5.3 Comparison with simulations
5.3.1 Multipactor bands
Standard multipactor simulations show distinct multipacting bands. Experiments show a continuous multipactor current with peaks and troughs but no gaps in the spectrum. Once multipactor appears (experiments gave a lower power limit of 80-200kW, depending on the degree of processing the waveguide has been exposed to), the current remains unless the entire wall processes to such a point that no multipactor current remains regardless of the power level.
Experimentally, band-like behaviour was occasionally observed. On such example can be seen on Figure 59 in the jumps from one level of current to another depending on RF power, time, or the level of cleanliness of the surface at a given moment. No distinct band structure was observed, but peaks and troughs are clearly visible in the various power scans of the waveguide (examples of this are visible in Figure 56, Figure 97 and Figure 98). This suggests that the phenomenon is much more complex than simple simulations might suggest. It is very probably also a result of the fact that the multipactor that can occur in the waveguide is a high order multipactor, its order being between 7 and 9 depending on the power level. High order multipactor bands are close together (as can be seen in Figure 16, the high order bands being the ones to the left of the figure, as they require less power to send the electron across the waveguide). That closeness leads to the increased possibility of blurring the bands, due to such processes as out of phase electrons having the possibility of bouncing off the surfaces (high low energy backscattering probability) until they drift back into the multipacting electrons. Simulations carried out with MAGIC, as well as other codes [31], show the possibility of cross talk between the stable multipactor phases. Another factor acting in favour of blending the bands is the fact that the electric field envelope in the waveguide has a cosine distribution across the width of the waveguide in the TE10 mode (maximum in the centre,
no field near the sidewall). This allows different wall-to-wall trajectory transit times to exist in the waveguide, and can be compared to having electric fields equivalent to a variety of power levels in a two-plate system across the width of the waveguide.
1 10 100 1 10 100 250 300 350 400 450 500 550 600
Comparison between MAGIC simulation of multipactor
and experimental data
Central strip
P2 probe signal from WG3 (10_30_CuPlate)
Acc u mu lat e d ch arge o n t he cen tral st rip of th e w a ve gui de ( A U) P2 p ro b e sig na l fro m W G 3 (mV) (1 0_ 30 _C u P la te ) Power (kW)
Figure 70: MAGIC simulation of multipactor with only a 3.04cm strip on the centreline having a non-zero secondary electron yield, compared to a measurement from P2 (located on the centreline) on a plain copper waveguide
The introduction of low energy electron reflection widens the bands in standard simulations, while the early MAGIC simulations that did not incorporate such a low energy reflection showed little or no multipactor. MAGIC simulations show only minor effects on the charge ‘accumulated’ on the walls in a given time at different power levels, as can be seen on Figure 70 (‘accumulated’ is in brackets as the charge is not conserved by the wall, which is a perfect conductor, but only counted by the code for the purpose of the measurement). That particular series of points was taken after 100ns of simulation at the various power levels. It also restricted multipactor to distinct sections of the waveguide width. The simulation shows a continuum of multipactor current similar to
what was observed in the experiments (a curve showing similar behaviour on a plain copper waveguide is added for comparison).
5.3.2
Location of electron multipactor
MAGIC simulations conducted in a rectangular waveguide show the drift of electrons towards the sidewall of the waveguide. That effect was already observed in previous particle tracking simulations, but MAGIC and the possibility of making videos of the phase-space make it even more obvious. It is readily apparent in Figure 71, which shows a majority of electrons following nearly direct wall-to-wall trajectories in the centre of the waveguide, but also a number of completely off-phase electrons travelling slowly across the breadth of the waveguide. It is also apparent that as we look at electrons further away from the centre of the waveguide, the rate at which they head towards the sidewall (i.e. the angle of their trajectory compared to a vertical line) increases dramatically. This helps explain the high current picked up by the probes located off-centre and on the sidewall.
Off-phase electrons Cloud of sidewall electrons
Main multipacting electrons
Figure 71: Trajectories of multipacting electrons after 105ns of simulation time (~5 impacts of the main multipactor mode)
Simulations have also been conducted measuring the accumulated charge on small areas of the surface placed at the same location as the electron probes in WG3. While the results (shown in Figure 72) show quite a lot of noise, it is apparent that P1 to P4 show very similar levels of charge. This is to be expected because they are all on the same line in the middle of the simulated waveguide. The levels measured in WG3 experiments tend to show similar levels between the probes composing the pairs P1-P4 and P2-P3. The pairs P1-P4 and P2-P3 may however show different signal levels, even in cases where they theoretically should not measure any difference (as in Figure 73). Causes for that difference may include the greater proximity of P1 and P4 to the Mylar windows, as well as the fact that the actual stainless steel waveguide body is closer to
P1-P4 than P2-P3 that measure electrons coming almost exclusively from the sample plate. The kink apparent in the figure around 375kW appears to be more than a glitch of the code (nearby power levels confirm its presence, but no explanation was found for it.
Figure 72: MAGIC simulation measuring the accumulated charge at the location of P1-P8 after 100ns of simulation run-time
Figure 73: Measurement of P1-P8 from a plain copper plate
It is also interesting to notice from Figure 72 that P5-P8 in the simulation, that has a uniform secondary electron yield along the waveguide surface, shows a higher signal level than P6-P7. This tends to show that the higher P5-P8 signal consistently measured by experiments is a fundamental property of rectangular waveguides and not exclusively due to variations in the secondary electron yield of the surface due to differences in processing (as suggested in Section 5.2.3). The higher signal measured may well be due to the observed accumulation of electrons towards the sidewall of the waveguide (as described above). It is however notable that the MAGIC simulations also show that the signal from P6-P7 is much lower than P1-P4, while in the experiments the signal from P6-P7 was often greater than that from P1-P4 (but always lower than P5-P8 as discussed above). This tends to support the theory that the secondary electron yield of
the surface is indeed uneven due to uneven processing of the waveguide, but that the higher current present near the waveguide wall may indeed be a fundamental property of multipactor in rectangular waveguides.