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Electrodynamic tethers are long conducting wires, such as the one deployed from the tether satellite, which can operate on electromagnetic principles as generators, by converting their kinetic energy to electrical energy, or as motors, converting electrical energy to kinetic energy. Electric potential is generated across a conductive tether by its motion through the Earth's magnetic field. The choice of the metal conductor to be used in an electrodynamic tether is determined by a variety of factors. Primary factors usually include high electrical conductivity, and low density. Secondary factors, depending on the application, include cost, strength, and melting point.

## Tether propulsionEdit

Main article: Tether propulsion

As part of a tether propulsion system, crafts can use long, strong conductors (though not all tethers are conductive) to change the orbits of spacecraft. It has the potential to make space travel significantly cheaper. It is a simplified, very low-budget magnetic sail. It can be used either to accelerate or brake an orbiting spacecraft. When direct current is pumped through the tether, it exerts a force against the magnetic field, and the tether accelerates the spacecraft.

## Tethers as generatorsEdit

Main article: Electrical generator

An electrodynamic tether is attached to an object, the tether being oriented at an angle to the local vertical between the object and a planet with a magnetic field. When the tether cuts the planet's magnetic field, it generates a current, and thereby converts some of the orbiting body's kinetic energy to electrical energy. As a result of this process, an electrodynamic force acts on the tether and attached object, slowing their orbital motion. The tether's far end can be left bare, making electrical contact with the ionosphere via the phantom loop. Functionally, electrons flow from the space plasma into the conductive tether, are passed through a resistive load in a control unit and are emitted into the space plasma by an electron emitter as free electrons. In principle, compact high-current tether power generators are possible and, with basic hardware, 10 to 25 kilowatts appears to be attainable.

### Voltage and currentEdit

NASA has conducted several experiments with Plasma Motor Generator (PMG) tethers in space. An early experiment used a 500 meter conducting tether. In 1996, NASA conducted an experiment with a 20,000-meter conducting tether. When the tether was fully deployed during this test, the orbiting tether generated a potential of 3,500 volts. This conducting single-line tether was severed after five hours of deployment. It is believed that the failure was caused by an electric arc generated by the conductive tether's movement through the Earth's magnetic field.

When a tether is moved at a velocity (v) at right angles to the Earth's magnetic field (B), an electric field is observed in the tether's frame of reference. This can be stated as:

E = v * B = vB

The direction of the electric field (E) is at right angles to both the tether's velocity (v) and magnetic field (B). If the tether is a conductor, then the electric field leads to the displacement of charges along the tether. Note that the velocity used in this equation is the orbital velocity of the tether. The rate of rotation of the Earth, or of its core, is not relevant. In this regard, see also homopolar generator.

### Voltage across conductorEdit

With a long conducting wire of length L, an electric field E is generated in the wire. It produces a voltage V between the opposite ends of the wire. This can be expressed as:

$V = \mathbf{E}\cdot\mathbf{L} = EL \cos \tau = vBL \cos \tau$

where the angle τ is between the length vector (L) of the tether and the electric field vector (E), assumed to be in the vertical direction at right angles to the velocity vector (v) in plane and the magnetic field vector (B) is out of the plane.

### Current in conductorEdit

An electrodynamic tether can be described as a type of thermodynamically "open system". Electrodynamic tether circuits cannot be completed by simply using another wire, since another tether will develop a similar voltage. Fortunately, the Earth's magnetosphere is not "empty", and, in near-Earth regions (especially near the Earth's atmosphere) there exist highly electrically conductive plasmas which are kept partially ionized by solar radiation or other radiant energy. The electron and ion density varies according to various factors, such as the location, altitude, season, sunspot cycle, and contamination levels. It is known that a positively charged bare conductor can readily remove free electrons out of the plasma. Thus, to complete the electrical circuit, a sufficiently large area of uninsulated conductor is needed at the upper, positively charged end of the tether, thereby permitting current to flow through the tether.

However, it is more difficult for the opposite (negative) end of the tether to eject free electrons or to collect positive ions from the plasma. It is plausible that, by using a very large collection area at one end of the tether, enough ions can be collected to permit significant current flow through the plasma. This was demonstrated during the Shuttle orbiter's TSS-1R mission, when the shuttle itself was used as a large plasma contactor to provide over an ampere of current. Improved methods include creating an electron emitter, such as a thermionic cathode, plasma cathode, plasma contactor, or field electron emission device. Since both ends of the tether are "open" to the surrounding plasma, electrons can flow out of one end of the tether while a corresponding flow of electrons enters the other end. In this fashion, the voltage that is electromagnetically induced within the tether can cause current to flow through the surrounding space environment, completing an electrical circuit through what appears to be, at first glance, an open circuit.

### Tether current flowEdit

The amount of current (I) flowing through a tether depends on various factors. One of these is the circuit's total resistance (R). The circuit's resistance consist of three components:

1. the effective resistance of the plasma,
2. the resistance of the tether, and
3. a control variable resistor.

In addition, a parasitic load is needed. The load on the current may take the form of a charging device which, in turn, charges reserve power sources such as batteries. The batteries in return will be used to control power and communication circuits, as well as drive the electron emitting devices at the negative end of the tether. As such the tether can be completely self-powered, besides the initial charge in the batteries to provide electrical power for the deployment and startup procedure.

The charging battery load can be viewed as a resistor which absorbs power, but stores this for later use (instead of immediately dissipating heat). It is included as part of the "control resistor". The charging battery load is not treated as a "base resistance" though, as the charging circuit can be turned off at anytime. When off, the operations can be continued without interruption using the power stored in the batteries.

## ChallengesEdit

One complication to these techniques is that if the tether rotates, the direction of current must reverse (such as is the case in alternating currents of alternators). Others include pendular motion instability and electrical surges.

### Pendular motion instabilityEdit

Electrodynamic tethers deployed along the local vertical ('hanging tethers') suffer from dynamical instability. Pendular motion causes the tether vibration amplitude to build up under the action of electromagnetic interaction. As the mission time increases, this behavior can compromise the performance of the system. Over a few weeks, electrodynamic tethers in Earth orbit can also build up vibrations in many modes, as their orbit interacts with irregularities in magnetic and gravitational fields.

One plan to control the vibrations is to actively vary the tether current to counteract the growth of the vibrations. Electrodynamic tethers can be stabilized by reducing their current when it would feed the oscillations, and increasing it when it opposes oscillations. Simulations have demonstrated that this can control tether vibration.

See also: Error: Template must be given at least one article name This approach requires sensors to measure tether vibrations, which can either be an inertial navigation system on one end of the tether, or satellite navigation systems mounted on the tether, transmitting their positions to a receiver on the end.

Another proposed method is to utilise spinning electrodynamic tethers instead of hanging tethers. The gyroscopic effect provides passive stabilisation, avoiding the instability.

### SurgesEdit

As mentioned earlier, conductive tethers have failed from unexpected current surges. Unexpected electrostatic discharges have cut tethers (eg. see Tethered Satellite System Reflight (TSS-1R) on STS-75), damaged electronics, and welded tether handling machinery. It may be that the Earth's magnetic field is not as homogeneous as some engineers have believed.