Direct observation of electrons in microwave vacuum components Free

High voltage breakdown of a medium under alternating fields has been a topic of interest as it ultimately governs the maximum power capabilities of many RF components.^1–4 At sufficiently high pressures, electron multiplication is primarily governed by electron impact ionization of the background gas, ultimately establishing a conducting path, thus shorting the microwave component. An initial seed electron may appear owing to the ever present background radiation or due to electron detachment.⁵ In the case where the mean free path of the electrons is much larger than the interior dimension of the microwave component, typically for pressures below ∼10⁻³ Pa, the source of electrons must be sought elsewhere. In the extreme, at macroscopic field amplitudes of tens of $kVcm$⁠, the electron number growth is governed by electron field emission from the component’s metal surfaces. The onset for such cold field emission will depend on the work function of the metal surface, the surface roughness, possible oxidation, and dielectric inclusions, just to name a few. Due to heating and possible ion bombardment, the field emission may become more intense as time progresses. Furthermore, unless carefully prepared, the metal surfaces are covered by adsorbed layers of gas that are partially desorbed under the electron bombardment. As a consequence, the local gas pressure may increase, thus giving rise to a final gaseous type electron multiplication.

At field amplitudes too low to affect significant field emission, the propagation of microwaves may still be upset due to multiplication of an initial seed electron via secondary emission.^6,7 That is, in 1934, Farnsworth recognized that a resonant condition of secondary emission with the RF field may occur. However, electrons would oscillate between two surfaces in sync with some RF field. This synchronicity relies on the transit time of the electrons being an odd half cycle of the RF signal, which sustains or grows its population through secondary emission. Known as multipactor, the synchronized electrons impacting the walls of the vacuum microwave component again desorb gas molecules from the walls, generate heat, eventually leading to localized plasma generation and finally gaseous electric breakdown.^8–16 

It is obvious that the above-described electron multiplication mechanisms may cause damage to onboard components of systems. Thus, in addition to a strong modeling and numerical simulation effort, the detection of the appearance electrons in a vacuum microwave component becomes necessary.

Present detection techniques incorporate local or global detection methods. Global detection relies on close-carrier-noise detection, nulling detection, and harmonic detection methods. Hence, such methods usually diagnose that the overall system is suffering from electron effects but fail to pinpoint where electron generation originated in the system. To this extent, local detection methods are superior; however, they are typically more intrusive and have limited temporal resolution, ∼μs time scale, as discussed below.^17–21 It is briefly noted that the presented detection method is a local detection method with nanosecond temporal resolution.

Presently implemented local detection schemes include an electron probe in the form of a charged wire. The wire is positively biased and attracts free electrons, an approach that comes with drawbacks, however. That is, free electrons are accelerated to the wire and strike the probe surface. Hence, the probe itself may emit secondary electrons, which in the case of Ref. 21 is coated in multiple layers of carbon to mitigate secondary emission. Of course, at very high powers and electric fields, avoiding interaction of the probe with any electron growth becomes a daunting task. Furthermore, such probes may be only a few millimeters away from the electron generating surfaces which will perturb the local RF electric field. Finally, the temporal resolution of the electron probe is limited, owing to the necessary solid state amplification of the weak electron signal as the needed gain leads to slew rates on the order of microsecond. That is, the temporal resolution is sacrificed in the local detection method.

The experimental technique presented here utilizes an electron multiplier tube, EMT, with a rise time on the order of single nanosecond to avoid sacrificing temporal resolution such as the case with a wire probe. To access the electron flow directly, a custom fabricated waveguide structure employs an electron guiding aperture with the EMT as the final diagnostic device. Testing the presented method, a microsecond RF pulse is applied at rather high electric field amplitudes (tens of $kVcm$ rms field), which revealed that field emission is directly initiated without the noticeable onset of the multipactor on the rising edge of the RF pulse amplitude.

The local detection method is suited to observe electron avalanches via vacuum breakdown, or the generation and saturation of electrons through the multipactor effect. While being able to observe both phenomena, it is important to differentiate between the mechanics causing the electron multiplication. In this manuscript, electron energies conducive to multipactor are generated by the microwave pulse during the rising and falling edge only, while the major portion of the microwave pulse yields electron energies higher than that needed for the multipactor effect, as shown in the susceptibility graph in Fig. 1. At the onset of the experiment, it was unclear if multipactor would be observed on the rising pulse edge. It was since revealed that the 500 ns pulse risetime moves conditions directly toward vacuum breakdown too rapidly for multipactor to develop. The main factor to note is the level of the electric field amplitude within the waveguide, steering secondary electron generation toward resonance, field emission, or both.

For the sake of the argument, one may neglect the spatial variation in the electric field amplitude and simply assume that secondary emission occurs between two parallel plates, separated by a waveguide height of b. One may further assume that the two plates have the same secondary emission characteristics and that an initial electron(s) exists at the zero phase of the RF signal close to one of the walls. Due to operation in the dominant TE₁₀ mode, the waveguide height can be adjusted without affecting the cutoff frequency as shown in Eq. (1), where m is 1 and n is 0. Equation (2) is used to estimate the electric field inside a WR-284 waveguide

where E_RMS is the rms electric field in the center of a WR-284 waveguide, E_ref is a reference rms field of 90 $kVcm$⁠, P_ref is a reference input power of 90 MW, and α is a scaling factor for which the waveguide height was scaled down from the standard WR-284 waveguide dimensions (for this experiment, $α=$ 5.657).²² 

To observe multipactor, several necessary conditions must be met. Not only must the mean free path of an electron be greater than the waveguide gap, but it must also be accelerated to cover the gap distance in multiples of one half cycle of the RF signal frequency. For the former, as an example, the mean free path of electrons in diatomic oxygen shown in Ref. 23 yields a mean free path greater than 1 km at 273 K and 10⁻⁴ Pa. Since the pressure in the experiment is kept at similarly low levels, it is assured that electron collisions with the walls are much more frequent than collisions in the volume owing to a gap of mere millimeters.

For the latter, an electron needs to be able to cover the gap distance within a multiple of one half cycle of the RF signal frequency. We shall refer to the number of half cycles as N or the order of multipactor. Limiting the Lorentz force equation to the electric force only (the electron speed is low), we can find an expression for the needed rms field for an electron to travel a specified gap distance within a number of N half cycles

where E_RMS is the rms electric field, q_e is the magnitude of elementary electron charge, m_e is the mass of an electron, f is the operating frequency, and x is the gap size. The impact energy of an electron impacting the wall(s) must also be taken into account as a function of gap distance and number of half cycles. Manipulation of the standard kinetic energy formula yields

where N is an integer representing the number of half cycles. Using copper walls with SEY crossover points from 150 eV to 2.5 keV, with an operating frequency of 2.85 GHz, and the desired gap size of 6 mm, one can use Eq. (3) to find that an rms field of 12.13 $kVcm$ is required for an electron to cross the gap in one half cycle.¹¹ Using the calculated E-field and Eq. (4), the impact energy of the electron will be 3.326 keV, which is not between the crossover points of copper. Thus, in the presented geometry, higher orders of multipactor would need to be observed to have impact energies between the crossover points of copper. From Eq. (3), with N = 3, or third order multipactor, an impact energy of 370 eV is calculated, falling between the crossover points at rms fields of 4 $kVcm$⁠. Further reading regarding the motion of electrons in an RF field can be found in Ref. 11. Using these equations will determine the lower limit of the E-fields that the source must be able to produce. From the rms field calculated previously, Eq. (2) is used to determine roughly 33 kW which is needed from the RF source to attain an E-field that in principal may lead to a third order multipactor.

Within the same vacuum environment, one can discuss electron behavior at much higher E-fields than those needed for multipactor, leading to electron energies higher than the second crossover point of copper (≫2 keV). The secondary electron yield at these energies, δ, will be lower than unity. Thus, the electron population will decrease due to wall losses, unless mechanisms other than multipactor gain dominance.

At sufficiently high applied fields, the surface barrier of metals used in the experimental setup is lowered. The lowering of the surface barrier requires very high field strengths (upward of $GVm$⁠), in which surface field enhancements due to material irregularities, achieve large microscopic field strengths with E-fields being insufficient for field emission at the macroscopic scale. Surface irregularities such as machining marks, whiskers, edges, cracks, impurities, and grain boundaries provide these surface field enhancements. These allow for electrons within a solid to overcome the work function of the material, in this case a metal, and transition into the test chamber vacuum. Electron emission from cold metal surfaces due to large electric fields was originally treated as quantum tunneling phenomena by Fowler and Nordheim. An RF conversion of the Fowler-Nordheim equation seen in Refs. 24 and 25 is used to calculate the average field-emitted current density. A more rigorous derivation of this equation is shown in Refs. 26–28 

where $j¯F$ is the average field-emitted current density [$Am2$], ϕ is the work function of a metal in eV, E_s is the applied field within the waveguide, and β is the surface field enhancement factor. For temperatures ranging up to a few hundred Kelvin, the average emitted current would not be expected to change by more than a few percent. This is discussed in more detail in Ref. 27. Calculating the β of a material is accomplished assuming idealized geometries of field enhancements and measurements of material surfaces. For a clean surface, depending on the detailed surface conditions, the value of β may realistically range from single digits to 250, as per Latham.²⁹ The onset of field-emission due to surface field enhancements is discussed in further detail in Sec. III.

The setup needed for this experiment was to mimic a space-based RF environment, with measurements being taken at pressures kept in the range from 10⁻⁴ to 10⁻⁷ Pa. While results demonstrated in this manuscript are with electron energies that push beyond the crossover points of copper, the operating power floor would produce electrons with energies within the copper crossover points. With this in mind, the designs were carried out to satisfy third-order multipactor requirements. Space-based communication system downlinks predominantly use S-band frequencies, which are within the operating frequency range of the WR-284 waveguide.^30–33 A pre-existing traveling wave resonator was constructed from the WR-284 waveguide, in which a 2.85 GHz signal will operate in the dominant TE₁₀ mode.^34–37 A travelling wave resonator is incorporated due to its sensitivity in regard to small changes in the quality factor (Q) through absorption and phase shifts caused by the multipactor effect. The traveling wave resonator incorporates a 14.6 dB sidewall coupler and a ring loss per round trip of ∼0.22 dB. The round trip time of this ring is about 15 ns, which causes very little energy to be stored even at high powers, e.g., 15 mJ at 1 MW power. This ring is able to support upward of 50 MW, which allows the user to step up the power delivered to the test section at much higher levels, approximately a factor of 20, than the source can supply. This high power coupled with a large mean free path will produce high energy electrons in the test section on the order of keV.

Although the magnetron is able to supply high power to the test setup (3 MW nominal without the resonator ring), the electric field produced in the waveguide will not be able to achieve electrons traveling the gap distance in one half cycle at the standard WR-284 waveguide height.^7,38,39 In order to also test less powerful, more frequency, and phase agile sources in the future, an impedance transformer is used to reduce this gap size to 6 mm, which subsequently increases the E-field by $α$ as shown in Eq. (2). Due to operation in the dominant TE₁₀ mode, the waveguide height can be manipulated without affecting the operating cutoff frequency as previously discussed in Eq. (1).

The described method used to find the impedances was developed by Graves and demonstrated in Ref. 40. Using Grave’s method, the full range of impedances from WR-284 height (34.04 mm) to a 6 mm gap is 260 Ω, 168.3 Ω, 70.7 Ω, and 45.8 Ω. These impedances correlate with waveguide heights of 34.04 mm, 22.05 mm, 9.26 mm, and 6 mm, respectively at 2.85 GHz. Simulations using High Frequency Electromagnetic Field Simulation (HFSS) were carried out with the impedance transformer geometry. While the calculations take into account orthogonal corners between each impedance step, care must be taken in mitigating field enhancements from the impedance transformer to not only avoid high voltage breakdown but inhibit the multipactor effect occurring in undesirable locations along the test section. The impedance steps were modified with a fillet that has a 15 mm radius. Simulations with the fillet edges demonstrate the peak E-field in the center of the test piece, with results shown in Fig. 2. From here, the apparatus was constructed so that the impedance transformer could be machined into copper inserts that are placed into the waveguide structure. A collar (in this version made of brass) was brazed to the copper waveguide, as to provide a housing for the inserts to lie in. This setup allows for the user to “plug and play” in which new impedance transformers or inserts are easily machined, without having to construct an entirely new test piece. Both inserts are sealed off by stainless steel plates and a Viton O-ring to ensure vacuum seal. A threaded hole was also machined into the center of the broadside wall of the bottom transformer plate so that electrodes with differing shapes may be added for extra field shaping/enhancement. These electrodes may be easily switched out with versions made from variety of materials or surface geometries. Figure 3 shows a photograph of the completed test piece with collar and a copper impedance transformer insert.

A local detection method incorporated by this experimental setup utilizes an electron multiplier tube (EMT) to detect secondary electrons being generated within the waveguide structure. Unlike an electron detection probe used in multipactor experiments which can be as close as 0.1 cm away from the multipactor area, the EMT is within an entirely separate chamber from the waveguide, connected by a 1 mm aperture whose cutoff frequency is well above 2.85 GHz. Electron detection probes can be intrusive, where it is possible to perturb the electric field within the waveguide. The EMT on the other hand is not only isolated from the waveguide fields but is also a much larger target than commonly implemented electron detection probes.⁶ 

The EMT is housed in its own vacuum chamber to which electrons can enter through a 1 mm aperture in the broadside wall of one of the waveguide surfaces. This isolation avoids the issues discussed above with the charged electron probe. It will be shown that the fields within the WR-284 waveguide are not perturbed by its presence and that secondary emission from the EMT dynodes will not feed back into the chamber due to proper biasing. Since the broadside aperture is circular, we can calculate the cutoff frequency of a circular waveguide

where f_c is the cutoff frequency of the circular waveguide, c is the speed of light, and r is the radius of the circular waveguide, in this case the 1 mm aperture. The resulting cutoff frequency using this equation is 1.75 THz, which is far beyond the operating frequency of 2.85 GHz. HFSS simulations using the 1 mm aperture that is 2.36 mm deep show that a maximum E-field of 6 $Vcm$ is measured between the aperture and the EMT housing. This field is negligible compared to the 200 V bias placed on the first dynode of the EMT, which provides a comparable field between dynodes (compared to 6 $Vcm$⁠). This aperture will allow for accelerated electrons to pass through and then be accelerated toward the EMT. Figure 4 shows the electron trajectories from the 6 mm gap to the EMT housed behind the 1 mm aperture. The electron trajectory simulation was carried out in COMSOL. Trajectories of electrons are shown with their respective energies in kilo-electron volt.

The setup allows for accelerated electrons to travel through the 1 mm aperture into the EMT chamber, where it is then accelerated into the first dynode of the EMT itself.⁴¹ Figure 5 presents an overview of the constructed detection scheme. The test section houses the copper bars which were machined to the dimensions of the impedance transformer, while the 1 mm aperture is located in the top, broadside wall of the waveguide. From here, the EMT is suspended from a high voltage feedthrough ∼6.36 mm from the aperture. The supply voltage for the EMT as well as the signal output is connected to a high voltage feedthrough via a cable connection located at the top of the tube on a standard ConFlat-flange (CF-flange) for the transition from the vacuum environment to atmospheric conditions.

A Hamamatsu R5150-10 electron multiplier tube was incorporated into the experimental setup. It is a box and line dynode structure with a typical rise time of 1.7 ns and a typical gain of 10⁶. In Fig. 6(a), biasing to the internal dynodes is provided by R1 and R2 at 3 MΩ and 1.5 MΩ, respectively, while R3-R17 are 1 MΩ. The output P represents the anode. In Fig. 6(b), 2 kV DC is supplied to the EMT so that there is a voltage drop between each dynode to provide continuous acceleration of incident electrons toward the anode. The 3 MΩ resistor was placed in the external circuit so that there is a positive voltage on the first dynode. The three capacitors at the top of the circuit act as DC blocking caps, only allowing fluctuations from the anode through to an O-scope.

In addition to the EMT, similar to the setup described elsewhere,³⁴ the forward and reverse power in the ring was measured along with the signal from a nanosecond risetime PMT (Photo Multiplier Tube). The PMT, with a sensitivity from 180 to 800 nm, had an end on view into the test region through a fused silica window. A strong PMT signal was expected when electron impact induced outgassing from monolayers adsorbed to the surfaces, followed by a gaseous breakdown in the expanding gas cloud.⁴² Note that such gas-monolayers certainly exist in the test section since the surfaces were neither plasma-cleaned nor baked out at high temperatures.

Experiments were carried out with varying incident power levels fed into the traveling ring resonator. Measurements were taken using the previously discussed power couplers, EMT, and PMT (cf. Figs. 7–9). At higher pressures (6.6 × 10⁻³ Pa), a strong PMT signal was measured, cf. Fig. 7, whereas the PMT signal is hardly noticeable at the lower pressures (3.3 × 10⁻³ Pa), see the inset in Fig. 8. While the argument could be made that photons produced within the waveguide affect the output current of the EMT, it is demonstrated in Fig. 7 that this is not the case. Although the material of the EMT’s first dynode (Cu–BeO) is susceptible to photoionization in the range of soft X-rays to approximately 300 nm wavelength, the EMT output signal dies off as breakdown occurs. Noting the peak measured voltage of 0.6 V into 50 Ω in Fig. 9, and assuming an EMT gain of roughly 5 × 10⁵, one may estimate that a maximum of about 1.5 × 10¹¹ electrons/s finds their way through the aperture separating the waveguide and EMT vacuum spaces. With this electron rate impacting the walls, the number of X-ray photons emitted into the solid angle from the aluminum electrode toward the aperture is estimated utilizing the results of the spectrally resolved measurements reported elsewhere, see Ref. 43. Adopting an incident electron energy of ∼20 keV, cf. trajectory simulation of Fig. 4, a total rate of roughly 2.2 × 10⁴ X-ray photons per second will pass through the aperture connecting the waveguide volume with the EMT.

Owing to the low quantum efficiency of a Cu–BeO dynode, reported by the manufacturer to be less than 1% for 20 keV photons, the contribution of X-ray stimulated EMT current to the overall observed electron stimulated current is estimated to be below 20 nA. This current is seen as negligible for the 12 mA total current amplitudes.⁴⁴ 

Without breakdown, the measured forward and reverse power signals follow the power fed into the ring, cf. the inset waveform in Fig. 9, albeit at increased amplitude. Due to the developing plasma within the test section, the actual power signals in the ring are much more complicated, cf. Fig. 8, and a consequence of the interplay between the resonant ring properties and field emission/plasma development.

One may infer from the signals that the initial rise in power amplitude is due to the ring being pumped by the magnetron, until the conditions are just right. This would be at about 35 $kVcm$ rms field amplitude for the data set depicted in Fig. 9. Note that such a field amplitude is roughly three times the calculated field for first order multipactor with a 6 mm gap in Eq. (3). A further increase in the power/electric field is hindered through field emission detuning the ring by the associated additional phase shift. Thus, the power in the resonant ring diminishes and as such the emission amplitude. Nevertheless, the magnetron is still pumping power into the ring where the nonlinear interaction between field emission and the resonator leads to oscillations in the EMT signal at relatively low amplitudes, cf. Fig. 9. These oscillations have an approximately 83 ns period (∼12 MHz), which is well below the maximum bandwidth of the detection system. One might argue that the plasma/field emission is reignited repeatedly due to complex electric field interaction between the microwave field and the developing plasma within the microwave resonant ring.

As it was desired to test a technical surface, plasma cleaning or any bakeout of the waveguide structure was purposefully omitted, but rather, the surface was mechanically polished with sandpaper followed by CeO microparticle buffing. While the electron emission from a clean surface would be adequately captured by the Fowler-Nordheim model, the surface layer contaminants or inclusions give rise to a significantly more complex process resulting, for instance, in a “switch-on” mechanism between the metal, insulator, and vacuum interfaces. Unlike a clean metal surface in which the geometry of surface structures determines the microscopic field, a metal-insulator microstructure model provides a more accurate representation of the metal surfaces.^45,46 The reported Fowler-Nordheim plots with these inclusions show larger surface field enhancements than their clean surface counterparts, while also showing a decrease in the emission area. Note that such large field enhancement values (in excess of 10³, Refs. 29 and 46) would be physically unrealistic with the standard Fowler-Nordheim theory but are shown to be the result of multiple enhancement factors between the metal, insulator, and vacuum regions when taking into account surface inclusions. The reported emission areas and field enhancement factors with a 15 mm Cu electrode show a β and emission area of 400 and 2 × 10⁻¹¹ mm² for a clean surface, respectively. While reports for a dirty surface are on the order of 10³ and 6 × 10⁻¹² mm², respectively.⁴⁶ The number of emitters can be back-calculated with these reported values and then applied to Eq. (5) determining the β and emission areas with the measured emitted current presented here using a 1 mm Al electrode. In order to match the observed 1.5 × 10¹¹ electrons/s, we assume a macroscopic field of 4 × 10⁶ $Vm$ and a ϕ of 4 eV. It is calculated that an emission area of 8 × 10⁻¹⁴ mm² is required for a clean surface, while a dirty surface has an emission area of 2.5 × 10⁻¹⁴ mm². Both values of β for the clean and dirty surfaces are in excess of 10³, which is consistent with the metal-insulator microstructure model, but not the Fowler-Nordheim model surface structure aspect ratio for a clean surface. A much more rigorous explanation of metal-insulator microstructures and other inclusion effects is provided in Refs. 45–48.

Note that the experiment was performed without employing an external electron seed, but rather, the high electric field itself ∼35 $kVcm$ is reasonably sufficient to provide some initial electron emission. Also note that any visible to UV light emission could not be detected by the PMT for this and all other experiments conducted at lower pressures.

It is worth noting that the field emission amplitude rises very quickly, taking a few nanoseconds only to reach peak amplitude. Considering that the microwave period is about 350 ps, a developing electron sheet has about 10–15 collisions with the two surfaces during that period. Of course, the EMT itself has a rise time limit of 1.7 ns such that the field emission signal may increase faster than what is indicated in Fig. 9. In future work, one may consider other faster electron detectors, such as microchannel plates, that are available with a subnanosecond temporal resolution that would at least be able to temporally resolve a high order multipactor and rapid field emission at 2.85 GHz.

Overall, the presented detection method enables detecting field emission onset with nanosecond temporal resolution and high sensitivity.

A local electron detection method was demonstrated with results discussed. Advantages of this method avoid the perturbation of the fields within the waveguide structure, providing an alternative setup to those required for noise detection, as well as forward and reverse power detection. In order to achieve sufficient E-fields at relatively low input powers, a step impedance transformer is utilized in order to provide a 6 mm waveguide height. For the detection of electrons, an EMT is housed in a separate chamber from the test section waveguide and is connected through a 1 mm aperture drilled into the broadside wall of the copper insert. Results demonstrate that field emission is directly observed before a plasma is formed via desorbed gas on the metal surfaces. For future work, the plasma development may be mitigated through a vacuum bakeout of the test piece. Future work will include investigating the multipactor regime in more detail by driving the setup with a 2 kW output power source with a pulse length exceeding 100 μs. This should provide a more significant time frame in which the multipactor effect is observed, while quelling field emission within the test section. The “plug and play” aspect of the presented assembly will enable testing of different periodic structures such as filters, irises, and other common waveguide-based communication components found in space-based applications.

This research was supported by the Air Force Office of Scientific Research under Contract No. FA9550-18-1-0062.