Preliminary study on possible multipactor effects inside the output

It is concluded from the previous section that the reason for the melting of the two coupling metal rods when the glass dome is replaced by a ceramic one cannot be due to the RF current, which is only of the order of 40 Amps. It seems that if the RF current in the coupling loop was the reason for the loop melting the small diameter input leads should melt first.

Other possible explanations for the observed melting could be a spurious resonance due to the ceramic window, anomalous field distributions around the loop with higher order modes, multipactor effects and plasma discharge, possibly affected by any stray magnetic field in the region of the loop. The present hypothesis is that the localised multipactor causes some gas evolution and a gas discharge is sustained by the RF power generated by the magnetron and this melts the surface of the rods. The computer modelling has therefore been concentrated on investigating the possibility of multipactor

in the output system.

The Multipactor discharge is a resonant vacuum discharge frequently observed in microwave systems, such as RF windows, accelerator structures, microwave tubes and other devices. The underlying mechanism is an avalanche caused by secondary electron emission. Primary electrons accelerated by RF fields upon impact on a surface, release a large number of secondary electrons, which may in turn be accelerated by the RF fields and impact again, releasing even more electrons, and so on. The discharge can take place on a single surface or between two surfaces [1–4]. Multipactor is usually undesirable. It can dissipate substantial amounts of energy or detune a microwave signal. The discharge also heats the surface, possibly increasing noise level and causing damage by destroying vacuum.

What concerned us most is how the multipactor may develop on the metal rods of the output system of the S band magnetron and the electro-magnetic conditions which accompany it. Figures 4.11(a) to 4.11(b) show vector plots of the electric field excited inside the output system when a 3GHz RF signal is applied through the input ports.

Figure 4.11(b) is half RF period later than Figure 4.11(a).

The multipactor possibilities between different metal rods and surfaces can be ana-lyzed by calculating the electron transit time in the first instance. Because the electric field distribution between the metal rods is not uniform, strict analytical calculation of the electron transit time in this area is not feasible. A simple calculation has been car-ried out to estimate the electron transit distance within half RF period. The RF voltage oscillation between the central support rod and the coupling rod is shown in Figure 4.12, with peak value of 4.7kV.

The distance between the two rods is 10.98mm. Assuming the electric field between the central support rod and the coupling rod is uniformly distributed. We obtain Emax = 4.7kV /10.98mm = 428kV /m. Within one half of the RF period, the distance the electron

(a) (b)

Figure 4.11: A cross section of the electric vector field just below the dipole antenna where the melting points are situated. (a) t=1.660ns (b) t=1.820ns

Figure 4.12: Voltage oscillation between the central support rod and one of the coupling rods. The applied signal operates at 2.998GHz with peak power of 4MW.

can travel is calculated using Eq. 4.6.

s = v₀t +1

2at² (4.6)

where v₀ is the initial velocity, t equals to half RF period and a is the acceleration caused by the electric field.

In computer modelling, secondary electrons are released from the coupling rod with initial energy 0.5eV. Therefore the initial velocity can be obtained, v₀ = 4.2e5m/s. With operating frequency 2.998GHz, the half RF period is t = 1/(2f ) = 0.167ns. For a crude estimation, considering only the effect of the electric field, the acceleration speed of the electron is a = eE/m = 7.5e16m/s², where e is the electron charge and m its mass. The approximate distance an electron can travel within half RF period is therefore s ≈ 1mm.

Due to the complexity of the electromagnetic field distribution, computer modelling seems to be the only feasible approach to identify the areas where multipactor might take place and to discover the required electro-magnetic field conditions.

In the output system, all the surfaces of the metal rods and the waveguides are set to be able to emit secondary electrons when struck by primary electrons. A typical value for the secondary emission coefficient of copper has been used for the metal rods and the waveguides, its maximum value is 1.3 with a primary energy of 500 eV.

Simulations with different levels of RF input power and different emission phases of the primary electrons have been conducted. Simulations have shown that the primary electrons released from the melting regions seem to knock off a large number of secondary electrons at the point where the central support rod joins the dipole; also the secondary electrons then back bombard the melted region. Simulations have also shown that the yield of the secondary electrons is more sensitive to the phases of the RF field than to the power level of the RF field. The phase of 0.5π seems to be a favorite one, which generates the largest number of secondary electrons which then keep bombarding the coupling rods. This process is shown in Figure 4.13, where red dots represent primary electrons and purple dots the secondaries. The dome is ceramic, with ǫr= 9.

In order to compare the effect of different domes, simulation with a glass dome has been carried out with the same conditions as those for the ‘ceramic’ simulation. Fig-ure 4.14 shows the electron bombardment when a glass dome is present. Comparing Figure 4.13(f) with Figure 4.14(f), it seems that the secondary electron cloud is more

(a) (b)

(c) (d)

(e) (f)

Figure 4.13: Snap shots of electron clouds (RF power: 4MW; Phase of RF field while primary electrons are released: 0.5π; Ceramic dome: ǫ_r = 9 ; Red colour represents primary electrons; Purple colour represents secondary electrons.) (a) t= 1.940ns (b) t=2.500ns (c) t=2.900ns (d) t= 3.140ns (e) t=3.300ns (f) t=4.000ns

(a) (b)

(c) (d)

(e) (f)

Figure 4.14: Snap shots of electron clouds (RF power: 4MW; Phase of RF field while primary electrons are released: 0.5π; Glass dome: ǫ_r= 4 ; Red colour represents primary electrons; Purple colour represents secondary electrons.) (a) t= 1.940ns (b) t=2.500ns (c) t=2.900ns (d) t= 3.140ns (e) t=3.300ns (f) t=4.000ns

condensed when the ceramic dome is used than in the case of the glass dome. If this form of electron bombardment is allowed to continue, it is quite likely to result in multipactor effect and thus the melting of the metal rods.

According to the analysis above, the most likely reason for the melting is multipacting inside the structure. The Multipactor effect is a complicated physical phenomenon. The simulation conducted here is only a preliminary study.