The Electromagnetic Effects of TVAC and Space on Passive Waveguide Devices and How Each Can be Simulated

Designing and manufacturing components to withstand the harsh environment of outer space is an additional challenge compared to ground-based equivalent products. Before the components even reach outer space, they are subjected to continuous mechanical vibrations from the launch and experience a large pressure difference from leaving the atmosphere. Finally, once the spaceship has achieved its final orbit, extreme conditions are now to be accounted for. Conditions such as a near perfect vacuum, oscillating high-temperature ranges, and high energy particles originating from the Sun or further beyond the Solar System [1]. This article will focus on the aspect of simulating waveguide devices to design them for use in harsh outer space environments by considering electromagnetic effects such as thermal heating and multipaction.

Introduction

A radio frequency (RF) waveguide is a type of electrical transmission line which transmits electromagnetic waves, generally in the GHz to THz frequency range, down a conductive metal tube. They have many inherent benefits over other types of transmission lines, for example, coaxial cables, for space-based applications. Waveguide has an inherent lower loss than coaxial cable due to the extra dielectric loss present especially when working at higher frequencies [2], this is an important property when working with the limited power and link budgets of satellites. 

The lack of atmospheric attenuation also means, in the future, higher frequencies and therefore wider bandwidths can be used. Due to waveguides simplistic design it can already operate far beyond 1 THz, such as Flann’s sub-millimeter extruded waveguide (figure 1), which is far exceeding the current limit 166 GHz of 0.8 mm coaxial cable connector. 

The construction of a waveguide helps provide an advantage of immunity against external RF interference or producing interference to other nearby electrical components. This isolation of the signal is due to the metal walls of waveguide giving a benefit over more open topological transmission lines, such as microstrip and slotline.

Figure 1. Flann's Extruded Sub-millimetric Waveguide

Depending on the orientation of the object with the Sun and Earth, it can experience both intense heat from radiation and extreme coldness from the temperature of space. The source of this radiation is primarily solar radiation straight from the Sun, however, secondary radiation occurs from the albedo effect from the Earth and Earth’s thermal radiation [3]. To be able to test devices before launch a thermal vacuum chamber (TVAC) can be used. TVAC is a specific type of vacuum chamber that can regulate the temperature of the objects inside to allow for the thermal behavior of the object in a radiative vacuum environment, outer space, to be analysed. 

As waveguide is a metal tube it is a mechanically robust transmission line; when operated in a standard atmospheric environment generally the only damage caused is when the medium within the waveguide undergoes electrical breakdown. This is caused by the electric field strength between two points, the voltage being higher than the breakdown voltage of that material causing the once dielectric to conduct a current and causing a voltage arc [4]. 

However, in a vacuum there is no longer any medium to undergo electrical breakdown which also means the mean free path of particles, such as electrons, within the waveguide channel has increased. This can cause a phenomenon known as multipaction (sometimes known as the multipactor effect) which is an exponentially cascading electron multiplication effect caused by an oscillating electric field. Like electrical breakdown multipaction can damage, or even destroy, the RF device and can cause other problems such as noise and additional signal loss. There are also secondary effects that multipaction can allow for such as corona discharge and others.

The multiplication of electrons is caused by an impact of a primary electron into the walls of the waveguide (or object such as dielectric within the waveguide). Dependant on the initial energy, angle, and surface roughness the impact can release one or more secondary electrons. This process then repeats each cycle causing the increase of free electrons within the waveguide. Each material can have its own secondary electron emission distribution which compares the multiplicative effect of secondary electrons by the energy of the primary electron, known as a secondary electron yield (SEY) curve [5]. 

As multipaction is reliant on the oscillating electric field, the time between collisions of the electron and H-plane metal walls are required to be synchronised to an odd multiple of half the period of oscillation, causing a resonance effect. To find an approximation for the electric field strength that could cause a possible multipaction breakdown to occur, the frequency-gap equation can be used:

Derived from Newton’s 2^nd law, it shows the maximum resonance occurs when the frequency gap (fd) between two plane parallel surfaces is proportional to the square root of the maximum potential between the surfaces [5]. 

If a dielectric is present within the waveguide a different type of multipaction could occur using a single surface. Known as the ‘tripple point effect’ due to the presence of three medium, metal, dielectric, and vacuum. It occurs due to a slightly positively charged dielectric attracts the electrons causing a collsion between the surface and primary electrons, releasing secondary electrons [6].

To conform with the strict requirements of space-based products, ESA (European Space Agency) and NASA (National Aeronautics and Space Administration) have both developed their own detailed sets of standards for space activities. These are compiled on ECSS (European Cooperation for Space Standardization) [7] and NTRS (NASA Technical Reports Server) [8] which are readily available online. 

Simulation of Waveguide Devices in Thermal Vacuum Environments

With the current abilities of computational physics, more specifically electromagnetic and multi-physics simulations, TVAC testing can begin long before the component is finally assembled and can become integral to the design stage. Popular commercial simulation software is developed by Ansys, COMSOL, and Dassault Systèmes Simulia, to name a few.

Thermal Simulation

Due to waveguide’s compariable large thermal mass for the size of the transmission line and low insertion loss they can take a high CW (continuous waveform) power, with the maximum dependant on the waveguide size. However, once features are added into the waveguide, such as impedance matching steps for a waveguide to coaxial transition, regions of higher temperature will arise. These ‘hot-spots’ can be caused by greater loss due to the internal features or a less conductive thermal path that is unable to transfer the heat away from a specific area of the device, or a combination of both. 

To be able to simulate temperature of a waveguide body multiphysics simulation involving electromagnetic simulation of radio waves, sometimes known as high frequency electromagnetic simulation, and heat transfer are used together. The results can then be used to calculate the maximum possible temperature, therefore maximum power, the device can handle. 

There are generally two types of mechanisms responsible that generate heat in waveguide. The first mechanism is from the imperfect conduction of the walls of the metal waveguide, known as joule heating (or ohmic heating). The effect is caused by the magnetic field inducing a current in the walls of the waveguide causing a loss from the resistivity of the metal. The currents are generally simulated as surface currents due to the small skin depth distance at microwave frequencies and to simplify the simulation. The second type of mechanism is known as dielectric heating and is the same principle that microwave ovens use to warm food. As the oscillating EM wave travels down the waveguide through the dielectric material, it causes the electric dipoles of the dielectric to align with the field of the wave. This constant movement of the electric dipoles in the dielectric is driven by a loss of energy for the wave which in turn heats up the dielectric, the dielectric loss is quantified by an angle known as the loss tangent [3][9].

To be able to find the maximum temperature the devices reach in a simulation, the output of heat also needs to be considered. In a vacuum environment there are two methods to remove heat from a system or from a specific area of the system, these are via thermal conduction (diffusion) and radiation. Waveguides are always connected to at least one adjoining component, so there is always a path for the heat generated at ‘hot spots’ to diffuse to the greater volume of the system, such as through the flange faces. The other method of heat transfer present is through the emission of electromagnetic radiation, normally in the infrared region. The radiative heat transfer is the only transfer method to remove heat away from the hot component when suspended in a vacuum. At Flann we can design the system to suit your needs and if required add additional cooling to make sure the heat is transported away from the hotter areas of the waveguide system.

Here at Flann, we use COMSOL Multiphysics to simulate the theoretical maximum temperature expected at the waveguide component’s ‘hot-spots’. COMSOL solves coupled partial differential equations within specified domains depending on the user’s chosen physics for the problem at hand. The user then selects certain boundary conditions to define the limits of the problem from which COMSOL numerically solves via the finite element method (FEM). An example of a 0.8 mm coaxial end-launch waveguide adapter simulated in COMSOL is shown in figure 2 using a multiphysics simulation of high frequency electromagnetics and heat transfer. To model Flann’s waveguide adapters in COMSOL the boundaries are chosen as such so the worse possible rated conditions are simulated and so the device will reach its highest temperature. The possible heat flow paths are therefore restricted to only the waveguide flange face and coaxial interface, both held at 85 °C and the radiative heat transfer is not considered.

Figure 2. A cross-section of Flann’s WG27 (WR10) 0.8 mm coax end-launch waveguide adapter undergoing a COMSOL Multiphysics simulation for RF heating at a frequency of 84 GHz. The flange face and adjoining coaxial cable is set at 85 °C for the rated maximum continuous waveform power of the device. The red arrows show the direction of the electric field at a chosen phase.

Figure 3. A line graph resulting from the COMSOL Multiphysics simulation showing how the maximum temperature of Flann’s WG27 (WR10) 0.8 mm coax end-launch adapter varies as the frequency increases across the WG27 band.

The ‘hot-spot’ and therefore design limitation of the adapter can be shown with the increase in temperature of the coax’s centre conductor gets much hotter than the rest of the adapter body. Simulation allows a much greater understanding of devices than just testing alone would allow, being able to probe into area that are unable to be monitored. The simulation also allows for variations of external temperature values and power requirements, allowing for a quicker answer when the environmental requirements of the waveguide device change. Simulation will also show the effects of frequency on temperature, for the example 0.8 mm coaxial end-launch waveguide adapter figure 3 shows a steady increase in ‘hot-spot’ temperature with frequency. This is expected as the device contains a coaxial transmission line section which increases in loss with respect to frequency, especially when approaching its high frequency cut-off, dominating the waveguide loss which generally decreases with respect to frequency. 

Multipaction Simulation

Depending on the complexity of the model and the orientation of the gap to the electric field, it will influence the type of modelling required to validate a possibility that multipaction could cause a problem in a waveguide device. A basic tool that is used to verify if multipaction could cause an issue has been developed by ESA, known as the ECSS Multipactor Tool, which is based off their ECSS multipactor design and test standard [10]. The ESA tool returns a pass or fail, including the additional safety margin defined by the test standard, that is based on the user inputs of gap height, frequency, power, and material type which will define the SEY curve for electron distribution.

Figure 4. A SEY curve for aluminium based upon the ESA SEY dataset [6] included in the Multipactor Tool and extrapolation to higher energies using Vaughan’s formula. The maximum SEY coefficient and the two coefficients that are equal to one are clearly marked on the curve. Note that the zero SEY value is not present in original dataset due to the step size chosen for the measured data.

Waveguide components are not always simple and do not contain a uniform field so sometimes require complex three-dimensional finite element analysis to be able to fully simulate the problem. The Multiphysics software mentioned previously all have their own packages that can simulate multipaction such as Spark3D for CST (Dassault), COMSOL’s particle tracing module, and the inbuilt multipaction analysis in Ansys HFSS. Depending on the software chosen they use a combination of particle-in-cell techniques [11] and/or Monte-Carlo simulation [12] along with ray tracing to simulate the particles in the pre-solved electromagnetic fields using a time-domain solver, keeping track of the total number of particles.

Using Ansys HFSS multipaction as an example, the simulation is first required to be solved in the frequency domain to find the solutions for the electromagnetic fields for the particle-in-cell techniques. Much like the temperature simulation in COMSOL that was discussed above, certain boundary conditions and domains are now required to be selected so the secondary electron emission and particle properties and locations are both included in the simulation. 

To model the secondary electron emission, the distribution of a number of secondary electrons can be found from the energy of the primary electron and the SEY curve, as mentioned previously. In Ansys and other multipaction simulation software the SEY curve can generally either be based upon a user’s input dataset, such as previously measured data, or based on Vaughan’s SEY formula [13] and Vaughan’s minor revision to their formula [14]. 

Figure 5a. An internal ‘air model’ of the filter based on the design present in the ESA multipaction handbook. The black particles are the simulated electrons present at the specific timestep and the arrows show the direction and magnitude of the electric field. Notice that the smaller gaps have the higher number of particles.

Figure 5b. An example of a result for a multipaction simulation in Ansys HFSS for the filter design, showing a clear multipaction breakdown of continuous waveform powers above 75 W. Note that the higher the power the greater the exponential increase of number of electrons due to multipaction.

The basic mathematical form of Vaughan’s formula is based upon a continuous piecewise function, defining two regions above and below the incident particles energy that releases the maximum secondary emission. Each of these individual regions are themselves exponential functions, they depend on the defining energy of the incident particle when zero secondary electrons are released and the energy at which the maximum number of secondary electrons are released. Two other important points are the two corresponding energies to which the secondary emission is equal to one, evidently only valid if the maximum secondary electron emission is itself greater than one. All these parameters can be experimentally found to create a curve like the example shown in figure 4. 

Ansys then simulates the multipaction of a defined number of electrons over a chosen time period for different indicident field energies. This produces a line graph, shown in figure 5, of the variation of total electron count over time. The multipaction breakdown is now clearly visable with a exponentially increasing number of electrons when the energy is over a certain threshold, and beneath the threshold an attenuation of the number of electrons. 

Conclusion

Depending on the original aims and environments that the waveguide components are going to be subjected to over their lifetimes and the safety margins present with the FEM simulation, physical testing might also be required to test for both multipaction and thermal limitations using TVAC equipment. An example of the types of testing required can be found in the ECSS multipactor handbook [6]; depending on the margin present unit testing, batch testing, or only qualification testing could be required. There are also many other aspects of the design that are required to be analysed before the waveguide can be subjected to a TVAC environment or even space. Mechanical vibrations and resonance need to be analysed and reduced so the device does not shake itself apart, materials and manufacturing methods need to be accounted for to keep the mass of the item to a minimum for example via 3D printing methods, and to limit outgassing of chosen materials. Designing waveguide components for space-based applications causes many new and interesting challenges to classical waveguide design.

References

[1] Meseguer, José, Isabel Pérez-Grande and Ángel Sanz-Andrés. “Spacecraft thermal control.” (2012).
[2] Pozar, David M. “Microwave Engineering 4^th ed.” (2011). 
[3] Chisabas, R.S.S, et al. “Development of a Thermal-Vacuum Chamber for testing in Small Satellites.” (2017).
[4] Kuffel, E, Zaengl, WS, Kuffel, J. “High Voltage Engineering Fundamentals 2^nd ed.” (2000). 
[5] Vaughan, J.R.M. “Multipactor.” IEEE Transactions on Electron Devices, vol. 35, no. 7 (1988).
[6] ECSS. “Space engineering, Multipactor handbook.” ECSS-E-HB-20-01A (2020).
[7] ECSS website https://ecss.nl/. Accessed 10/2023.
[8] NASA NTRS website https://ntrs.nasa.gov/. Accessed 10/2023.
[9] Griffiths, David J. “Introduction to Electrodynamics 4^th ed.” (2013). 
[10] ECSS. “Space engineering, Multipactor design and test.” ECSS-E-ST-20-01C (2020).
[11] Ahmed, S. “HFSS ENABLES MULTIPACTION ANALYSIS OF HIGH POWER RF/MICROWAVE COMPONENTS.” 5th North American Particle Accel. Conf. (2022).
[12] COMSOL. “Particle Tracing Module User’s Guide 6.1.” (2022).
[13] Vaughan, J.R.M. “A New Formula for Secondary Emission Yield.” IEEE Transactions on Electron Devices, vol. 36, no. 9 (1989).
[14] Vaughan, J.R.M. “Secondary Emission Formulas.” IEEE Transactions on Electron Devices, vol. 40, no. 4 (1993).