Is it possible to use a particle beam to push a sail to interstellar velocities? Back in the spring I looked at aerospace engineer Alan Mole’s ideas on the subject (see Interstellar Probe: The 1 KG Mission and the posts immediately following). Mole had described a one-kilogram interstellar payload delivered by particle beam in a paper in JBIS, and told Centauri Dreams that he was looking for an expert to produce cost estimates for the necessary beam generator. Jim Benford, CEO of Microwave Sciences, took up the challenge, with results that call interstellar missions into doubt while highlighting what may become a robust interplanetary technology. Benford’s analysis, to be submitted in somewhat different form to JBIS, follows.
by James Benford
Alan Mole and Dana Andrews have described light interstellar probes accelerated by a neutral particle beam. I’ve looked into whether that particle beam can be generated with the required properties. I find that unavoidable beam divergence, caused by the neutralization process, makes the beam spot size much larger than the sail diameter. While the neutral beam driven method can’t reach interstellar speeds, fast interplanetary missions are more credible, enabling fast travel of small payloads around the Solar System.
Dana Andrews proposed propulsion of an interstellar probe by a neutral particle beam and Alan Mole later proposed using it to propel a lightweight probe of 1 kg [1,2] The probe is accelerated to 0.1 c at 1,000 g by a neutral particle beam of power 300 GW, with 16 kA current, 18.8 MeV per particle. The particle beam intercepts a spacecraft that is a magsail: payload and structure encircled by a magnetic loop. The loop magnetic field deflects the particle beam around it, imparting momentum to the sail, and it accelerates.
Intense particle beams have been studied for 50 years. One of the key features is that the intense electric and magnetic fields required to generate such beams determine many features of the beam and whether it can propagate at all. For example, intense charged beams injected into a vacuum would explode. Intense magnetic fields can make beam particles ‘pinch’ toward the axis and even reverse their trajectories and go backwards. Managing these intense fields is a great deal of the art of using intense beams.
In particular, a key feature of such intense beams is the transverse velocity of beam particles. Even though the bulk of the energy propagates in the axial direction, there are always transverse motions caused by the means of generation of beams. For example, most beams are created in a diode and the self-fields in that diode produce some transverse energy. Therefore one cannot simply assume that there is a divergence-less beam.
What I will deal with here is how small that transverse energy can be made to be. The reason this is important for the application is that the beam must propagate over the large distances, to accelerate the probe to 0.3 AU or 45,000,000 km. That requires that the beam divergence be very small. In the original paper on the subject by Dana Andrews (2), the beam divergence is simply stated to be 3 nanoradians. This very small divergence was simply assumed, because without it the beam will spread much too far and so the beam energy will not be coupled to the magsail. (Note that at 0.3 AU, this divergence results in a 270 m beam cross-section, about the size of the magsail capture area.)
Just what are a microradian and nanoradian? A beam from Earth to the moon with microradian divergence would hit the moon with a spot size of about 400 m. For a nanoradian it would be a very small 0.4 m, which is about 15 inches.
One method of getting a neutral particle beam might be to generate separate ion and electron beams and combine them. But two nearby charged beams would need to be propagated on magnetic field lines or they would simply explode due to the electrostatic force. If they are propagating parallel to each other along magnetic field lines, they will interact through their currents as well as their charges. The two beams will experience a JxB force, which causes them to spiral about each other. This produces substantial transverse motion before they merge. This example shows why the intense fields of particle beams create beam divergence no matter how carefully one can design them. But what about divergence of neutral particle beams?
Image: A beamed sail mission as visualized by the artist Adrian Mann.
Neutral Beam Divergence
The divergence angle of a neutral beam is determined by three factors. First, the acceleration process can give the ions a slight transverse motion as well as propelling them forward. Second, focusing magnets bend low-energy ions more than high-energy ions, so slight differences in energy among the accelerated ions lead to divergence (unless compensated by more complicated bending systems).
Third, and quite fundamentally, the divergence angle introduced by stripping electrons from a beam of negative hydrogen or tritium ions to produce a neutral beam gives the atom a sideways motion. (To produce a neutral hydrogen beam, negative hydrogen atoms with an extra electron are accelerated; the extra electron is removed as the beam emerges from the accelerator.)
Although the first two causes of divergence can in principle be reduced, the last source of divergence is unavoidable.
In calculations I will submit to JBIS, the divergence angle introduced by stripping electrons from a beam of negative ions to produce a neutral beam, giving the resulting atom a sideways motion, produces a fundamental divergence. It’s a product of two ratios, both of them small: a ratio of particle masses (≤10-3) and a ratio of neutralization energy to beam particle energy (≤10-7 for interstellar missions). Divergence is small, typically 10 microradians, but far larger than the nanoradians assumed by Andrews and Mole. Furthermore, the divergence is equal to the square root of the two ratios, making it insensitive to changes in ion mass and ionization energy.
In Alan Mole’s example, the beam velocity is highest at the end of acceleration, 0.2 c, twice the ship final velocity. Particle energy for neutral hydrogen is 18.8 MeV. The energy imparted to the electron to drive it out of the beam, resulting in a neutral, is 0.7 eV for hydrogen. Evaluation of Eq. 3 gives beam divergence of 4.5 microradians.
This agrees with experimental data from the Strategic Defense Initiative, SDI. The observed divergence of a 100 MeV neutral beam as 3.6 microradians; for a Triton beam (atomic weight 3), 2 microradians.
The beam size at the end of acceleration will be 411 km. Alan Mole’s magnetic hoop is 270 m in diameter. Therefore the ratio of the area of the beam to the area of the sail is 2.3 106. Only a small fraction of the beam impinges on the spacecraft. To reduce the beam divergence, one could use heavier particles but no nucleus is heavy enough to reduce the beam spot size to the sail diameter.
Laser Cooling of Divergence?
Gerry Nordley has suggested that neutral particle divergence could be reduced by use of laser cooling. This method uses lasers that produce narrowband photons to selectively reduce the transverse velocity component of an atom, so must be precisely tunable. It is typically used in low temperature molecular trapping experiments. The lasers would inject transversely to the beam to reduce divergence. This cooling apparatus would be located right after the beam is cleaned up as it comes out of the injector. They would have substantial powers in order to neutralize the beam as it comes past at a fraction of the speed of light. Consequently, the coupling between the laser beam and the neutral beam is extraordinarily poor, about 10-5 of the laser beam. This highly inefficient means of limiting divergence is impractical.
Fast Interplanetary Sailing
Beam divergence limits the possibilities for acceleration to interstellar speeds, but fast interplanetary missions look credible using the neutral beam/magsail concept. That enables fast transit to the planets.
Given that the beam divergence is fundamentally limited to microradians, I used that constraint to make rough examples of missions. A neutral beam accelerates a sail, after which it coasts to its target, where a similar system decelerates it to its final destination. Typically the accelerator would be in high Earth orbit, perhaps at a Lagrange point. The decelerating system is in a similar location about another planet such as Mars or Saturn.
From the equations of motion, To get a feeling for the quantities, here are the parameters of missions with sail probes with microradian divergence and increasing acceleration, driven by increasingly powerful beams.
|θ||1 microradian||1 microradian||1 microradian|
|acceleration||100 m/sec2||1000 m/sec2||10,000 m/sec2|
|Ds||270 m||270 m||540 m|
|V0||163 km/sec||515 km/sec||2,300 km/sec|
|R||135,000 km||135,000 km||270,000 km|
|t0||27 minutes||9 minutes||4 minutes|
|mass||3,000 kg||3,000 kg||3,000 kg|
|EK||4 1013 J||4 1014 J||8 1015 J|
|P||24 GW||780 GW||34 TW|
|particle energy||50 MeV||50 MeV||50 MeV|
|beam current||490 A||15 kA||676 kA|
|time to Mars||8.7 days||34 hours||8 hours|
The first column shows a fast interplanetary probe, with high interplanetary-scale velocity, acceleration 100 m/sec2, 10 gees, which a nonhuman cargo can sustain. Time required to reach this velocity is 27 minutes, at which time the sail has flown to 135,000 km. The power required for the accelerator is 24GW. If the particle energy is 50MeV, well within state-of-the-art, then the required current is 490A. How long would an interplanetary trip take? If we take the average distance to Mars as 1.5 AU, the probe will be there in 8.7 days. Therefore this qualifies as a Mars Fast Track accelerator.
An advanced probe, at 100 gees acceleration, requires 0.78 TW power and the current is 15 kA. It takes only 34 hours to reach Mars. At such speeds the outer solar system is accessible in a matter of weeks. For example, Saturn can be reached by a direct ascent in the time as short as 43 days.
A very advanced probe, an Interstellar Precursor, at 1000 gees acceleration, reaches 0.8% of light speed. It has a power requirement 34 TW and the current is 676 kA. It takes only 8 hours to reach Mars. At such speeds the outer solar system is accessible in a matter of days. For example, Saturn can be reached by a direct ascent in the time as short as a day. The Oort Cloud at 2,000 AU, can be reached in 6 years.
The rough concepts that have been developed by Andrews, Mole and myself show that neutral beam-driven magnetic sails deserve more attention. But the simple mission scenarios described in the literature to date don’t come to grips with many of the realities. In particular, the efficiency of momentum transfer to the sail should be modeled accurately. Credible concepts for the construction of the sail itself, and especially including the mass of the superconducting hoop, should be assembled. As addressed above, concepts for using laser cooling to reduce divergence are not promising but should be looked into further.
A key missing element is that there is no conceptual design for the beam generator itself. Neutral beam generators thus far have been charged particle beam generators with a last stage for neutralization of the charge. As I have shown, this neutralization process produces a fundamentally limiting divergence.
Neutral particle beam generators so far have been operated in pulsed mode of at most a microsecond with pulse power equipment at high voltage. Going to continuous beams, which would be necessary for the minutes of beam operation that are required as a minimum for useful missions, would require rethinking the construction and operation of the generator. The average power requirement is quite high, and any adequate cost estimate would have to include substantial prime power and pulsed power (voltage multiplication) equipment, a major cost item in the system. It will vastly exceed the cost of the magnetic sails.
The Fast Interplanetary example in table 1 requires 24 GW power for 27 minutes, which is an energy of 11 MW-hours. This is within today’s capability. The Three Gorges dam produces 225 GW, giving 92 TWhr. The other two examples cannot be powered directly off the grid today. So the energy would be stored prior to launch, and such storage, perhaps in superconducting magnets, would be massive.
Furthermore, if it were to be space-based the heavy mass of the high average power required would mean a substantial mass System in orbit. The concept needs economic analysis to see what the cost optimum would actually be. Such analysis would take into account the economies of scale of a large system as well as the cost to launch into space.
We can see that there is in Table 1 an implied development path: a System starts with lower speed, lower mass sails for faster missions in the inner solar system. The neutral beam driver grows as technology improves. Economies of scale lead to faster missions with larger payloads. As interplanetary commerce begins to develop, these factors can be very important to making commerce operate efficiently, counteracting the long transit times between the planets and asteroids. The System evolves.
We’re now talking about matters in the 22nd and 23rd centuries. On this time scale, neutral beam-driven sails can address interstellar precursor missions and interstellar itself from the standpoint of a much more advanced beam divergence technology than we have today.
Alan Mole, “One Kilogram Interstellar Colony Mission”, JBIS, 66, pp.381-387, 2013
Dana Andrews, “Cost Considerations for Interstellar Missions”, Acta Astronautica, 34, pp. 357-365, 1994.
Ashton Carter, Directed Energy Missile Defense in Space–A Background Paper, Office of Technology Assessment, OTA-BP-ISC-26, 1984.
G. A. Landis, “Interstellar Flight by Particle Beam”, Acta Astronautica, 55, pp. 931-934, 2004.
G. Nordley, “Jupiter Station Transport By Particle Beam Propulsion”, NASA/OAC, 1994. And http://en.wikipedia.org/wiki/Laser_cooling.