Magnetohydrodynamic Ion Drive As A Main Propulsion Unit For A Space Vehicle

Daniel Neuman
SFSU Physics Dept.
Spring '97

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Abstract | Introduction | Theory | Electron Bombardment Ion Engine | Conclusion | References

Abstract

For future interplanetary missions to Mars and beyond a new method of spacecraft propulsion must be implemented. Current chemical reaction based rockets will not be able to provide sufficient levels of performance to meet mission critical needs. This paper examines an alternative propulsion method, electric propulsion. Electric propulsion is the acceleration of propellant by electrostatic and electrodynamic body forces. The theory behind as well as the implementation and pros and cons will be discussed. It will be shown that electric propulsion is the only viable alternative to chemical rockets for large total impulse- high _ v missions.


Introduction

To understand the benefits of electric propulsion we must first understand some basic concepts of rocketry. The equation of motion of a spacecraft in a gravitational field is,[ ]

m = + Fg (I-1)

Where = acceleration of the rocket

= rate of change of rocket mass by exhaust of propellant

ue = exhaust velocity relative to rocket

Fg = local force of gravity

The term is the thrust T of the rocket,

T = (I-2)

The integral of the thrust over a complete trip is called the total impulse,

(I-3)

The specific impulse is defined to be the ratio of the thrust T to the rate of use of the sea level weight of propellant:

(I-4)

where g0 is the sea level acceleration of gravity. Specific impulse is essentially an indication of how much a rocket's velocity can be increased by a given amount of fuel[ ]. Specific impulse can be thought of as the gas mileage of the engine. From (I-3) we see that to obtain a large total impulse we can either have a large exhaust velocity or a large rate of change of the rocket mass. Equation (I-1) can be solved for the fraction of the original total rocket mass which can be accelerated through a velocity increment _ v

(I-5)

In the literature aerospace engineers are always talking about the `delta-v' of a particular propulsion system. Equation (I-1) can also be solved for delta-v, the change in velocity as a function of expended propellant mass.

_ v = ue ln (I-6)

Delta-v will tell an aerospace engineer how much mass needs to be expelled in order to bring about a desired change in velocity. Equation From (I-5) we see that ue has to be of the same order as _ v in order to bring a large fraction of the original mass to the final velocity. Here are some theoretically predicted values of _ v for impulsive missions over minimum propellant semiellipse trajectories[ ].

_ v values for a few long range missions

MISSION VELOCITY meters/sec
Earth orbit to Mars orbit and return 1.12 104
Earth surface to Mars surface and return 3.4 104
Earth orbit to Venus orbit and return 1.6 104
Earth orbit to Mercury orbit and return 3.1 104
Earth orbit to Jupiter orbit and return 6.4 104
Earth orbit to Saturn orbit and return 1.1 105

 

Now, for comparison here are some exhaust velocities of a few chemical rockets[ ].

Exhaust velocities for chemical rockets

Propellant type ue meters/sec
Liquid mono-propellants 1.7- 2.9 103
Solid propellants 2.1- 3.2 103
Liquid bi-propellants 2.9 - 4.5 103
State-of-the-art space shuttle 5.0 103

 

We see that for chemical rockets their exhaust velocities are not on the same order of magnitude as _ v. Chemical rockets can not bring a large fraction of their original mass up to a desired final velocity. Chemical rockets get around this limitation by using a staged propulsion system. As each stage is used up it is jettisoned and the total mass of the rocket decreases. But the staged system itself adds mass and complexity and is more expensive to build than a single stage system.

For long duration missions such as interplanetary travel or satellite station keeping where the total impulse and _ v are large, chemical rockets will not work efficiently.

The exhaust velocity of a chemical rocket is limited by several factors: (1) the total amount of energy available from a chemical reaction, (2) how much thermal stress the engine itself can withstand, and (3) the energy lost in internal modes. With all of these intrinsic limiting factors working against you, has to be very large to obtain large total impulse. Correspondingly their specific impulse is small. Typical values are on the order of a few kilograms/sec[ ]. Having large is very disadvantageous because the spacecraft will have to carry a large amount of fuel. With a larger mi the rocket will have to expend more fuel to escape earth's gravity well and there will be less available space for payload. Conventional rockets change their velocity by having a very large amount of thrust over a short time. What if you could really increase ue? If ue could be made large enough then would not have to be very large and you avoid the large penalties. You could build a spacecraft that can be smaller and lighter and obtain a higher final velocity. Figures(1-a,b,c) show the difference, in some critical mission parameters between, small ue chemical rockets and a large ue propulsion system. It is seen that with high ue and large specific impulse the trip time to Mars is drastically reduced.

Electric propulsion, the acceleration of propellant by electrostatic and electrodynamic body forces, is the answer. Typical ue and values are 3.0 104 m/s and a few milligrams/sec respectively[ ], numbers that are good enough to take us to the surface of Mars and back with a single stage. Electric propulsion devices do not suffer from the same limitations as chemical rockets. There is not such a strict limit to their ue, and there is no heating of the engine walls. They do have limitations, fundamentally different from chemical rockets. These limitations will be discussed in a later section of this paper.

Ion drives are a subfield of the larger electric propulsion device group. In a nutshell, ion drives work by ionizing a gaseous fuel such as Xenon and then accelerating it in an electric field and ejecting it out the back of the spaceship. One scheme, called the electron-bombardment method, ionizes the Xenon by bombarding it with energetic (~40eV) electrons. The ions and electrons are then accelerated, in different directions, through a potential difference. The accelerated ions leaving the unit provide the thrust. To keep the exhaust neutral, electrons need to be added to the exhaust stream shortly after leaving the thruster. This can be done by placing a thermionic cathode on the periphery of the ion beam. The thrust available using this method depends only on the exhaust speed, on the mass of the ion, and on the total ion flux that can be accommodated by the source-accelerator-neutralizer system.

Ion drives are a good idea because they can provide high specific impulse and very low thrust. With the ion drives high it can obtain the same or greater total impulse as a chemical rocket by thrusting for a longer period of time. The ion drives small allows it to obtain this velocity with a small amount of propellant mass ejected. This can translate into smaller, lighter propulsion systems. From a business point of view ion drives are cost-effective because with less space being taken up by engines there is more room for commercial payloads and thus more profit.

Historically the theory of electric propulsion has been around since 1906. Robert H. Goddard is considered the inventor. During the great space race of the 50's and 60's scientists knew about the benefits of electric propulsion but could not implement them for a few technical reasons. First, where was the electricity going to come from to accelerate the propellant? The thousand volt potential difference needed for acceleration of propellant could not be generated with the technology of the time. A small compact, light-weight power source was needed. Small nuclear reactors could power such a system but environmental concerns effectively grounded a nuclear fission powered rocket. Not until the invention of efficient solar cells and modern batteries-fuel cells can we have practical electric propulsion. Even so, electric propulsion powered by solar cells will only work out to about 3 AU's because of the decrease of solar flux with distance.


Theory

 

The basic theory of how ion engines work is almost embarrassingly simple. The equations of electrodynamics concerned with the motion of a charged particle in a constant electric and magnetic field are all we need. The equation of motion of a particle with charge q and mass m in a region of space with constant E and B is[ ],

 

The particle will undergo a circular orbit at a frequency called the cyclotron frequency.

With a radius, called the larmor radius given by,

 

An ion engine can be thought of as a cylindrical plasma where the E field and B field are in the same direction say the z direction(see figure(3)). If an ion was given an initial velocity purely in the z direction then the equation of motion simplifies to,

 

That is to say, if we can keep the component of velocity perpendicular to the direction of B and the magnitude of B very small the propellant ions will basically move in a straight trajectory. The electrons, on the other hand, are injected into the plasma nearly perpendicular to B. The electrons will follow a helical orbit in the opposite direction from the ions. The B field is of such strength that rl is equal to the radius of the plasma. Even when the ion's velocity has a perpendicular component, B is so small and their mass is so large compared with electrons that they still travel in basically a straight line. The end result is that the ions are accelerated out of the rocket by the electrostatic E field and electrons follow a much longer helical path to the anode.

We have learned about why we need electric propulsion and some of the general theory now lets get more specific.


Electron Bombardment Ion Engine

Space charge limited flows:

The electron bombardment Thruster can be seen in figures(2-a,b,c).

The propellant velocity is given by the equation for a charged particle that is accelerated through a potential difference.

 

One of the parameters that effect the thrust that an ion engine can produce is the ion flux that the engine can accommodate. Child's law[ ],

 

Where M = mass of the ion

q= charge of the ion

= Potential at ion source

= distance between accelerating grids

originally determined for electron current in a vacuum diode, represents one fundamental limit on the current that can be drawn across a given plane gap by a given potential difference. This is called the space-charge limited current. With this limit on the ion density there will be a corresponding limit on the thrust density. The limit on thrust density can be found from the relations for velocity, current and thrust[ ]. 

where A is the area of the beam and = NaMue is the mass flow rate per unit area. Note that the thrust density does not depend on the charge to mass ratio of the ions. This equation describes how the performance of the engine depends on the electric field strength that can be sustained in the gap. The exhaust velocity ue and the power required per unit area however, do depend on the charge to mass ratio[ ].

We see that if we could improve the charge to mass ratio there would be corresponding improvements in the power and exhaust velocity.

Production of positive ions:

How will the ions needed be created? What qualities will our ion source need to have? The ion source should be capable of producing an ion density that corresponds to the space charge limited current. The ion source must be efficient. The energy needed to create an ion must be less than the kinetic energy it receives from being accelerated through the potential difference. The ion source must produce a ratio of ions to neutrals that is very large. If there are neutrals in the propellant stream the ions will collide with them thereby randomizing both of their velocities. The out of focus ions and the neutrals, which will not be affected by any fields, can impinge on the accelerating electrode and cause sputtering damage. Finally, the ion source must maintain these characteristics over the lifetime of the thruster. Lifetimes can be many years for geosynchronous satellites.

Electron bombardment source:

The type of ion source used is the electron bombardment source. The electron bombardment source is derived from a magnetron discharge tube[ ](see figure ). Electrons are emitted on the center axis of the ionization chamber by a thermionic cathode. The electrons are attracted radially outward to a concentric cylindrical anode but can not reach it due to an applied weak magnetic field. The magnetic field causes the electrons to spiral back and fourth until a collision occurs. Depending on the collision cross section of the propellant atoms and the energy of the electrons some fraction of these collisions cause the propellant atoms to be ionized. In the steady state then, the ionization chamber is filled with a plasma of ions, electrons, and neutrals. The ions are extracted out of the ionization chamber by means of a strong electric field established between the accelerating grids at one end of the chamber. This field can provide the primary acceleration of the ion beam. To prevent the axial loss of electrons the inner grid and the opposite wall of the ionization chamber are kept at the same potential.

There are some engineering difficulties to over come. The erosion of the electron emitting cathode shortens the useful lifetime of the thruster. At the thermionic temperatures needed to sustain a desired electron discharge rate most metals have a large sublimation rate. Because the field that drives the electrons outward also drives the ions inward, serious sputtering damage can occur to the cathode. The accelerator grids also suffer sputtering damage in the course of their normal operation. There is some worry about the effects of low energy ions, created through charge-exchange phenomenon in the exhaust plume, impinging on spacecraft surfaces. This impingement could lead to a decrease in the useful life of the solar cells that would power such a craft. Research into cathodes and accelerating grids made out of exotic carbon-carbon compounds[ ] and the spatial characteristics of the exhaust plume[ ], is now being performed to address these issues.

The accelerating field:

An interesting problem presents itself in the design of the accelerating field. What should the geometry of the accelerating electrodes and the source surface be so that the ion beam with a specific current density and cross section, can be accelerated to a given velocity with optimum uniformity and with a minimum of impingement on the electrode surface? An analytic solution can be found by solving simultaneously the equations for ion flux, Newton's law and Poisson's equation. For given input parameters, ion velocity and beam size, equipotential surfaces are found. If a physical electrode were placed there at that potential and with the same shape, the ion flow would have the same characteristics as the input parameters. In this way we could design electrodes to produce propellant streams with the desired characteristics of high velocity, low divergence and minimum impingement of the grid surface.

Neutralizing the ion beam:

To produce useful thrust an ion engine must emit large amounts of positive ion current. Yet the total capacitance of a typical spacecraft is only 1 x 10-9 Farads. With such a small capacitance the spacecraft will quickly acquire a large negative potential at the rate

9 volts per sec per amp of ion current.

Very quickly the entire spacecraft would be charged to such a large negative potential that it would be impossible to eject any additional ions. This charge-up can be circumnavigated by emitting an identical electron current into the exhaust stream. Where this neutralization occurs is also important. If the unneutralized ion beam gets to far from the electrode, positive space-charge potentials in the beam will cause it to stall and or reflect back on itself. It has been found that the ion flow needs to be neutralized within a few multiples of the acceleration gap xa[ ]. This limit is not as strict as it may seem because the electrons will tend to migrate upstream and neutralize the ions before the electron source.

Ideally, we would inject electrons with the same velocity and density as the ion stream and charge neutrality would be guaranteed. Unfortunately thermionic emitters tend to emit electrons in all directions with a wide dispersion in velocities, most of them much higher than the mean ion velocity. In real world tests[ ] it has been found that the neutralization of the ion beam is much easier. Macroscopic mixing due to space-charge forces mix the two beams very efficiently so that the neutralization is not so dependent on the geometry. The ions are easily neutralized with just a simple thermionic cathode placed on the peripheral of the beam.

Acceleration-deceleration concept

What about the possibility of the injected electrons moving past the accelerating grid? If the electrons could make it past the grids and into the ionization chamber they would be strongly accelerated toward the ion source. These electrons would distort the potential profile in the acceleration gap, they would be a current drain on the power supply with no corresponding thrust, and they could damage the ion source through sputtering.

If a second grid were placed downstream of the accelerating ions, but before the electron source, at a lower potential then it could exclude the neutralizer electrons. This would also reduce the ion speed but without a loss in space-charge current thus giving a higher thrust density at lower specific impulse levels. It is possible to have the neutralizing filament act as a deaccelerator and an electron source. The neutralized ion beam plasma created near the source can act as a virtual deaccelerator grid. In this manner the beam can become space-charge neutralized before it is current-neutralized, meaning that virtual deaccelerators can neutralize the ion beam ahead of their actual physical placement. The net effect is to produce a higher thrust than a single stage thruster of the same exhaust velocity with no neutralizer electrons in the accelerator gap.

The Future

NASA has several proposed missions in the near future that will need electric propulsion. The New Millennium project, to launch a spacecraft in 1999 for an asteroid rendezvous mission,(see figure ( )) will need electric propulsion. All the planned missions to Mars(see figure( )) would benefit greatly from electric propulsion. Small, station keeping thrusters(see figure( )) for geosynchronous satellites need electric propulsion.

Work is being done at JPL to increase the specific impulse. If a larger mass propellant can be used the specific impulse will increase correspondingly. JPL is looking at C60, Buckminsterfullereen, as a potential propellant. With their much larger mass than Xenon and uncomplicated storage they are an attractive possibility.


Conclusion

If we want to go to Mars, if we want to do comet rendezvous missions, we need a better rocket engine technology. For the large total impulse missions NASA has planned for the near future, chemical rockets just will not do. With their low specific impulse and correspondingly high they cannot perform as needed. Electric propulsion can provide us with the necessary performance. Xenon ion bombardment thrusters have a specific impulse of at least an order of magnitude higher than chemical reaction engines and an of several orders of magnitude smaller. Spacecraft using them will not suffer the penalties of having most of their mass as fuel. They can have a large _ v, which is necessary for interplanetary missions. In this paper I have tried to show why electric propulsion is advantageous over chemical rocket engines.


References

[a ]"Overview of Electric Propulsion Devices and Power Systems " http://asao.lerc.nasa.gov/resources/ep-devices.html (1 April 1997).

[b ]Telc, Haifang "Ion Propulsion" http://gear.mae.cornall.edu/Boydgroup/sbala/IonPropulsion.html (1 April 1997).

[ c]Liang, Paul "Research" Plasmadynamics & Electric Propulsion Laboratory. March 1997. http://www.engin.umich.edu/dept/aero/spacelab/ (1 April 1997)

[ d]Viddeleer, R. "Ion Propulsion Diagnostic Sensor" Preparing for the Future Vol. 6 No.3. Sept. 1996. http://esapub.esrin.esa.it/pff/pffuv6n3/vidv6n3.htm (1 April 1997)

[ e]Szabo, James "Solar Electric Propulsion Systems" Nov. 1995. http://www.afbmd.laafb.af.mil/xrt/xrts/spclft/tnprop8.htm (1 April 1997)

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[g ]Santarius, John F. "Summary of lectures 28--31" May 1996. http://elvis.neep.wisc.edu~jfs/neep602/Summary.html (1 April 1997)

[h ]"The Student Electric Propulsion Project" http://vega.lpl.arizona~collins/eplab.html (1 April 1997)

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[j ]Jahn, Robert G.: "Physics of electric Propulsion," McGRAW-HILL BOOK COMPANY, New York 1968.

[k ]Blums, Elmars: "Heat and mass transfer in MHD flows," WORLD SCIENTIFIC PUBLISHING Co. Pte. Ltd, Singapore 1987.

[l ]Woods, L. C.: "Principles of Magnetoplasma Dynamics," OXFORD UNIVERSITY PRESS, New York 1987.

[m ]Rosa, Richard J.: "Magnetohydrodynamic Energy Conversion," McGRAW-HILL BOOK COMPANY, New York 1968.

[n ]Rose, David J. and Clark, Melville: "Plasmas and Controlled Fusion," JOHN WILEY & SONS, New York 1961.

[o ]Kristein, Peter T. et. Al.: "Space-Charge Flow," McGRAW-HILL BOOK COMPANY, New York 1967.



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