Dear Kristian

In order to define the rectenna characteristics, a reasonable value for the power flux at the centre of the rectenna system has to be assumed. Different values have been proposed, between 230 W/m² and 1000 W/m² [1, Table 2.3.2]. Here, a conservative value of 300 W/m² (which is less dangerous from a biological point of view: see [1, Section 4.3]) is adopted for the central power flux. Assuming a Gaussian distribution of the power at the ground, and assuming further that the power flux at the edge of the rectenna is equal to 10 W/m² (for safety reasons, which are discussed in [1, Section 4.3]), after a simple calculation one arrives at a radius of the rectenna of km. If L is the altitude of the geostationary orbit (km) and if is the radius of the transmitting antenna, one has that approximately , where is the RF wavelength (m at 2.45 GHz). Therefore, m (a more accurate estimate would arrive at 1200 m: see [1, Section 3.1.1]). The assumed sizes are summarised in Table 2.

Table 2. The size of the SPS components being considered.

Quantity	Size
Solar-cell array	10 km^2 area
Transmitting antenna on satellite	2.4 km diameter (for 2.45 GHz)
Rectenna	4 km diameter (independent of frequency in the above estimate)

The last number to be introduced is the desired pointing accuracy of the transmitting antenna. In most projects, one assumes that the allowed displacement of the centre of the beam is a small fraction of the diameter of the rectenna system. In [1, Section 2.1.1], the adopted value of this displacement was 300 m, so that the required pointing accuracy for a geostationary power station is 0.0005°. It should be noted that the above estimate for the rectenna size does not take into account any safety margin due to the pointing accuracy of 300 m.

2.5 Economic Issues
As already stated in Section 2.2, economic-related issues are outside of URSI’s scientific domain. Some important aspects are therefore touched on only briefly in this section, with some figures quoted from the available literature.
There are four main factors that determine the power-production costs of an SPS system: photovoltaic module efficiency and costs, mass-specific power production (W/kg) of the solar modules and the transmission system, microwave power-transmission efficiency, and launch costs. The target is an efficiency of about 50% for the total microwave power transmission dc-microwave-dc conversion (see Section 3.1), and a specific power output of 1 kW/kg for the whole microwave power-transmission system. The published SPS cost estimates are based on a launch cost of USD150/kg [1, Section 2.1.4]. All these assumptions lead to an estimated energy-generation cost of approximately USD0.1-0.2 per kWh for an SPS system[23]. These estimates remain controversial. For example, present-day launch and space-assembly costs are greater than two orders of magnitude higher than the desired USD150/kg (present-day launch costs are USD10,000/kg [24]). While NASA expects the launch costs to decrease by a factor of 100 by 2025 and by a factor of 1000 by 2040 [25], ESA is less optimistic. In a corresponding ESA report, the energy-generation costs for a 500 GW SPS system were estimated to be USD0.40/kWh, assuming transportation costs of USD1,500/kg, and a mass-specific power production of 0.2 kW/kg [26]. In the same report, it was stated that transportation costs may be reduced to USD200/kg in the future.
A direct comparison of the output power from a space-based solar power unit with that from a terrestrial photovoltaic array with equal area is not straightforward. On one hand, a simple estimate of the energy output yields an advantage of about a factor 2.5 for the SPS. For the SPS system,
1.37 kW/m² solar power flux in space × 0.07 overall SPS efficiency (Table 1) × 24 h = 2.3 kWh/m²/day.
For a terrestrial solar-cell array,
5 kWh/m²/day average solar power flux at a sunny place (Arizona [27]) × 0.17 solar cell efficiency = 0.85 kWh/m²/day.
On the other hand, a detailed economic comparison of the costs turns out to be very complicated and dependent on many factors, such as launch costs (see above), SPS concept, power-consumption profile (base-load versus non-base-load power-supply systems), storage technology (for base-load power supply), terrestrial power-transmission system (depending on the location of the terrestrial power plant), energy payback times, and others. ESA conducted several corresponding studies (including also terrestrial solar thermal plants) (e.g., [28, 29]. One of these came to the conclusions that (i) for a base-load power supply, SPS systems above 5 GW and launch costs between USD824 and USD1023/kg would be required for an SPS to be competitive with terrestrial plants; (ii) for non-base-load power supplies, SPS systems above 50 GW and launch costs between USD206 and USD2146/kg would be required for an SPS to reach a competitive level with terrestrial plants [28]. More-detailed results of these comparisons are presented and discussed in [1, Section 2.4.3 and Appendices E.5-E.7].

2.6 Key SPS Technologies
The most important key technology concerns the infrastructure to launch, assemble, transport, and maintain the SPS system. Since this topic is beyond URSI’s scientific domain, it will not be dealt with here.
The key elements in the dc power generation for the SPS system are the solar cells. Thin-membrane (amorphous) silicon solar cells are expected to be the most suitable type for the SPS system because of their good performance for a given weight, and because of conservation of natural resources, although their conversion efficiency is lower than the figures for Si cells (17.3% [7]) and GaAs cells (20% [7]). Mass-production feasibility is also an important aspect in choosing the most suitable solar-cell type. A sunlight concentrator would enhance the power output. Therefore, two types of power-generation systems have been studied: (a) a massive light-concentration type [9], and (b) a super-light-weight thin-membrane type [30]. An increase of the total power-conversion efficiency is to be greatly desired. However, it should be noted that solar cells in space deteriorate, due to accelerated solar-wind particles and solar radiation. Radiation-hardened cells are already available for long-term space missions, but at considerably higher costs than cells for terrestrial use.
The thermal design and control of the SPS system will also be of importance, particularly if sunlight concentration is applied. One method for thermal control of the generator is blockage of the infrared radiation from the sun, either by effective reflection or by band-elimination filters for infrared radiation.
The radio science and technology of an SPS system, such as the microwave power transmission, microwave power devices, rectennas, and beam control, will be discussed in detail in Section 3.
A very important detail of an SPS is the proper orbit in space. A geostationary orbit has been proposed for most of the systems envisioned so far. However, a more-remote orbit, an L2-halo orbit [31], was also considered. It is generally assumed that the SPS is assembled at a low Earth orbit, with subsequent transportation to a geostationary orbit. Modern SPS concepts rely on robotic assembly and maintenance systems, rather than human astronauts for the assembly task. For transportation, suitable orbit-transfer vehicles have to be developed to transport a very large structure from a lower to a higher orbit. Solar electric-propulsion orbital-transfer vehicles have been suggested for this purpose. Some corresponding prototype propulsion systems, such as a magneto-plasmadynamic thruster, a Hall thruster, and a microwave-discharge ion engine, have been tested ([1, Section 2.3.1.2).
It should also be noted that the selection of the final working orbit of an SPS may have important implications for the antenna design and its characteristics (far-field or Fresnel region).
Other key issues of SPS technology are lifetime and maintenance. The limited lifetime of solar cells has already been mentioned, but a long-term radiation hazard also exists for any solid-state device on the SPS, such as dc-to microwave converters, for instance. In addition, there is the problem of the long-term mechanical stability of the very large structures of the solar panels and the microwave transmitting antenna. The long-term influence of tidal effects and radiation pressure have to be examined. In principle, both effects can deform the structure as well as change its orientation. In particular, the radiation pressure exerts a force that changes continuously in direction with respect to the line joining the satellite and the rectenna. This may pose serious problems concerning the control of the orbit and the orientation of the RF beam. The amplitude of this force is of the order of 100 N for a solar-cell area of 10 km² (2 × solar radiation power flux × 10 km²/velocity of light). Regarding maintenance, the present-day experiences for low Earth orbits with the Hubble space telescope and the International Space Station indicate that maintaining and servicing a much larger system in a much higher orbit may be very difficult and much more expensive than for low Earth orbits. A completely new approach to space maintenance may be required to maintain assets at geostationary orbit. Currently, progressive replacement is the only viable option.

3. SPS Radio Technologies
3.1 Microwave Power Transmission
Wireless communication uses radio waves as carriers of information. However, in the microwave power-transmission system, radio waves would be used as carriers of energy. In principle, the energy-carrying microwaves would be monochromatic waves, without any modulation. The microwave power transmission would use power densities at the surface of the transmitting antenna that are three or four orders of magnitude higher than the corresponding levels in wireless-communication systems, and up to 25 orders of magnitude higher than power densities received by the radio-astronomy and remote-sensing services.
The main parameters of the microwave power-transmission system for the SPS system are the frequency, the diameter of the transmitting antenna, the output power (beamed to the Earth), and the maximum power-flux density. In addition to the system parameters described above, the weight per unit power of the microwave devices is also of importance [1, Section 3.2].
Efficiency is very important for the microwave power-transmission system. Assuming the SPS transmitting-antenna-to-rectenna propagation path is optimum, the following efficiencies will be important: dc-to-radio-frequency (RF) conversion, RF-to-dc conversion, and beam-collecting efficiencies. Conversion efficiencies higher than 80% for both RF-dc and dc-RF conversions are necessary to make the cost of the SPS system reasonable (see Section 2.4).
Various types of transmitting antennas have been considered, such as slotted-waveguide antennas, dipole antennas with reflectors, and microstrip antennas. The most suitable antenna type depends on the chosen microwave generator and amplifier, but also on weight. A possible concept seems to be the active integrated antenna technique, combing the dc power generation, microwave conversion, and radiation and control in one multi-layered plate [32].
As mentioned in Section 2.4, the diameter of a transmitting antenna array of a 1 GW SPS system would be about 2 km. The average microwave power-flux density at the array of the SPS would then be about 300 W/m² on the surface of the transmitting antenna. A phased antenna array is planned for the SPS system, in order to obtain high-efficiency beam collection under the condition of fluctuating SPS attitudes. Depending on the frequency of the microwave power transmission, e.g. 2.45 GHz or 5.8 GHz, the number of antenna elements per square meter would need to be of the order of 100 or 400, where the power delivered by a singe element would be 10 W or 2.5 W, respectively [1, Section 3] . Thus, the total number of elements could be of the order of several hundreds of millions (this number could be substantially reduced if single klystrons of more than 1 kW output power were used to feed one antenna element). Such a large phased array has neither been developed nor constructed up until now, even on Earth. It is uncertain if simple scaling of already realised arrays is possible, or whether it may lead to unexpected problems.
Hence, realising the SPS system will require overcoming many engineering challenges, such as arrays with a dc-RF conversion efficiency higher than 80%, a phase-shifting system with very low root-mean-square errors for accurate beam control, phase synchronisation over millions of elements, and very-low-cost mass production of these elements.

3.2 Microwave Power Devices
Many possibilities have been proposed for the microwave generators, such as microwave vacuum tubes (klystrons, magnetrons, travelling-wave tube amplifiers), semiconductor transmitters, and combinations of both technologies. These types of generators have been compared with respect to their efficiency, output power, weight, and emitted harmonics [1, Section 2.3.4.2]. The dc-to-RF conversion efficiency for microwave vacuum tubes can be as high as 65% to 75%; the power of a single tube can be more than 100 kW. For semiconductor transmitters, the best achievable efficiency is 40%, the power from a single transmitter being below 100 W. Better efficiencies may be possible with new devices, such as wide-bandgap devices using GaN, which have significant power output, in particular at microwave frequencies of 2.45 GHz and 5.8 GHz [1, Section 2.3.4.2 (4)].
Compared to semiconductor technologies, a microwave tube has higher efficiency, lower cost, and a smaller power-to-weight ratio (kW/kg), even if one includes the power source, the dc-dc converter, the cooling system, and all the other elements needed to drive the system. Some of the SPS concepts are based on a microwave power transmitter with microwave tubes, such as klystrons and magnetrons. For example, a new concept for a microwave transmitter has been developed. It is called a phase-controlled magnetron, and it satisfies both the requirements of high efficiency and beam controllability [33]. A hybrid tube-semiconductor system is also a possible solution currently under investigation [34].
For the high-efficiency power transmitters, a design that generates a low amount of harmonics, and low-loss phase shifters, are particularly important and would need to be developed. Manufacturability would be one of the important considerations in the implementation of particular technologies for the microwave power-transmission system. Since the SPS requires huge investments, even in electronic parts, the availability of particular materials and the manufacturability need to be examined. From a manufacturing point of view, recent semiconductor technologies could be useful for SPS systems. However, their reliability in space would need to be investigated. For the microwave power-transmission technology, the reduction of the weight per unit of generated power would also be of importance to ensure a reasonable cost for a given performance.
In any case, thousands of microwave tubes or millions of solid-state amplifiers and oscillators have to be phased and controlled, which is a large technical challenge.

3.3 Rectennas
The rectenna (located on the Earth) receives the microwave power from the SPS and converts it to dc electricity (e.g., [35]). The rectenna is composed of an RF antenna, a low-pass filter, and a rectifier. It is a purely passive system (apart from a low-power pilot beam: see Section 3.4) and needs no extra power. A low-pass filter is necessary to suppress the microwave radiation that is generated by nonlinearities in the rectifier. Most rectifiers use Schottky diodes. Various rectenna schemes have been proposed, and the maximum conversion efficiencies anticipated so far are 91.4% at 2.45 GHz [36] and 82% at 5.8 GHz [37]. However, the actual rectenna efficiency will also depend on various other factors, such as the microwave input power intensity and the load impedance.
The single elements of the rectenna can be of many types, such as dipoles, Yagi antennas, microstrip antennas, or even parabolic dishes.
The rectenna array, with a typical radius of approximately 2 km, is an important element of the radio technology for which high efficiency is essential. The efficiency depends on the input power, and the input-power flux density is not constant over the entire rectenna site for the SPS system. Further research will be required into rectennas that maintain high efficiency under various input-power conditions. Recently, development has started on a low-power (only 100 µW or less), high-efficiency rectenna system for the perimeter of the rectenna site [38]. Studies and experiments have also been performed for a hybrid technique [39].

3.4 Control and Calibration
Another important issue concerning the space-based microwave antenna is the necessarily high precision of the control of the beam direction. This is important for two reasons: to maximise the energy transferred to the Earth; and to limit radiation in undesired directions, in order to avoid adverse effects on existing telecommunications, passive radio-detection systems, and biological systems. This goal may be achieved with the concept of a retrodirective array, in which the rectenna sends a pilot signal to the SPS in order to indicate its position before the power beam is transmitted. This pilot beam is then used to direct the power beam back along exactly the same path as the pilot beam: in the retrodirective direction. The effect of this is to automatically remove perturbations to the direction of the propagating beam, assuming that the perturbing factors along the propagation path do not change during the round-trip transit time. For this to work, retrodirective beam-forming techniques have to be developed in order to suppress sidelobes and to maximise the transmission efficiency. In addition, control measures have to take the delay of commands into account, which is a considerable fraction of a second for an SPS in geostationary orbit.
Emergency procedures should be defined and have to be applied when the beam direction is not contained within the predefined angle of 0.0005°. Ordering an interruption of the RF transmission may be a possible solution, but the detrimental effects that could be caused by a sudden interruption of the dc-to-RF conversion onboard the satellite have to be evaluated, not forgetting that the load to the grid will also need to be managed carefully.
The centre of the microwave beam should be confined to a region within 0.0005° of the centre of the rectenna. This corresponds to less than one-fourth of the 8-arc-seconds half-power beamwidth of a 1000-m-diameter parabolic SPS antenna. Achieving such pointing accuracy and stability would currently pose a major technical challenge. The required beam-control accuracy of the SPS microwave power-transmission system may be achieved using a very large number of power-transmitting antenna elements, and by limiting the total phase errors over the antenna array to a few degrees. Technologies to achieve these goals are presently under study [18]. Beam-collection efficiency is as important as the beam-control accuracy, and the efficiency depends on the power lost in sidelobes and grating lobes.
Measurement and calibration are important issues for the SPS and microwave power-transmission systems, because the SPS’s microwave power-transmission system requires accurate beam control with a large phased array. The testing of large SPS antennas presents not only the usual difficulty of making accurate RF measurements over a substantial aperture, but also the unusual problems of devising tests that can accurately predict the performance of the antenna under the harsh mechanical, thermal, and radiation conditions in the space environment. New methods of measurement and calibration would therefore need to be developed. Microwave measurements and calibration would be necessary for the evaluation of power, interference, and spurious emissions from the SPS and rectennas.
The proposed antennas – both the transmitting antenna and the rectenna – are expected to be so large that testing them in their entirety will pose significant challenges. Computer simulations can give accurate predictions of the performance of the antennas in terms of gain, beamwidth, and near sidelobes. However, the transmitting antenna can only be accurately tested once in orbit, and to achieve this, special antenna-measurement and calibration techniques will need to be developed.

4. Radio Science Influences and Effects of SPS
4.1 Interaction with the Ionosphere and Atmosphere
To a first approximation, it is generally considered that the interaction of the SPS system with the medium – space, ionosphere, and atmosphere – will be negligible. However, as noted in Section 2.6, SPS subsystems may be affected by accelerated solar-wind particles and solar radiation. Space is a harsh environment, with large temperature gradients and ionising radiation (geostationary satellites are in the solar-wind regime during large geomagnetic storms). On the other hand, currents created by SPS may locally affect the medium [40].
Power loss due to normal atmospheric absorption over the distance from a geostationary orbit to the ground is assumed to be below 2%. In abnormal circumstances, significant departures might be expected when, for instance, the beam encounters scintillations in the ionosphere and rain cells in the troposphere, as explained in the following.
Very few groups have worked on the effects of powerful microwaves on the atmosphere and ionosphere, and the few studies presently available refer to potential effects via the heating of ionospheric electrons or via ionisation of the air. The expertise is limited, but it exists. However, at a time where new observations (transient luminous events, terrestrial gamma-ray flashes) raise new questions about energy coupling between the atmosphere and the space environment [41], studies are needed on all phenomena that may influence the atmospheric electrical conductivity and chemical composition.
In the process of SPS construction, large high-power electric propulsion systems would be needed to move the structures from a low Earth orbit to the geostationary orbit. These would inject heavy ions perpendicular to the Earth’s magnetic field (around the equator). The injection could strongly disturb the electromagnetic environment surrounding the ion engine in the ionosphere and the magnetosphere, through interaction between the heavy-ion beam and the ambient plasmas. Some of these effects are discussed in [1, Section 4.1.3].
A thorough and systematic theoretical analysis of possible ionospheric effects was published under an ESA contract [42]. This analysis indicated several possible relevant effects, but simultaneously stated that “the natural variability of the ionosphere, as well as the fundamental unpredictability of nonlinear effects certainly limit the accuracy with which the performance of SPS systems and their environmental impact can be estimated.”
In principle, radio waves passing through the ionosphere are absorbed due to ohmic heating, i.e., wave energy heats the electrons. This effect is strongest in the ionospheric D and E layers, but the effect is assumed to be small for radio-wave frequencies above 1 GHz, since the heating efficiency varies as the inverse square of the frequency. No ground-based measurements of electron heating by high-power microwaves are available in the GHz range; only theoretical estimates exist for a frequency of 3 GHz [43]. These estimates indicate that an electron-temperature increase from 200 K to 1000 K in the E layer might occur for a power-flux density of 500 W/m². Test microwave injections from a sounding rocket have been carried out in Japan [12]. Although ohmic-heating effects were not observed, plasma waves were excited by the injected microwaves. This was in agreement with several theoretical predictions that high-power microwaves may produce plasma instabilities in the ionosphere (e.g., [42]). Several types of such instabilities produce secondary electromagnetic waves, which could be a source of interference to other radio services. The instabilities might also result in additional electron heating and density irregularities, which could have an effect on other radio waves propagating through the region. It is uncertain if the SPS microwave power-flux density would be high enough to cause such effects, or whether these effects could affect the SPS microwave transmissions.
Another problem may be defocusing of the microwave power beam, due to naturally occurring electron-density irregularities causing rapid signal-strength fluctuations (scintillations). This could have severe implications for the beam control described in Section 3.4, but, again, it is not known if this effect is important for the envisioned frequency of the SPS microwave beam. Theoretical considerations show that a 2.45-GHz SPS system would be more strongly affected than a 5.8-GHz system [42]. The effects of defocusing and scintillation on natural irregularities will be there for all power densities. What is uncertain is whether the high SPS power densities would enhance the effect through nonlinear interactions and feedback.
Some effects of powerful microwaves on the stratosphere have been studied both theoretically and experimentally [44]. These investigations have been carried out for a quite different purpose, namely to study the effects of ozone-destroying pollutants in the troposphere, and to create an artificial ozone layer in the stratosphere by high-power electromagnetic waves. The field strength necessary for this is much higher than the values that would be used by an SPS. Therefore, such effects on the atmosphere are not expected.
In the troposphere, refraction and scintillation effects on the beam (or even those induced by the high-power beam itself) need to be considered. Also, absorption and diffraction by atmospheric gases, aerosols, (water/ice) clouds, and precipitation must be studied. For instance, Recommendation ITU-R P.619 states the following about interference from an SPS: “Using available data on likely harmonic content, it can be shown that – even at the 4^th harmonic – the interfering signal at a distance of 50 km from the rain cell can be comparable with the level of the received signal in the fixed satellite service. At the fundamental frequency, however, direct radiation from the side lobes of the SPS to the terrestrial station will probably exceed the signal due to precipitation scatter.” In addition, two other effects have to be taken into account: beam attenuation and beam diffusion due to rain. As an example, for a cloud temperature of 0° C and a path length under rain of 4 km, the absorption at 5.8 GHz is 0.16 dB, 1.2 dB, and 2.8 dB for precipitation rates of 10 mm/h, 50 mm/h, and 100 mm/h, respectively [45]. Although rain rates of 100 mm/h are rare [1], it has to be stated that the last figure corresponds to a power loss of almost 50%. The beam diffusion at a dBW level can be as large as 4-6 km in diameter for precipitation rates of 50-100 mm/h [45].