System-Level Design Considerations for Asteroid Despin via Neutral Beam Emitting Spacecraft Christine M. Hartzell Clark School of Aerospace Engineering University of Maryland- College Park College Park, Maryland 20740 301-405-4647
[email protected]
Anthony J. DeCicco Clark School of Aerospace Engineering University of Maryland- College Park College Park, Maryland 20740 301-405-1390 Email:
[email protected]
1. I NTRODUCTION
Abstract—Asteroids have gained significant interest during the past several years in the areas of planetary defense, mining, and civil space. Hundreds of asteroids are discovered each year and that rate is increasing exponentially as technology improves. However, Chelyabinsk is a reminder that not every asteroid is observed and that the technology to prevent collision events has not been developed. Asteroids are not all likely to be monolithic boulders, but a large number are probably rubble piles held together by gravity and cohesion. To protect Earth, we must find ways to alter the trajectories of asteroids so that significant impact events never occur. Controlling smaller asteroids can be done through propulsive methods in proximity operation. However, as all asteroids spin, with some rotating on more than one axis, the thrust vector necessary to deflect an asteroid will likewise rotate. To thrust along the deflection vector for a long period of time, we must first despin the asteroid. This study investigates a novel concept for asteroid despin using spacecraft equipped with neutral beam emitters. While other methods for asteroid control employ vehicles that attach to the body, our proposed method only requires spacecraft to hover above the surface and induce a torque to stabilize the complex spinning behavior of asteroids. As the despin methods will cause considerable stresses inside the rubble pile, we present the maximum stress allowable before asteroid disaggregation due to Drukker-Prager failure calculated from gravitational and van der Waals (VDW) attraction. We provide relations for thrust and Isp as related to neutral beam application. The projected power required for a given beam energy is likewise presented to scale our system and concept. The time required to despin an example asteroid as dependent on force applied is also presented. In order to despin the asteroid to decrease the required power and time to despin, we then consider the possibility of multiple spacecraft working together. While there are several concepts for Earth defense in the event of a probable asteroid impact, most require a precursor mission to determine the size and composition of the asteroid to design systems that latch on or bag the body. Launch opportunities to Near Earth Asteroids can vary anywhere from years to decades making such concepts difficult to implement if there is a limited time frame from discovery to orbital characterization to the likelihood of Earth impact. Our concept requires no such precursor mission as there is no need for direct contact with the asteroid. This work discusses the system-level trades and requirements of an asteroid despin mechanism that shows distinct operational advantages when compared to other designs.
The nature of asteroids’ low structural strength, rotational characteristics, uncertainty in composition and shape, and orbital path variability provide challenges to designing effective planetary defense measures. Current proposals for controlling asteroids can be divided into two general categories: high impulse and slow-push. A prime example of a high impulse method is that of the nuclear explosive device concept from Wie [1]. Large asteroids (∼ 1 km) require a significant force to alter their trajectories, something that a nuclear explosive device is capable of providing. In Wie’s [1] concept, two spacecraft are sent to the hazardous asteroid: one spacecraft acts as the impactor and creates a significant crater while the other contains a nuclear explosive which aims for the newly formed crater. These types of nuclear concepts are likely the best solution for a large asteroid with a short lead time for deflection but may not be suitable for smaller asteroids (100m-500m) due to the risk of fragmentation. For these bodies, the slow-push methods are better suited to move asteroids over a period of years. One possible slow push method is to use mirrors to enhance the Yarkovsky effect, as described by Vasile and Maddock [2]. In this proposal, a large mirror reflects sunlight onto the surface causing sublimation which acts as a thruster. Thermal emission, also known as the Yarkovsky effect, assists in acting as a weak thruster for this concept. Vasile and Maddock’s [2] method is not without its challenges. Sublimated gases will inevitably contaminate the mirror leading to a less effective reflector, which will eventually cease to have the required power to sublimate the surface. Another challenge is that the mirror required to significantly alter the asteroid trajectory would be tens of meters in size. Another slow push method is the gravity tug [3, 4]. By placing a spacecraft in a halo orbit above the asteroid and using thrusters on the spacecraft to maintain distance, the gravitational force between the two bodies causes the asteroid to be attracted to the spacecraft thus altering its trajectory. The propellant mass needed to maintain this tug can be offset through the use of a solar sail [4]. Olympio [3] further defines optimal deflection by alternating between coast and thrust phases. The operational time required to alter the trajectory of an asteroid by 100km or more is five or more years at the asteroid. Though the solution is elegant, both the time requirement and the small deflection (∼100 km) would constitute a high degree of risk with its implementation.
TABLE OF C ONTENTS 1. I NTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. N EUTRAL B EAM D ESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. C ONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 R EFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 B IOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
The use of thrusters to control an asteroid have been also proposed by Scheeres and Schweickart [5] and by Bombardelli et al [6]. Bombardelli et al [6] propose using an electric thruster positioned several asteroid radii away to push the asteroid over the coarse of several years. They also compare the per-
c 978-1-4673-7676-1/16/$31.00 2016 IEEE
1
formance of such a method to a gravity tractor for asteroids (whose size is on the order of hundreds of meters) and demonstrate that such propulsive methods are more effective. These studies consider roughly spherical asteroids (something that is usually not the case for 102 m order asteroids) and show that there is minimal propulsion loss due to the half angle expansion of the thrust cone. However, these losses would become high if the target asteroid was ellipsoidal and they maintained their position of several asteroid radii away. This distance could help prevent sputtered asteroid volatiles from traveling back in the ion beam to deposit on the spacecraft. Another challenge is electrostatic lofting of the surface dust grains. While it is true that electric thrusters can be thought of as a quasi-neutral plasma, those assumptions break down below the Debye length of the plasma. Grains on the surface of the asteroid smaller than the Debye length would interact with the electric field on their scale and could potentially loft from the surface as investigated by Hartzell and Scheeres [7] and DeCicco and Hartzell [8]. This would create a fine dusty environment about the asteroid probably only about 10m from the surface.
Does not require a scouting mission Does not require physical contact between the spacecraft and asteroid • Can be throttled on and off (to evaluate effectiveness) and is efficient • Can translate about asteroid to modify thrust vector • Does not create an unsafe environment for spacecraft during operation • Does not require large technology hurdles for power, mass, or thrust • Can be accomplished in similar time scales to current slowpush methods • •
To meet all of these outlined conditions, we propose a hovering neutral beam emitter for asteroid control (NBAC) to despin the asteroid. Neutral beams are typically used in fusion research as the primary heating source for tokamaks and are plasma beams that have been entirely neutralized. Our analysis will scale down the typical megawatt neutralizer and determine the thrust, Isp , propellant mass, and time required to fully despin an asteroid. Section 2 determines asteroid strength to set the limit on allowable stress that NBAC can exert, focuses on maximizing neutralization of the beam, outlines our estimates for mass flow rates of neutral gas into the neutralizer, focuses on thrust and Isp estimates as well as power requirements, and applies our neutral beam to despinning asteroids.
If we want to employ proximity operations to an ellipsoidal asteroid in order to change its trajectory, then the asteroid rotation becomes important. As the asteroid rotates, so too does the thrust vector (in the asteroid rotating frame) required to deflect the asteroid. This is especially important for using a mass-driver or thruster to alter the asteroid trajectory. For the mass driver, material is ejected from the asteroid surface which acts as a thruster on the asteroid. To do this over a long period of time the asteroid must be oriented such that the ejected mass acts along the desired thrust vector. Additionally, if a thruster is used in the rotating frame it too must act a long a certain vector for a period of time to deflect the asteroid. Control of the thrust direction becomes especially difficult if the asteroid rotates about more than one axis [5]. Therefore, despinning the asteroid ensures that we can deflect along the correct vector for an extended period of time. Additionally, a rotating asteroid induces a centrifugal force thus weakening the structural strength of the asteroid. Scheeres and Schweickart [5] propose despinning and controlling their example asteroid through a tethered thruster attached to the surface. Such a system would require advanced knowledge of the asteroid surface properties, likely requiring a precursor mission.
2. N EUTRAL B EAM D ESIGN Asteroid Strength and its Effect on Despin Design Developing models for asteroid structural strength is an ongoing field of research with nearly all work using Discrete Element Method (DEM) approaches to solve the asteroid failure and re-accumulation problem [9–11]. If we understand the structural strength, we can ensure that any method used to despin or deflect an asteroid does not cause it to disaggregate initially. Though a disaggregated asteroid appears to be a good solution for planetary defense, the issue remains that there would be uncertainty as to whether each part is small enough to burn up in the atmosphere or whether we have exacerbated the problem by creating boulders that will impact several locations on Earth. To determine conservative estimates for asteroid structural strength, we will use the analytical estimates from Sanchez and Scheeres [10] and refined cohesion estimates from DeCicco and Hartzell [8]. First we modify the yield stress due to cohesive strength as given by Sanchez and Scheeres [10]:
Asteroid control methods that require any knowledge of an asteroid besides a mass and size estimation carry a fair amount of risk. According to JPL’s Small Body Database, of the 13,065 Near Earth Asteroids (NEAs) only 325 have a SMASS-II or Tholen spectral class definition. This is problematic for any method whose main thrust comes from the sublimation of volatiles like the mirror scheme from Vasile and Maddock [2] which relies on the assumption that their target asteroid is volatile rich. It is also problematic for any method that makes assumptions on the asteroid composition in order to attach a thruster like Scheeres and Schweickart [5]. Both concepts would require extensive pre-mission observations and/or a precursor mission to obtain spectral data and a detailed shape model. Vasile and Maddock [2] would also require a large launch mass to deliver a mirror tens of meters in diameter which may not be possible with current launch vehicles. Here, the hovering electric thruster idea from Bombardelli et al [6] has an advantage, but it could cause an unsafe environment as discussed previously.
σY =
0.125AC# φD r¯p
(1)
where A is the Hamaker constant, C# is the average number of neighboring particles, φ is the packing fraction, D is a cohesion multiplier from DeCicco and Hartzell [8], and r¯p is the average grain size. The cohesion multiplier was determined in [8] by varying eccentricity and orientation of two ellipsoidal grains in contact and comparing their cohesion to that of two spheres in contact. The yield stress, σY , is the strength of a matrix of small grains holding together larger boulders. The principal stress due to gravitation and rotation is given by [10]:
We must despin the asteroid in order to control it. The ideal deflection method must satisfy several requirements:
ρ σx = − (ωα2 − ω 2 )a2 2 2
(2)
ωα2 = 2πGρab2
∞ 0
(a2
+ x)
dx (a2 + x)(b2 + x)2
(3)
where ρ is the bulk density, ωα represents a rotation rate limit where a cohesionless body would destabilize, ω is the rotation rate, a is the semi major axis of the ellipsoidal asteroid, is the internal stress variation (typically close to 1), G is the gravitational constant, and b is the semi minor axis of the ellipsoidal asteroid. By using Drucker-Prager failure criterion, we can then find the maximum applied stress allowable: σapp ≥ σY −
4σx sin α − σx 3 − sin α
Figure 1: The structural strength of the asteroid is highly dependent on the average grain size and on assumptions for the bond strength (ratio of cohesive strength to gravity). Our minimum and maximum cohesive estimates provide further bounding ranges for the overall structural strength.
(4)
where α is the internal friction angle of the cohesive substance. The asteroid parameters are given by:
electron capture and ionization reactions occur. For an argon target:
Table 1: Asteroid Parameters Hamaker Constant, A Average # Neighbor Particles, C# Packing Fraction, φ Cohesion Multiplier, D Density, ρ Rotation Rate, ω Semi Major Axis, a Semi Minor Axis, b α Mass of Asteroid, Mast
0.036 N/m 4.5 (cubic) 0.55 (cubic) 0.33 - 4 2000 kg/m3 6 hrs 100 m 50 m 1 90◦ 2.09·109 kg
Ar + Ar → Ar+ + Ar + e− Ar+ + Ar → Ar + Ar+
Ionization
Electron Capture
The electron capture reactions dominate and a majority of the beam flux becomes neutrally charged without a reduction in the beam’s momentum. The beam then travels through magnetic deflectors and the remaining ions are deflected onto ion dumps. Menon [12] provides an analytical relation for the neutralization fraction, ηn in an ionization/electron capture reaction:
We pick the internal friction angle to be 90◦ even though this is non-physical as a conservative estimate as it maximizes sin α for the structural strength; additionally, we use cubic packing parameters. The size and rotation rate of the asteroid were chosen to represent a medium-sized asteroid with a moderate spin. The asteroid strength is highly dependent on the average grain size. We plot the strength results for the minimum and maximum cohesion multiplier to determine a range dependent on grain size. Fig 1 presents a large variability of asteroid strength. A typical range of bond numbers (the ratio of cohesive strength to gravitation), B, are plotted to their equivalent average grain size. In situ data has shown that asteroids follow a cubic distribution for grain size [10]. Fig 1 demonstrates how rapidly the strength can drop off as cohesion becomes the less dominant binding force. If we assume that the smallest grain size is 1 μm, then it can be shown that the average grain size is approximately r¯p = 1.5rmin . This corresponds to a strength of approximately 2 - 30 kPa and will serve as our metric for the yield strength of the asteroid. The yield strength dictates the maximum torque that we can apply during the despin maneuver to avoid fragmenting the asteroid.
ηn =
Γ0 C10 = (1 − e−nL(C10 +C01 ) ) Γ1 C10 + C01
(5)
where Γ0 is the flux of neutrals, Γ1 is the flux of singly charged ions, C10 is the reaction cross section for electron capture, C01 is the reaction cross section for ionization, and nL is the linear number density of the neutral gas in the neutralization chamber (n being the number density and L being the chamber length). The reaction cross sections are typically found experimentally through beam target experiments and are highly dependent on the incident beam energy and the species. Our goal is to find a linear density in Eqn 5 that maximizes the neutral fraction. We will focus on Argon as data on its reactions over a spread of energies is widely available. In Phelps [13], reaction cross sections are given for ionization and electron capture over wide energy intervals. By numerically fitting the Argon cross sections as a function of energy, E, C10/01 = f (E), we can get the following empirical relations up to 10 keV:
Maximizing Neutralization The goal of our initial analysis is to determine the linear density of our neutral target that maximizes neutralization and is a function of the beam energy. Neutral beams are comprised of four modules: an ion source, neutralization chamber, magnetic deflectors, and an ion dump. In its operation, the neutral beam takes an ion source of given energy and density and sends it through a neutralizer filled with neutral gas (also referred to as the ‘neutral target’) where
C01 = 0.6432 ln(E) − 2.4453
[10−16 cm2 ]
(6)
C10 = −4.819 ln(E) + 59.674
[10−16 cm2 ]
(7)
When Eqn 6 and 7 are substituted into Eqn 5, we find that Γ0 /Γ1 reaches an asymptote. However, by using Eqn 6 and 7 in Eqn 5, holding the energy constant, and varying the linear density we can find the numerical derivative and the linear density that achieves the maximum efficiency. By stepping through several energies, we may then develop a power law relation for the linear density that maximizes the efficiency: 3
nL = 8 · 1014 E 0.1315
[cm−2 ]
from 500mA to 1000mA), and the maximum neutralization that corresponds with the beam energy. In Figure 2 we demonstrate that the theoretical thrust for our neutral beam provides tens of millinewtons throughout our entire energy range. This is due to the fact that in our energy range for Argon, electron capture is the dominant reaction allowing for the beam to achieve 80% - 95% neutralization.
(8)
This gives us the required linear density of neutral gas in the neutralizer in order to maintain maximum neutralization of the beam for any energy as Eqn 5 is now only a function of energy. Mass Flow Rates of Neutral Gas If we analyze the neutral beam as an extension to an electric propulsion device, an important characteristic we need to understand is the mass flow rates to determine our specific impulse (the ratio of thrust to mass flow). We can model our neutralization chamber as a cylinder with gas inputs that ensure constant neutral gas density across the chamber. We assume that the mass flow rate of neutral gas is large enough that the gas remains quasi-neutral. The end of the chamber is in vacuum so the time for the gas input to escape, τesc scales with the sound speed, us : τesc
L us
Figure 2: Thrust Achieved by Neutral Beam - With moderate currents, we are theoretically able to achieve tens of millinewtons of thrust with the neutral beam owing to the fact that the neutralization efficiency ranges from 80% to 95% and it decreases with increasing energy.
(9)
In order to maintain maximum neutralization we require a number density, n (which we calculate from Eqn 8): nus (10) L where n˙ is the number density flow rate. We can then determine the mass flow rate for the neutralizer using the cross-section area, A, and mass of our species, M :
Given that a neutral beam is a low thrust application, we must understand the specific impulse, Isp , in order to later determine mass requirements for this despin method. Our Isp is given by:
n˙ −
M nf AL m˙n τesc
Isp = (11)
By setting the neutralizer length, we investigate the range of Isp for our beam ionization energy and source current. Figure 3 presents data for a small neutralizer, which would also require a higher mass flow rate of neutral gas to maintain neutral density. Therefore, the Isp achieved by such a neutral beam would not be suitable for long-term use but would be useful for a table-top proof of concept.
Thrust and Isp The past two sections set up our investigation into neutral beams by determining the neutralization efficiency. This efficiency determines our ion beam input loss and the mass flow to maintain neutralization: a key component to determining our specific impulse. The fundamental equations for electric propulsion are given:
2QE M
m˙ b =
IM Q
F = ηn vef m˙ b
(13)
where g0 is the gravitational acceleration at Earth. From our previous work, we now have a manageable Isp relation that is only a function of three variables: allowing us to compare how energy, current, and neutralizer length affect the specific impulse of a neutral beam.
With this, we now have a relation for the mass flow rate as m ˙ = f (E, AL) meaning that we can find the mass flow rate for the optimal neutralization at a specific energy by setting the dimensions of our neutralization chamber.
vef =
F (E, I) g0 [m˙ b (I) + m˙n (E, L)]
As we lengthen our neutralizer to 50 cm and 100 cm in Figures 4 & 5, respectively, we see a marked increase in the Isp . However, as we increase the length of the neutralizer, the gain in Isp per change in thrust level decreases. An assumption we have made in these calculations is that the beam maintains constant cross-sectional area through the neutralizer which is fair for short distances, but may not be appropriate for longer neutralizers. As the half angle is non-negligible, this would either require beam shaping in the neutralizer or a conical-bored neutralizer. In either case, the benefits of a longer neutralizer are clear as it provides reasonable Isp , a key consideration for our application to asteroid despin.
(12)
where vef is our effective velocity, Q/M is our charge to mass ratio (fixed for our species), m˙ b is the mass flow from our source, I is our current, ηn is our neutralization efficiency, and F is thrust. For the effective velocity, we have fixed our analysis to consider an input beam of singly charged Argon ions. The momentum is conserved through the neutralizer so our effective velocity is not altered. The thrust is affected by this form of neutralization as there is loss in beam mass due to magnetic deflection of the imperfectly neutralized portions of the beam. We then plot our output thrust as a function of the energy, mass flow of the source (with a range of current
We next calculate the power requirements of the proposed NBAC design. Our analysis begins back at the ion source which we have, until now, considered as a black box. The input power to the ion source, Pin , is given by: 4
power to be achieved; Petro and Sedwick [14] have compiled such conversion efficiencies for modern electric propulsion. Our power requirements are given in Table 2. Table 2: Power Requirements Beam Energy 2 keV 8 keV 10 keV
Input Power 2.5 - 3.85 kW 6.15 - 10.13 kW 6.94 - 12.66 kW
This range of power is easily achievable with modern solar arrays, however, the issue becomes in achieving these powers in a laboratory setting for proof of concept. For our future research, we will focus upon the 2 keV neutral beam to achieve our metrics for thrust and Isp .
Figure 3: Isp for 10cm Neutralizer - The 10 cm neutralizer provides sub-1000s Isp which is not suitable for a long duration burn required to control an asteroid. Such Isp is considered sub standard for plasma propulsion devices
Time Required for Complete Asteroid Despin Scheeres and Schweickart [5] worked extensively on the control dynamics for despinning and deflecting asteroids. The time to despin is highly dependent on the maximum moment of inertia, I3 : Mast 2 (a + b2 ) (15) 5 where Mast is the mass of the asteroid, a is the semi-major axis, and b semi-minor axis. The time required to despin the asteroid can be calculated from conservation of angular momentum. We modify Scheeres and Schweickart’s [5] equation for despin time to account for multiple spacecraft acting on the asteroid: I3 =
Figure 4: Isp for 50cm Neutralizer - Lengthening the neutralizer to 50 cm improves our theoretical Isp to a range that is suitable for plasma propulsion whilst maintaining good thrust levels.
ω0 (16) aF N where F is the thrust, ω0 is the initial rotation rate and N is the number of spacecraft applying the NBAC torque. Finding the total fuel mass required to despin the asteroid: t = I3
Mtot =
T (E, I) t(E, I, N ) Isp (E, I, L)g
(17)
Here we fix the asteroid parameters (shape, mass, and rotation rate) to facilitate our investigation of using a neutral beam to fully despin while simultaneously changing the ion source of energy level, current, length of the neutralizer, and number of spacecraft. Thus, this Mtot is a measurement of fuel mass required per spacecraft. Figure 5: Isp for 100cm Neutralizer - At a length of 100 cm, there is a moderate increase in the Isp from the 50 cm neutralizer. Longer neutralizers would be fairly cumbersome and even at the 100 cm length we may need to further investigate if beam spread may be a significant problem due to the half angle.
Pin =
Pout ηp
Using Eqn 16 and 17, we can determine if neutral beams would be a feasible method of despinning a moderately-sized asteroid from a time and fuel mass requirement standpoint. In Figure 6, we investigate using a 2 keV ion source with different size neutralizers over the 500mA-1000mA range with varying numbers of spacecraft. The number of spacecraft decreases the time for despin and the fuel mass per spacecraft, both expected results, importantly, the 50cm neutralizer allows for us to achieve sub-metric ton fuel mass requirements. As we add more spacecraft to the system, we not only decrease the per spacecraft fuel requirements, but we add operational capability to controlling the asteroid. For example, if the asteroid starts precessing as we try to despin it because of imperfect thrust vectors, we can redistribute
(14)
where ηp is the power conversion efficiency and Pout is our output power from the ion source into the neutralizer. The power conversion efficiency is dependent strictly on the 5
(a) 2 keV Despin Time
(b) 2 keV Required Fuel
Figure 6: (a) Despin time as dependent on thrust and the number of spacecraft (b) Required fuel mass (Metric Tons) as dependent on thrust, neutralizer length, and number of spacecraft (abbreviated as s/c). Using a 2keV ion source with a capability of 500mA-1000mA, despin times are prohibitively long. However, fuel mass use (given here in metric tons) is reasonable. The difference in mass usage simply by lengthening the neutralization chamber from 10cm to 50cm provides large fuel savings.
(a) 8 keV Despin Time
(b) 8 keV Required Fuel
Figure 7: (a) Despin time as dependent on thrust and the number of spacecraft (b) Required fuel mass (Metric Tons) as dependent on thrust, neutralizer length, and number of spacecraft (abbreviated as s/c). Using a 8keV ion source with a capability of 500mA-1000mA, we see a marked decrease in despin time as well as fuel requirements with the majority of results in the sub-500kg range. spacecraft to counter that precession while still maintaining the desired torque. Though the 2 keV system would have good fuel mass requirements, the time required to despin would not be suitable for planetary defense.
savings which is directly evinced from the Isp data in Fig 5 and displayed in Fig 8. The Isp starts to level off at these increasing energies with our fixed range of current. The theoretical neutralization is steadily decreasing as electron capture starts to become the less dominating effect in the Argon reactions due to the increasing incident energy of the beam onto the neutral target. Thus, the useful beam that we can extract likewise decreases driving down the thrust that would otherwise be attainable had we not neutralized the beam. The advantage that we gain from increasing energy to these higher levels is evident in the time to despin as the 10 keV beam drives this metric down to 2 years.
As we increase our energy to 8 keV, despin times with multiple spacecraft become more manageable. Also, many of the configurations require less than 500kg of fuel. As the fuel mass per spacecraft decreases, it becomes feasible to deliver multiple spacecraft with one launch vehicle on a direct transit to the asteroid. This reduces the inherent risk associated with multiple mission-critical payloads. Increasing the energy to 10 keV does little for our fuel mass 6
(a) 10 keV Despin Time
(b) 10 keV Required Fuel
Figure 8: (a) Despin time as dependent on thrust and the number of spacecraft (b) Required fuel mass (Metric Tons) as dependent on thrust, neutralizer length, and number of spacecraft (abbreviated as s/c). Using a 10keV ion source with a capability of 500mA-1000mA, the advantage over the 8 keV system lies in the time required to despin the asteroid rather than any large decrease in fuel mass.
3. C ONCLUSION In our pursuit of developing a concept to despin an asteroid, we have conducted a preliminary design study. Our neutral beam does not require a massive propellant requirement (
