## Magnetic Field for power and propulsion

An electrodynamic tether, which is basically a long electrically conducting wire, can propel a spacecraft by virtue of the force a magnetic field exerts on the wire when it is carrying an electrical current. This phenomenon was first explained scientifically by Ampere, one of the pioneers in the study of electromagnetism, around 180 years ago. The physics describing the nature of this force, which acts on any charged particle moving through a magnetic field (including the electrons moving in a current-carrying wire), was described by Hendrik Lorentz in 1895 in an equation that now bears his name. The force acts in a direction perpendicular to both the direction of current flow and the direction of the magnetic field (Figure 15.1). Electric motors make use of this force: a wire loop in a magnetic field is made to rotate by the torque the Lorentz force exerts on it due to an alternating current in the loop interacting with the field

FIGURE 15.1 The Lorentzforce (F) on a charged particle (P) is perpendicular to the magnetic field and the particle velocity V (the direction of current flow). The magnetic field direction is down, into the page.

produced by a magnet. The motion of the loop is transmitted to a shaft, thus producing a motor. Michael Faraday demonstrated this first electric motor about 1821.

Given that the fundamental physics was worked out almost two centuries ago, the working principle of an electrodynamic tether propulsion system is not new, but its application to space propulsion may change the way we plan space missions. In essence, a tether thruster is just a clever way of getting an electrical current to flow in a long orbiting wire (the tether) so that the Earth's magnetic field will accelerate the wire and, consequently, the payload attached to the wire. The direction of current flow in the tether, either toward or away from the Earth along the local vertical, determines whether the magnetic force will raise or lower the orbit. The key point is that all of this is done without the need for fuel. An electrodynamic tether provides propulsion by interacting with the natural space environment and does not require any resupply! They have even been tested in space.

To understand how they work, a short description of the space environment in which they operate is in order. First of all, electrodynamic tethers work best when they are in the presence of space plasma. Plasma is nothing more than a collection of freely moving ions and electrons. In a system without external energy coming in, these ions (which are positively charged) and electrons (which carry a negative charge) would attract one another and produce electrically neutral atoms without a net charge. When energy is freely available—typically from the Sun in the form of ultraviolet light—electrons are stripped from atoms, creating the plasma and sustaining it. The residual atmosphere in low Earth orbit contains plasma. Another natural environmental factor required for electrodynamic tether propulsion is a magnetic field. The Earth is surrounded by a fairly strong magnetic field that is thought to be produced by our planet's molten iron core,. The strength of the field decreases with distance, making it fairly strong in low Earth orbit and weak at geostationary orbital altitudes.

Electrodynamic tethers were successfully demonstrated in space by flights of the Plasma Motor Generator (PMG) in 19931 and the Tethered Satellite Systems (TSS-1 and TSS-1R) in 1992 and 1996.2,3 All three missions deployed long conducting tethers from orbiting spacecraft and successfully generated a current, though none used the current to provide measurable propulsion. Readers with a background or knowledge of electricity and magnetism will immediately question how this system can produce net thrust since a loop is required for current to flow. Attaching a wire to only one terminal on your car battery does not produce a current flow—the wire(s) must be connect to both terminals or one terminal and the ground. In such a loop, the force on the tether resulting from the current flowing through it in one direction would be exactly canceled by the current flowing back through the wire loop in the other direction (which "closes" the circuit) producing no net thrust! The answer is that, in space, the tether forms only one half of the loop; the space plasma in the ionosphere forms the other. The tethered system extracts electrons from the plasma at one end (upper or lower, depending upon the deployment direction and intended thrust motion) and carries them through the tether to the other end, where they are returned to the plasma. Currents in the plasma then complete the circuit. The net force caused by a magnetic field acting on a current-carrying closed loop of wire (i.e. a normal circuit) would be zero, since the force on one length of the wire would be canceled by that on the other through which the current was flowing in the opposite direction. However, since there is no mechanical attachment of the tethered system to the plasma, magnetic forces on the plasma currents do not affect the tether motion. In effect, we have a length ofwire with a unidirectional current flowing in it, and this wire is accelerated by Earth's magnetic field (Figure 15.2).

Imagine a spacecraft in low Earth orbit, traveling at 8 kilometers per second immediately after being launched into space by a rocket. A spring

1 McCoy, J.E. et al., "Plasma Motor Generator (PMG) Flight Experiment Results,'' 4th International Conference on Tethers in Space, Smithsonian Institution, Washington, DC, 10— 14 April, 1995.

2 Strim, B., Pasta, M. and Allais, E., "TSS-1 vs. TSS-1R,'' 4th International Conference on Tethers in Space, Smithsonian Institution, Washington, DC, 10—14 April, 1995.

3 Raitt, W.J. et al., "The NASA/ASI TSS-1 Mission: Summary of Results and Reflight Plans,'' 4th International Conference on Tethers in Space, Smithsonian Institution, Washington, DC, 10—14 April, 1995.

electron emitter

s/c electron flow electrodynamic tether electron collector s/c s/c velocity

Earth

FIGURE 15.2 An electrodynamic tether in low Earth orbit, with a unidirectional current flow. The spacecraft (s/c) is attached to the tether. The spacecraft's acceleration (As/c) is caused by the interaction with Earth's magnetic field.

ejects upward a small payload attached to the spacecraft by a conducting tether. The tether deploys upward from the spacecraft by the forces exerted due to the difference in gravitational attraction between the payload and the spacecraft (technically known as the "gravity gradient force"). This occurs because the force of gravity decreases with distance. And the distance created initially by the spring ejection is sufficient to produce a significantly different gravitational force acting on the spacecraft versus the payload—effectively pulling the tether from a spool to virtually any length desired. Tethers as long as 20 kilometers in length have been deployed this way in space.

But what is the source of the voltage required to drive the current? The voltage across a vertically deployed conducting tether, which results just from its orbital motion through Earth's magnetic field, is positive at the top and negative at the bottom. This is once again due to the Lorentz force acting on the electrons in the tether. The magnetic force on the tether wire has a component opposite to the direction of motion, and therefore slows down the system, lowering its altitude, leading eventually to reentry. In this "generator" mode of operation the Lorentz force serves both to drive the current and then act on the current to decelerate the system. The TSS and PMG missions described above demonstrated this in space, but, as stated previously, no measurements were made to quantify the relatively small orbital changes. And that was a shame!

In addition to not requiring any fuel, no onboard power source is required to drive the electrical current flow in either the orbit-raising or orbit-lowering modes. Again, the environment provided by nature gives us all we need—sunlight. To raise the orbit, sunlight falling on a solar array can be converted to the electrical energy required to drive the tether current in the opposite direction. To lower the orbit, the power comes from the orbital energy of the spacecraft (supplied by the Earth-to-orbit launcher when it placed the system into orbit).

Having established that an electrodynamic tether system can provide essentially "free" propulsion around any planet with both a plasma and a magnetic field, what might it be used for? The short answer is "lots of things!'' From extending the orbital lifetime of large space structures like the International Space Station, to providing a lightweight deorbit system for use at the end of a space mission (so as to not create more space junk), they can be used by virtually any spacecraft in low Earth orbit.

The International Space Station, or ISS, experiences significant aerodynamic drag in its approximately 400-kilometer altitude orbit. In this low Earth orbit, the vacuum is not perfect. At space station altitudes, the atmospheric pressure is very low, but it is not zero—contrary to popular misperception, Earth orbit is not a perfect vacuum! When the ISS, having a very large surface area, passes through this tenuous gas traveling at 8 kilometers per second, it experiences a continuous drag force of approximately 1 newton. The drag is caused by the collision of the space station with the residual atmosphere. It is no different from the drag a car experiences when it is moving through the air on the freeway—though the magnitude ofthe drag force in space is significantly less because there is so little atmosphere at these altitudes. It is a very small force, approximately the same force that a piece of notebook paper exerts on the palm of your hand. But it is a constant 1 newton force, causing a slow but steady braking force on the station. As a result, the space station's altitude slowly decays until a reboost maneuver is performed. Without reboost, the ISS would sink ever lower until it finally burned up in the atmosphere. Reboosting something as massive as the space station requires a propulsion system and, conventionally, fuel—lots of fuel.

Outfitting the space station with a tether propulsion system would significantly reduce or eliminate its dependence on Earth-launched propellant resupply, which is needed to accomplish the required reboost.4 The ISS can supply its own electrical power using solar arrays but not its own propellant. A 7-kilometer tether and 6 kilowatts of electrical power could reduce the number of fuel resupply flights to the ISS, potentially saving \$1 billion over a decade of operation! Even if the planned frequency of resupply flights to the ISS is maintained, putting a tether propulsion system on board would then provide the option to trade power for increased payload capacity. Resupply vehicles might then deliver useful cargo like scientific instruments, replacement parts, and crew supplies rather than fuel.

Another critical application of tether propulsion might be for use during the assembly of large space vehicles going to the Moon or Mars. Many of the options being considered for such exploration involve putting together large vehicles from many smaller pieces launched from Earth. A tether reboost system would allow these pieces to remain in orbit indefinitely while the remaining pieces are launched from Earth and thus provide mission flexibility if a launch delay is encountered. And no launch costs would be incurred for the massive amounts of fuel that would otherwise be required.

A tether might also be used on an orbital tug to move payloads in LEO after launch. The tug would rendezvous with the payload and launch vehicle, dock with the payload, and maneuver it to a new orbital altitude or inclination within LEO without the use of boost propellant. The tug could then lower its own orbit to rendezvous with the next payload and repeat the process. Such a system could perform multiple orbital-maneuvering assignments without resupply, substantially lowering costs.5 Current technology requires that a new upper stage be built, used, and thrown away for each of these mission phases.

Tether propulsion would also be useful for one of the most propulsively intense orbital operations—changing a spacecraft's orbital inclination.

4 Johnson, L. and Herrmann, M., International Space Station Electrodynamic Tether Reboost

Study. NASA/TM-1998-208538.

5 Johnson, L., "The Tether Solution,'' IEEE Spectrum, July 2000.

When a rocket is launched from the ground, some of the Earth's rotational energy is carried with it, lowering the amount of energy that must be added to achieve orbital velocity. This is why spacecraft are almost always launched eastward, and not westward, where the rocket would be acting against the Earth's rotation. The launch point also determines the inclination, or tilt relative to the ground, of the spacecraft's orbit as it moves around the Earth. Recall that the Earth is tilted on its axis by approximately 24 degrees. (It is this axial tilt that provides our seasons.) As a spacecraft orbits, the tilted Earth rotates beneath it, circumscribing an orbital trace that appears to move up and then down across the face of the Earth. The higher the latitude of the launch, the more northerly the trace appears. This is the orbital inclination of the spacecraft, and to change this inclination in space after launch requires a large amount of propulsive thrust, hence propellant. Given that most US launches occur in Florida, which has a 28.5-degree latitude, the easiest attainable orbit has a 28.5-degree inclination. A spacecraft equipped with an electrodynamic tether could selectively flow current through the wire to maximize the thrust out of the orbital plane, resulting in an inclination change. And no fuel would be required!

Electrodynamic tether propulsion does, however, have limits. It can only be used where the magnetic field is strong and the plasma current densities are rather large. For Earth, this limits their use to between approximately 400 and 2,000 kilometers. Below 400 kilometers, the atmosphere is too dense and the atmospheric drag on the tether exceeds its ability to produce thrust. Above 2,000 kilometers the plasma density gets so low that there are simply not enough electrons to collect and produce the required current.

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