Getting enough power to a climber such that it can travel from Earth to geosynchronous orbit in a reasonable amount of time is one of the technological challenges of building and using a space elevator. When considering the situation we are discussing, we find the only realistic method for getting power to the climbers is to beam it up. Alternatives that have been suggested include running power up the cable, solar or nuclear power onboard and using the cable's movement in the environment's electromagnetic field. None of these methods are feasible on further examination due to efficiency or mass considerations.
There are two scenarios we have been considering for beaming power to the climbers, microwave and laser beaming. In this section we will go through the driving constraints of both systems. In examining power beaming we found both of these techniques have been considered in the literature as possible methods for transferring power across large distances. In the laser beaming case we even found a system under construction that meets our needs.Laser Power Beaming
First, we will examine the laser beaming system. Our preliminary examination of this scenario suggested the power beaming station may need to be located at a high-altitude sight (greater than 5 km altitude) to focus a beam tight enough to efficiently deliver power to a climber. High altitude operations are not impossible but do cause numerous difficulties and limitations. Power beaming from sea level would be much preferred. In this study we will examine this possibility.
The primary difficulty in beaming laser power up to the climbers specifically from sea level is atmospheric distortion. Atmospheric distortion will broaden the beam and reduce the power delivery efficiency.
From The Infrared and Electro-Optical Systems Handbook: Atmospheric Propagation of Radiation, we find a discussion of exactly the problem we are investigating. The problem of sending a laser beam from Earth to space.
The long-term beam radius can be expressed as:
where rD is the transverse coherence length, L is the distance from the transmitter to the receiver, D is the diameter of the transmitter, the diffraction limited spot radius is
Following the example in the book we use the stated CLEAR I night model (this model may have some problems in our situation because the model starts at1.2 km altitude):ro = 2.76cm for l = 0.5mm
The beam will have about 20 times the radius (400 times the area) of our originally proposed receiver. With this spot size the wander is not significant but will be significant if the spot size is reduced. To beam up power from sea level we will require adaptive opticsD&B; or we must live with an efficiency of <0.25%. The next step is to examine adaptive optics.
From the work of Robert Fugate and others we find that adaptive optics (AO) have experimentally demonstrated a spatial resolution of 25 cm at 1000 km [Angel, 2000]. This is an order of magnitude better than our application requires at 1000 km and this system can focus the laser into the precise spot size we need at 10,000 km. With this accuracy we can place the power we need onto the 3 meter diameter solar array we have designed into the smallest climber. By the time the beam expands to fill the photovoltaic array of our smallest climber (12,000 km altitude) the power requirements of the climber are lower due to reduced downward acceleration (~0.1g). In addition, at this altitude the next climber can start its ascent and the speed of the first climber is less critical (again reducing the power requirement).
Fugate and others have examined the problem of power beaming using lasers and find the same basic AO techniques work for power beaming that have worked for observing. They are currently planning a power beaming demonstration from Earth to a geosynchronous satellite [Lipinski, 1994]. The major problems that hinder AO applications are the lack of a bright guide star and tracking moving satellites. We have neither of these in our application. The climbers will be at known, slowly-varying positions and can be made to retroreflect part of the pump beam or emit a similar kind of tracking beacon. The only thing that has not been demonstrated is the complete beaming of a high-power laser. The primary problems that may be encountered in this next stage include thermal blooming of the atmosphere, and production of the high-power laser. In our application, thermal blooming will not be a problem with a large beam size and the power we will be using.
A complete power beaming system with 200 kW of power is the aim of Compower, a private company [Bennett, 2000] (see figure 4.1). The laser power will come from a 200 kW freeelectron laser (FEL) which University of California - Berkeley will be supplying for a fixed price of $120M. The 0.84 micron output from this laser will be directed and focused with a 12 m mirror based on the Hobby-Eberly telescope. The mirror is being modified to have more closely spaced actuators to accommodate the adaptive optics system. The system will deliver 200 kW (3ps pulses every 1 ns) into a 7 m diameter spot at geosynchronous with a 3% wallplug to laser power efficiency. The design of the laser is also readily expandable to 1MW (with possibly 30% efficiency). The current design only uses one fifth of the system (one of five wigglers) to produce the 200 kW. If all five wigglers are utilized 1 MW of laser power should be produced. This system has a five year construction schedule and its planned use is for delivering power to geostationary satellites. To expand to higher powers either the system can be redesigned or multiple identical lasers can be used with their pulses interlaced in time. In our scenario we will need 2.4 MW of power delivered to our 20,000 kg climbers so three of these systems would need to be brought on-line and their pulses interlaced. For the longer-term a 1x106 kg climber would require 120 MW of power delivered. We are only considering the first 20,000 kg capacity space elevator but the long-term aspects of the program must be kept in mind. It is conceivable that subsystems such as the power beaming facility or the large climbers might become the schedule driver in construction of a 1x106 kg capacity space elevator.
The receiver system must also be considered when examining the power beaming system. There are several photovoltaic cells that can be used as receivers and the choice depends on the laser being used, cell mass and the desired operational lifetime.
If the Compower FEL system is selected, specifically designed AlGaAs photovoltaic cells can be used with 59% conversion efficiency, 82% filling factor and 54 W/cm2 power densities [D'Amato, 1992]. These cells would also work well with a large laser diode array as proposed by Kwon, 1997.
One additional problem that we need to address is lost transmitting time because of overcast skies. At our proposed anchor location where it would be best to also place the power beaming facility, the percentage of overcast skies appears to be low (figure 4.2) but to insure continuous operations a second beaming facility located in a separate weather zone would be advisable.
In our proposed situation the second beaming facility could also be located on a movable ocean platform (see Chapter 6: Anchor) roughly hundreds to thousands of kilometers from the anchor or in the mountains of Ecuador (10,000 ft altitude). An additional power beaming system in the United States (Mojave desert [Bennett, 2000]) could also be used for supplying power to climbers above 10,000 km.
Several studies have been conducted on the beaming of power from space using microwaves [Brown, 1992: Glaser, 1992]. These studies have looked at frequencies of 2.4, 35 and 94 GHz primarily and utilize dish, flat or phased array transmitting and receiving antenna [Brown, 1992: Koert, 1992]. If we consider our specific situation of beaming power to space and not from space in these same terms we start with the equation:
where Pr is the power received, Pt is the power transmitted, Ar is the area of the receiving antenna, At is the area of the transmitting antenna, d is the distance between the transmitting and receiving antenna and l is the wavelength. A low-mass receiving antenna is required so we will select a baseline 3 meter diameter area (Ar =7m2, 30 kg). We also need 50 kW delivered to an altitude of 15,000 km (for the initial climber, 40 times this for the final climbers). To deliver this power to our receiver we will need a phased array transmitting antenna of at least 1x106 m2 (1 km2). Including rectenna (rectifying antenna) efficiency (50% [Koert, 1992: Koert, 1999]) and transmission efficiency (30% [Koert, 1992]) we find we will need 1.7x105 MW, 792 MW, and 110 MW, going to the transmitters for 2.4 (l= 12.5 cm), 35 (l= 8.6 mm), and 94 (l= 3.2 mm) GHz respectively for the first climbers. This system is expandable as required by putting more power through the phased array and the received power is inversely proportional to the transmitting antenna area. A frequency of 94 GHz is preferable from the numbers above. Considerable effort has gone into developing rectifying antenna at 35GHz for use as lightweight receivers. These rectennas have 50% total efficiency and similar results should be achievable at 94 GHz [Koert, 1999]. The mass of a the rectenna would be comparable to lightweight solar panels at 33 kg for a 50 kW receiver [Koert, 1999].
Microwaves at frequencies above 10 GHz are readily absorbed by water vapor (easily 50% absorption at 94 GHz) so careful high-altitude or dry site selection is required. If we go to the longer wavelengths where absorption is less of a problem we find the efficiency of the system drops dramatically unless a very large transmitter (1600 km2) can be built, a difficult proposition.Power Beaming Summary
In examining the two possible systems we see that there are performance, maturity and operational differences. An overall summary of the two systems is shown in table 4.1. It is clear that at this time the laser power beaming system is the better choice of the two. The higher efficiency, smaller transmitter, and maturity of the laser beaming system are all distinct advantages over the microwave system. Construction of the Compower system would eliminate any concerns on the construction or performance of the power beaming system.
|Table 4.1: Laser vs. Microwave Power Beaming|
|Operating Wavelength||0.84 microns||3.2 mm (94 GHz)|
|Transmitter System||Free-Electron laser / deformable mirror||Phased Array|
|Transmitter Area||12 m diameter||1 km diameter|
|Receiver System||Tuned solar cells||Rectennas|
|Overall system efficiency||2%||0.05%|
|High altitude operation||Preferred||Preferred|
|Development level||Under construction||Design stage|