Coulomb Formation Flying

A GEO satellite is scatha image A GEO satellite is exposed to the space plasma environment which contains positively charged ions and negatively charged electrons. The faster electrons will accumulate more rapidly on the craft than the slower positively charged ions. This causes in a negative electric charge build-up to occur within the spacecraft. At steady-state charging conditions, the negative electric field about the spacecraft will repel a sufficiently large number of electrons such that a zero net current to the craft will result. Depending on the space plasma density, the steady-state charges can vary from near-zero to several kilovolts. In 1979 the SCATHA satellite was launched. One of its goals was to measure the build-up and breakdown of electrostatic charge on various spacecraft components, as well as to actively control the spacecraft charge using an electron beam. This mission was able to flight verify that it is possible to actively control the spacecraft charge. If another spacecraft had been present with a separation distance of about 20 meters, the natural uncontrolled SCATHA voltage levels would have been enough to impose inter-spacecraft forces in the milli-Newton level.

CFF plasma image The amount of electrical power required to generate these active electrical fields in less than 1 Watt. An ion engine operates by expelling charged particles (ions) at a very high velocity. The force generated is due to the momentum exchange between the particle and the spacecraft. The required large exit velocity of the ion particles results in the ion engines having a large electrical power requirement. To control the spacecraft charge, a comparable device to an ion engine would be used. However, here the ion exit velocity only would have to be large enough for the particle to escape the local electrical potential field. The massive reduction in required exit velocity results in a power requirement which is orders of magnitude smaller than that of an ion engine. The force exerted onto the Coulomb spacecraft due to momentum exchange with the expelled particle is negligible. The Coulomb satellite will only experience a force if additional charged spacecraft are in the vicinity. Similarly, the amount of mass expelled (charge ion particles) is so small that this mode of navigation control is referred to as being “essentially propellantless.”

CFF attitude image Note that such Coulomb forces will only control the relative motion of the satellite cluster, not the inertial motion of the cluster center of mass. For example, it would be impossible to use such Coulomb forces to boost the cluster orbit radius. However, it is possible to control the relative motion between the Coulomb satellites by changing the satellite charges. Thus, the Coulomb Formation Flying (CFF) concept allows for very fuel-efficient relative navigation with a very high control bandwidth. For example, a 1 meter spacecraft was found to be able to charge to 6 kV in as little as 8 ms using only 200 mW of power. The CFF concept could be used for general proximity flying (fly a sensor about a larger craft) or for controlling the relative motion of swarms or clusters of satellites. Since the magnitude of the Coulomb electrostatic force diminishes with 1/r2 of the separation distance, it is only effective for relatively tight formation/proximity flying scenario of 10-100 meters. For minimum separation distances larger than that, the required spacecraft charging levels simply become impractical. Further, the Coulomb force effectiveness is diminished in a high density space plasma environment. This is typically measured through the Debye length which indicates the exponential decay of the electrostatic field strength in a plasma environment. This decays is in addition to the natural point charge 1/r2 field strength reduction. For example, at LEO the Debye length is on the order of centimeters, thus preventing electrostatic forces from being an effective relative motion control method. At GEO, in comparison, the Debye length is between 100 and 1000 meters, depending on the current plasma density conditions.

Six Sat Image Developing control laws for such CFF concepts are challenging in that the charge dynamics are highly nonlinear and coupled. By changing the charge of a single satellite, the net resulting electrostatic force experienced by all other charged craft in the cluster will be changed as well. Static equilibrium solutions have been presented of the CFF concept where the formation center of mass is assumed to be in a circular orbit. Interesting in-plane two dimensional solutions, as well general three-dimensional solutions are found. However, none of the equilibrium solutions found so far are stable and would require an active charge control law to be developed. A control solution for a simplified two-spacecraft formation with equal satellite mass has been developed. Virtual Coulomb Structure The control law is based on an orbit element difference description of the relative motion and applies to both circular and elliptical cluster center of mass motion. While this control was shown to be globally stabilizing, it was not asymptotically stabilizing for all initial conditions. For example, if the initial formation has only in-plane satellite motion, and the final formation is to have out-of-plane motion, then such a relative orbit correction cannot be achieved with only inter-satellite forces. However, for the case of controlling only the semi-major axis of the satellites, it was shown that the control was indeed asymptotically stabilizing in differences in semi-major axes. As a result, the two-spacecraft control law was able to balance the semi-major axes of both satellites and achieve bounded relative motion.

The study of the CFF concept is just in the infancy. The charging technology is very feasible. However, a Coulomb spacecraft will need to be designed from the ground up to be able to handle a higher voltage level than is typical currently. Differential charging is to be minimized to avoid arcing. The potential benefits to tight proximity flying or formation flying are tremendous. The challenge is for the control engineer to exploit this concept and develop a relative navigation method that will utilize very little power, has very high bandwidth, and consumes essentially no fuel.

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