Can you imagine the science we could do if we had the capability of sending a probe to Jupiter with travel time of less than a month? How about Neptune in 18 weeks? Alex Tolley has been running the numbers on a concept called Wind Rider, which derives from the plasma magnet sail he has analyzed in these pages before (see, for example, The Plasma Magnet Drive: A Simple, Cheap Drive for the Solar System and Beyond). The numbers are dramatic, but only testing in space will tell us whether they are achievable, and whether the highly variable solar wind can be stably harnessed to drive the craft. A long-time contributor to Centauri Dreams, Alex is co-author (with Brian McConnell) of A Design for a Reusable Water-Based Spacecraft Known as the Spacecoach (Springer, 2016), focusing on a new technology for Solar System expansion.
by Alex Tolley
In 2017 I outlined a proposed magnetic sail propulsion system called the Plasma Magnet that was presented by Jeff Greason at an interstellar conference . It caught my attention because of its simplicity and potential high performance compared to other propulsion approaches. For example, the Breakthrough Starshot beamed sail required hugely powerful and expensive phased-array lasers to propel a sail into interstellar space. By contrast, the Plasma Magnet [PM] required relatively little energy and yet was capable of propelling a much larger mass at a velocity exceeding any current propulsion system, including advanced solar sails.
The Plasma Magnet was proposed by Slough  and involved an arrangement of coils to co-opt the solar wind ions to induce a very large magnetosphere that is propelled by the solar wind. Unlike earlier proposals for magnetic sails that required a large electric coil kilometers in diameter to create the magnetic field, the induction of the solar wind ions to create the field meant that the structure was both low mass and that the size of the resulting magnetic field increased as the surrounding particle density declined. This allowed for a constant acceleration as the PM was propelled away from the sun, very different from solar sails and even magsails with fixed collecting areas.
The PM concept has been developed further with a much sexier name: the Wind Rider, and missions to use this updated magsail vehicle are being defined.
Wind Rider was presented at the 2021 Division of Planetary Sciences (DPS) meeting by the team led by Brent Freeze, showing their concept of the design for a Jupiter mission they called JOVE. The December meeting of the American Geophysical Union was the venue for a different Wind Rider concept mission to the SGL, called Pathfinder.
The main upgrade from the earlier PM to the Wind Rider is the substitution of superconducting coils. This allows the craft to maintain the magnetic field without requiring constant power to maintain the electric current, reducing the required power source. Because the superconducting coils would quickly heat up in the inner system and lose their superconductivity, a gold foil reflective sun shield is deployed to shield the coils from the sun’s radiation. This is shown in the image above with the shield facing the sun to keep the coils in shadow. The shield is also expected to do double duty as a radio antenna, reducing the net parasitic mass on the vehicle.
The performance of the Wind Rider is very impressive. Calculations show that it will accelerate very rapidly and reach the velocity of the solar wind, about 400 km/s. This has implications for the flight trajectory of the vehicle and the mission time.
The first mission proposal is a flyby of Jupiter – Jupiter Observing Velocity Experiment (JOVE) – much like the New Horizons mission did at Pluto.
Figure 1. The Wind Rider on a flyby of Jupiter. The solar panels are hidden behind the sun shield facing the sun. The 16U CubeSat chassis is at the intersection of the 2 coils and sun shield.
The JOVE mission proposal is for an instrumented flyby of Jupiter . The chassis is a 16U CubeSat. The scientific instrument payload is primarily to measure data on the magnetic field and ion density around Jupiter. The sail is powered by 4 solar panels that also double as struts to support the sun shield and generate about 1300 W at 1 AU and fall to about 50W at Jupiter.
Figure 2. Trajectory of the Wind Rider from Earth to Jupiter
The flight trajectory is effectively a beeline directly to Jupiter, starting the flight almost at opposition. No gravity assists from Earth or Venus are required, nor a long arcing trajectory to intercept Jupiter. Figure 2 shows the trajectory, which is almost a straight-line course with the average velocity close to that of the solar wind.
Although the mission is planned as a flyby, a future mission could allow for orbital insertion if the craft approaches Jupiter’s rotating magnetosphere to maximize the impinging field velocity. Although not mentioned by the authors, it should be noted that Slough has also proposed using a PM as an aerobraking shield that decelerates the craft as it creates a plasma in the upper atmosphere of planets.
How does the performance of the Wind Rider compare to other comparable missions?
The JUNO space probe to Jupiter had a maximum velocity of about 73 km/s as Jupiter’s gravity accelerated the craft towards the planet. The required gravity assists and long flight path, about 63 AU or over 9 billion km, mean that its average velocity was about 60 km/s. This is not the fairest comparison as the JUNO probe had to attain orbital insertion at Jupiter.
A fairer comparison is the fastest probe we have flown – the New Horizons mission to Pluto — which reached 45 km/s as it left Earth but slowed to 14 km/s as it flew by Pluto. New Horizons took 1 year to reach Jupiter to get a gravity assist for its 9 year mission to Pluto, and therefore a maximum average velocity of 19 km/s between Earth and Jupiter.
Wind Rider can reach Jupiter in less than a month. Figure 2 shows the almost straight-line trajectory to Jupiter. Launched just before opposition, Wind Rider reaches Jupiter in just over 3 weeks. Because opposition happens annually, a new mission could be launched every year.
As the Wind Rider quickly reaches its terminal velocity at the same velocity as the solar wind, it can reach the outer planets with comparably short times with the same trajectory and annual launch windows.
The Wind Rider can fly by Saturn in just 6 weeks, and Neptune in 18 weeks. Compare that to the Voyager 2 probe launched in 1977 that took 4 years and 12 years to fly by the same planets respectively. Pluto could be reached by Wind Rider in just 6 months.
Because of its high terminal velocity that does not reduce during its mission, the Wind Rider is also ideally suited for precursor interstellar missions.
The second proposed mission is called Pathfinder , proposed to ultimately reach the solar gravity focal line around 550 AU from the sun. Flight time is less than 7 years, making this a viable project for a science and engineering team and not a multi-generation one based on existing rocket propulsion technology. As the flight trajectory is a straight line, this makes the craft well suited to follow the focal line while imaging a target star or exoplanet using the sun’s diameter as a large aperture telescope to increase the resolving power.
As the Wind Rider reaches the solar wind velocity, it may even be able to ride the gusts of higher solar wind velocities, perhaps reaching closer to 550 km/s.
While solar sails have been considered the more likely means to reach high velocities, especially when making sun-diver maneuvers, even advanced sails with proposed areal densities well below anything available today would reach solar system escape velocities in the range of 80-120 km/s . If the Wind Rider can indeed reach the velocity of the solar wind, it would prove a far faster vehicle than any solar sail being planned, and would not need a boost from large laser arrays, nor risky sun-diver maneuvers.
I would inject some caution at this point regarding the performance. The performance is based entirely on theoretical work and a small scale laboratory experiment. What is needed is a prototype launched into cis-lunar space to test the performace on actual hardware and confirm the capability of the technology to operate as theorized.
It should also be noted that despite its theoretical high performance, there is a potential issue with propelling a probe with a magnetic sail. Compared to a solar sail or a vehicle with reaction thrusters, the Wind Rider as described so far has no crosswind capability. It just runs in front of the solar wind like a dandelion seed in the wind. This means that it would have to be aimed very accurately at its target, and subject to the vagaries of the strength of the solar wind that is far less stable than the sun’s photon emissions. Like the dandelion, if the Wind Rider was very inexpensive, many could be launched in the expectation that at least one would successfully reach its target.
However, there is a possibility that some crosswind capability is possible. This is based on modelling by Nishida . This paper was recommended by Dr. Freeze .
The study modeled the effect of the angle of attack of the magnetic field of a coil against the solar wind. The coil in this case would represent the induced circular movement of the solar wind induced by the primary Wind Rider/PM coils.
Theoretically, the angle of attack has an impact on the total force pushing past the magnetic field.
Figure 3 shows the pressure and on the field as the coil is rotated from 0 through 45 and 90 degrees to the solar wind.
The force experienced is maximal at 90 degrees. This is shown visually in figure 3 and graphically in figure 4.
Figure 4. Force on the coil effected by angle of attack. A near 90 degrees angle of attack increases the force about 50%.
The angle of attack also induces a change in the thrust vector experienced by the coil, which would act as a crosswind maneuvering capability, allowing for trajectory adjustments as well as a longer launch window for the Wind Rider.
Figure 5. The angle of attack affects the thrust vector. But note the countervailing torque on the coil.
If the coil can maintain an angle of attack with respect to teh solar wind, then the Wind Rider can steer across the solar wind to some extent.
Figure 6. (left) Angle of attack, and steering angle. (right) angle of attack and the torque on the coil.
Figure 6 shows that the craft could steer up to 12 degrees away from the solar wind direction. However, maintaining that angle of attack requires a constant force to oppose the torque restoring the angle of attack to zero or 90 degrees. The coil therefore acts like a weather vane, always trying to align itself with the solar wind. To maintain the angle of attack would be difficult. Reaction wheels like those on the Kepler telescope could only act in a transient manner. Another possibility suggested is to move the center of gravity of the craft in some way. Adding booms with coils might be another solution, albeit by adding mass and complexity, undesirable for this first generation probe. Jeff Greason has an upcoming paper to be published in 2022 on theoretical navigation with possible ranges of steering capability.
In summary, the Wind Rider is an upgraded version of the Plasma Magnet propulsion concept, now applied to a reference design for 2 missions, a fast flyby of Jupiter, and an interstellar precursor mission that could reach the solar gravity lens focus. The performance of the design is primarily based on modelling and as yet there is no experimental evidence to support a finite lift/drag ratio for the craft.
Having said that, the propulsion principle and hardware necessary are not expensive, and there seems to be much interest by the AIAA. Maybe this propulsion method can finally be built, flown and evaluated. If it works as advertised, it would open up the solar system to exploration by fast, cheap robotic probes and eventually crewed ships.
1. Freeze, B et al Wind Rider Pathfinder Mission to Trappist-1 Solar Gravitational Lens Focal Region in 8 Years (poster at AGU – Dec 13th, 2021). https://agu.confex.com/agu/fm21/meetingapp.cgi/Paper/796237
2. Freeze, B et al Jupiter Observing Velocity Experiment (JOVE), Introduction to Wind Rider Solar Electric Propulsion Demonstrator and Science Objective.
3. Vulpetti, Giovanni, et al. (2008) Solar Sails: A Novel Approach to Interplanetary Travel. New York: Springer, 2008.
4. Nishida, Hiroyuki, et al. “Verification of Momentum Transfer Process on Magnetic Sail Using MHD Model.” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2005.
5. Slough, J. “Plasma Magnet NASA Institute for Advanced Concepts Phase I Final Report.” 2004. http://www.niac.usra.edu/files/studies/final_report/860Slough.pdf. See Figure 2.
6. Tolley, A “The Plasma Magnet Drive: A Simple, Cheap Drive for the Solar System and Beyond” (2017).
7. Generous email communications with Dr. Brent Freeze in preparation of this article.
What a beautiful thing to see moving toward fruition! This sounds like a Golden Age of Sail waiting to come to life, when a navigator’s skill and intuition (in concert with a large army of forward solar probes) make the difference between success and ruin of great enterprises.
Tacking is the key issue. This article describes a different method than the last, which stacked magnetospheres into engineered arrays. Though I’m rather unclear about how multiple rotating magnetospheres would interact with one another, I can’t help but wonder: could that be used to *concentrate* solar wind? If you build a triangle of these drives in a tethered or statite position in space, can you use it to generate a small, dense beam of particles in the middle for industrial uses or redirection as a propellant?
That is an interesting idea. The spacing is going to be important. Too wide and you just get separate magnetospheres or ones with “bent” edges. Too close and the fields act more like a single coil and the that tends to act as a sail.
My sense is that it probably doesn’t buy you anything, as the coils’ magnetic field causes divergence and even if several coils spaced near each other could create a beam, would there be any net thrust against the sail repulsion? Even if static and the beam was used to propel another vehicle, there is still divergence between the protons and electrons that will effectively disperse the beam to equilibrate with the surrounding solar wind.
Tacking such a sail is not trivial. It is like trying to force a weather vane to point at an angle to the wind. This needs a constant force if steady. It is possible a smaller force can be employed if the weather vane “bounces” back and force with an intermittent force. If the weathervane is given other vanes on struts, changing the angle of those sub vanes may keep the main vane at some angle of attack. Think of the classic kite design solar sails with small sails at the ends of the struts to steer the orientation of the sails. The same effect was achieved by IKAROS with differential reflecting material on the sail, an elegant solution IMO. Whether such an approach would work with a magsail, IDK. It needs some simulation. It is particularly difficult with the PM approach of the Wind Rider as the magnetosphere generated is many kilometers in radius and changes with the density of the solar wind. This means the structs would have to be very long and stiff, and their mass alone would not be trivial, perhaps many times that of the rest of the craft. Having said that, tailoring the shape of the magnetosphere or even redirecting the solar wind downstream (like an aircraft tail stabilizer’s elevator, or a front canard wing) might be an option. Another option might be to disrupt the induced ring current of the solar wind so that the magnetosphere is not symmetric across the diameter of the magnetic sail. That should induce a trim torque against the torque forcing the sail back to its stable orientation.
Worst case is that the Wind Rider is not steerable. Just as with a toy sailboat that has no control over the sail or rudder, you point it in the direction you want it to go and hope it gets close to where you want it to be. One can always add other steering mechanisms, e.g. conventional monopropellant maneuvering thrusters for small course corrections.
I think of these early designs as prototypes to test the concept. If they work, then it is worth looking at how to add components to enable more control. If it works, it could be a classic disruptive propulsion technology that is either “cheap and good enough” and/or has a huge performance boost. With market success it can be improved to incorporate the features of mature technologies to eventually dominate.
I realize it’s too soon to test any of it with Wind Rider, but ultralight space megastructures need a lot of work. In theory you could make a carbon filament suitable for a space elevator, which ought to be worth testing for keeping magnetospheres together at vast distances. In theory you should be able to sight a pair of very good corner reflectors along the filament, and use a small laser bounced many thousands of times to supply the complementary compressive strength needed to mimic a solid strut. Could you use this to balance the torques of your magnetospheres against each other?
More strangely … I don’t understand nearly well enough to know this, but I’m thinking some of the publications on optics lately, with notions like light bending 180 degrees in free space ( https://phys.org/news/2019-10-free-space-data-carrying-bendable.html ), might even allow for an “optical tweezer” that stations the satellites with no physical contact. (Apparently the bent light is an optical illusion, but it’s the kind of optical illusion you can use to expand optical tweezer capability and … burn a curved hole through an object with a laser? https://www.science.org/content/article/light-bends-itself )
Of course, using light to precisely change and measure the distance between satellites should have more useful applications in VLBI astronomy. And if possible, it would be interesting to see if concentrated and fractionated solar wind can be used in industrial processes, maybe even controlled transmutation ( would https://ui.adsabs.harvard.edu/abs/2015LPICo1878.2027W/abstract be applicable?)
carbon nanotube is great under tension, but would need a some sort of truss structure to ensure stiffness over 10s of kilometers. “Outrigger” steering mechanisms won’t need perfectly rigid supports, but enough to ensure that they operate as intended. Would it be sufficient to allow for the laser pointing accuracy, and don’t forget the needed laser power supply that will decline as the craft travels away from the sun?
I’ve read mirrors can be more than 99.9999% reflective ( https://www.rp-photonics.com/supermirrors.html ). Breakthrough Starshot’s program depends on this to keep their probes from vaporizing. If a light beam could be bounced between two corner reflectors (perhaps with some adaptive optics) about 100,000 times before attenuating, I’m guessing you could take a 1-watt laser, 1 J/s divided by 3E+8 m/s, times 1E5 bounces, times 2 (reaction), and get I think 0.6 millinewtons of force from the light beam to keep the nanotube moderately taut. With sufficient leverage between the beam and the tether, this might instead transfer quite a bit of torque between probes (for example, if they are fired as a “chain shot” or “bolas” at a distant target). Even if both probes need to steer the same way, transferring the torque should be able to direct the angular momentum into moving one probe forward relative to the other; if they are a hundred km apart the moment of inertia for the combined system should be something ridiculous.
Also… what happens when the probes fully catch up with the solar wind moving outward? Do they become painted ships on a painted ocean, unable to use any trick discussed to change course, or does solar weather and turbulence give them continued opportunities to change course (or resist the offer)?
Bouncing lasers light hundreds of times between mirrors is in itself an interesting way to vastly improve momentum transfer from the light to the spacecraft. Near perfect reflectivity and and collimation would be required. Even 10 or 15 round-trip reflections would reduced laser power by a huge factor.
This has been done in a lab with carefully aligned mirrors quite close together. It is a very different proposition applying this to mirrors in space, many kilometers apart and aligned by a semi-rigid strut/tether. Maybe it can be done by paying out the tether after the light is applying force and using some actuators to maintain alignment. IDK.
I’ll admit there’s a fair amount of daydream here, but to me it looks like in the past 25 years optics has gone from a standard-issue physics field that was all about what was impossible, to being one where any crazy thing – beat the diffraction limit, form photons into something like a molecule, bend light, form skyrmions, or (in some contexts) self-collimate a laser beam – seems to be doable. Making a probe center itself on a light beam seems easier for me to believe than most things ( https://www.space.com/laser-sail-centering-breakthrough-starshot.html ), and I’m thinking some clever optics ought to be able to do the converse. Alternatively the light might be bounced back and forth inside some tensile structural element to keep it confined.
Very impressive performance. Apart from the NIAC, has this or the previous plasma magnet concept been proposed to Breakthrough Starshot for funding?
I don’t know, Antonio. But I doubt it. I haven’t heard any plasma magsail discussion coming via Breakthrough, but of course that doesn’t mean it won’t popup at the next Breakthrough Discuss in a session.
Probably not fast enough. Will not go faster than the solar wind. Great for “close by” exploration though.
One big question; What is this beautiful ship capable of at solar maximum? With what would be the equivalent of a typhoons winds from flux tube opening up from the sun and magnetic reconnections blasting the craft, speeds could be much faster to the Solar Lens. Launch time could be coordinated with solar flare blasts to give the maximum boost…
Bear in mind that the size of the induced magnetosphere and the thrust remains constant as it adapts to the particle density. While transient effects may increase thrust, a CME that creates a higher density of particles should simply reduce the size of the magnetosphere and maintain a constant thrust.
Having said that, the authors note (and I included this in the posts) that “gusts” with higher velocity could increase the terminal velocity of the craft.
Also note that the higher velocity solar wind emanates more consistently from the sun’s poles. This should mean that a craft flying out of the ecliptic plane should reach a higher velocity. I understand that Jeff Greason has been looking into this regime for missions.
Yes, I was thinking about that after commenting but it would seem better to increase power to the wind rider while close to the sun with possible solar arrays. The solar array could be ejected after getting further from the sun but could help boost the ship to a much higher speed. The enlarged magnetic field from the coil would be able to take advantage of the solar flares and also protect the equipment from damage. Maybe the bottom sun shield could be made of some new solar power film that would not add much to the total weight of the wind rider. Lightweight Flexible Holographic Lens could be stowed and when reaching the suns gravitational lens, stretched out a crossed the round coils to help generate a usable image…
A flat sheet with a holographic lens might best be deployed and stiffened by rotation. The Pathfinder mission assumes a small nuclear (RTG) power source rather than solar PV. The sun shield is intended to become an antenna and needs to be away from the sensor/lens to avoid interfering with the image acquisition.
I expect to be receiving the 2 mission studies after publication to get any more details on the craft design and mission parameters.
Paul & Alex
A striking concept. A couple of references seem to be missing. There does not seem to be a  or a  in the body of the text?  and later seem to be there but the first two are absent, I believe?
John, it’s now fixed. Sorry about that.
How scalable? Multi-ton payloads would be cool.
Theoretically very scalable. The principle way to scale upwards is to use more power to generate a stronger primary magnetic field which in turn increases the size and strength of the induced field in the rotating captured solar wind particles. An increase in the size and x-section of the coils is probably also required which increases mass. In principle I don’t see why it shouldn’t scale up to allow large robot probes and even crewed vehicles (the magnetosphere protecting the crew from solar flares).
Bear in mind that the rotating captured solar wind particles is not a rigid structure like a coil, so there may be issues with this stream of rotating ions being deformed and with it the magnetosphere. That may be a problem, or possibly a benefit for some steering solutions.
There was a recent NAIC paper on how a kilometer wide structure could fit in Falcon Heavy. Might that be adapted? Folks want lasers for starshot. Might masers and particle beams be useful here…making this a physical “cursor” of sorts?
The sail field is dipole shaped, like the earth’s. What about the following scheme for functional plasma sail rudders: four smaller field generators that are spaced around the main ring, spaced out from it by about 10km (main induced field diameter) plus the diameter of the smaller induced fields. Two of them in the plane of the ecliptic, opposite each other, two in the plane perpendicular to the ecliptic, also opposite each other. They could be on all the time to add to the general thrust, turned off or turned down asymmetrically to give a turning thrust, or only turned on asymmetrically when needed if power/energy is an issue, when steering is desired. The sticking point I see is their mechanical connection to the main sail equipment and each other, but perhaps someone else will point to another problem. A modification of this idea might be to have just an annular ring of smaller field sails, all in parallel, aperture adding up to the desired total for thrust, selectively throttled for steering. Again their mechanical connection is perhaps a problem. If either idea worked it would presumably allow a return trip in-system, and not just on a spiral path, as mentioned in Tolley’s prior 12/29/17 article.
I thought about a mag sail idea a while back, the coil was wound onto two bobbins. The contra rotation of the two bobbins on the same shaft opened the coil at the same time a current was set up, a sun shield of solar cells was used to allow superconductivity earlier and power the coil. The issue with mag sails is the low momentum of the solar wind, other than that a wonderful idea.
That issue of momentum is solved by the plasma magnet approach. (See my first 2017 article on the technology). Relatively small coils “capture” and induce the solar wind particles to rotate around the craft, in turn generating the main magnetic field. As this field is much greater in size than that generated by the primary coils, the thrust from the pressure of the solar wind is that much greater. Moreover, the size of the trapped solar particles is determined inversely by the density of the solar wind particles,. As the craft travels away from the sun, the solar wind density falls, but the magnetosphere increases in size to compensate, maintaining a constant thrust. In practice, the trapped particles are both being added to by the solar wind and being lost, a dynamic situation that maintains a residency of particles. The idea is very elegant, harnessing the medium by coopting it.
Whether this works as advertised needs to be tested with relatively inexpensive hardware. I suspect the main costs are the launch to a position outside the Earth’s magnetosphere (not a common satellite destination) and the overhead of the ground facilities and personnel to monitor the craft, similar to the that of the Planetary Society’s LightSail project. (Several technical staff with computers. LightSail got a free piggyback to LEO, but the Wind Rider prototype needs a lift to much further out. Piggybacked with a free flight on the way to L2 with the JWST would have been nice).
I suppose then having two sets of bobbins in a cross formation with the two coil joined at the top would be an effective means of deployment.
Thank you Mr Tolley for a very good presentation.
I think it’s known on at least this site that I am a strong advocate for magnetic sail propulsion. While there’s been interesting ideas presented,
it was Pekka Janhunen proposal that was the game changer in my perspective.
If the method described here turn out to be feasible, the change is comparable to from doing exploration by foot – to taking a high speed train. Not Tau zero, but at least TAU. =)
Putting the thrust into perspective.
From reference 4, a 100km radius coil (equivalent to the radius of the trapped rotating solar ions) generates a thrust of 225 N. This is several orders of magnitude lower compared to a main engine of any launcher, but similarly the same orders of magnitude larger than ion engines. It is roughly comparable to the thrust of the Gemini spacecraft reaction control system thrusters.
So imagine those thrusters firing continuously for days or months.
As with any electric system, there is an energy cost. The modeled values for the coil in reference 4 is 40 kA (no kW given). (Resistance heating would be very high and the x-section of the coil large and hence massive to cope with the amperage). Although the power is much lower for the plasma magnet approach as only the primary coils are needed to be powered, there is an obvious advantage in using superconducting materials for the coils of the Wind Rider, an engineering solution suggested by a number of traditional magsail designs.
Thank you for the clarification, I did suspect that nano- and picosatellite designs was the idea that gave this such a huge advantage over any other means – by low mass. And indeed, the proposal for a Jupiter mission was a Cubesat.
If high temperature super conductors could be utilized, then Nitrogen, alternatively Argon cooling also need to be incorporated into the design. While a super conductor could mean smaller power use, the cooling system it could affect the need of power as well. Yes there’s one room temperature superconductor candidate, and one just under freezing point – but both need extreme pressure to conduct.
Remember that the background temperature of space is 4K. Sufficient shielding from energy sources, primarily the sun, allows an object to cool towards this temperature. This is why the cold traps on the Moon occur – permanently shadowed areas where only conduction through the ground occurs. On the Moon, surface temperatures during the night drop to -173C (100K) 23C higher than LN2. Using higher temperature superconductors one could operate even during the lunar night. At Saturn, the lowest temperatures are 82K. Well-shielded objects should be able to fall to even lower temperatures.
I always say that bringing innovative propulsion concepts to higher TRL does much more good than trying to squeeze everything out of chemical propulsion and plan multi-decadal outer Solar system missions. If a single flagship-class investment goes the right way, then everything with arrival time later than 2040 will be outrun.
The highest wind speeds I’ve seen while monitoring space weather and hunting for auroras are something around 800 km/s. Riding these gales would bring spacecraft almost into direct exhaust nuclear propulsion territory!
Are there any differences with earlier M2P2 inflated magnetosail concept, aside of superconducting coils?
I think there would be many options for lateral thrust, starting from using solar wind inhomogenities (allowing maybe an one-degree cone of trajectories). Interactions with pockets of interplanetary magnetic field embedded in solar wind, rotating tethered configurations, controlled bounces off Jovian magnetosphere, and likely many more ways.
But of course, all of this brings us back (or forward?) from precisely-calculated trajectories and maneuvers to the art akin to sailing the globe and getting from point A to point B through all winds and storms.
I imagine space regatta on wind riders. Traditional Earth-based sailing contests are something to watch, but solar wind racing is infinitely more rich than that. The first who makes it from Earth’s L2 to Jupiter gets the main prize, but the first does not always mean the most spectacular and epic, because all kinds of solar winds, shock waves and disturbances, with different velocities, densities and interplanetary magnetic field polarities, are in the way.
Winglee’s M2P2 used onboard material to form the ion particles needed. The principle improvement of the PM was to dispense with the need for this by using the solar wind particles themselves.
Re: steering sailing ships. As you are aware, even square-rigged sail allow a ship to change direction against the wind, primarily by use of the keel to prevent side-slip, and the rudder to push against the water. There is no equivalent in space, although planetary magnetic fields and even gravity can be harnessed in some way to change direction. Even on Earth, large merchant sailing ships did not sail up to the dock, but rather were towed in by various means, as steering under wind is too crude to allow a gentle docking with the facilities. Steering the Wind Rider is going to be an issue, although there are options. In the far future, there may even be tugs to steer them safely and gently into space docks!
So, if I get this correct, the basic concept is just magnetobraking in reverse. Solar wind plasma runs up against magnetic field, and the secondary current is induced almost like when a neodymium magnet is dropped through a thick copper tube. The difference is, the more dilute is the plasma, the wider is the secondary current, just because of conductive properties of completely ionized plasma.
The removed center-of-gravity certainly looks like a solution for crosswind capability. Maybe if a payload is suspended at some distance in front of ring coil from Fig.6, like on a chute or even a paraglider, then crosswind is achieved by tugging suspension lines. The coil needs not to be rigid, it could be inflated by magnetic field pressure, and not much is needed with these gentle accelerations. It could be spread out or contracted by winding the wire onto compact coils with magnetic-field-canceling configuration, distributed along it’s length. Then, the spacecraft could fly into magnetotail of a gas giant, decelerate there using trapped particles, and achieve orbital insertion by using conventional electric propulsion or even inward-moving streams of plasma. There is multitude of possible ideas, largely unexplored. The braking still requires much harder loads than acceleration, but for orbital insertion missions, reduced cruise speeds could be used to make the braking load manageable. Even 50 km/s from Earth to Neptune is something.
I cannot hold myself from imagining wind-riding races of the future again and again. “That year winds were calm and a dull race could result if not for a contestant from Space-Omega who steered aside to catch a fast-moving posket of solar wind and darted outwards at 600 km/s but missed the target by tenth of degree, unable to get exactly back on track…”
Are those gusty winds associated with the 11/22 year sunspot cycle? If so, it suggests certain favorable launch windows.
This was probably one of the most difficult articles that I have ever had to look at within the Centauri Dreams long list of articles that have ever been posted. I found myself with a lot of questions and very little understanding of the explanations offered here. Additionally I do have a few comments based on what I believe I understand. To start with, this method of propulsion is totally inexplicable to me.
Are you saying to the reader that the principal concept is to induce a continuously flowing current with in a set of superconducting coils which must be continuously shielded from principally the heat energy of the sun? I assume, that what you are attempting to do with the superconducting coils is to continuously generate a standing magnetic field which will interact with the solar when and somehow or another create propulsion. So my first question to you is if you have a flowing current in a superconducting coil which is generating a magnetic field wouldn’t you eventually lose energy in the coil?
The reason for me saying this is that is not a principle of physics that a moving current will radiate electromagnetic radiation from itself due to the motion of charges? Isn’t that the principal for example behind radio and TV? If so, then how do you expect this coil to maintain its energy for a long period of time such that it can serve to generate a magnetic field? Or do I have my conception of physics incorrect?
Additionally, doesn’t seem really practical to be able to shield your superconductoring coil from all radiation from the sun? Especially over the many months you expected to be in operation. Especially if you are talking about tracking which I understand has to do with tilting the entire craft to permit it to turn-dozen that in turn result in having the coils being exposed to heat? And finally how do you expect (if you wish to) to insert yourself into an orbit about a planetary body that you wish to observe?
Finally, who is the author of this article and whose picture is that at the beginning of the article? It’s common practice for Paul to usually introduce when he writes an article both who is the author and to identify with the caption the picture of individuals included with the article.
Actually, when I do a guest post, I always cite the author’s name at the top, with his or her picture directly below, unless the author prefers no photo. So the author here is Alex Tolley, and the image is Alex.
So the WIND RIDER can reach speeds as that of the solar wind, which is 400,000 km/s?
I thought the speed of light was just under 300,000 km/s.
400 km/s is the figure Alex cited, not 400,000 km/s.
So anyway, I did look at your 2017 entry on this same plasma engine that you are talking about here currently as well as the YouTube video which got into a little bit more detail on what this whole thing is about and now I have somewhat more of a (relative) clear picture of what is going on with regards to this. I don’t quite follow why a rotating conductor is required to create a rotating magnetic field which then in some fashion interacts with the solar wind and creates thrust. I can see how in a regular motor you have a counter rotation due to the push on the permanent magnets on the (stator?) which induces rotary motion, but I’m not sure exactly how that translates into an interaction with solar plasma that creates thrust.
It would seem that a rotating conductor would have a counter torque on whatever it was attached to and you would have to in some fashion provide a relatively “stationary” platform against which the rotating conductor would rotate against, but again the devil is in the details.
All that being said this is seemingly almost too good to be true in terms of its potentiality but if it is in fact true it would represent a revolutionary new development which would be capable of getting where you wanted to go (at least within the solar system) in a very, very quick fashion. Obviously there be a lot of details that would need to be addressed to make it viable but I feel assured that someone is looked into it. The question here is as was pointed out in the comments section of the video is: why hasn’t this been touted from the mountain tops and stressed as a priority project ?? Quite strange, if you asked me. As for interstellar travel the man in the video made a very intriguing comment near the end of the video in which he suggested that lithium-deuterium pallets could be fired at the magnetic field which would induce thermonuclear fusion creating a temporary plasma which in effect would drive the craft to at least one half velocity of light speed. Again, quite imaginative and if realizable would certainly be a game changer.
30 years ago the same was being said of solar sails. The idea had been around for a long time. Eric Drexler was pounding the table on this back in the 1980s. Arthur C Clarke edited a book with a mix of fact and fiction called Project Solar Sail. What happened? Nada. But the Planetary Society started work on a real sail – Cosmos-1, which after 2 failures succeeded with a much smaller CubeSat version. The delays allowed JAXA to be first with a real sail (IKAROS) that was navigated into deep space. Sometimes things take a long time to gain traction against established ideas. Launchers that could be reused and land on their tails was ignored by the industry until SpaceX proved the concept. (The Space Shuttle was reusable, but hugely expensive and complicated by comparison). Now all the launch providers are designing their own versions to reduce costs and stay in business. Similarly, even though electric cars were better than ICE vehicles around the beginning of the 20th century, they fell into disfavor due to poor batter performance. Even GM could not successfully revive the concept. Tesla almost singlehandedly made electric cars “sexy” and conquered much of the range anxiety with LiOn batteries. Now every major car manufacturer is committed to making the electric vehicle the main product to be powered by renewable energy in the global Net Zero by 2050 strategy.
We know why some good ideas get stalled – vested interests satisfied with the status quo and the barriers to entry of competing technologies. Sometimes they remain stalled. Sometimes they can gain traction if resources are provided and the technology nurtured. The barrier in this case is the cost to reach a testing ground.
“I don’t quite follow why a rotating conductor is required to create a rotating magnetic field which then in some fashion interacts with the solar wind and creates thrust. I can see how in a regular motor you have a counter rotation due to the push on the permanent magnets on the (stator?) which induces rotary motion, but I’m not sure exactly how that translates into an interaction with solar plasma that creates thrust.
It would seem that a rotating conductor would have a counter torque on whatever it was attached to and you would have to in some fashion provide a relatively “stationary” platform against which the rotating conductor would rotate against, but again the devil is in the details.
As for interstellar travel the man in the video made a very intriguing comment near the end of the video in which he suggested that lithium-deuterium pallets could be fired at the magnetic field which would induce thermonuclear fusion creating a temporary plasma which in effect would drive the craft to at least one half velocity of light speed. ”
Alex, could you possibly throw some light or possible further explanation upon some of the points that I have raised here above from my understanding of what you have written and/or the points brought out in the video at the conference on these plasma magnetic sales ??
Speculation ahead. A rotating sphere or cylinder in a fluid stream can generate a force perpendicular to the direction of fluid flow (think of a curve ball thrown by a pitcher). Could the magnet field rotate using multiple magnets as done in 3-phase motors? The rotating field could possibly accelerate the wind on one side and retard the wind on the other side resulting in a net force analogous to a rotating ball or cylinder in a fluid flow field.
All fine dreams described here are sound very nice, but have one huge problem – “Plasma Magnet” idea will not work as it is described in this (and reference) article.
The some parody on current loop is possible only for charged particles that has relative (to vehicle) speed vector close to zero all particles that have speed higher and lower that vehicle will be deflected only – will not form any huge (relatively to coil diameter) “current loop” , probably the charged particles that moves with vehicle’s speed to same direction will be form a small sized current loop located close to the electromagnet, no more, so finally expected thrust is defined by electromagnets physical dimensions and magnetic field strength only.
So idea that looks fine for wishful thinker has no theoretic ground under it.
I have 2 answers to your point that at the solar wind speed, the large field might “collapse” due to a lack of trapped ions.
1. The solar wind is a distribution of ion speeds, not a homogenous bulk object. The craft speed theoretically maxes out at the average wind speed, i.e. there are ions that it is traveling faster than, and ions that are still impinging on the craft’s magnetic field, as well as replacing any ions that are lost. It is therefore at some equilibrium.
2. Suppose you are correct and that this is indeed a flaw in the theory. So the craft’s maximum velocity is perhaps some fraction of the average solar wind speed. How low a fraction of the solar wind velocity can the craft reach is tolerable before you say it is unacceptable? 50%, 25%, 10%?
Having said that, the theory paper (reference 4) on the dynamics of a fixed size electric coil in the solar wind assumes that the wind is flowing past the coil’s magnetic field. The drag (i.e. thrust) is dependent on that velocity, as one would expect. However, when the coil is replaced by a stream of ions, it is possible that this model breaks down. That is the purpose of building a prototype to test reality. How does a physical craft’s performance match theory and where does it break down? Given the potential theoretical high performance and the relatively low cost of the craft, it seems well worth testing the concept.
Last thought. Best to test actual vehicles versus theory. It can be counterintuitive. Earlier in the 20th century it was thought than no aircraft could fly faster than the speed of sound. The best more recent example I can give is that a wind powered vehicle on land that can move downwind faster than the wind. This seems impossible, and many thought so, but it is not: Blackbird.
There are any theoretical problem with interaction between magnetic coil and solar wind, but this interaction will be limited by coil dimensions and close distance from it.
Due to huge relative speed difference between magnetic coil and solar wind – there will be no any “plasma current loop”, this “loop” will be blown out by solar wind there will be nothing to extend…
Whole idea of “plasma magnet” is based on this loop – that is not theoretically possible in open and very dynamic environment.
I believe that in physical laboratory the plasma media in CLOSED and very limited VOLUME can form something similar to described plasma current loop.
The “plasma magnet / current loop” idea described in this concept is directly related to “Perpetuum mobile” concept – i.e. violating thermodynamic laws
What you are saying is that the lab experiment was not truly a demonstration of the PM effect at scale and that Winglee and Slough were mistaken about the mechanism, and that this error has propagated to fool others into believing in this propulsion scheme.
But would you not also agree that the best way to test this is to build a scaled up model to test in space where the effect can be measured and the performance assessed? If you are correct about the theory, then the model will fail to demonstrate the acceleration predicted and barely move. If the model works, then your belief about the theory is wrong and progress has been made to move forward and build the JOVE CubeSat model and fly the mission.
Yes, it is what I mean.
By the way the data provided in reference document #5 is more similar to Volt-Ampere characteristic of vacuum (or gas discharge) tube. There are results of behavior of closed system, where particle free fly distance is hardly limited by chamber volume. It is very ridiculous to met there some reference to 30km open space loop radius , based on closed space tests :-)
Summary no physical theory supporting Slough’s proclamations, so there is nothing to test in the space – this is the main problem of discussed attractive idea.
“The “plasma magnet / current loop” idea described in this concept is directly related to “Perpetuum mobile” concept – i.e. violating thermodynamic laws.”
With regards to your comment directly above, is there any reference here to the idea (that a moving current will radiate electromagnetic radiation from itself due to the motion of charges? ):
“Are you saying to the reader that the principal concept is to induce a continuously flowing current with in a set of superconducting coils which must be continuously shielded from principally the heat energy of the sun? I assume, that what you are attempting to do with the superconducting coils is to continuously generate a standing magnetic field which will interact with the solar when and somehow or another create propulsion. So my first question to you is if you have a flowing current in a superconducting coil which is generating a magnetic field wouldn’t you eventually lose energy in the coil?
The reason for me saying this is that is not a principle of physics that a moving current will radiate electromagnetic radiation from itself due to the motion of charges? Isn’t that the principal for example behind radio and TV? If so, then how do you expect this coil to maintain its energy for a long period of time such that it can serve to generate a magnetic field? Or do I have my conception of physics incorrect?” ???
Superconducting magnets only need a tiny additional power feed to compensate for resistive losses on non-superconducting parts, as well as any requirement to maintain refrigeration.
source: Superconducting Coil
What I am not clear about is whether the induced flow of solar wind ions to create the inflated magnetosphere creates a counter force against the moving coils and this needs to be offset with more power to keep the coils rotating.
The design of the JOVE mission craft that has just 1300 W to start and a mere 50 W at 5AU near Jupiter suggests that any counter force must be very small assuming all the forces have been calculated. 50W must also power the science instruments and any data communication to Earth. The required power for keeping the induced magnetosphere operating is given in the Slough paper equations (for non-superconducting coils).
Assuming the sun shield can keep the coils in shadow, there seems no reason to expect that any power is required to maintain refrigeration of the high temperature superconducting coils, even at 1 AU.
Hopefully, access to the full paper will resolve this and related questions.
“a moving current will radiate electromagnetic radiation”
EM radiation require charge acceleration. Motion isn’t good enough. Place a resistor and a battery in series and the only EM radiation is during the brief instants when you connect and disconnect the circuit (on and off).
Electrons that are running in “your” (battery resistor) circuit are changing direction during their trajectory from one pole to another, so they have acceleration, but create only constant magnetic field.
As well as charged particle that moves around cyclic trajectory (so it has acceleration) in perpendicular to constant magnetic field – does not radiate EM waves… (there is only constant magnetic field)…
So your definition is not full.
By the way the current running in resistor – will create heat – that is EM waves , so even in this case your example is not correct :-)
So only ideal conditions can satisfy “no energy loss” state.
Yes, you are correct. I was attempting a simple example to illustrate the concept, but of course in the real world these “ideal” situations do not exist.
charlie – I suppose you are asking your questions in wrong place – I am not author of Plasma Magnet idea.
My point – that this idea does not have any theoretical support at least in modern physic.
J. Slough created plasma current inside huge magnetron-like gas discharge tube and decided that it is engine – so you should ask idea’s author about his theory.
I certainly understood that you were not the author of the paper presented here. Rather I was addressing the idea that you mention a perpetual motion machine. Your comment got me to wondering whether or not the superconducting coil for the magnetic field would eventually dissipate its current energy by the omission of electromagnetic radiation. That’s what I was wondering if you had a idea about.
Superconducting conductors have perpetual current running in them and that got me to thinking that the perpetual current would radiate EM radiation and eventually exhaust its energy. I thought you (or someone else) might have a answer to that
There is no EM radiation from an electric current. The magnetic field is not like the emission of photons that requires energy. If there was, rapidly moving a superconducting conducting wire with another superconducting coil with a flowing current would result in some heating as the em radiation from the magnet was absorbed by the wire. If it was non-superconducting, the wire would only heat up due to ohmic resistance from the induced current. As there is no resistance in a superconducting wire, there would be no heating, nor would the coil generating the magnetic field heat up or cool.
As you probably know, the changing magnetic fields in a tokamak reactor heat the plasma. The only heating effect on the magnetic coils (assuming superconducting) is due to the em radiation of the plasma heating the reactor components. There is no concomitant em emission from the superconducting magnets AFAIK.
In the case of the Wind Rider’s PM approach, the solar wind ions impinging on the magnetosphere and those circulating to create that magnetosphere, could theoretically experience “heating” although this means something rather different in this situation as the temperature of the ions is measured by their velocity. [Similar to the thermosphere in the upper atmosphere, and the medium at the boundary of the heliosphere and the ISM.] The trapped ions circulating in the PM might actually be cooler than the solar wind if their velocity is reduced at all. Although the Nishida paper does not show it, the solar wind impinging on the magnetosphere is likely slowing, and therefore “cooling” as their momentum is transferred to the craft.
@charlie – please find tin this comments two messages above Ron S. comment and my notes to his comment – you will find there answer.
To test the idea in real space – someone need to design the new engine using some theory , but when we are talking about this specific “Plasma magnet” engine – there is no any theory standing after this concept, it is not supported by modern physic.
Most bothering fact that this concept can be seriously discussed…
You may disagree with the theory, but the theory has been explained and it has been validated experimentally in the lab by both Winglee (M2P2) and Slough (PM). There seems little doubt to me that the idea works in principle, it just needs testing the performance in space.
I have read various critiques of various propulsion approaches by Alexander Bolonkin who seems to reflect your thinking about false theories. For example:
Source: Non-Rocket Space Launch and Flight (2005)
[There are no exact mathematical solutions to the Navier–Stokes equations for all fluid flow and turbulence conditions either, but fluid dynamics can be simulated, and the simulations around airframes do seem to closely match actual wind tunnel test results. Simulations work well for wind turbine designs, and racing yacht hulls and sail designs as just 3 further examples.]
Fun – all name there are Alex :-)
Dear Alex Tolley, in you quote Alexander Bolonkin is talking about more reasonable variant – problem to calculate drag caused by interaction between real coil and solar wind.
When Slough’s idea even more problematic – to create drag it uses virtual huge sized “Plasma Magnet” growing up from small sized physical coil – it is much more nonsense.
Everything in “Plasma Magnet” is funny, it is hard to decide from which fail in this idea to start…
Yes it will work for real electromagnet , but will not work for virtual “plasma magnet” – that is difference.
Slough experiments for NASA are not about engine, it is about measuring volt-ampere characteristics of gas-discharge (or vacuum) tube.
Whole Slough’s idea tells as: “we do not need to build huge electromagnet – we will grow it up from plasma, so this “plasma magnet “ will create huge drag from solar wind”.
P.S. Every schoolboy can build simplest model of EMD engine using two electrodes, battery and strong permanent magnet. I am sure same principles can be scaled to space.
I’ve vaguely followed the progress of the plasma magnet idea for the last few years. I can’t say I’ve been super convinced that it will definitely work in a real space environment, but neither have i been convinced that it definitely won’t work. My understanding of what literature I’ve read is that the concept is theoretically sound, limited simulations and small scale lab tests suggest it works, but no authoritative and thorough full simulations work (ie full magnetic+electrostatic plasma simulations that allow the plasma loop to build up naturally rather than inserted on an ad hoc basis). But you sound very confident that it won’t work, AlexTru. Is there some literature you can point to that shows clearly it won’t work? (And it’s worth explicitly noting that we’re talking about the “plasma magnet” concept here, not the mini mag sphere inflatable bubble concept)
I do not have any special literature that is dedicated to this special case, be such such devices are not exists in reality.
Author gave you some reference materials to study, if you will look at the reference about laboratory tests and will analyze the content, you will find that laboratory tested device is in reality not engine, but huge gas discharge tube and authors succeed to measure it’s Volt-Ampere characteristics.
So reference to laboratory results as prof of “plasma magnet” engine – is pointing nowhere, none tested any engine here.
My question on the ability to steer based on the work of the Nishida paper (ref 4) concerns the different between a rigid coil and the stream of circulating ions of the PM drive.
A symmetric force seems OK, but is an asymmetric one that torques on the ion stream going to work the same way or distort the stream? The effect may work for or against the desired vectoring effect. One way to model this might be to assume different shapes for the rigid coil or make the coil non-rigid in the simulations. (Or just test a real vehicle!)
One can understand the need for rigidity in wind and solar sails. A wind sail of any design is stretched with masts and lines under tension. Release those forces on the sail and it flaps about in the wind. All contemporary kite designs for solar sails are the same.
NASA once proposed the heliogyro solar sail for the Comet Halley rendezvous in 1986, a large design that used rotation of the sail to provide the forces to put it under tension. Theoretically one could spin up a wind sail to do the same, although I don’t think it has even been attempted and would probably fail in a strong wind even it it was a desirable design.
The circulating ions in the PM are entrained by various magnetic forces, but will also be subjected to forces that impinge on the magnetic field they generate. Are they held more like the masts and tension lines of wind and solar sail craft designs, or those of the heliogyro? How resistant are they to distortion (like a storm breaking a wind sail mast)?
We can probably model this to some extent, but testing a real craft will give us the best answers at this point, just as any aircraft design that has passed all the modeling and wind tunnel tests still needs to be run through test flights to confirm its performance.
Unlike solar sails, I see more end of life uses of these. Mine metal rich asteroid mass to cables and loop around Jupiter back to Earth as Dyson Harrops. Coils lined up at Jupiter, etc.
Would there be any utility in this craft as an asteroid redirect candidate?
Either high velocity impactor, or alternatively, send craft via traditional means to rendevouz with candidate asteroid, anchor and deploy to alter trajectory over time etc.
Asking as there’s a potential source of funding NASA may have available if there’s a viable possibility here.
Interesting idea. Especially the anchor and push scenario. I have passed this on to the authors.
I heard back from the authors that they thought it was a very interesting idea and that their group has already been looking at it. There was a paper submitted to the conference by one of their members but it was rejected. So you are definitely on the right ideas track. No mention of possible Nasa funding though.
There should have been a paper on that but i believe they missed the conference window. so, yes.
How long would a Wind Rider take to reach the various trans-Neptunian dwarf planets? Eris? Haumea? Makemake? and so on.
Assume that the Wind Rider travels at 400 km/s, in a straight line. Divide the chosen body’s distance by this velocity and you get your answer. You can do this for any celestial body in orbit outside of Earth’s.
I do have one question concerning mag sails.
While they can ride the solar wind to high (velocities taking only weeks or months to reach the outer planets with zero fuel costs) and they can use plasma breaking in the atmosphere or magnetic field of their destination planet upon arrival – how the heck do they return home to Earth going against the solar wind stream?
How do you configure a magnetic jib that will allow them to tack into the solar wind and return home?
Can this device be used as the ram scoop for an intersteller ramjet?
If this is possible, then collecting the ions and accelerating them to oppose the solar wind could provide a braking system. This would overcome one of the original problems with this concept
Something that has always fascinated me is some type of large magnetic field being used for atmospheric reentry.
Reference  has the wrong date (1970) which should be 2004 and is also Phase I to the study. Figure 12 from the URL has the following caption: “A schematic and photograph of the SWS device used as the solar wind simulator. The orange segment is the copper cathode with the molybdenum disk secured. The black region is the stainless steel anode. The gray tungsten disk is placed at the end of the copper cathode to reduce sputtering. ” Was this the intended reference?
Phase II of the study (2006) can be accessed at the following URL. It contains updates to theoretical results as well as the experimental results:
The 2005 presentation http://www.niac.usra.edu/files/library/meetings/annual/oct05/917Slough.pdf is also good and clarifies citations from references and has good graphics and concise explanations.
Thanks for this, Dave, and the URLs. Will check on the reference, which may need to be changed.
Aloha, Paul. Wasn’t sure if this thread was still active. I can post some responses to AlexTru referencing specific equations and pages of the phase II report if that would be helpful.
Aloha, Dave. Sure, I’d welcome your responses to get them into the record. Many thanks!