SWIMMERs: A Thought Experiment on the Potential and Limitations of Propellantless Interstellar Travel

Can we tap ionized particles in the interstellar medium as a way of exchanging momentum for propulsion? It’s a concept with a lot of pluses if it can be made to work, chief among them the fact that such a device would be propellantless. Looking at the topic today is Drew Brisbin, a postdoctoral researcher in astronomy who received his PhD from Cornell University in 2014. Dr. Brisbin has since gone on to work towards better understanding his field of specialization: the study of galaxy evolution in the early universe. He currently works at Universidad Diego Portales, in Santiago Chile, where he collaborates closely with other researchers using some of the most sensitive telescopes in the world, located in the mountainous Chilean desert. In addition to his formal work and outdoors-oriented hobbies, he also enjoys dreaming about the future of humanity. One particular dream recently seemed to warrant some further investigation, leading him to the ideas he explains today.

By Drew Brisbin

Foreword

This article represents a distillation of a work published in April 2019 in the Journal of the British Interplanetary Society (reference [0]). Some technical details have been omitted for brevity, but interested readers are encouraged to read the original publication which is freely available at https://arxiv.org/abs/1808.02019. Additional commentary has been included to address what the author sees as a critical flaw in Dr. Robert Zubrin’s “Dipole Drive” concept.

Abstract

In particular light of the recent public excitement and ensuing disappointment regarding the exotic “EM drive” it is worthwhile to point out that space travel without on-board propellant is eminently possible based on well established physical principles. Here a new mode of transport is proposed which relies on electric-field moderated momentum exchange with the ionized particles in the interstellar medium. The application of this mechanism faces significant challenges requiring industrial-scale exploitation of space but the technological roadblocks are different than those presented by light sails or particle beam powered craft. This mode of space travel is well suited to energy efficient travel at velocities below about five percent the speed of light (0.05 x c) and compares exceptionally well to light sails on an energy expenditure basis. It therefore represents an extremely attractive mode of transport for slow (of order multi-century long) voyages carrying massive payloads to nearby stellar neighbors. This will be a useful niche for missions that would otherwise be too energy intensive to carry out, including initial forays into nearby stellar systems with observatory probes, or long term transport of bulk materials as a precursor mission to set up colony infrastructure.

Introduction

The tyranny of the rocket equation has long been recognized as an impediment to becoming a truly spacefaring species. Due to the exorbitant reaction mass required for traditional rockets in interstellar travel, there has been considerable attention to methods of space travel that circumvent the rocket equation. Laser-driven light sails are a prominent and long-standing idea (see for example [1] and references therein). While light sails are well established and also the engines of the widely publicized Breakthrough Starshot program [2] and Project Dragonfly [3], their thrust is fundamentally limited to 6.67 N/GW. For comparison, the Three Gorges Dam, the largest capacity power plant currently in operation, has a capacity of about 22.5 GW. If this power was transmitted with perfect efficiency to a light sail it would provide thrust equivalent to the force required to lift a 15 kg mass on Earth. Scaling light sails up to larger-than-gram-scale spacecraft therefore necessarily depends on humanity’s ability to harness incredible power. Furthermore, since light is only able to push, it is very difficult for light sail spacecraft to slow down at their destination, limiting missions to fly-bys unless complicated reflecting infrastructure can be sent ahead of the craft. Alternatively, direct sunlight could be used as a source of photon pressure. Unfortunately, the material properties suggested to be necessary for a practical interstellar solar sail require materials with extremely low areal densities with σ≲10-3 g/m2 [4]. Current state-of-the-art reflective films developed for light sails reach areal densities of order 10 g/m2, or four orders of magnitude too dense even without including any support structure or payload, so it is uncertain when if ever suitable materials will be developed for an interstellar solar sail [5].

Another idea using external reaction mass is the particle-beam powered spacecraft. This hinges on a sail formed by an extended electric or magnetic field which is able to deflect a remotely-beamed stream of charged particles. Since charged particles carry much more momentum per unit energy than photons this could have much lower power requirements than light sails. This concept has its origins in the Magsail, a large loop of current carrying wire which deflects passing charged particles in the interstellar medium (ISM), eliciting a drag force which could be used as a brake to slow spacecraft down to rest with respect to the ISM after a high speed journey [6]. To provide acceleration, one could simply supplant the ISM with a beamed source of high velocity charged particles [7]. Providing a long distance beam of charged particles is, however, quite difficult because of beam divergence due to particle thermal motion, interaction with interplanetary or interstellar magnetic fields, and electrostatic beam expansion in the case of non-neutral particle beams. Andrews (2003) suggests that it would be necessary to construct a highway of beam generators at least every AU or so along the route on which the craft accelerates [8]. The related concept of the electric sail instead uses an electric field generated by a positively charged grid of wires or wire spokes extending from a central hub to push against the outward streaming solar wind [9]. This concept has the near term potential to allow travel within our own stellar neighborhood with very low energy costs. The electric sail, like the Magsail however, ultimately relies on a drag force, decelerating the spacecraft to rest with respect to the surrounding medium (the outward moving solar wind in this case). It is therefore unable to accelerate beyond the heliosphere, nor can it accelerate directly inwards towards the sun while in the heliosphere.

It would be possible to overcome these obstacles by actively pushing against the charged particles of the ISM, rather than passively coming to rest with respect to the medium. These spacecraft with interstellar medium momentum exchange reactions (SWIMMERs) can accelerate with respect to the ISM, are significantly more energy efficient than light sails, would be able to decelerate at their destination, do not require pre-established infrastructure along the route and are based on elementary physical principles. Recently Dr. Robert Zubrin discussed his independent work on a “dipole drive” concept which is similar to the SWIMMER concept described here [10,11]. Although the two ideas are related and even share a similar geometry, they were arrived at independently. Furthermore the dipole drive as described, suffers from a flaw which prevents its successful acceleration in the stationary ISM. The work presented here concerns the conceptual mechanism which allows SWIMMERs to accelerate through a stationary ISM.

Both the Magsail and electric sail concepts rely on the fact that there is significant mass in the ISM (or the heliosphere) which can interact with relatively low mass structures consisting of charged or current carrying wires. How, then, could a spacecraft interact to accelerate rather than decelerate with respect to the surrounding medium?

The need for a time varying electrical voltage

Quite generally this will require a time varying electric field which can do work on the surrounding particles of the ISM. As a thought experiment, imagine a spacecraft consisting of a pair of conducting plates arranged in a parallel-plate capacitor style configuration with a switchable power source connecting them and able to charge and discharge them at will. The conducting plates, rather than being solid, are composed of a wire mesh with the vast majority of the area taken up by open space rather than metal, such that particles are easily able to pass through the plate mesh without collision. The spacecraft is moving face on through a stationary medium of charged particles (like the interstellar medium), as shown schematically in Fig. 1. For the moment take the charged particles to be macroscopic and extremely dispersed so we can easily see individual particles and identify when they are in the vicinity of the spacecraft — charged pebbles rather than atoms or elementary particles. As the spacecraft moves through the field of charged particles we can strategically switch the power source on and off to create an electric field and push on charged particles as they pass between the conducting plates, accelerating the particles backward and creating thrust to push the spacecraft forward (Fig. 1). This scenario is perfectly in line with conservation laws. momentum is conserved since the particle gains momentum in the backward direction and the spacecraft gains momentum in the forward direction. Energy is conserved as the increase in kinetic energy (of the particle and the spacecraft) is drawn directly from the power source depleting whatever energy source is being used (depleting a battery’s chemical energy, or converting beamed laser light for instance).

In practice of course, the ISM is not made of macroscopic, easily separable pebbles, but microscopic ions and electrons with tens of thousands per cubic meter or more, so we cannot consider manually switching the charged plates based on the positions of individual particles. The possibility of simply leaving the plates continuously charged, front facing plate positive, back plate negative, may initially seem workable, and this appears to be the scenario imagined in the “Dipole Drive” [10]. Introductory electricity courses train us to think about parallel plate capacitors as having a strong field in one direction between a pair of charged plates, and no field outside the plates, so it is easy to initially imagine that a positively charged ion would approach the front plate while feeling absolutely no force, feel a strong force backwards while between the plates, and then feel absolutely no force again as it recedes beyond the back plate. In fact, however, a set of finite parallel plates will indeed have electric fields outside of their gap which directly oppose the electric field inside the gap, and would perfectly negate the thrust generated by particles transitioning the gap.

This is made more clear by considering the electrical voltage rather than electric fields. Fig. 2 (top) shows schematically the voltage through the center of an idealized infinite parallel plate capacitor charged to a potential difference of 2V. Positive charges will want to “slide down” the potential ramp located between the plates, accelerating rightward. For a finite sized set of parallel plates the voltage extends a bit to the left and right of the gap, continuously decaying from the voltage at the plates to a voltage of zero at great distances as shown in Fig. 2 (middle). Note that these voltage ramps tilt in the other way than the region between the plates and will tend to accelerate positive charges in the opposite direction. For a particle entering in from the left and making it all the way through to exit out the right side, would it end up with more or less rightward velocity? Remember that voltage (often referred to as electric potential) is simply potential energy divided by charge (in SI units 1 volt = 1 joule/coulomb). Starting out very far on the left in Fig. 2, the rightward traveling particle with charge q will have some kinetic energy, KE, and zero potential energy.

As it approaches the front plate, it will begin slowing down as it rises up the potential ramp and converting kinetic energy to potential energy, eventually reaching a peak potential energy of +qV (with a kinetic energy of KE-qV). As it traverses the gap it is accelerated rightward as it slides down the potential, eventually reaching a potential energy of -qV and a kinetic energy of KE+qV. It then exits the parallel plate gap and is again forced up a potential ramp, converting kinetic energy back into potential energy, until it finally reaches distances far away from the plates where the voltage is 0 at which point it has potential energy 0 and kinetic energy KE — exactly the same as it started.

This is not a minor fluke of this particular geometry either. Any arrangement of charged plates – so long as the voltage is finite and the plate volume is finite – will leave the potential 0 at infinity. In [11] Zubrin has suggested that Debye shielding (the phenomenon of oppositely charged free particles in a plasma tending to cluster around charged objects and screen out the electric field) would somehow ameliorate this issue, but that is not the case. The effect of Debye shielding will be for the front facing positive plate to accumulate a cloud of electrons and the back plate to accumulate a cloud of positive ions, making the voltage ramps just outside the plate pair more steeply return to zero, as shown in Fig. 2 (bottom). Nonetheless, the potential remains 0 at large distances and in the end passing particles enter and leave the system with the exact same kinetic energy. This does not preclude the particles from changing direction, either being reflected back in the direction they came, or deflected to the side if they interact with the parallel plates at an angle, so such a configuration could certainly be used to either steer or decelerate with respect to the charged particle medium, but such a system with constant voltages cannot do work on charged particles which begin and end far away, and cannot accelerate with respect to them (it could still be useful to accelerate up to the velocity of the solar wind inside our heliosphere, much like the electric sail).

If the goal is to accelerate in the dead of the ISM, it is essential that a time-varying electrical potential be used to do work on the passing particles. There are multiple ways to do this, but one simple implementation, illustrated in Fig. 3, could feature a pusher plate made of a large grid of wires moving face-on through the ISM (much like the proposed geometry of a standard electric sail). Unlike a standard electric sail, however, the grid of wires would actually be two identical layers of wire sandwiching a strong insulator between them to keep the two layers physically apart and electrically isolated. These wire grids or tethers could be made from very fine superconducting wire and the entire ensemble could be spun to create tension and keep the wire grids extended without heavy support structure. The two faces of the pusher plate would be charged and discharged cyclically. In the “primer” portion of the operation cycle, the front layer in the pusher plate is raised to a positive potential and the back layer to an equal negative potential. Due to edge effects of the finite plates and the self-shielding behavior of plasmas, this results in a decaying electric potential of opposite sign on either side of the plates. Ions streaming towards the front positively charged layer slow down, building up an overdense clump in front of the pusher plate while an underdensity forms at the immediate location of the pusher plate. Then in the “pull” stage of the cycle the potential difference across the layers is reversed and significantly increased. The ion clump that was formed in front of the plate will be attracted to the negative front layer, pulling the spacecraft forward. As the clump approaches the pusher plate, the potential difference is turned off and the clump is allowed to coast through the plate to the other side. In the final “push” stage the same potential difference is applied and the clump is further pushed backwards by the positive back layer of the pusher plate. The clump drifts away beyond the influence of the pusher plate and the cycle repeats. Fig. 4 shows the electric potential and ion density at various cycle stages for a simple model.

By intentionally setting up clumps in the oncoming ISM we can interact with it much more like in our initial thought experiment with charged pebbles. The spacecraft gains momentum by giving backward momentum to the ISM (pushing ion clumps to the right in Fig. 4). The source of the potential difference does work in the primer stage when it sets up the positive potential, raising the electrical potential energy of the ions in front and again in the push stage when it raises the ion clump to a higher potential. Electrons encountering the potential ramps will largely be reflected but this causes only a negligible momentum drag since they are far less massive than the protons and other positively charged ions. In a real three dimensional case, there will also be loss of efficiency due to particles which do not interact perfectly in one dimension, but instead are pushed off to the side as they pass by the charged wires. Furthermore, this qualitative conceptual analysis does not account for the self influencing behavior of plasmas. This will undoubtedly strongly affect the ion (and electron) distributions and the extended electric potential. Detailed particle-in-cell simulations will be necessary to investigate the optimal tuning of cycle timings, electrical potentials, and even geometry of the charged plates as it may be advantageous in some cases to accelerate ion clumps across a series of potential differences to gain more thrust per ion, at the expense of a more complex and massive pusher plate. These simulations are beyond the scope of this work but will be a critical step in transitioning the concept from a thought experiment to a practical real world device.

Mathematical expression of an idealized case

While the effectiveness and geometry of a SWIMMER will ultimately need to be tested thoroughly by simulation, it is straightforward to represent the force on an idealized system which is able to efficiently convert electrical power, P, into backwards acceleration of nearby particles. The resulting force, F SWIMMER , is

where m p is the particle mass (of order the proton mass for the ISM), n is the density of particles, v is the velocity of the spacecraft (with respect to the stationary-particle frame), and A is the cross sectional area over which the system can interact with particles (or equivalently v x A is the volume rate of particles swept out by the spacecraft through time). The positive sign is used when accelerating with respect to the the stationary-particle frame, and the negative sign is used when decelerating. The derivation of this relationship is shown in [0].

The power referred to throughout this work is the delivered electrical power. Thus far the source of power for a SWIMMER has been ignored. There is no reason a SWIMMER could not use an onboard power source, making it totally independent of external infrastructure. This, of course, would require an exceptionally energy dense fuel source as well as a very efficient generator to achieve useful velocities for interstellar travel. Beaming power remotely to the SWIMMER is possibly a more viable strategy for interstellar travel, which invites a direct comparison to light sails. In this case an additional P/c term is included in eq. 2, corresponding to the photon pressure of the beamed energy being absorbed by the spacecraft. The total force is then:

Where P/c is either added or subtracted depending on if the beamed energy source is coming from the origin or the destination respectively. It will also be useful to consider the ratio, R, of the force on a SWIMMER to the force on an ideal light sail with equal delivered power (F=2 P/c). This ratio can be written as:

where we have used the the positive signs in the SWIMMER and photon forces indicating the spacecraft is accelerating and beamed energy is coming from the origin (as would be the case for an initial out-bound journey to another star system). In Fig. 5 R is shown as a function of velocity for a few values of A/P. There is some uncertainty surrounding the structure and properties of the local ISM, but there is general consensus that a journey to Cen A will involve passage through some combination of the Local Interstellar Cloud, the Circum-Heliospheric Interstellar Medium and the G Cloud. Therefore, a conservatively low ion density of n=0.07 cm-3, consistent with the estimated densities in these clouds, (see for example [13]) is used in Fig. 5. Fig. 5 shows the force initially rising with velocity due to the fact that at higher velocities the SWIMMER plates are sweeping out larger volumes of the ISM faster and able to interact with more particles per second. The force peaks at some velocity, and then decreases since it takes more and more energy to accelerate the passing ions to yet higher velocities to get the same momentum change. Due to this initial rise in force with velocity, it may be useful to give SWIMMERs an initial velocity boost through other means (such as conventional rockets, gravitational assists, or particle beam assists) to take advantage of the forces at higher velocities.

Larger A/P values give significantly better performance at lower velocities, but trend together as velocity increases, with the force approaching (P/v) x (c+v)/c (the ratio R approaches (c+v)/(2v), shown by the red line in Fig. 5). This high velocity limit implies an order of magnitude larger force for SWIMMERs relative to light sails up to v=c/19 or about 5% the speed of light.

Example mission

To illustrate the potential of SWIMMERs for interstellar travel, it is helpful to consider a possible future mission. Further details and technical considerations are available in the published manuscript, but here we simply assume the the engineering difficulties of beaming power to interstellar distances is solved, and the onboard energy converter has a specific power capacity of 4 kW/kg (every 4 kW of delivered power requires an increase of 1 kg in the mass of the power converter equipment). The ISM is assumed to be uniform with a density of 0.07 cm-3, a temperature of 7000 K and therefore an electron Debye length, λ D =21.8 m.

A relatively lower mass SWIMMER mission might have the goal of transporting a modest space probe, m pay =1000 kg to α Cen A. Accelerating within our heliosphere and decelerating at the destination are possible, and in fact relatively energy efficient but discussion of these will be left for the main publication, [0], for brevity. A modest electrical power delivered to the SWIMMER of 10 MW is assumed. The pusher plate will be made up of several long tethers. In practice these tethers will consist of very fine braided filaments to prevent failure due to micrometeoroid and interstellar dust collision, as described for the electric sail [9]. From a material mass standpoint these are considered to be single wires with an effective diameter of 30 μm. This is equivalent in material to eight filaments with diameters of about 10 μm. Given the pulsed nature of the SWIMMER electric field, the wire tethers should be made out of superconducting materials. A single charged wire will interact with charged particles passing within about λ D on either side of it. The total cross sectional interaction area is given by

where L is the summed length of all the tethers. This cross sectional interaction area is somewhat of an idealization as the Debye length does not represent a hard cut off where particles suddenly cease to be effected by an electric field, and in regions where tethers intersect, part of their cross sectional areas will overlap. Nonetheless it is a sufficient estimate for our rough calculations. The mass devoted to this pusher plate will be m pusher = ρ x L x π r wire 2. Where r wire represents the effective radius of the wire tether (15 μm in our case), and ρ represents the density of the tether material, which we will take to be 2570 kg/m3, the density of the popular superconducting material, magnesium diboride.

The total mass of the SWIMMER ship is comprised of m pay =1000 kg, m power =2500 kg (given by the 10 MW supplied electric power and a 4 kW/kg specific power), and m pusher . We will take 7400 kg as the mass of the pusher plate which provides for a total summed tether length of 4.1 x 109 m. While this is seemingly a very long tether, it does not in any way represent the spatial scale of the SWIMMER, as the pusher plate will be made up of several thousand tethers, possibly splitting off from each other at greater radial distances. The summed length is merely a useful value for determining the total cross sectional area in plasmas of different temperatures and densities. In this case, from eq. 4 our SWIMMER tether length corresponds to a cross sectional interaction area of 180,000 km2 (about the size of Uruguay or the state of Washington).

We will begin our voyage as the SWIMMER enters the ISM at 100 AU with a velocity of 4.0 x 105 m/s (0.133% the speed of light and consistent with typical velocities of the solar wind). Iteratively integrating using eq. 3, we find that after just less than 300 years the spacecraft will be on the doorstep of Alpha Centauri after having travelled one parsec and achieving a final velocity of 1.66% the speed of light. Including time to initially accelerate from rest within the heliosphere and decelerate at the destination marginally increases the trip time, but we could also shorten the trip slightly by systematically shedding mass and reducing the size of the pusher plate enroute. As Fig. 5 shows, at higher velocities larger plate areas provide diminishing returns, so as the spacecraft reaches higher velocities the larger area of the pusher plate becomes dead weight. A total journey of about 300 years starting from rest in the solar system to being gravitationally captured by Cen A is reasonable for the overall journey [0].

While 300 years is a significant amount of time for a scientific endeavor, there is good precedent for multi-century science projects for worthwhile investigations (c.f. [14-16]). Furthermore, the energy expense is a pittance compared to an equivalent mission using laser-pushed light sails. An equivalent, 7400 kg probe pushed by 10 MW of laser light incident on ideal light sails (and starting with a velocity 4 x 105 m/s) would take about 1600 years to travel 1 parsec and reach a final velocity of 0.28% the speed of light. To reduce the light sail travel time to 300 years would require an average power consumption of nearly 700 MW (70x higher).

Conclusion

SWIMMERs represent a new mode of interstellar transport. By disposing of onboard reaction mass they circumvent the rocket equation, and by exchanging momentum with ions in the ISM they improve by orders of magnitude over the energy efficiency of traditional light sails at relatively low velocities. The key to this momentum exchange is the time varying electric field which allows SWIMMERs to create inhomogeneities in the surrounding plasma and then push on these inhomogeneities to create thrust.

SWIMMERS perform exceptionally well at lower velocities, with their advantage over light sails diminishing quickly at v > 0.05 c. Furthermore, by relying on the ambient ISM as a momentum exchange medium, they are quite versatile, able to accelerate either away or towards a beamed energy source, opening up myriad opportunities to serve as one-way transport, roundtrips or even statites remaining in stationary positions with respect to the Sun and serving as useful waypoints with infrastructure for other potential space transportation networks.

The example discussed here only scratches the surface of the possible roles for SWIMMERs in our spacefaring future. Their characteristics make them ideal for any mission with large masses in which relatively low velocities are acceptable. They are unlikely to be the sole mode of space transport due to their diminishing advantages at high velocities and their structural complexity which requires onboard power conversion systems with significant mass. They can play the role of the proverbial Mack trucks of space, transporting goods slowly and reliably at a low energy cost, while more time sensitive cargo can make use of fast yet inefficient light sails – the Ferraris of space. SWIMMERs might, for instance, be well suited to aiding the construction of a fast interstellar highway by transporting massive particle beam stations along with their fuel supply out to stationary positions between us and our target destinations. These particle beam stations could be used to swiftly carry low mass Magsails along the path or augment the power of future SWIMMERs by replacing the stationary ISM with a corridor of fast moving beamed particles.

The mission analyzed here regards a one-way interstellar trip. While it does push the limits of current technology by assuming relatively high specific power electrical systems, very thin mass-produced super conducting wire, and low mass electrical insulators which can resist large potential differences (as well as very large laser array optics which are addressed in other works regarding light sails) there is no obvious material or theoretical limits which would prevent such missions from realization. Future work in this vein will need to examine several issues ignored here. Areas of further investigation, include the efficiency of the SWIMMER drive in three dimensions; the electrical potential and cycle timings during the pulsed SWIMMER operation and how they effect the required current density of the tethers; the expected impact of interstellar dust collisions and redundant tether configurations to avoid catastrophic damage from tether breakage; and realistic limits on power conversion system capabilities.

As our understanding of interstellar travel develops, we must face the realization that, not only is it difficult, but there is no one-size-fits-all solution. Where SWIMMERs excel in one metric, other methods may excel in another. Ultimately our best strategy is to develop all possible methods in the hope that their synergy will provide a means to accomplish our goals.

References

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