URSI GASS 2020, Rome, Italy, 29 August - 5 September 2020 Harvesting Electromagnetic Energy from Hypervelocity Impacts for Solar System Exploration Sean A. Q. Young*(1), Nicolas Lee(1), and Sigrid Close(1) (1) Department of Aeronautics & Astronautics, Stanford University, Stanford, California, USA, 94305 Abstract CubeSats have opened new opportunities for solar system exploration by decreasing mission development and launch costs. While they have proven successful in the inner so- lar system, providing sustained power to these spacecraft Figure 1. Graphical representation of the HVI energy har- at large distances from the sun requires novel power gener- vesting concept. ation methods. Solar power is dramatically diminished at these distances and radioisotope thermoelectric generators do not scale well to spacecraft with small dimensions. The CubeSats as free-flying sensors can produce plasma mea- space environment could provide a solution; by harnessing surements spread over hundreds of kilometers — a signif- energetic hazards in the environments under investigation, icant improvement over the tens of meters that a boom- the spacecraft could forgo traditional power sources. Radio mounted sensor would provide. This concept has heritage frequency emissions are abundant in the space environment in the Cluster [1] mission for example. with sources originating from planetary aurora, particle dy- namics in the magnetosphere, and electromagnetic pulses Power presents a challenge to small spacecraft in the outer (EMPs) associated with hypervelocity impacts between mi- solar system. The extreme distance from the sun precludes crometeoroids and spacecraft. A case study of a mission the use of solar panels for Cubesats, and radioisotope ther- to the rings of Saturn is presented and analyzed for feasi- moelectric generators are expensive, difficult to handle, and bility. Upper bounds on the power emitted by the hyper- bulky relative to the amount of power delivered. Another velocity impact EMPs are produced by combining results approach under consideration is to use the power within the from ground-based experiments and Saturnian environment space environment to power these spacecraft. Radio fre- models. We find that although the kinetic energy of hyper- quency (RF) sources within the space environment present velocity impacts is significant, the conversion efficiency to a tempting target considering their abundance. EMPs is too low for spacecraft to effectively use. Hypervelocity impacts (HVIs) are one such source of radio 1 Introduction and Motivation frequency emissions. HVIs on spacecraft surfaces and air- less bodies occur frequently in the space environment due Exploration of the outer solar system is an expensive en- to micrometeoroids, dust, and orbital debris (referred to col- deavor and maximizing the science return of the few mis- lectively as impactors throughout this paper). As described sions that will make the journey is of paramount importance in detail in [2], HVIs on metallic targets emit an electro- to mission designers. Nanosatellites (spacecraft between 1- magnetic pulse (EMP) which can interfere with spacecraft 10 kg in mass) such as CubeSats (spacecraft made up of cu- electronics, resulting in mission anomalies. Given that the bic units 10 cm to a side) succeeded in driving down costs emitted energy is significant enough to be destructive, we for missions to Earth orbit and provided platforms for ex- aim to characterize the amount of energy carried by the perimentation with mission concepts, hardware, and pay- EMP and to determine whether it can be harnessed to power loads. While solo flights to the outer planets may be cur- nanosatellites. Figure 1 illustrates this concept using a rently infeasible for them, Cubesats traveling with larger surface-mounted patch antenna. motherships have the potential to advance science while controlling costs. This study analyzes the amount of expected energy avail- able to spacecraft traversing Saturn’s rings from impact For example, nanosatellites can enable distributed sensing EMPs. First, we present general expressions for the up- missions to the outer planets. Magnetospheres are large- per bound of energy available to a spacecraft given an im- scale, complex structures whose properties are constantly in pactor flux model and EMP measurements from laboratory flux. Understanding physical processes that drive the mag- experiments. Characteristics of the Saturnian space envi- netosphere requires resolution of spatial gradients in plasma ronment are derived from spacecraft data while our own properties. Distributed sensing missions using swarms of measurements provide the expected EMP energy. Synthe- sizing these elements resutls in an estimate of the power where A is the impact area and available to these spacecraft. 1 Z a A = rDWdr (3) eff 2 2 Methodology 0 is the effective power collection area. In the small space- A = a2= = A= The physics governing the generation of the EMPs are not craft limit, eff p 4 4. well understood, nor is the Saturnian impactor mass and ve- locity distribution completely known. In addition, the de- 3 Physical models sign space of harvesting circuit topologies is too vast to enu- merate completely or optimize for the harmonic structure Models for the electromagnetic field energy EEMP and the of the EMP. A number of simplifying assumptions, there- meteoroid flux density F(m;u) are needed to proceed fur- fore, are required to obtain a usable power estimate. En- ther. The former can be estimated using detections of EMPs ergy conservation allows us to constrain the EMP energy to from terrestrial impact experiments while the latter is con- a fraction of the impactor kinetic energy, resulting in an up- structed using data from spacecraft measurements. per bound on available energy. Using spacecraft geometry and physical models for the EMP energy as a function of 3.1 Electromagnetic pulse energy impactor properties and the ambient impactor environment, we can compute the expected RF energy flux to a rectify- An empirical power law relation between the equivalent ing antenna (rectenna). This analysis assumes that EMPs isotropic radiated power, the mass m, and velocity u of a b result from every HVI event, that the EMP radiation pattern the impactor is PEMP ∝ m u where a ≈ 1 and b ≈ 3:5 is isotropic, and that HVI measurements from lower veloc- [3]. This relationship agrees with similar empirical laws ity ground-based experiments can be extrapolated to orbital describing the amount of charge produced in HVI exper- speed HVI events on spacecraft. Model-specific assump- iments [4]. We use this proportionality to estimate EEMP tions are presented in their respective sections. over a range of masses and velocities. a b EEMP = Cm u (4) The amount of energy in the electromagnetic fields EEMP is less than the combined impactor kinetic energy and en- Data from experiments can be used to determine the con- ergy stored in the electrostatic field due to spacecraft charg- stant of proportionality C. We recently conducted a set of ing. Since the charging state is variable, we use the kinetic experiments using the light gas gun at the NASA Ames Ver- energy alone as a weak upper limit. Experimental measure- tical Gun Range (AVGR). In these tests, small, 1.6 mm di- ments of EMPs can be used to compute a tighter bound. The ameter aluminum spheres were fired in partial vacuum (0.5 Torr) at speeds between 4-6 km/s. Targets were made of amount of energy Ec stored by a rectenna with frequency- various materials and biased to different voltages mimick- dependent efficiency h0( f ) is ing spacecraft charging conditions. A suite of RF sensors Z ¥ DW — including patch antennas, dipole antennas, and a 0.9- Ec = h0( f )ESD( f )d f < h0;max EEMP (1) 0 4p 1.8 GHz log-periodic monopole antenna (LPMA) — was placed inside the chamber about 1 m from the target. We where ESD( f ) is the energy spectral density of the incident detected EMPs on two of the thirteen shots (m = 5:9 mg, signal, DW is the solid angle subtended by the antenna el- u = 5:4 km/s) on aluminum targets biased to -300 V. ements, and h0;max = max f h0( f ) is the peak efficiency of the antenna and rectifying electronics. In the far-field, DW Given its broadband characteristics, the LPMA was used to would simply exhibit the usual inverse square attenuation estimate the EMP energy. The signal energy within a short with distance. For small spacecraft, however, the rectenna temporal window around the EMP was computed, account- is more likely to be in the near-field. As an example, for an ing for amplifier gain, cable losses, and space losses. For antenna element with height ` and diameter d protruding at ◦ these shots, EEMP ≈ 70 nJ. Using Equation (4), this results 90 from the spacecraft, DW ≈ p sr for nearby impacts and −15 2 in a proportionality constant C ≈ 1 × 10 when m and u asymptotically approaches 2`d=r as the distance r ! ¥. are measured in SI units. Orbital impactors can travel at speeds up to about tens of km/s, bringing with them com- When more than one impactor impinges upon the surface, paratively higher EMP energies. In addition, the flux of the power collected by the rectenna is computed using a impactors can be quite high, especially in the rings of Sat- model of the impactor flux density F(m;u)dudm (number urn. of particles with mass m and u impacting per area per sec- ond). Deployable structures can increase the number of im- 3.2 Saturn environment characteristics pacts on the spacecraft and thus the harvested energy. As- suming that the deployable surface is circular with radius Equation (5) gives the in-plane density profile of im- a with the antenna at its center, the power per unit impact pactors within Saturn’s rings derived from Cassini Radio area can be derived from (1) as and Plasma Wave Science data [5].