Download Radio Waves for Space-Based Construction

Radio Waves for Space-Based Construction
Narayanan M. Komerath, Sameh S. Wanis
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0150, USA.
404-894-3017, [email protected]
Abstract. This paper follows up on the idea of using potential fields for automatic construction of massive objects of
desired shape in Space. In STAIF03, we showed the commonality between the theories for acoustic and optical
positioning/shaping methods. Using this theoretical framework, we developed a simple engineering estimation scheme to
predict the acceleration per unit intensity. The radiation pressure is achieved by interaction of electromagnetic waves and
particles of a given dielectric material and size. The theory was limited to the Rayleigh domain, where particle size is
much less than the wavelength, and isotropic scattering could be assumed. With this theoretical framework in hand, we
now consider how electromagnetic waves could be utilized in a Space-based construction project. In the test case
project, the question of how to construct a safe radiation shelter for humans, in the Near-Earth Object (NEO) region is
considered. NEO material, pulverized to an average particle size of 0.1m radius, is formed into desired shapes using the
radiation pressure and gradient forces experienced by dielectric objects in a standing-wave field of radio waves. The
force field is produced by solar-powered transmitter/antenna carrying spacecraft, which are positioned in formation
around the particle cloud to set up a resonant field of the desired mode. As a test case, formation of cylindrical shells is
considered. The field level is set to induce an average particle acceleration of a millionth of an Earth-surface
gravitational acceleration. Once in position, the particles are fused by solar-powered energy beams through a sintering
process. Results show that 50m diameter, 50m-tall cylinders can be formed in the course of 12 to 13 hours per cylinder.
Order-of-magnitude arguments show that the selected acceleration level is adequate to overcome noise from all other
forces in this region. The paper also begins the consideration of tradeoffs between solar collector area, number of
resonators, and capacitive storage-discharge of energy in the fabrication process.
INTRODUCTION
In our previous STAIF paper (Komerath, 2003), we have shown that the theory for radiation pressure in beams and
standing-wave fields is essentially the same in general electromagnetic fields as they are in the acoustic fields.
Reduced-gravity flight test data are available on the formation of desired wall shapes from random-shaped particles
in a resonant acoustic field. Thus, we postulated that complex shapes of stable “trap” surfaces can be generated in
electromagnetic fields as well. A common estimating scheme was developed to compare the acceleration per unit
incident intensity available from different types of force fields and particle sizes. These calculations provide a
simple basis for estimating the power required to accelerate particles of given size using radiation of given
wavelength, assuming Rayleigh scattering for simplicity. 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 and comparisons with Rayleigh regime could be performed.
Under the constraint of Rayeigh scattering (wavelength >> particle radius) the smallest wavelengths to manipulate
10-cm diameter particles are in the radio wave regime, with wavelengths on the order of meters. The assumption of
Rayleigh scattering, which implies isotropic scattering independent of particle shape and orientation, also reduces
the problem from a 3-dimensional eigenvalue problem to multiple 1-dimensional eigenvalue problems. The
multiplicity of 1-D resonators depends on the complexity of the surface geometry of the desired object as illustrated
in Figure 1.
The test case which we have chosen to focus development of the above concept in the context of a future Space
Economy, is the construction of a cylindrical Shell in the Near-Earth Object (NEO) region in Earth’s orbit around
the Sun. There is considerable interest in the community of astronomers and those interested in Space resource
utilization, in the objects found at the stable L-4 and L-5 regions of Earth’s orbit around the Sun. Objects there are
believed to include those with high concentrations of high-value materials such as metals, carbon and water ice, all
critical to future development. It is also fairly safe to assume that there are plenty of objects which are simply
gravity-tied accumulations of rocks and soil.
The signal round-trip time from Earth is on the order of 20 minutes; and visual observation has proved quite difficult
at the scale of the objects in question. The diversity of resources in the region also demands intelligent presence.
Objects in this region, however small on a solar-system scale, are still widely scattered, and exploration and
development will require long-term human presence. Any human mission to this region will take quite a long
residence time in this region. Being as close to the Sun as Earth is, this region is subject to intense solar radiation.
Thus, heavily radiation-shielded, and fairly spacious, habitats are essential precursors to human presence and
resource development. No present technology will enable construction or shipping of such a shield. Hence this is a
relevant test case for our technology. It is assumed that by the time NEO resource extraction on a commercial scale
is considered seriously, there will already exist a substantial lunar resource infrastructure for building such items as
solar-cell arrays.
FIGURE 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.)
Suitable construction material for our purposes would be dielectrics such as metal oxides or silicon dioxide.
Electromagnetic fields separate different materials based on their dielectric properties. Electromagnetic fields move
the desired materials near the nodal planes of the resonator, which depend on the driving frequency. The material
forms surfaces along and parallel to the nodal surfaces. 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. With the basic cylinder design, 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 resonant
electromagnetic cavity longest dimension would be 100m. This field would be classified within the electromagnetic
spectrum as radio waves in the 3MHz range. In this regime, high-power transmitters can be built with excellent
conversion efficiency from solar-generated electricity.
PHYSICAL PROBLEM
Constructing surfaces in space using an appropriately tailored radio wave field is fundamentally based on solving
the electromagnetic problem of a resonant cavity. This reduces the problem to a typical 3-dimensional eigenvalue
problem. In an ideal resonator, the maximum electrical energy density is equal to the maximum magnetic energy
density stored in the resonator. Energy is converted or flows from one state to the other periodically, and thus
generates the desired electromagnetic oscillation.
The electric and magnetic field energy densities are found using plane wave expressions for both fields:
!
1 2
U electric = o E 2 =
B = U magnetic ,
(1)
2
2µo
using Poynting’s vector we get the energy flux in the wave:
ur ur
ur E " B
S=
= ! o cE 2 ,
(2)
µo
which is basically the total energy density times the speed of light. The momentum density is given by:
ur
ur ur !
P = !o E " B = o E 2 ,
(3)
c
which is also obtainable from governing expressions for general wave motion relating energy density, energy flux,
momentum density, and momentum flux.
This may be related to the trapping force in an optical resonant cavity given by Wright et al (1993):
ur nQP
F=
,
(4)
c
where n is the refractive index of the particle, Q is a trap efficiency factor, and P is power carried in the wave.
Dielectric particles with radius much smaller than the wavelength, placed in a 1-D resonant field, act as Rayleigh
scatterers. The problem to be solved then becomes equivalent to an electric dipole in a uniform electric field. This
scattering problem has been solved and the force on the particles is expressed as the sum of a gradient force and a
scattering force, (Gomez-Medina, 2001):
ur
S
2
,
(5)
F ~! E +
c
Finally, we arrive at the expressions previously reported (Zemanek et al (1998)) for Fgrad and Fscat:
2! n2 a 3 " m 2 $ 1 #
Fgrad ( z , r ) =
&
' %I ( z , r ) ;
c ( m2 + 2 )
2
16 n2 4 6 # m 2 " 1 $ P "2 r 2 / w2 2
Fscat ( z , r ) =
k a % 2
(! " 1).
& 2e
3 c
' m +2( w
(6)
CALCULATION OF RADIO WAVE INTENSITY AND SOLAR ENERGY
REQUIREMENTS
The estimation technique described in (Komerath, 2003) is used below to obtain the acceleration per unit radiation
intensity for a particle inside a resonator, with the particle radius being much smaller than the 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 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 secondary sources of acceleration
noise will be minimal.
TABLE 1. Estimate of acceleration per unit intensity for radio wave TFF.
Refractive index of the construction particles, n1
Refractive Index of medium (vacuum), n2
Particle material density, (kg/m3)
Ratio of refractive indices, m = n1 / n2
Ratio of wavelength to particle effective radius
1.51
1
2000
1.51
1000
(assumed to stay inside Rayleigh domain)
Effective Particle radius, a (m)
Wavelength, λ (m)
Acceleration per unit intensity (m/s2/W)
0.1
100
3E-14
An example of the power needed is given below in Tables 2 and 3. 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: it is intended for sparse inhabitation, primarily by trained professionals,
and primarily for shelter in the NEO region. Given the need for artificial gravity at such a station (1-g with less than
1 RPM dictates a large station size), the habitat construction must be modular. A permanent habitat may be built by
connecting several cylinders arranged around a circle, with artificial gravity due to rotation. The present concept of
the construction method envisages a resonator set up using large moveable antenna arrays - spacecraft which can be
individually positioned and oriented. 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 2.
TABLE 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)
Particle Effective Radius for construction, (m)
Wavelength, (m)
Acceleration selected, (m/s2)
Intensity needed, (w/m2)
Beam diameter, (m)
1380
0.1
100
9.81E-06
3.28E+08
100
These results are translated to radio wave and solar power requirements in Table 3. The choice of beam diameter
with respect to object size is such that the particles remain inside the resonant field. Previous reduced-gravity flight
test results using acoustic fields and random-sized particles (Komerath, 2003) show that the walls formed can be
nearly as large as the resonator dimensions.
TABLE 3. Radio-Frequency Power and Solar Power Requirements.
Power required, (w)
Assumed resonator Q factor
Power input needed, (w)
Solar converter efficiency (10%)
Solar collector area, (m2)
Collector side, (km)
Collector materials and mass per unit area
Collector mass, (kg)
Time needed to assemble structure, (hours)
Total energy needed, (kWh)
Structure total mass, (kg)
2.58E+12
10000
2.58E+08
0.1
1866770
1.36
6
11200620.6
6.27
1.62E+05
1296640
The collector mass is calculated, assuming a nominal panel thickness made of lunar regolith-derived material. Thinfilm solar collectors may be an option, but the manufacture cost must be traded off against the shipping cost – an
issue to be studied further. 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
acceleration level chosen above, particles will drift into position within about 1 hour. A total construction time 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.
Magnitudes of Other Accelerations Expected in the NEO Region
Magnitudes of other accelerations are estimated in Table 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 4. Data for Solar Effects on Particle Acceleration.
Mechanism and effect
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.
Basis for calculation
g=
!Gmsun
= 0.00593
m
"
r
sec 2
Where r is the average distance from Earth’s orbit to the Sun
(1 AU = 1.496E+11 m)
2
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
Zeilik et al (1997), took an average of 40.0E6 m-3 and
500km/s respectively.
Mass of proton is 1.6726231E -27 kg
Radiation:
Zeilik et al (1997) gives: 1.7361E-8 m/s2.
# !" rparticle 2 Rsun 2Tsun 4
%
%
c
'
aR =
d2
Note: the assumed solar intensity value of 1380
watts/m2 gives 1.755E-8m/s2
A # V = ! # rparticle 2 # Vsolarwind # " solarwind
$
&
&
( /m
particle
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 the rest of the
mass accumulated into a sphere and the last particle is right at the surface of this sphere. Assuming 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/m3.
Volume = 15079.7 m3, therefore mass of cylinder, or sphere = 3E7 kg
Therefore, radius of equivalent mass sphere = 15.3 m
Gravitational force on last particle at surface = 8.6E-6 m/s2
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. This
provides a gravitationally-stable structure, reducing the electromagnetic field required to hold it in place until the
fusing of the structure is complete.
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 rectangular resonator,
using the methods given by Gomez-Medina, (2001) and shown in equation (6) above. 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 opposite reflective boundary: 100 m
Structure to be formed: Cylinder 50m in diameter and 50m in height
Wavelength of field, λ = 70.8 m  radio range (f = 4.24 MHz)
(a) Field Intensity for mode 2 2 0
(b) Time to Reach Stable Point vs. Power
(c) Time Savings due to Drift Velocity > 0
FIGURE 2. Calculations for the time taken to form cylindrical walls inside an electromagnetic resonator operated at the 2 2 0
mode. Note conservative estimates were used for sources of radio intensity – range is from 5MW to 500MW sources. (a)
Instantaneous intensity field plot showing mode shape for 2 2 0 mode; (b) Time taken in hours to reach stable location as a
function of source power (5MW to 500MW shown); (c) Effect of including particle drift velocity before field is switched on
(source power selected is 50MW, and drift velocity range is 0 - 0.5 m/s towards stable point is shown) – done to examine order of
magnitude of time savings.
As seen in Figure 2, the time taken is well under 1 hour for currently available power sources (MW range).
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, labeled scenario 2, is illustrated in Table 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 6.
TABLE 5. Scenario 2: Collect & Store Solar Energy for Discharge During Construction, One Project Per Six Months.
Parameter
Energy collection time (months)
Collector area for 1.67million kWh (m2)
square kilometers
Collector side required (km)
value
6
2735.682
0.002736
0.0523
TABLE 6. Technology Needs for Different Approaches to Designing Radio-Wave TFF System.
Resonator Q
Solar cell area, sq. km
Storage amplifier system
Antenna technology level
Solar collector technology
level
Transport cost
High Resonator Q
10,000
1
none
Low Q, large collector
100
100
none
V. high
low
Medium Q, storage
1000
1
Collect for 130 hours, exhaust in
13 hours
High
moderate
low
moderate
high
moderate
high
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.
Antenna / Generator Technology
There has been at least one demonstration that such radio power levels are possible: The Arecibo Transmission. In
1974, the Arecibo observatory transmitted a message into outer space, as part of the Search for Extraterrestrial
Intelligence (SETI) program. The power of the transmission was 20 TW. The frequency was 2380 MHz – the
wavelength was roughly 12.6 cm. The signal duration was 169 seconds. This power level is well above that
projected in the previous pages. Certainly, the hurdles of constructing such a transmitter at the Earth-Sun L-5 region
will be a challenge, but it is well within feasibility. The Arecibo facility is shown in Figure 3.
FIGURE 3. Arecibo Space Radio Telescope, Puerto Rico. Credits: Courtesy of the NIAC - Arecibo Observatory, a facility of the
NSF. (David Parker / Science Photo Library)
CONCLUDING REMARKS ON RADIO TAILORED FORCE FIELDS FOR
CONSTRUCTION
Several possibilities are opened up by the finding about radio waves for Space-based construction. The realization
that such tailored force fields are indeed within practical conception is new. Further work is needed to brainstorm
the implications of this finding, and develop architectures for exploiting this finding. The needed solar energy can be
collected using large-array Space mirrors (Chilton, 1977). While such construction may be scientifically feasible,
any architecture to reach that horizon must first deal with nearer-term issues of building a Space-Based Economywhich will provide the “how” and “why”.
NOMENCLATURE
a: particle radius (m)
E: electric field intensity (W/m2)
B: magnetic field intensity (W/m2)
I: intensity (W/m2)
k: wave number (m-1)
m: ratio of refractive indices: particle n1 to medium n2
P: beam power (W)
r: radial distance (m)
w: beam width (m)
z: axial distance (m)
ε: permittivity (Farads/m)
µ: magnetic permeability (Henrys/m)
λ : wavelength (m)
ψ: phase (radians)
σ: specific conductance
ρ: absolute value of Fresnel reflection coefficient of
surface; used in forming standing wave.
Rsun: radius of the Sun (6.9599*108 m)
Tsun: temperature of Sun (5800 K)
c: speed of light (m/s)
d: distance from the sun (1 AU in this case)
σ: Stefan-Boltzmann Constant (5.6705*10-8 W / (m2 K4))
ACKNOWLEDGMENTS
This work is supported by the Universities Space Research Association through a NASA Institute of Advanced
Concepts Phase 1 grant, and one of the authors (Wanis) is supported by the NASA Georgia Space Grant
Consortium. Dr. Robert Cassanova of NIAC is the project technical monitor. The contributions of the Georgia Tech
student teams and NASA / Space Grant personnel under the NASA Reduced Gravity Flight Opportunities program
and the NASA Means Business Program are gratefully acknowledged.
REFERENCES
Chilton, F., Hibbs, B., O’Neill, G., Phillips, J., “Space-Based Manufacturing from Nonterrestrial Materials,” Prog. in
Astronautics and Aeronautics, 57, AIAA, (1977).
Gomez-Medina, R., San Jose, P., Garcia-Martin, A., Lester, M., Nieto-Vesperinas, M., Saenz, J. J., “Resonant Radiation Pressure
on Neutral Particles in a Waveguide,” Physics Review Letters, 84, 4275 (2001).
Komerath, N., Wanis, S., Czechowski, J., “Tailored Force Fields for Space-Based Construction,” in proceedings of Space
Technology and Applications International Forum (STAIF 2003), edited by M. El-Genk, AIP Conference Proceedings 654,
Albuquerque, New Mexico, (2003).
Wright, W.H., Sonek, G.J., “Radiation Trapping Forces on Microshperes with Optical Tweezers,” Applied Physics Letters, 63
(6), p. 715-717, (1993).
Zeilik, Michael and Stephen A. Gregory. Introductory Astronomy & Astrophysics, Brooks/Cole Thomson Learning, 4th Edition,
(1997).
Zemanek, P., Jonas, A., Sramek, L., Liska, M., “Optical Trapping of Rayleigh Particles Using a Gaussian Standing Wave,”
Optics Communications, 151 p. 273-285, Elsevier Science , (1998).