric (LiF) surface (curves 1', 1) and bounding metal (Cu) walls (h = 1.5 cm) (curves 2', 2), calculated for two values of εosc without and with allowance for electron reflection (dashed and solid curves, respectively).
the tails is about 3εosc. It is also seen that the development of the two-surface multipactor at εosc = 128 eV results in a relative increase in the number of electrons incident onto the metal walls as compared to those incident onto the dielectric.
ACKNOWLEDGMENTS This work was supported by the Program of Fundamental Research of State Academies of Sciences of the Russian Federation for 2014–2016 (state contract no. 01200953486).
4. CONCLUSIONS
REFERENCES
(i) A 2D3V PIC code has been developed for simulation of multipactor discharge on a dielectric placed in a parallel-plate waveguide with allowance for SEE from the dielectric surface and waveguide walls, finite temperature of secondary electrons, electron space charge, and elastic and inelastic reflection of electrons from the dielectric and metal surfaces. (ii) It is shown that the threshold for the development of a single-surface multipactor on a dielectric placed in a low-profile waveguide with absorbing walls increases as compared to that in the case of an unbounded dielectric due to escape of electrons onto the bounding walls. (iii) It is found that, depending on the amplitude of the microwave field and SEE properties of the waveguide walls, the discharge can operate in two modes: (a) a single-surface multipactor on the dielectric, in the course of which the dielectric acquires a positive potential with respect to the waveguide walls and (b) a combined (single-surface + two-surface) multipactor, in which the dielectric and the interwall space acquire a negative potential. (iv) It is shown that taking into account electron scattering from the dielectric surface and waveguide walls results in the appearance of high-energy tails in the EEDF. PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
1. J. Puech, D. Anderson, M. Buyanova, D. Dorozhkina, U. Jordan, L. Lapierre, M. Lisak, V. Semenov, J. Sombrin, and R. Udiljak, in Proceedings of the 5th International Workshop on Multipactor, Corona, and Passive Intermodulation in Space RF Hardware (MULCOPIM2005), Noordwijk, 2005, p. 235. 2. F. Piro and Y. Brand, in Proceedings of the 8th European Conference on Antennas and Propagation, Hague, 2014 (European Microwave Association, Louvain-laNeuve, 2014), p. 1643. 3. M. Thumm, State-of-the-Art of High Power GyroDevices and Free Electron Masers (Karlsruhe Inst. of Technology, Karlsruhe, 2013). 4. A. P. H. Goede, W. A. Bongers, B. S. Q. Elzendoorn, M. F. Graswinckel, and M. R. de Baa, Fusion Eng. Design 85, 1117 (2010). 5. G. Giruzzi, M. Lennholm, A. Parkin, G. Aiello, M. Bellinger, J. Bird, F. Bouquey, H. Braune, A. Bruschi, P. Butcher, R. Clay, E. De La Luna, G. Denisov, T. Edlington, J. Fanthome, et al., Nucl. Fusion 51, 063033 (2011). 6. A. Neuber, J. Dickens, D. Hemmert, H. Krompholz, L. L. Hatfield, and M. Kristiansen, IEEE Trans. Plasma Sci. 26, 296 (1998). 7. B. W. Hoff, P. J. Mardahl, R. M. Gilgenbach, M. D. Haworth, D. M. French, Y. Y. Lau, and M. Franzi, Rev. Sci. Instrum. 80, 094702 (2009). 8. X.-W. Hao, G.-J. Zhang, H.-J. Huang, J.-Y. Fang, C.-H. Chen, and W.-H. Huang, in Proceedings of the 24th International Symposium on Discharges and Electrical Insulation in Vacuum, Braunschweig, 2010, p. 113.
618
SAKHAROV et al.
9. J. R. M. Vaughan, IEEE Trans. Electron. Dev. 35, 1172 (1988). 10. R. A. Kishek and Y. Y. Lau, Phys. Rev. Lett. 80, 193 (1988). 11. R. A. Kishek, Y. Y. Lau., L. K. Ang, A. Valfells, and R. M. Gilgenbach, Phys. Plasmas 5, 2120 (1998). 12. V. E. Semenov, E. I. Rakova, D. Anderson, M. Lisak, and J. Puech, Phys. Plasmas 14, 033501 (2007). 13. A. S. Sakharov, V. A. Ivanov, Yu. A. Tarbeeva, and M. E. Konyzhev, in XXXVIII International Zvenigorod Conference on Plasma Physics and Controlled Fusion, Zvenigorod, 2011, Book of Abstracts, p. 319. 14. A. S. Sakharov, V. A. Ivanov, and M. E. Konyzhev, in Proceedings of the VIII International Workshop “Microwave Discharges: Fundamentals and Applications,” Zvenigorod, 2012, p. 75. 15. G. M. Batanov, V. A. Ivanov, M. E. Konyzhev, and A. A. Letunov, JETP Lett. 66, 170 (1997). 16. V. A. Ivanov, M. E. Konyzhev, V. P. Gavrilenko, and E. Oks, in Proceedings of the 5th International Workshop
17.
18.
19. 20. 21.
on Multipactor, Corona, and Passive Intermodulation in Space RF Hardware (MULCOPIM-2005), Noordwijk, 2005, p. 169. V. A. Ivanov, A. S. Sakharov, and M. E. Konyzhev, in Proceedings of the VII International Workshop “Strong Microwaves: Sources and Applications,” Nizhny Novgorod, 2008, Vol. 2, p. 620. V. A. Ivanov, A. S. Sakharov, and M. E. Konyzhev, in Proceedings of the VII International Workshop “Microwave Discharges: Fundamentals and Applications,” Hamamatsu, 2009, p. 34. J. R. M. Vaughan, IEEE Trans. Electron Dev. 36, 1963 (1989). I. A. Kossyi, G. S. Luk’yanchikov, V. E. Semenov, N. A. Zharova, D. Anderson, M. Lisak, and J. Puech, J. Phys. D 43, 345206 (2010). A. S. Sakharov, V. A. Ivanov, Yu. A. Tarbeeva, and M. E. Konyzhev, Plasma Phys. Rep. 38, 1090 (2012).
Translated by A. Sakharov
PLASMA PHYSICS REPORTS
Vol. 42
No. 6
2016
