Power Beaming 199 Independent Research Project
Design of a FEL System Capable of Delivering 1kW of Electrical Power to Satellites in GEO.
Chris Muller
UCLA Department of
Physics and Astronomy
Abstract:
Power beaming refers to the practice of transferring power from one place to another. The concept of power beaming has been around since the 1950.s but technical and economic hurdles prevented implementation. Recent advances in Free Electron Laser, FEL, and conventional laser technology have lowered some of these hurdles. Finding the optimal parameters for power beaming is a complex task because of the correlations between parameters that are not immediately obvious. The desired result is the maximum efficiency for energy transferred from the transmitter to the receiver.
Intro:
Power beaming is the process of transferring power from one place to another with out wires. The field can be separated into two distinct subfields; where power is transferred from earth, and where power is transferred to earth. When transferring power from earth the applications are mainly the powering of satellites or moon bases, asteroid deflection by vaporization of small portions of the asteroid, orbital raising without the use of chemical propellant, etc. For the subfield of transferring power to earth the main application is that of a large solar array beaming collected solar power to conversion stations located on earth.
In this paper study we will look at the application of beaming power from earth. The powering of existing and future satellites is an economically interesting subject. This causes an increase in the likely hood of funding for this type of research because of the immediately realizable returns for investors. According to a paper by Geoffrey A. Landis of NASA.s Glenn Research Center this technology could significantly decrease the cost of transporting a satellite to orbit by .Eliminating the requirement for an energy storage system [which] could reduce satellite mass by 10%.(1). According to this paper this energy storage system which constitutes 10% of the mass is used to power the satellite for 1% of its run time.
Once the technology that this research produces has been tested it can be used to perform other tasks that do not have a large, quick return on investment. The initial investment to decrease the cost of launching a satellite into orbit and to extend the life of satellites already in orbit will have many other far reaching implications. The technology can be used to perform such tasks as orbital raising, powering of a moon base during the 354 hour lunar night, location of orbital debris, interplanetary probe launch, interstellar launch, etc. (2)
High Average Power:
In order for a laser to be useful for power beaming applications it must have a high average power. This is due to the large fraction of energy lost in the transfer from .wall outlet. power to .usable. power received by the receiver. Power is lost due to atmospheric absorption, diffraction, coupling in the undulator, solar panel inefficiencies, ground optics, and wall power to beam power conversion. These losses combine to necessitate a high average power beam to .beam. any appreciable power to space.
Efficiency Calculation:
Two efficiencies that don.t have as large an influence on the cost of beamed power are the efficiency of converting outlet power to electron beam energy and electron beam energy to laser energy. These efficiencies are not as important because of the relative cost of producing power on earth as opposed to the cost of producing/storing it in space. These two processes are still difficult but can be done for a relatively little money.
The efficiency of converting outlet power to beam energy comes from the coupling of the particles to the RF. If we take the example of an electron accelerator we see that first the electrons must be freed from the cathode by using a laser to eject them, heating the cathode (generally LaB6), or pulling them off the cathode by strong electric field gradient (dark current). Then these electrons must be accelerated by the electric field in the gun. This is done by pumping RF power into the gun creating a strong electric field to accelerate the electrons. The efficiency of this comes in two parts, the efficiency due to converting electrical outlet power into RF power (about 60%), and then the coupling efficiency of the electrons to the RF power (about 10%). This leads to an over all efficiency of outlet power to beam power of 6%.
The coupling efficiency of the electron beam to the undulator constitutes the second portion of this inefficiency. Typical efficiencies range from .1-1%. This can be improved by implementing tapering and increasing the length of the undulator. With these two changes the efficiency can be increased to more than 10%. For this paper study we will assume that the coupling efficiency is 10%, this claim will be justified in the prototype section.
Directing the beam at the satellite has multiple inherent inefficiencies. This consists of pointing the transmitting dish at the satellite and the inefficiencies due to ground optics. For this paper we will assume that the tracking system is sufficiently precise to keep the entire solar array illuminated at all times. The energy loss due to ground optics, however, will not be ignored. We will assume that the tracking system is not composed of any exotic components; it is composed of only mirrors and lenses. For this situation we can assume that the system will have efficiency greater than 50%. If we take the transmission efficiency of a lens and mirror to be 98% and 99% respectively, the over all efficiency will be,
where l and m are the number of lenses and mirrors respectively. In order to have an efficiency greater than 50% there can be no more than ~ (l + 2m = 68) optical components. This equation comes from the fact that = .9801 and ~ ( = .505). This number of optical components is most likely more than enough to focus and direct any laser of this type.
Atmospheric absorption accounts for another sizeable fraction of the energy loss. Even while working with a frequency free from absorption from molecules such as H2O, CO, CO2, O3, etc. there is still a significant portion of the energy that gets absorbed or scattered. These atmospherically .transparent. regions can be found by examining Figure 2. For 0.84 microns the atmosphere has a transmisivity of about 80%.
The inefficiency due to the laser spot size when it reaches the solar array is a major component of the energy loss. There is a fundamental limit to the area that the laser illuminates at the solar array (Figure 1); meaning that there is energy loss due to inefficiency in illuminating the array. An idealized minimum area that is illuminated by the laser due to the diffraction limit is given by (4)
where
is the distance from the earth to the satellite,
is the wavelength of the laser,
is the diameter of the dish, and
is the minimum amount of area that the laser illuminates at the satellites distance from the earth. For a simple case study we will use a 500cm transmitting dish and a laser with a wavelength of 0.84 microns. This gives a diameter spot size of 7.37m leading to, assuming a circular spot, an area of 42.7
. If we assume a square, maximum area per side length, solar array with edge length of
,
where
is the diameter of the circle that the laser illuminates.
was chosen because it gives the largest square that can fit into the illuminated area covered by the laser. Using these numbers the square would have an area of 27.2 leading to a maximum geometric efficiency of 63.7%. This limit can be approached and surpassed with the use of edge focusing techniques.
An additional inefficiency comes from the conversion of laser light into usable electric power. While the efficiency of a solar panel converting laser light is much higher than of a panel converting light of a black body spectrum, such as from the sun, it is still only has a maximum efficiency of around 50%. GaAs solar panels have a maximum efficiency of about 50% near 0.84 microns. (5) This coupled with the ~80% transmisivity of the atmosphere in this region made this frequency a logical choice for our theoretical design.
When multiplying all of these efficiencies together there are two important efficiencies. The most important of these two efficiencies is the efficiency from laser beam to electrical power in the receiver, this turns out to be on the order of 12.74% when using the assumptions stated above. The other important efficiency is the total efficiency from the outlet power to useable electrical power in the receiver; this comes out to be .076% of the power that was used to produce it.
| Power Transport/Conversion Method |
Percent Transported/Converted |
| Geometric (Diffraction) |
<63.7%
|
| Solar Panel Conversion Efficiency |
~50% |
| Atmospheric Transmission Efficiency |
~80% |
| Ground Optics Transmission Efficiency |
>50% |
| Beam to FEL Conversion Efficiency |
defined as 10% |
| Wall to Beam Conversion Efficiency |
(60% Wall to RF, 10% RF to Beam) = 6% |
| Laser to Electrical Power in Space |
12.74% |
| Outlet Power to Electrical Power in Space |
.076% |
Why High Gain:
The state of current FEL's is that they are 0.1-1% efficient. For every megawatt of power that is pumped into them only 1-10 kilowatts is turned into coherent radiation. This is not so much of a concern due to the comparative costs of producing energy in space as opposed to the cost of production on earth. However, if the wall power to beam efficiency were to be increased the cost of transporting power from earth to space would be reduced accordingly.
One way to increase the efficiency of a FEL is to use energy recovery techniques. The most logical way to do this is to .recycle. the beam after it passes through the undulator. This is typically done by injecting electrons into a linac where they are accelerated to the desired energy the beam is then passed through the undulator where .1-1% of the energy is converted into coherent light. The beam that exits the undulator is therefore essentially the same beam that entered the undulator, less the .1-1% energy loss. This is not completely true however because the beam will not be as uniform as the original beam. This can be corrected by conditioning the beam before it is passed through the undulator again, if the uniformities are sufficient. The beam can also be passed through the undulator multiple times and then conditioned and passed through more times, if the undulator does not perturb the beam too much. This system creates a situation where the entire beam that is being passed through the undulator no longer has to be ejected from the cathode and accelerated to ~40MeV each time it is passed through the undulator allowing for a substantial efficiency increase of about double that of non-energy recovery linac beams. (6)
This technique is also not without its problems. With the implementation of energy recovery linac techniques many more complications, trivial as they are, arise from the non-trivial increase in vacuum space, magnets, and power sources. These problems are technical in nature and are dealt with on a daily basis in labs across the world. The only real down sides to the energy recovery techniques is the amount of start up money required to set up the FEL, the number of people required for maintenance, and the increased space requirement. All of these problems are economic in nature and have no intrinsic physical limitations.
Paths to Higher Power Gain:
High brightness beams are difficult to construct and no one has yet to build a high brightness FEL. This is not to say that high brightness FELs are impossible, there are multiple ways in which to achieve these high power lasers. They can be achieved by tapering the undulator, increasing the duty cycle efficiency, increasing the beam acceleration efficiency, propagating higher quality beams through the undulator, etc.
- Tapering:
In a FEL the efficiency of the energy transfer is limited by the quantity of the order of 1/2N, where N is the number of the undulator periods. With the typical number of the undulator periods of about 100 this leads to the energy transfer efficiency of less than 1%.. (7) This relation is caused by the release of energy from the electrons in the form of photons. This photon ejection caused the electron to loose energy and speed. This reduced energy electron fails to satisfy the resonance condition of the undulator, assuming that the undulator has a constant resonance frequency, and therefore does not continue to emit photons that contribute to the laser. In order to correct for this and increase the efficiency of the energy conversion either the magnetic field of the undulator and/or the period length must be varied allowing the electron to fulfill the resonance conditions even after its energy has decreased. This process of varying the undulator frequency and the period length is called tapering.
- High Average Duty Cycle
A second method to increase the power of the laser is to increase the duty cycle. The current PEGASUS laser fires a 5ps beam at 5Hz. This means that the laser is only firing for 25ps per second. This is equivalent to running for 
% of the time. If the duty cycle were increased the average power would be increased proportionally. This is the area where the easiest gains can be made because relatively little engineering must be done to accomplish it. Heat dissipation is the only major obstacle inhibiting an increased duty cycle.
Heat dissipation is a problem because of the RF energy that is dissipated into the gun chamber. If the amount of energy dissipated into the cavity is greater than the amount that can be removed, this extra heat energy causes the electron gun to deform and therefore detune. When the cavity detunes the resonance frequency of the cavity increases from the frequency, 2.856GHz for S-band, of the RF used to power it because of the expansion of the material used to construct the chamber. This heating deformation causes the chamber to distort its defined shape and become less and less excited by the RF, which is distributed like a delta function around 2.856GHz, as the resonant frequency is increased. The detuning effectively negates the ability of the cavity to accelerate electrons, unless the RF is varied along with the heating fluctuations.
This problem can be solved by increasing the capacity of the temperature regulating systems employed by these guns. Water cooling, heat sinks, etc. can be utilized in this effort. There are different sets of problems associated with each solution, but they are not unsolvable.
Applications:
In order for a technology to be .interesting. in an economic sense it must have a practical application. Power beaming is not an exception to this rule. Power is an invaluable resource that can be produced at varying costs depending on location. The cost of producing power in space from solar panels is free, provided they are in a location that receives solar radiation; however the cost of placing those solar panels there is not. The cost of producing power from a hydro electric damn is merely the cost of the installation of the facility and maintenance. The applications of power beaming lie in the transferring of power from places where it is inexpensive to convert power to places where it is extremely expensive to convert power.
- Power Beaming:
One of the proposed applications of high power FEL.s is remote powering of satellites, lunar bases, space stations, etc. when they are in the earth or moon.s shadow. These FELs can be used to irradiate their solar panels with wavelengths that are much more efficient than the sun.s black body spectrum, increasing the power conversion from 14% to about 50%. Allowing for the possibility of powering lunar bases during the 354 hour lunar night, or the powering satellites in Geosynchronous Earth Orbit, GEO, while they are in eclipse.
- Near Earth Object, NEO, Deflection:
A second application for high power FELs is NEO deflection. It can be used as a way to slowly move asteroids out of the path of earth. These lasers can accomplish this by vaporizing small portions of the asteroid creating a force from the small explosions. This could over time adjust the asteroid.s path enough to cause it to miss the earth.
- Ship Board Defense:
A third application for power beaming is ship board defense. An alternative to transferring power from one location to another to facilitate the running of machines is to use the power to heat a material, similar to the process used by a microwave. If a material is sufficiently heated it will liquefy or vaporize, depending on the atmospheric pressure and intrinsic material properties. This can be used for ship board defense in ways that traditional defensive weapons fail. Unlike metal, light travels essentially equivalently in air and water; obviously corrections must be made for refraction, but these are trivial. The speed of light in water is much faster than the speed of a submarine and similarly light traveling in air is essentially infinitely faster than the speed of an airplane in the air, thus this technology can be used in replacement of traditional missiles, guns, depth charges, etc. It can be used for attacking enemy forces in any environment.
Prototype:
In order to beam 1 Kilowatt of useful electrical power to a satellite in space the required electrical outlet power is 1 Kilowatt/.00076 ~ 1.3 Megawatt and the required coherent laser beam power is 1 Kilowatt/.1274 ~ 7.8 Kilowatt, assuming the given 10% undulator efficiency. The coherent radiation was picked to be 840 nanometers to maximize the transmission efficiency of the atmosphere and the energy conversion efficiency of the GaAs solar panels. The beam energy was chosen to be about 226MeV because it is a relatively easy energy to achieve, it leads to a high powered beam with less beam charge, and it is easier to achieve a higher quality beam because small perturbations effect the beam less than if the energy were lower. This necessitates a large gamma because gamma = Beam Energy/ .511 MeV = 443 for the chosen energy. These parameters then lead to an undulator parameter of 3 and an undulator period of 6cm.
With these parameters the required laser power can be produced with the parameters described in the table below.
| |
Frequency (Hz) |
Energy (MeV) |
Bunches |
Charge/Bucket (C) |
Average Output LASER Power (W) |
Total Electrical Energy Transfered (W) |
| PEGASUS |
5 |
15 |
1 |
1E-09 |
0.0075 |
0.000955 |
| Base Line |
5 |
226.373 |
1000 |
1E-09 |
113.1 |
14.4 |
| Maximum Bunches |
5 |
226.373 |
7140 |
1E-09 |
808.1 |
102 |
| Maximum Charge |
5 |
226.373 |
1 |
1E-08 |
1.131 |
0.144 |
| Maximum Frequency |
400000 |
226.373 |
1 |
1E-09 |
9054 |
1153 |
| Proposed #1 |
100 |
226.373 |
1000 |
3.45E-09 |
7809 |
995 |
| Proposed #2 |
69 |
226.373 |
5000 |
1E-09 |
7809 |
995 |
| Proposed #3 |
345 |
226.373 |
1000 |
1E-09 |
7809 |
995 |
| Proposed #4 |
35 |
226.373 |
2000 |
5E-09 |
7923 |
1010 |
The first case in the above uses parameters similar to the ones available at the University of California Los Angeles PEGASUS laser. The second case is a base line for beams at the energy that the theoretical beam for this paper study was picked to have. The third row is a list of parameters and output for a beam with the maximum acceptable bunches, as are the fourth and fifth for charge and RF frequency respectively. The final 4 rows represent viable beam parameters for achieving the 1 Kilowatt to space scenario.
The final average power in the above table is calculated by using the five parameters preceding it. A 10% beam power to laser power is assumed and beam power is calculated by
,
where
,
,
leading to
.
In order to achieve the average power displayed in the table above the duty cycle must be increased in such a way as to achieve those goals. In order to do this a procedure called macro bunching is utilized. It is a process by which the RF is used more efficiently. Instead of firing one shot during each RF cycle multiple buckets are accelerated during every RF cycle. With a RF cycle similar to that of the PEGASUS laboratory at UCLA, the chamber is filled with RF for a time on the order of 4 micro-s, thousands of 5ps shots can be produced to increase the duty cycle. This process of macro bunching is visually explained in Figure 3.
Genesis Simulation
After determining all of the parameters for transmitting power from earth to space utilizing a FEL operating at 840 nanometers, undulator optimization simulations were run to attempt to achieve the 10% electron beam to Electro Magnetic, EM, beam efficiency. Multiple simulations were run using the GENESIS 1.3 code. A beam energy extraction efficiency of 13.09% was achieved with an unrealistic 150m undulator. More realistic 20m and 40m simulations were also performed. The greatest energy extraction efficiency that was achieved with a 20m undulator was 2.64%, while the greatest achieved efficiency for the 40m undulator was 6.71%. All of these simulations utilized similar input parameters. The only differences were in undulator length, amount of taper and seed laser power. The seed laser was set to be 1kW at a wavelength of 844nm. The taper for the undulators were 5% starting at 12.5m, 15% starting at 12.5m, and 26% starting at 15m for the 20m, 40m, and 150m undulators respectively. The beams for the 20m and 40m undulators had a peak current of 500A and a uniform emittance of .00001 (units).
When utilizing the efficiencies given above for the parameter study of transferring 1kW of electrical energy to space the initial table turns into the two tables below for the 20m and 40m undulators. The parameters must be increased in both instances to account for the difference in energy extraction efficiencies compared to the assumed 10%. However, there seem to be many plausible solutions to this laser energy problem. None of the required changes seem to be pushing much past the envelope of technology that is currently in existence.
| |
Frequency (Hz) |
Energy (MeV) |
Bunches |
Charge/Bucket (C) |
Average Output LASER Power (W) |
Total Electrical Energy Transfered (W) |
| PEGASUS |
5 |
15 |
1 |
1E-09 |
0.00198 |
0.000252 |
| Base Line |
5 |
226 |
1000 |
1E-09 |
29.88 |
3.81 |
| Maximum Bunches |
5 |
226 |
7140 |
1E-09 |
213.4 |
27.2 |
| Maximum Charge |
5 |
226 |
1 |
1E-08 |
0.2988 |
0.0381 |
| Maximum Frequency |
400000 |
226 |
1 |
1E-09 |
2390 |
305 |
| Proposed #1 |
550 |
226 |
1000 |
2.5E-09 |
8217 |
1050 |
| Proposed #2 |
106 |
226 |
5000 |
2.5E-09 |
7919 |
1010 |
| Proposed #3 |
300 |
226 |
1755 |
2.5E-09 |
7866 |
1000 |
| Proposed #4 |
265 |
226 |
2000 |
2.5E-09 |
7918 |
1010 |
The parameters that were adjusted for the 20m undulator were tweaked more than the parameters for the 40m undulator because of the difference in efficiency of both undulators. The 20m undulator achieved a maximum efficiency of 2.64% while the 40m undulator achieved a maximum efficiency of 6.71%. However, even with the added adjustments that were necessary for the 20m undulator these adjustments still are not out side of the realm of what has either been accomplished in labs or is slightly beyond the scope of where current labs are at.
| |
Frequency (Hz) |
Energy (MeV) |
Bunches |
Charge/Bucket (C) |
Average Output LASER Power (W) |
Total Electrical Energy Transfered (W) |
| PEGASUS |
5 |
15 |
1 |
1E-09 |
0.005032 |
0.000641 |
| Base Line |
5 |
226 |
1000 |
1E-09 |
75.94 |
9.68 |
| Maximum Bunches |
5 |
226 |
7140 |
1E-09 |
542.3 |
69.1 |
| Maximum Charge |
5 |
226 |
1 |
1E-08 |
0.7595 |
0.0968 |
| Maximum Frequency |
400000 |
226 |
1 |
1E-09 |
6076 |
774 |
| Proposed #1 |
104 |
226 |
2000 |
2.5E-09 |
7899 |
1010 |
| Proposed #2 |
52 |
226 |
4000 |
2.5E-09 |
7899 |
1010 |
| Proposed #3 |
300 |
226 |
750 |
2.5E-09 |
8544 |
1090 |
| Proposed #4 |
103 |
226 |
2010 |
2.5E-09 |
7862 |
1000 |
Conclusion:
This paper study produced parameters for transporting 1 Kilowatt of energy from a ground based transmitting station to a satellite in GEO. These parameters were for an 840 nm laser of the FEL variety. The expected efficiency was determined and explained. The only subsystem in the paper study that has not been demonstrated to work as stated was the specialized undulators that were simulated using Genesis 1.3.
These high efficiency undulators were designed around a set of input and output parameters. The input parameters were the beam energy, charge, and emittance. The output parameter was the wavelength of light to be produced by the FEL. The efficiencies of the undulator for the 20 m and the 40 m were 2.64% and 6.71% respectively. These efficiencies were optimized by changing the tapering and position where the tapering began.
The idea of a ground based power beaming station utilized for powering of satellites or a moon base is a goal that can easily be realized by the end of the decade. We already have the technology and ability to produce all of the required elements to produce such a system have been demonstrated in labs throughout the world. The only necessity would be to bring all of these systems together and get them to work with each other. This task is not easy but neither is it impossible. If sufficient funding was applied to this project it could be completed in a matter of years. There are also plans to utilize groups of systems such as this to not only power space stations, moon bases, and satellites but to eventually propel satellites and space crafts into orbit. The future of power beaming is one of interest to all people interested in the future of space exploration.
Refrences:
1 Space Power by Ground-based Laser Illumination
2 Space Propulsion and Power Beaming Using Millimeter Systems
3 Atmospheric Absorption Spectrum
4 Telescope Differential Limit
5 FEL
6 FEL Tapering
