7.1 Introduction

In Chapter 3, we have shown that the theory for radiation force in beams and standing-wave fields is essentially the same in electromagnetic fields as it is in acoustic fields. Thus, we postulate that complex shapes of stable "trap" surfaces can be generated in electromagnetic fields as well. The calculations in section 3 provide a simple basis for estimating the power required to accelerate particles of given size using radiation of given wavelength, as long as the scattering is still in the Rayleigh regime (particle diameter less than 10% of wavelength). The choice of the Rayleigh regime is made to simplify the calculations. If the radiation wavelength is reduced for a given particle size, the acceleration per unit intensity is higher, but it is harder to predict, and perhaps to control. With advancements in prediction capability, it should be possible to take advantage of the Mie regime where the wavelength is the same order of magnitude as the particle diameter.

7.2 Radio Wave Tailored Force Fields

Small asteroids in the Near-Earth Object region in Earth’s orbit around the Sun may be used as the source of raw materials for building large, radiation-shielded habitats. The NEO region is chosen because this is the most likely region for the first large-scale resource exploitation efforts of humanity, beyond the Moon. The L-5 region of the Earth-Sun system is believed to have entrained thousands of objects which are either asteroid fragments or cometary fragments. Some are believed to contain water ice and carbon, while others may have substantial metallic resources. Suitable construction material for our purposes would be metal oxides such as silicon dioxide. The signal round-trip time from Earth is on the order of 20 minutes; the diversity of resources in the region demand intelligent presence. For these reasons, this region is most likely to have the greatest need for a permanent, large, radiation-shielded habitat. 

Figure 7.1 Conceptual drawing of a large radiation-shield being formed using radio waves, from pulverized asteroidal material. Earth is shown much larger than it would be seen from the Near-Earth Object region at the Earth-Sun L-5

A conceptual drawing is shown in Fig. 7.1. Magnetic fields separate different materials. Electromagnetic fields move the desired materials near the nodal planes of the resonator, which depend on the driving frequency. The material forms walls along and parallel to the nodal planes. Energy at other frequencies is beamed to melt and fuse the walls; radiant cooling hardens them into rigid structures. Radiation-shielded habitats could be formed for the first resource-prospectors and extraction crews to live in this region. Spaceship structures could be formed for long-duration missions.

For a single-point design example, we assume that the basic construction material to build a radiation shield will be blocks roughly 0.2m in diameter, obtained by breaking pieces off asteroids. The appropriate radiation for this would be radio waves in the 2MHz to 5MHz range. In this regime, high-power transmitters can be built, with excellent conversion efficiency from solar-generated electricity. 
 

Abstract	Intro	Theory	Near-term: Acoustic
Mid-Term: L2 Habitat	Space Economy	Far-Term: Radio-Wave Construction	Comments
Issues	Conclusions	Acknowledgements	References

7.3 Calculation of Radio Wave Intensity and Solar Energy Requirements.

The estimation technique developed in Section 3 is used below to obtain the acceleration per unit radiation intensity for a particle inside a resonator, with the particle radius being 5% of wavelength in order to keep the calculation in the Rayleigh regime.  In this regime, the shape of the particle is not significant, and hence an effective radius is used as a characteristic dimension.  The results are shown in Table 7.1. Clearly, a very high intensity of radio waves will be required to cause any significant acceleration. This is why the first applications of this technique will probably be in a region of vacuum where g-jitter and other acceleration errors will be minimal.

Table 7.1 Estimate of acceleration per unit intensity for radio wave TFF
 

Refractive index of  the particles n1	1.51
Refractive Index of medium (vacuum) n2	1
Particle material density, kg/m3	2000
m = n1 / n2	1.51
Ratio of wavelength to particle effective radius (assumed to stay inside Rayleigh domain)	1000
Effective Particle radius a  (m)	0.1
Wavelength  (m)	100
Acceleration per unit intensity (SI units)	2.99E-14

An example of the power needed is given below. To form a cylinder 50 m in diameter and 50 m long we would excite a 220 mode in a rectangular cavity of dimension comparable to 50 x 100 x 100 m.  In the below power calculation a radio beam 100 meters in diameter was conservatively used for comparisons with conventional data. The choice of habitat dimension in this case is argued as follows: Unlike the 1km-radius cylinder considered in Section 5, this one is intended for sparse inhabitation, primarily by technical people, and primarily for shelter in the NEO region. It is not intended as a permanent habitat. The present conception of the construction method envisages a resonator set up using large moveable antenna arrays – thus the size of the structure built in one formation operation, will be limited by the resonator size. It is also likely that these structures, once assembled, may have to be propelled to different regions. In this case, it is more practical to build the shelter in modules, then attach them using tethers and set them in a 1-rpm revolution with a 1km radius, in order to obtain 1-G. These considerations justify the selection of a 50m diameter by 50m long cylinder as the initial test case. The results are shown in Table 7.2.

Table 7.2 Parameters for building 50m long cylinder at the NEO site at the Earth-Sun L-5 region
 

Solar intensity at site orbit, w/m2	1380
Particle Effective Radius for construction: (m)	0.1
Wavelength (m)	100
Acceleration per unit intensity	1.50E-12
Acceleration selected, m/s2	9.81E-06
Intensity needed, w/m2	3.28E+08
Size of object in beam, m	50
Beam dia, m	100

These results are translated to radio wave and solar power requirements in Table 7.3. The choice of beam diameter with respect to object size is arbitrary - there must be a criterion that can be used to optimize resonator size and Q-factor in this regard. This is an issue for further study in Phase 2.

Table 7.3 Radio-Frequency Power and Solar Power Requirements
 

Power required, w	2.58E+12
Resonator Q factor	10000
Power input needed, w	2.58E+08
Solar converter efficiency (10%)	0.1
Solar collector area, m2	1866770
Collector side, km	1.3663
Collector materials and mass per unit area	6
Collector mass, kg	11200620.6
Time needed to assemble structure, hours	6.27
Total energy needed (kWh)	1.62E+06
Structure total mass, kg	12,96,640

The collector mass is calculated, assuming a nominal panel thickness made of lunar regolith-derived material. Thin-film solar collectors may be an option, but the manufacture cost must be traded off against the shipping cost – an issue for Phase 2.  The assembled structure itself is assumed to be a 2m thick cylinder. The particle acceleration level is chosen to be well above the acceleration level due to any background radiation. With the level chosen above, particles will drift into position within about 1 hour.  The total of 13 hours is chosen to provide enough time to fuse critical portions of the structure in place (using focused beams not considered in the above power calculation), so that the rest of the structure can be completed after the field is turned off.
 
   

Abstract	Intro	Theory	Near-term: Acoustic
Mid-Term: L2 Habitat	Space Economy	Far-Term: Radio-Wave Construction	Comments
Issues	Conclusions	Acknowledgements	References

7.4 Magnitudes of other accelerations expected in the NEO region

Magnitudes of other accelerations are estimated in Table 7.4 and the following discussion. It is easily seen that an acceleration of 10^-6 G’s is adequate to overcome the worst of these.

Table 7.4 Data for solar effects on particle acceleration
 

Mechanism and effect	Basis for calculation
Solar Gravitational Attraction  Balanced out in orbit around the Sun; jitter time scales are >> time scale for assembly of an object using TFF; jitter amplitude negligible.	Where r is the distance from the Sun (1 AU = 1.496E+11 m)
Solar Wind: Proton Density varies from 0.4 to 80*10^6 per m3 and velocity ranges from 300 to over 700 km/sec at Earth orbit ; particle of 0.1 m2 and a density of 2000 kg/m3 was used in these calculations. Acceleration= 6.2722E-11 m/s2	Refs: Zeilik, Michael and Stephen A. Gregory.  Introductory Astronomy & Astrophysics.  Brooks/Cole Thomson Learning, 4th Edition. Took an average so used 40.0E6 and 500,000 m/sec respectively from above. Mass of proton is 1.6726231E -27 kg
Radiation: Use the fullequation from Zeilik, gives: 1.7361E-8 m/sec2.  Note: the assumed solar intensity value of 1380 watts/m2 gives 1.755E-8m/s2	Wheresis the Stefan-Boltzmann Constant = 5.6705*10-8 W / (m2 K4) p*r2is the area of the particle Rsun = 6.9599*108 m = Radius of the Sun Tsun = 5800 K = Temperature of Sun 'c' is speed of light 'd' is distance from the sun (1 AU in this case)

The gravitational acceleration on the particles due to the rest of the particles in the "construction zone" is estimated as follows. The worst-case is the acceleration on the last 10-cm diameter construction particle due to all the rest. Assume that the largest single manufactured component is a hollow cylinder 50 m in diameter, 50 m long, with a wall thickness of 2 m, made of silicon dioxide, with a density of 2000 kg/m^3.

Figure 7.2 illustrates the worst-case situation where all construction material is agglomerated into a sphere, and the last particle is right at the surface of this sphere.

Figure 7.2 Worst-case model for gravitational acceleration on particles in the construction field.

Volume = 15079.7 m3, therefore mass of cylinder, or sphere = 3E7 kg

Therefore, radius of equivalent mass sphere = 15.3 m

Gravitational force at surface = 8.6E-6 m/s2

This is still below the 1.0E-6 g's selected. When the particle cloud is formed, some effort should be put into clearing the central region, so that the gravitational acceleration becomes a helpful feature in forming the cylinder, bringing material to the wall of the cylinder.  

Abstract	Intro	Theory	Near-term: Acoustic
Mid-Term: L2 Habitat	Space Economy	Far-Term: Radio-Wave Construction	Comments
Issues	Conclusions	Acknowledgements	References

7.5 Time to Form Structure: a more refined calculation

In the tables above, a first-order estimate was made of the time to form the structure, considering a uniform acceleration on all particles. Below, this calculation is refined using the radiation force in a resonator, using the methods given in [13]. The time taken for particles in all parts of the standing wave field to drift to the cylinder location in a 2,2,0 mode was computed. The following assumptions were made:

Particle diameter: 20 cm (= 2a)

Refractive index: 1.52 (= n1)

Cavity Mode: (2 2 0)

Spacing between source and reflective boundary: 100 m

Structure to be formed: Cylinder 50m in diameter and 50m in height

Wavelength of field, 1: 100m à Radio range

As seen in Figure 7.3, the time taken is well under 1 hour for currently available power sources (MW range).

Figure 7.3: Calculations for the time taken to form cylindrical walls inside an electromagnetic resonator operated at the 220 mode. (produced in Mathcad). The last curve shows the time taken (in hours) as a function of source intensity. Note conservative estimates were used for sources of radio intensity - above range is from 5MW to 500MW sources.

7.6 Tradeoffs

In the above calculation of radio power, the resonator Q can be traded directly against solar collector area, or a storage system can be developed so that the solar energy can be collected over several months and an intense field can be generated with a low Q-factor. There are at least 3 different design approaches to this, with different technology needs and emphases. One of them is illustrated in Table 7.5 - the energy is collected and stored for discharge during the few hours of construction operations. In this case, the collector area required is quite small. The different approaches to the design of the TFF system are summarized in Table 7.6

Table 7.5: Scenario 2: Collect & store solar energy for discharge during construction, one project per six months.

Table 7.6: Technology needs for different approaches to designing radio-wave TFF system

From the above numbers, the concept of using solar-powered radio waves to perform such large-scale construction appears to be quite feasible, provided there are markets and infrastructure elsewhere in orbit to provide the transportation and resource exploitation support. The above calculations are no doubt simplistic in terms of the final configuration needed in the future to perform such projects. Several issues for further work are discussed below.