Electrodynamic tether

Long conducting wires which can act as electrical motors or generators

Electrodynamic tethers (EDTs) are long conducting wires, such as one deployed from a 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 a planet's magnetic field. A number of missions have demonstrated electrodynamic tethers in space, most notably the TSS 1, TSS 1R, and Plasma Motor Generator (PMG) experiments.

As part of a tether propulsion system, craft 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. When direct current is applied to the tether, it exerts a Lorentz force against the magnetic field, and the tether exerts a force on the vehicle. It can be used either to accelerate or brake an orbiting spacecraft. In 2012 Star Technology and Research was awarded a $1.9 million contract to qualify a tether propulsion system for orbital debris removal.

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. The tether's far end can be left bare, making electrical contact with the ionosphere. When the tether intersects the planet's magnetic field, it generates a current, and thereby converts some of the orbiting body's kinetic energy to electrical energy. 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. As a result of this process, an electrodynamic force acts on the tether and attached object, slowing their orbital motion. In a loose sense, the process can be likened to a conventional windmill the drag force of a resistive medium (air or, in this case, the magnetosphere) is used to convert the kinetic energy of relative motion (wind, or the satellite's momentum) into electricity. In principle, compact high current tether power generators are possible and, with basic hardware, tens, hundreds, and thousands of kilowatts appears to be attainable.

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:

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.

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 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.

Understanding electron and ion current collection to and from the surrounding ambient plasma is critical for most EDT systems. Any exposed conducting section of the EDT system can passively ('passive' and 'active' emission refers to the use of pre stored energy in order to achieve the desired effect) collect electron or ion current, depending on the electric potential of the spacecraft body with respect to the ambient plasma. In addition, the geometry of the conducting body plays an important role in the size of the sheath and thus the total collection capability. As a result, there are a number of theories for the varying collection techniques. The primary passive processes that control the electron and ion collection on an EDT system are thermal current collection, ion ram collection effects, electron photoemission, and possibly secondary electron and ion emission. In addition, the collection along a thin bare tether is described using orbital motion limited (OML) theory as well as theoretical derivations from this model depending on the physical size with respect to the plasma Debye length. These processes take place all along the exposed conducting material of the entire system. Environmental and orbital parameters can significantly influence the amount collected current. Some important parameters include plasma density, electron and ion temperature, ion molecular weight, magnetic field strength and orbital velocity relative to the surrounding plasma. Then there are active collection and emission techniques involved in an EDT system. This occurs through devices such as hollow cathode plasma contactors, thermionic cathodes, and field emitter arrays. The physical design of each of these structures as well as the current emission capabilities are thoroughly discussed.

The concept of current collection to a bare conducting tether was first formalized by Sanmartin and Martinez Sanchez. is defined as the characteristic shielding distance in a plasma, and is described by the equation

This distance, where all electric fields in the plasma resulting from the conductive body have fallen off by 1/e, can be calculated. OML theory is defined with the assumption that the electron Debye length is equal to or larger than the size of the object and the plasma is not flowing. The OML regime occurs when the sheath becomes sufficiently thick such that orbital effects become important in particle collection. This theory accounts for and conserves particle energy and angular momentum. As a result, not all particles that are incident onto the surface of the thick sheath are collected. The voltage of the collecting structure with respect to the ambient plasma, as well as the ambient plasma density and temperature, determines the size of the sheath. This accelerating (or decelerating) voltage combined with the energy and momentum of the incoming particles determines the amount of current collected across the plasma sheath. The orbital motion limit regime is attained when the cylinder radius is small enough such that all incoming particle trajectories that are collected are terminated on the cylinder's surface are connected to the background plasma, regardless of their initial angular momentum (i. e., none are connected to another location on the probe's surface). Since, in a quasi neutral collisionless plasma, the distribution function is conserved along particle orbits, having all “directions of arrival” populated corresponds to an upper limit on the collected current per unit area (not total current). In an EDT system, the best performance for a given tether mass is for a tether diameter chosen to be smaller than an electron Debye length for typical ionospheric ambient conditions (Typical ionospheric conditions in the from 200 to 2000 km altitude range, have a T e ranging from 0.1 eV to 0.35 eV, and n e ranging from 10^10 m^ 3 to 10^12 m^ 3 ), so it is therefore within the OML regime. Tether geometries outside this dimension have been addressed. OML collection will be used as a baseline when comparing the current collection results for various sample tether geometries and sizes. In 1962 Gerald H. Rosen derived the equation that is now known as the OML theory of dust charging. According to Robert Merlino of the University of Iowa, Rosen seems to have arrived at the equation 30 years before anyone else.

For a variety of practical reasons, current collection to a bare EDT does not always satisfy the assumption of OML collection theory. Understanding how the predicted performance deviates from theory is important for these conditions. Two commonly proposed geometries for an EDT involve the use of a cylindrical wire and a flat tape. As long as the cylindrical tether is less than one Debye length in radius, it will collect according to the OML theory. However, once the width exceeds this distance, then the collection increasingly deviates from this theory. If the tether geometry is a flat tape, then an approximation can be used to convert the normalized tape width to an equivalent cylinder radius. This was first done by Sanmartin and Estes and more recently using the 2 Dimensional Kinetic Plasma Solver (KiPS 2 D) by Choiniere et al. This flowing plasma analysis as it applies to EDTs have been discussed.

The next step in developing a more realistic model for current collection is to include the magnetic field effects and plasma flow effects. Assuming a collisionless plasma, electrons and ions gyrate around magnetic field lines as they travel between the poles around the Earth due to magnetic mirroring forces and gradient curvature drift. They gyrate at a particular radius and frequency dependence upon their mass, the magnetic field strength, and energy. These factors must be considered in current collection models.

When the conducting body is negatively biased with respect to the plasma and traveling above the ion thermal velocity, there are additional collection mechanisms at work. For typical Low Earth Orbits (LEOs), between 200 km and 2000 km, the velocities in an inertial reference frame range from 7.8 km/s to 6.9 km/s for a circular orbit and the atmospheric molecular weights range from 25.0 amu (O+, O2+, & NO+) to 1.2 amu (mostly H+), respectively. Assuming that the electron and ion temperatures range from ~0.1 eV to 0.35 eV, the resulting ion velocity ranges from 875 m/s to 4.0 km/s from 200 km to 2000 km altitude, respectively. The electrons are traveling at approximately 188 km/s throughout LEO. This means that the orbiting body is traveling faster than the ions and slower than the electrons, or at a mesosonic speed. This results in a unique phenomenon whereby the orbiting body 'rams' through the surrounding ions in the plasma creating a beam like effect in the reference frame of the orbiting body.

Porous endbodies have been proposed as a way to reduce the drag of a collecting endbody while ideally maintaining a similar current collection. They are often modeled as solid endbodies, except they are a small percentage of the solid spheres surface area. This is, however, an extreme oversimplification of the concept. Much has to be learned about the interactions between the sheath structure, the geometry of the mesh, the size of the endbody, and its relation to current collection. This technology also has the potential to resolve a number of issues concerning EDTs. Diminishing returns with collection current and drag area have set a limit that porous tethers might be able to overcome. Work has been accomplished on current collection using porous spheres, by Stone et al. and Khazanov et al. It has been shown that the maximum current collected by a grid sphere compared to the mass and drag reduction can be estimated. The drag per unit of collected current for a grid sphere with a transparency of 80 to 90% is approximately 1.2 – 1.4 times smaller than that of a solid sphere of the same radius. The reduction in mass per unit volume, for this same comparison, is 2.4 – 2.8 times. This limit depends on the emission surface area, the potential difference across the plasma gap and the distance of that gap. Further discussion of this topic can be found.

There are three active electron emission technologies usually considered for EDT applications: hollow cathode plasma contactors (HCPCs), thermionic cathodes (TCs), and field emission cathodes (FEC), often in the form of field emitter arrays (FEAs). System level configurations will be presented for each device, as well as the relative costs, benefits, and validation.

Thermionic emission is the flow of electrons from a heated charged metal or metal oxide surface, caused by thermal vibrational energy overcoming the work function (electrostatic forces holding electrons to the surface). The thermionic emission current density, J, rises rapidly with increasing temperature, releasing a significant number of electrons into the vacuum near the surface. The quantitative relation is given in the equation

This equation is called the Richardson Dushman or Richardson equation. (ф is approximately 4.54 eV and AR ~120 A/cm2 for tungsten). Once the electrons are thermionically emitted from the TC surface they require an acceleration potential to cross a gap, or in this case, the plasma sheath. Electrons can attain this necessary energy to escape the SCL of the plasma sheath if an accelerated grid, or electron gun, is used. The equation

shows what potential is needed across the grid in order to emit a certain current entering the device. Here, η is the electron gun assembly (EGA) efficiency (~0.97 in TSS 1), ρ is the perveance of the EGA (7.2 micropervs in TSS 1), ΔVtc is the voltage across the accelerating grid of the EGA, and It is the emitted current.]] TC electron emission will occur in one of two different regimes: temperature or space charge limited current flow. For temperature limited flow every electron that obtains enough energy to escape from the cathode surface is emitted, assuming the acceleration potential of the electron gun is large enough. In this case, the emission current is regulated by the thermionic emission process, given by the Richardson Dushman equation. In SCL electron current flow there are so many electrons emitted from the cathode that not all of them are accelerated enough by the electron gun to escape the space charge. In this case, the electron gun acceleration potential limits the emission current. The below chart displays the temperature limiting currents and SCL effects. As the beam energy of the electrons is increased, the total escaping electrons can be seen to increase. The curves that become horizontal are temperature limited cases.

Hollow cathodes emit a dense cloud of plasma by first ionizing a gas. This creates a high density plasma plume which makes contact with the surrounding plasma. The region between the high density plume and the surrounding plasma is termed a double sheath or double layer. This double layer is essentially two adjacent layers of charge. The first layer is a positive layer at the edge of the high potential plasma (the contactor plasma cloud). The second layer is a negative layer at the edge of the low potential plasma (the ambient plasma). Further investigation of the double layer phenomenon has been conducted by several people. One type of hollow cathode consists of a metal tube lined with a sintered barium oxide impregnated tungsten insert, capped at one end by a plate with a small orifice, as shown in the below figure. The high electron velocities lead to electron currents much greater than xenon ion currents. Below the electron emission saturation limit the contactor acts as a bipolar emissive probe. Each outgoing ion generated by an electron allows a number of electrons to be emitted. This number is approximately equal to the square root of the ratio of the ion mass to the electron mass. It can be seen in the below chart what a typical I V curve looks like for a hollow cathode in electron emission mode. Given a certain keeper geometry (the ring in the figure above that the electrons exit through), ion flow rate, and Vp, the I V profile can be determined. [111 113]. [[File:Fig222 Hollow Cathode Curve. PNG|thumbnail|center|300px|Typical I V Characteristic curve for a Hollow Cathode. [[File:Fig223 Hollow Cathode Geometry. PNG|thumb|400px|Typical Schematic detailing the HC emission geometry. photoemission, secondary electron emission, and secondary ion emission.

In order to integrate all the most recent electron emitters, collectors, and theory into a single model, the EDT system must first be defined and derived. Once this is accomplished it will be possible to apply this theory toward determining optimizations of system attributes. There are a number of derivations that solve for the potentials and currents involved in an EDT system numerically. The derivation and numerical methodology of a full EDT system that includes a bare tether section, insulating conducting tether, electron (and ion) endbody emitters, and passive electron collection is described. This is followed by the simplified, all insulated tether model. Special EDT phenomena and verification of the EDT system model using experimental mission data will then be discussed.