Laser Thermal Propulsion for Rapid Transit to Mars: Part 1

Do the laser thermal concepts we discussed earlier this week have an interstellar future? To find out, applications closer to home will have to be tested and deployed as the technology evolves. Today we look at the work of Andrew Higgins and team at McGill University (Montreal), whose concept of a Mars mission using these methods is much in the news. Dr. Higgins is a professor of Mechanical Engineering at the university, where he teaches courses in the discipline of thermofluids. He has 30 years of experience in shock wave experimentation and modeling, with applications to advanced aerospace propulsion and fusion energy. His background includes a PhD (’96) and MS (’93) in Aeronautics and Astronautics from the University of Washington, Seattle, and a BS (’91) in Aeronautical and Astronautical Engineering from the University of Illinois in Urbana/Champaign. Today’s article is the first of two.

by Andrew Higgins

Directed energy propulsion continues to be the most plausible, near-term method by which we might send a probe to the closest stars, with the laser-driven lightsail being the Plan A for most interstellar enthusiasts. Before we use an enormous laser to send a probe to the stars, exploring the applications of directed energy propulsion within the solar system is of interest as an intermediate step.

Ironically, the pandemic that descended on the world in the spring of 2020 provided my research group at McGill University the stimulus to do just this. As we were locked out of our lab for the summer due to covid restrictions, our group decided to turn our attention to the mission design applications of the phased-array laser technology being developed by Philip Lubin’s group at UC Santa Barbara and elsewhere that has formed the basis of the Breakthrough Starshot initiative. If a 10-km-diameter laser array could push a 1-m lightsail to 30% the speed of light, what could we do in our solar system with a smaller, 10-m-diameter laser array based on Earth?

Image: Laser-thermal propulsion vehicle capable of delivering payload to the surface of Mars in 45 days.

For lower velocity missions within the solar system, coupling the laser to the spacecraft via a reaction mass (i.e., propellant) is a more efficient way to use the delivered power than reflecting it off a lightsail. Reflecting light only transfers a tiny bit of the photon’s energy to the spacecraft, but absorbing the photon’s energy and putting it into a reaction mass results in greater energy transfer.

This approach works well, at least until the spacecraft velocity greatly exceeds the exhaust velocity of the propellant; whenever using propellant, we are still under the tyranny of the rocket equation. Using laser-power to accelerate reaction mass carried onboard the spacecraft cannot get us to the stars, but for getting around the solar system, it will work just fine.

One approach to using an Earth-based laser is to employ a photovoltaic array onboard the spacecraft to convert the delivered laser power into electricity and then use it to power electric propulsion. Essentially, the idea here is to use a solar panel to power electric propulsion such as an ion engine (similar to the Deep Space 1 and Dawn spacecraft), but with the solar panel tuned to the laser wavelength for greater efficiency. This approach has been explored under a NIAC study by John Brophy at JPL [1] and by a collaboration between Lubin’s group at UCSB and Todd Sheerin and Elaine Petro at MIT [2]. The results of their studies look promising: Electric propulsion for spaceflight has always been power-constrained, so using directed energy could enable electric propulsion to achieve its full potential and realize high delta-V missions.

Image: Laser-electric propulsion, explored as part of a NIAC study by JPL in 2017. Image source:

There are some limits to laser-electric propulsion, however. Photovoltaics are temperature sensitive and are thus limited by how much laser flux you can put onto them. The Sheerin et al. study of laser-electric propulsion used a conservative limit for the flux on the photovoltaics to the equivalent of 10 “suns”. This flux, combined with the better efficiency of photovoltaics that could be optimized to the wavelength of the laser, would increase the power generated by more than an order of magnitude in comparison to solar-electric propulsion, but a phase-array laser has the potential to deliver much greater power. Also, since electric propulsion has to run for weeks in order to build up a significant velocity change, the laser array would need to be large—in order to maintain focus on the ever receding spacecraft—and likely several sites would need to be built around the world or perhaps even situated in space to provide continuous power.

I had spent my sabbatical with Philip Lubin’s group in Santa Barbara in 2018 and was fortunate to be an enthusiastic fly-on-the-wall as the laser-electric propulsion concept was being developed but—being an old-time gasdynamicist—there was not much I could contribute. There is another approach to laser-powered propulsion, however, that I thought was worth a look and suited to my group’s skill set: laser-thermal propulsion. Essentially, the laser is used to heat propellant that is expanded out of a traditional nozzle, i.e., a giant steam kettle in space. The laser flux only interacts with a mirror on board the spacecraft to focus the laser through a window and into the propellant heating chamber, and these components can withstand much greater fluxes, in principle, up to the equivalent of tens of thousands of suns. The greater power that can be delivered results in greater thrust, so a more intense propulsive maneuver can be performed nearer to Earth. The closer to Earth the propulsive burn is, the smaller the laser array needs to be in order to keep the beam focused on the spacecraft, making it more feasible as a near-term demonstration of directed energy propulsion. The challenge is that the laser fluxes are intense and do not lend themselves to benchtop testing; could we come up with a design that could feasibly handle the extreme flux?

Our effort was led by Emmanuel Duplay, our “Chief Designer,” who happens to be a gifted graphic artist and whose work graces the final design. We also had Zhuo Fan Bao on our team, who had just finished his undergraduate honors thesis at McGill on modelling the laser-induced ionization and absorption by the hydrogen propellant—the physics that was at the heart of the laser-thermal propulsion concept [3]. Heading into the lab to measure the predictions of Zhuo Fan’s thesis research was our plan for the summer of 2020, but when the pandemic dropped, we pivoted to the mission design aspects of the concept instead. Together with the rest of our team of undergraduate students—all working remotely via Zoom, Slack, Notion, and all the other tools that we learned to adopt through the summer of 2020—we dove into the detailed design.

Image: McGill Interstellar Flight Experimental Research Group meeting-up in person for the first time on Mont Royal in Montreal, during the early days of the pandemic, summer 2020.

Our design team benefitted greatly from prior work on both laser-thermal propulsion and gas-core nuclear thermal rockets done in the 1970s. Laser-thermal propulsion is well-trodden ground, going back to the seminal study by Arthur Kantrowitz [4], who is my academic great grandfather of sorts. In the 1970s, the plan was to use gasdynamic lasers—imagine using an F-1 rocket engine to pump a gas laser—operating at the 10-micron wavelength of carbon dioxide. With the biggest optical elements people could conceive of at the time—a lens about a meter in diameter—combined with this longer wavelength, laser propulsion would be limited to Earth-to-space launch or low Earth orbit. To the first order, the range a laser can reach is given by the diameter of the lens times the diameter of the receiver, all divided by the wavelength of laser light. So, targeting a 10-m diameter receiver, you can only beam a CO2 laser about a thousand kilometers. The megawatt class lasers that were conceived at the time were not really up to the job of powering Earth-to-orbit launchers, which typically require gigawatts of power. For many years, Jordin Kare kept the laser-thermal space-launch concept alive by exploring how small a laser-driven launch vehicle could be made. By the 1980s, most studies focused on using laser-thermal rockets for orbit transfer from LEO, an application that requires lower power[5].

Image: Concept for a laser-thermal rocket from the early 1980s, using a 10-micron-wavelength CO2 laser. Image Source: Kemp, Physical Sciences Incorporated (1982).

As a personal footnote, I was fixated with laser-thermal propulsion in the 1980s as an undergraduate aerospace engineering student studying Kantrowitz and Kare’s work and, in 1991, visited all of the universities that had worked on laser propulsion, hoping I could do research in this field as a graduate student. I was told by the experts—politely but firmly—that the concept was dying or at least on pause; with the end of the Cold War, who was going to fund the development of the multi-megawatt lasers needed?

The recent emergence of inexpensive, fiber-optic lasers that could be combined in a phased array changed this picture and—thirty years later—I could finally come back to the concept that had been kicking around the back of my mind. The fact that fiber optic lasers operate at 1 micron (rather than 10 microns) and could be assembled as an array 10-m in effective optical diameter means they could reach a hundred times further into space than previously considered. Greater power, shorter wavelength, and bigger optical diameter might multiply together as a win–win–win combination and open up the possibility to rapid transit in the solar system.

The other prior literature we greatly benefitted from is gas-core nuclear thermal rockets. Unlike classic, solid-core NERVA rockets that are limited by the materials that make up the heating chamber, gas core nuclear thermal rockets contain the fissile material as plasma in the center of the heating chamber that does not come into contact with the walls. Work on this concept progressed in the 1960s and early 1970s, and studies concluded that containing temperatures of 50,000 K should be feasible. The literature on this topic is extensive, but Winchell Chung’s Atomic Rockets website provides a good introduction [6]. Work from the early 1970s concluded specific impulses exceeding 3000 s were achievable, but leakage of fissile material and its products from the gas core were both a performance limiting issue and an environmental nonstarter for use near Earth. But what if we could create the same conditions in the gas core using a laser, without loss of uranium or radioactive waste to worry about? The heat transfer and wall cooling issues between gas core NTR and the laser-thermal rocket neatly overlap, so we could adopt many of the strategies previously developed to contain these temperatures while keeping the walls of our heating chamber cool.

Image: Gas-core nuclear thermal rocket. Image source: Rom, Nuclear-Rocket Propulsion, (NASA, 1968).

Laser-thermal propulsion is sometimes called the poor person’s nuclear thermal rocket. Given its lack of radioactive materials and associated issues, I would argue that laser-thermal propulsion is rather the enlightened person’s nuclear rocket.

With this stage set, in the next installment, we will take a closer look at the final results of our Mars-in-45-day mission design study.


1. John Brophy et al., A Breakthrough Propulsion Architecture for Interstellar Precursor Missions, NIAC Final Report (2018)

2. Sheerin, Todd F., Elaine Petro, Kelley Winters, Paulo Lozano, and Philip Lubin. “Fast Solar System transportation with electric propulsion powered by directed energy.” Acta Astronautica (2021).

3. Bao, Zhuo Fan and Andrew J. Higgins. “Two-Dimensional Simulation of Laser Thermal Propulsion Heating Chamber” AIAA Propulsion and Energy 2020 Forum (2020).

4. Arthur Kantrowitz, “Propulsion to Orbit by Ground-Based Lasers,” Astronautics and Aeronautics (1972).

5. Leonard H. Caveny, editor, Orbit-Raising and Maneuvering Propulsion: Research Status and Needs (AIAA, 1984).



Notes on the Magnetic Ramjet II

Building a Bussard ramjet isn’t easy, but the idea has a life of its own and continues to be discussed in the technical literature, in addition to its long history in science fiction. Peter Schattschneider, who explored the concept in Crafting the Bussard Ramjet last February, has just published an SF novel of his own called The EXODUS Incident (Springer, 2021), where the Bussard concept plays a key role. But given the huge technical problems of such a craft, can one ever be engineered? In this second part of his analysis, Dr. Schattschneider digs into the question of hydrogen harvesting and the magnetic fields the ramjet would demand. The little known work of John Ford Fishback offers a unique approach, one that the author has recently explored with Centauri Dreams regular A. A. Jackson in a paper for Acta Astronautica. The essay below explains Fishback’s ideas and the options they offer in the analysis of this extraordinary propulsion concept. The author is professor emeritus in solid state physics at Technische Universität Wien, but he has also worked for a private engineering company as well as the French CNRS, and has been director of the Vienna University Service Center for Electron Microscopy.

by Peter Schattschneider

As I mentioned in a recent contribution to Centauri Dreams, the BLC1 signal that flooded the press in January motivated me to check the science of a novel that I was finishing at the time – an interstellar expedition to Proxima Centauri on board a Bussard ramjet. Robert W. Bussard’s ingenious interstellar ramjet concept [1], published in 1960, inspired a generation of science fiction authors; the most celebrated is probably Poul Anderson with the novel Tau Zero [2]. The plot is supposedly based on an article by Carl Sagan [3] who references an early publication of Eugen Sänger where it is stated that due to time dilation and constant acceleration at 1 g „[…] the human lifespan would be sufficient to circumnavigate an entire static universe“ [4].

Bussard suggested using magnetic fields to scoop interstellar hydrogen as a fuel for a fusion reactor, but he did not discuss a particular field configuration. He left the supposedly simple problem to others as Newton did with the 3-body problem, or Fermat with his celebrated theorem. Humankind had to wait 225 years for an analytic solution of Newton‘s problem, and 350 years for Fermat’s. It took only 9 years for John Ford Fishback to propose a physically sound solution for the magnetic ramjet [5].

The paper is elusive and demanding. This might explain why adepts of interstellar flight are still discussing ramjets with who-knows-how-working superconducting coils that generate magnetic scoop fields reaching hundreds or thousands of kilometres out into space. Alas, it is much more technically complicated.

Fishback’s solution is amazingly simple. He starts from the well known fact that charged particles spiral along magnetic field lines. So, the task is to design a field the lines of which come together at the entrance of the fusion reactor. A magnetic dipole field as on Earth where all field lines focus on the poles would do the job. Indeed, the fast protons from the solar wind are guided towards the poles along the field lines, creating auroras. But they are trapped, bouncing between north and south, never reaching the magnetic poles. The reason is rather technical: Dipole fields change too rapidly along the path of a proton in order to keep it on track.

Fishback simply assumed a sufficiently slow field variation along the flight direction, Bz=B0/(1+ ? z) with a „very small“ ?. Everything else derives from there, in particular the parabolic shape of the magnetic field lines. Interestingly, throughout the text one looks in vain for field strengths, let alone a blueprint of the apparatus. The only hint to the visual appearance of the device is a drawing of a long, narrow paraboloid that would suck the protons into the fusion chamber. As a shortcut to what the author called the region dominated by the ramjet field I use here the term „Fishback solenoid“.

Fig. 1 is adapted from the original [5]. I added the coils that would create the appropriate field. Their distance along the axis indicates the decreasing current as the funnel widens. Protons come in from the right. Particles outside the scooping area As are rejected by the field. The mechanical support of the coils is indicated in blue. It constitutes a considerable portion of the ship’s mass, as we shall see below.

Fig. 1: Fishback solenoid with parabolic field lines. The current carrying coils are symbolized in red. The mechanical support is in blue. The strong fields exert hoop stress on the support that contributes considerably to the ship’s mass. Adapted from [5].

Searching for scientific publications that build upon Fishback’s proposal, Scopus renders 6 citations up to this date (April 2021). Some of them deal with the mechanical stress of the magnetic field, another aspect of Fishback’s paper that I discuss in the following, but as far as I could see the paraboloidal field was not studied in the 50 years since. This is surprising because normally authors continue research when they have a promising idea, and others jump on the subject, from which follow-up publications arise, but J. F. Fishback published only this one paper in his lifetime. [On Fishback and his tragic destiny, see John Ford Fishback and the Leonora Christine, by A. A. Jackson].

Solving the dynamic equation for protons in the Fishback field proves that the concept works. The particles are guided along the parabolic field lines toward the reactor as shown in the numerical simulation Fig. 2.

Fig.2: Proton paths in an (r,z)-diagram. r is the radial distance from the symmetry axis, z is the distance along this axis. The ship flies at 0.56 c (?=0.56) in positive z-direction. In the ship’s rest frame, protons arrive with a kinetic energy of 194 MeV from the top. Left: Protons entering the field at z=200 km are focussed to the reactor mouth at the coordinate origin, gyrating over the field lines. Particles following the red paths make it to the chamber; protons following the black lines spiral back. The thick grey parabola separates the two regimes. Right: Zoom into the first 100 m in front of the reactor mouth of radius 10 m. Magnetic field lines are drawn in blue.

The reactor intake is centered at (r,z)=(0,0). In the ship’s rest frame the protons arrive from top – here with 56 % of light speed, the maximum speed of the EXODUS in my novel [8]. Some example trajectories are drawn. Protons spiral down the magnetic field lines as is known from earth’s magnetic field and enter the fusion chamber (red lines). The scooping is well visible. The reactor mouth has an assumed radius of 10 m. A closer look into the first 100 m (right figure) reveals an interesting detail: Only the first two trajectories enter the reactor. Protons travelling beyond the bold grey line are reflected before they reach the entrance, just as charged particles are bouncing back in the earth’s field before they reach the poles. From the Figure it is evident that at an axial length of 200 km of the Fishback solenoid the scoop radius is disappointingly low – only 2 km. Nevertheless, the compression factor (focussing ions from this radius to 10 m) of 1:40.000 is quite remarkable.

The adiabatic condition mentioned above allows a simple expression for the area from which protons can be collected. The outer rim of this area is indicated by the thick grey line in Fig. 2. The supraconducting coils of the solenoid should ideally be built following this paraboloid, as sketched in Fig. 1. Tuning the ring current density to

yields a result that approximates Fishback‘s field closely.

What does it mean in technical terms? Let me discuss an idealized example, having in mind Poul Anderson’s novel. The starship Leonora Christina accelerates at 1 g, imposing artificial earth gravity on the crew. Let us assume that the ship‘s mass is a moderate 1100 tons (slightly less than 3 International Space Stations). For 1 g acceleration on board, we need a peak thrust of ~11 million Newton, about 1/3 of the first stage of the Saturn V rocket. The ship must be launched with fuel on stock because the ramjet operates only beyond a given speed, often taken as 42 km/s, the escape velocity from the solar system. In the beginning, the thrust is low. It increases with the ship’s speed because the proton throughput increases, asymptotically approaching the peak thrust.

Assuming complete conversion of fusion energy into thrust, total ionisation of hydrogen atoms, and neglecting drag from deviation of protons in the magnetic field, at an interstellar density of 106 protons/m3, the „fuel“ collected over one square kilometer yields a peak thrust of 1,05 Newton, a good number for order-of-magnitude estimates. That makes a scooping area of ~10 million square km, which corresponds to an entrance radius of about 1800 km of the Fishback solenoid. From Fig. 2, it is straightforward to extrapolate the bold grey parabola to the necessary length of the funnel – one ends up with fantastic 160 million km, more than the distance earth – sun. (At this point it is perhaps worth mentioning that this contribution is a physicist’s treatise and not that of an engineer.)

Plugging the scooping area into the relativistic rocket equation tells us which peak acceleration is possible. The results are summarised in Table 1. For convenience, speed is given in units of the light speed, ß=v/c. Additionally, the specific momentum ß? is given where

is the famous relativistic factor. (Note: The linear momentum of 1 kg of matter would be ß? c.) Acceleration is in units of the earth gravity acceleration, g=9.81 m/s2.

Under continuous acceleration such a starship would pass Proxima Centauri after 2.3 years, arrive at the galactic center after 11 years, and at the Andromeda galaxy after less than 16 years. Obviously, this is not earth time but the time elapsed for the crew who profit from time dilation. There is one problem: the absurdly long Fishback solenoid. Even going down to a scooping radius of 18 km, the supraconducting coils would reach out 16,000 km into flight direction. In this case the flight to our neighbour star would last almost 300 years.

Table 1: Acceleration and travel time to Proxima Centauri, the galactic center, and the Andromeda galaxy M31, as a function of scooping area. ß? is the specific momentum at the given ship time. A ship mass of 1100 tons, reactor entrance radius 10 m, and constant acceleration from the start was assumed. During the starting phase the thrust is low, which increases the flight time by one to several years depending on the acceleration.

Fishback pointed out another problem of Bussard ramjets [5]. The magnetic field exerts strong outward Lorentz forces on the supraconducting coils. They must be balanced by some rigid support, otherwise the coils would break apart. When the ship gains speed, the magnetic field must be increased in order to keep the protons on track. Consequently, for any given mechanical support there is a cut-off speed beyond which the coils would break. For the Leonora Christina a coil support made of a high-strength „patented“ steel must have a mass of 1100 tons in order to sustain the magnetic forces that occur at ?=0,74.

Table 2: Cut-off speeds ?c and cut-off specific momenta (ß?)c (upper bounds) for several support materials. (ß?)F from [5], (ß?)M from [7]. ?y/? is the ratio of the mechanical yield stress to the mass density of the support material. Bmax is the maximum magnetic field at the reactor entrance at cut-off speed. A scooping area of 10 million km2 was assumed, allowing a maximum acceleration of ~1 g for a ship of 1100 tons. Values in italics for Kevlar and graphene, unknown in the 1960s, were calculated based on equations given in [7].

But we assumed above that this is the ship‘s entire mass. That said, the acceleration must drop long before speeding at 0,74 c. The cut-off speed ?c=0,74 is an upper bound (for mathematicians: not necessarily the supremum) for the speed at which 1 g acceleration can be maintained. Lighter materials for the coil support would save mass. Fishback [5] calculated upper bounds for the speed at which an acceleration of 1 g is still possible for several materials such as aluminium or diamond (at that time the strongest lightweight material known). Values are shown in Table 2 together with (ß?)c.

Martin [7] found some numerical errors in [5]. Apart from that, Fishback used an optimistically biased (ß?)c. Closer scrutiny, in particular the use of a more realistic rocket equation [6], results in more realistic upper bounds. Using graphene, the strongest material known, the specific cut-off momentum is 11,41. This value would be achieved after a flight of three years at a distance of 10 light years. After that point, the acceleration would rapidly drop to values making it hopeless to reach the galatic center in a lifetime.

In conclusion, the interstellar magnetic ramjet has severe construction problems. Some future civilization may have the knowhow to construct fantastically long Fishback solenoids and to overcome the minimum mass condition. We should send a query to the guys who flashed the BLC1 signal from Proxima Centauri. The response is expected in 8.5 years at the earliest. In the meantime the educated reader may consult a tongue-in-cheek solution that can be found in my recent scientific novel [8].


Many thanks to Al Jackson for useful comments and for pointing out the source from which Poul Anderson got the idea for Tau Zero, and to Paul Gilster for referring me to the seminal paper of John Ford Fishback.


[1] Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.

[2] Poul Anderson: Tau Zero. Doubleday 1970.

[3] Carl Sagan: Direct contact among galactic civilizations by relativistic inter-stellar space flight, Planetary and Space Science 11 (1963) 485-498.

[4] Eugen Sänger: Zur Mechanik der Photonen-Strahlantriebe. Oldenbourg 1956.

[5] John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.

[6] Claude Semay, Bernard Silvestre-Brac: The equation of motion of an interstellar Bussard ramjet. European Journal of Physics 26 (1) (2005) 75-83.

[7] Anthony R. Martin: Structural limitations on interstellar space flight. Astronautica Acta 16 (6) (1971) 353-357.

[8] Peter Schattschneider: The EXODUS Incident. Springer 2021,
ISBN: 978-3-030-70018-8.


Crafting the Bussard Ramjet

The Bussard ramjet is an idea whose attractions do not fade, especially given stunning science fiction treatments like Poul Anderson’s novel Tau Zero. Not long ago I heard from Peter Schattschneider, a physicist and writer who has been exploring the Bussard concept in a soon to be published novel. In the article below, Dr. Schattschneider explains the complications involved in designing a realistic ramjet for his novel, with an interesting nod to a follow-up piece I’ll publish as soon as it is available on the work of John Ford Fishback, whose ideas on magnetic field configurations we have discussed in these pages before.

The author is professor emeritus in solid state physics at Technische Universität Wien, but he has also worked for a private engineering company as well as the French CNRS, and has been director of the Vienna University Service Center for Electron Microscopy. With more than 300 research articles in peer-reviewed journals and several monographs on electron-matter interaction, Dr. Schattschneider’s current research focuses on electron vortex beams, which are exotic probes for solid state spectroscopy. He tells me that his interest in physics emerged from an early fascination with science fiction, leading to the publication of several SF novels in German and many short stories in SF anthologies, some of them translated into English and French. As we see below, so-called ‘hard’ science fiction, scrupulously faithful to physics, demands attention to detail while pushing into fruitful speculation about future discovery.

by Peter Schattschneider

When the news about the BLC1 signal from Proxima Centauri came in, I was just finishing a scientific novel about an expedition to our neighbour star. Good news, I thought – the hype would spur interest in space travel. Disappointment set in immediately: Should the signal turn out to be real, this kind of science fiction would land in the dustbin.

Image: Peter Schattschneider. Credit & copyright: Klaus Ranger Fotografie.

The space ship in the novel is a Bussard ramjet. Collecting interstellar hydrogen with some kind of electrostatic or magnetic funnel that would operate like a giant vacuum cleaner is a great idea promoted by Robert W. Bussard in 1960 [1]. Interstellar protons (and some other stuff) enter the funnel at the ship‘s speed without further ado. Fusion to helium will not pose a problem in a century or so (ITER is almost working), conversion of the energy gain into thrust would work as in existing thrusters, and there you go!

Some order-of-magnitude calculations show that it isn‘t as simple as that. But more on that later. Let us first look at the more mundane problems occuring on a journey to our neighbour. The values given below were taken from my upcoming The EXODUS Incident [2], calculated for a ship mass of 1500 tons, an efficiency of 85% of the fusion energy going into thrust, an interstellar medium of density 1 hydrogen atom/cm3, completely ionized by means of electron strippers.

On the Way

Like existing ramjets the Bussard ramjet is an assisted take-off engine. In order to harvest fuel it needs a take-off speed, here 42 km/s, the escape velocity from the solar system. The faster a Bussard ramjet goes, the higher is the thrust, which means that one cannot assume a constant acceleration but must solve the dynamic rocket equation. The following table shows acceleration, speed and duration of the journey for different scoop radii.

At the midway point, the thrust is inverted to slow the ship down for arrival. To achieve an acceleration of the order of 1 g (as for instance in Poul Anderson’s celebrated novel Tau Zero [3]), the fusion drive must produce a thrust of 18 million Newton, about half the thrust of the Saturn-V. That doesn’t seem tremendous, but a short calculation reveals that one needs a scoop radius of about 3500 km to harvest enough fuel because the density of the interstellar medium is so low. Realizing magnetic or electric fields of this dimension is hardly imaginable, even for an advanced technology.

A perhaps more realistic funnel entrance of 200 km results in a time of flight of almost 500 years. Such a scenario would call for a generation starship. I thought that an acceleration of 0.1 g was perhaps a good compromise, avoiding both technical and social fantasizing. It stipulates a scoop radius of 1000 km, still enormous, but let us play the “what-if“ game: The journey would last 17.3 years, quite reasonable with future cryo-hibernation. The acceleration increases slowly, reaching a maximum of 0.1 g after 4 years. Interestingly, after that the acceleration decreases, although the speed and therefore the proton influx increases. This is because the relativistic mass of the ship increases with speed.

Fusion Drive

It has been pointed out by several authors that the “standard“ operation of a fusion reactor, burning Deuterium 2D into Helium 3He cannot work because the amount of 2D in interstellar space is too low. The proton-proton burning that would render p+p ? 2D for the 2D ? 3He reaction is 24 orders of magnitude (!) slower.

The interstellar ramjet seemed impossible until in 1975 Daniel Whitmire [4] proposed the Bethe-Weizsäcker or CNO cycle that operates in hot stars. Here, carbon, nitrogen and oxygen serve as catalysts. The reaction is fast enough for thrust production. The drawback is that it needs a very high core temperature of the plasma of several hundred million Kelvin. Reaction kinetics, cross sections and other gadgets stipulate a plasma volume of at least 6000 m3 which makes a spherical chamber of 11 m radius (for design aficionados a torus or – who knows? – a linear chamber of the same order of magnitude).

At this point, it should be noted that the results shown above were obtained without taking account of many limiting conditions (radiation losses, efficiency of the fusion process, drag, etc.) The numerical values are at best accurate to the first decimal. They should be understood as optimistic estimates, and not as input for the engineer.

Waste Heat

Radioactive high-energy by-products of the fusion process are blocked by a massive wall between the engine and the habitable section, made up of heavy elements. This is not the biggest problem because we already handle it in the experimental ITER design. The main problem is waste heat. The reactor produces 0.3 million GW. Assuming an efficiency of 85% going into thrust, the waste energy is still 47,000 GW in the form of neutrinos, high energy particles and thermal radiation. The habitable section should be at a considerable distance from the engine in order not to roast the crew. An optimistic estimate renders a distance of about 800 m, with several stacks of cooling fins in between. The surface temperature of the sternside hull would be at a comfortable 20-60 degrees Celsius. Without the shields, the hull would receive waste heat at a rate of 6 GW/m2, 5 million times more than the solar constant on earth.

Radiation shielding

An important aspect of the Bussard ramjet design is shielding from cosmic rays. At the maximum speed of 60% of light speed, interstellar hydrogen hits the bow with a kinetic energy of 200 MeV, dangerous for the crew. A.C. Clarke has proposed a protecting ice sheet at the bow of a starship in his novel The Songs of Distant Earth [5]. A similar solution is also known from modern proton cancer therapy. The penetration depth of such protons in tissue (or water, for that matter) is 26 cm. So it suffices to put a 26 cm thick water tank at the bow.

Artificial gravity

It is known that long periods of zero gravity are disastrous to the human body. It is therefore advised to have the ship rotate in order to create artificial gravity. In such an environment there are unusual phenomena, e.g. a different barometric height equation, or atmospheric turbulence caused by the Coriolis forces. Throwing an object in a rotating space ship has surprising consequences, exemplified in Fig. 1. Funny speculations about exquisite sporting activities are allowed.

Fig. 1: Freely falling objects in a rotating cylinder, thrown in different directions with the same starting speed. In this example, drawn from my novel, the cylinder has a radius of 45 m, rotating such that the artificial gravity on the inner hull is 0.3 g. The object is thrown with 40 km/h in different directions. Seen by an observer at rest, the cylinder rotates counterclockwise.


The central question for scooping hydrogen is this: Which electric or magnetic field configuration allows us to collect a sufficient amount of interstellar hydrogen? There are solutions for manipulating charged particles: colliders use magnetic quadrupoles to keep the beam on track. The symmetry of the problem stipulates a cylindrical field configuration, such as ring coils or round electrostatic or magnetic lenses which are routinely used in electron microscopy. Such lenses are annular ferromagnetic yokes with a round bore hole of the order of a millimeter. They focus an incoming electron beam from a diameter of some microns to a nanometer spot.

Scaling the numbers up, one could dream of collecting incoming protons over tens of kilometers into a spot of less than 10 meters, good enough as input to a fusion chamber. This task is a formidable technological challenge. Anyway, it is prohibitive by the mere question of mass. Apart from that, one is still far away from the needed scoop radius of 1000 km.

The next best idea relates to the earth’s magnetic dipole field. It is known that charged particles follow the field lines over long distances, for instance causing aurora phenomena close to earth’s magnetic poles. So it seems that a simple ring coil producing a magnetic dipole is a promising device. Let’s have a closer look at the physics. In a magnetic field, charged particles obey the Lorentz force. Calculating the paths of the interstellar protons is then a simple matter of plugging the field into the force equation. The result for a dipole field is shown in Fig. 2.

Fig. 2: Some trajectories of protons starting at z=2R in the magnetic field of a ring coil of radius R that sits at the origin. Magnetic field lines (light blue) converge towards the loop hole. Only a small part of the protons would pass through the ring (red lines), spiralling down according to cyclotron gyration. The rest is deflected (black lines).

An important fact is seen here: the scoop radius is smaller than the coil radius. It turns out that it diminishes further when the starting point of the protons is set at higher z values. This starting point is defined where the coil field is as low as the galactic magnetic field (~1 nT). Taking a maximum field of a few Tesla at the origin and the 1/(z/R)3 decay of the dipole field, where R is the coil radius (10 m in the example), the charged particles begin to sense the scooping field at a distance of 10 km. The scoop radius at this distance is a ridiculously small – 2 cm. All particles outside this radius are deflected, producing drag.

That said, loop coils are hopelessly inefficient for hydrogen scooping, but they are ideal braking devices for future deep space probes, and interestingly they may also serve as protection shields against cosmic radiation. On Proxima b, strong flares of the star create particle showers, largely protons of 10 to 50 MeV energy. A loop coil protects the crew as shown in Fig. 3.

Fig.3: Blue: Magnetic field lines from a horizontal superconducting current loop of radius R=30 cm. Red lines are radial trajectories of stellar flare protons of 10 MeV energy approaching from top. The loop and the mechanical protection plate (a 3 cm thick water reservoir colored in blue) are at z=0. It absorbs the few central impinging particles. The fast cyclotron motion of the protons creates a plasma aureole above the protective plate, drawn as a blue-green ring right above the coil. The field at the coil center is 6 Tesla, and 20 milliTesla at ground level.

After all this paraphernalia the central question remains: Can a sufficient amount of hydrogen be harvested? From the above it seems that magnetic dipole fields, or even a superposition of several dipole fields, cannot do the job. Surprisingly, this is not quite true. For it turns out that an arcane article from 1969 by a certain John Ford Fishback [6] gives us hope, but this is another story and will be narrated at a later time.


1. Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.

2. P. Schattschneider: The EXODUS Incident – A Scientific Novel. Springer Nature, Science and Fiction Series. May 2021, DOI: 10.1007/978-3-030-70019-5.

3. Poul Anderson: Tau Zero (1970).

4. Daniel P. Whitmire: Relativistic Spaceflight and the Catalytic Nuclear Ramjet. Acta Astronautica 2 (1975), 497-509.

5. Arthur C. Clarke: Songs of distant Earth (1986).

6. John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.


Magnetic Reconnection in New Thruster Concept

At the Princeton Plasma Physics Laboratory (PPPL) in Plainsboro, New Jersey, physicist Fatima Ebrahimi has been exploring a plasma thruster that, on paper at least, appears to offer significant advantages over the kind of ion thruster engines now widely used in space missions. As opposed to electric propulsion methods, which draw a current of ions from a plasma source and accelerate it using high voltage grids, a plasma thruster generates currents and potentials within the plasma itself, thus harnessing magnetic fields to accelerate the plasma ions.

What Ebrahimi has in mind is to use magnetic reconnection, a process observed on the surface of the Sun (and also occurring in fusion tokamaks), to accelerate the particles to high speeds. The physicist found inspiration for the idea in PPPL’s ongoing work in fusion. Says Ebrahimi:

“I’ve been cooking this concept for a while. I had the idea in 2017 while sitting on a deck and thinking about the similarities between a car’s exhaust and the high-velocity exhaust particles created by PPPL’s National Spherical Torus Experiment (NSTX). During its operation, this tokamak produces magnetic bubbles called plasmoids that move at around 20 kilometers per second, which seemed to me a lot like thrust.”

In magnetic reconnection, magnetic field lines converge, separate, and join together again, producing energy that Ebrahimi believes can be applied to a thruster. Whereas ion thrusters propelling plasma particles via electric fields can produce a useful but low specific impulse, the magnetic reconnection thruster concept can, in theory, generate exhausts with velocities of hundreds of kilometers per second, roughly ten times the capability of conventional thrusters.

Image: Magnetic reconnection refers to the breaking and reconnecting of oppositely directed magnetic field lines in a plasma. In the process, magnetic field energy is converted to plasma kinetic and thermal energy. Credit: Magnetic Reconnection Experiment.

Writing up the concept in the Journal of Plasma Physics, Ebrahimi notes that this thruster design allows thrust to be regulated through changing the strength of the magnetic fields. The physicist describes it as turning a knob to fine-tune the velocity by the application of more electromagnets and magnetic fields. In addition, the new thruster ejects both plasma particles and plasmoids, the latter a component of power no other thruster can use.

If we could build a magnetic reconnection thruster like this, it would allow flexibility in the plasma chosen for a specific mission, with the more conventional xenon used in ion thrusters giving way to a range of lighter gases. Ebrahimi’s 2017 work showed how magnetic reconnection could be triggered by the motion of particles and magnetic fields within a plasma, with the accompanying production of plasmoids. Her ongoing fusion research investigates the use of reconnection to both create and confine the plasma that fuels the reaction without the need for a large central magnet.

Image: PPPL physicist Fatima Ebrahimi in front of an artist’s conception of a fusion rocket. Credit: Elle Starkman, PPPL Office of Communications, and ITER.

Thus research into plasmoids and magnetic reconnection filters down from the investigation of fusion into an as yet untested concept for propulsion. It’s important to emphasize that we are, to say the least, in the early stages of exploring the new propulsion concept. “This work was inspired by past fusion work and this is the first time that plasmoids and reconnection have been proposed for space propulsion,” adds Ebrahimi. “The next step is building a prototype.”

The paper is Ebrahimi, “An Alfvenic reconnecting plasmoid thruster,” Journal of Plasma Physics Vol. 86, Issue 6 (21 December 2020). Abstract.


Propulsion for Satellite ‘Constellations’

A French company called Exotrail has been working on electric propulsion systems for small spacecraft down to the CubeSat level. As presented last week at the 13th European Space Conference in Brussels, the ExoMG Hall-effect electric propulsion system was flown in a demonstration orbital mission in November, launched to low-Earth orbit by a PSLV (Polar Satellite Launch Vehicle) rocket. A brief nod to the PSLV: These launch vehicles were developed by the Indian Space Research Organisation (ISRO), and are being used for rideshare launch services for small satellites. Among their most notable payloads have been the Indian lunar probe Chandrayaan-1, and the Mars Orbiter Mission called Mangalyaan.

Hall-effect thrusters (HET) trap electrons emitted by a cathode in a magnetic field, ionizing a propellant to create a plasma that can be accelerated via an electric field. The technology has been in use in large satellites for many years because of its high thrust-to-power ratio.

What catches my eye about ExoMG is its size, about that of a 2-liter bottle of soda as opposed to conventional Hall-effect thrusters that weigh in at refrigerator size and demand kilowatts of power. The Exotrail thruster, which was successfully fired during the November mission, runs on about 50 watts of power, and appears to be a propulsion system that can adapt to satellites in the range of 10 to 250 kg. Collision avoidance and deorbiting for satellites in the CubeSat range as well as flexible orbital operations become feasible with this technology.

Image: Satellite using Exotrail technology undergoing testing. Credit: Exotrail.

The company is calling ExoMG “the first ever Hall-effect thruster operating on a sub-100kg spacecraft,” and points to four missions slated to fly with the technology in 2021. I’m interested in how the diminutive thruster can be employed in constellations of satellites. We already rely on satellites working together as a system — GPS is a classic example. The needs of navigation and communication force the issue. Think Iridium and Globalstar in terms of telephony, or the Russian Molniya military and communications satellites. The list could be easily extended.

So what we have evolving is a set of constellation technologies with immediate application to satellites in low-Earth orbit. Exotrail talks about “high coverage telecommunication constellations or high revisit rate earth observation constellations at 600-2000km altitude,” enabled by orbit-raising via the new thrusters as well as necessary de-orbiting capabilities, but we should be looking as well at the controlling software and thinking in longer timeframes. Satellites working together is the theme.

Increasing miniaturization coupled with artificial intelligence and next-generation electric thrusters can be enablers for planetary probes flying in swarm formation in the outer system, perhaps using sail technologies as the primary propulsion to get them there. The one-size fits all purposes mission begins to give way to a fleet approach, tiny probes networking their data as they operate at targets as interesting as Neptune and Pluto. It’s also worth noting that the entire Breakthrough Starshot concept calls for not one but an armada of small sails in interstellar space, offering a hedge against catastrophic failure of any one craft, and conceivably drawing on swarm technologies that could facilitate data gathering and return.

So I keep an eye on near-term technologies that explore this space of miniaturization, efficient orbital adjustment and constellation operations. It will be intriguing to see how Exotrail’s operational software (called ExoOPS) deals with the interactions of such constellations. Likewise interesting is last fall’s firing of the European Space Agency’s Helicon Plasma Thruster, which ESA presents as a “compact, electrodeless and low voltage design” optimized for propulsion in small satellites, including “maintaining the formation of large orbital constellations.”

The HPT achieved its first test ignition back in 2015 at ESA’s Propulsion Laboratory in the Netherlands, and has been under development in terms of improved levels of ionization and acceleration efficiency ever since, using high-power radio frequency waves, as opposed to the application of an electrical current, to render propellant into a plasma for acceleration.

Image: A test firing of Europe’s Helicon Plasma Thruster, developed with ESA by SENER and the Universidad Carlos III’s Plasma & Space Propulsion Team (EP2-UC3M) in Spain. This compact, electrodeless and low voltage design is ideal for the propulsion of small satellites, including maintaining the formation of large orbital constellations. Credit: SENER.

Where will constellation and formation flying in Earth orbit take us as we adapt them for environments further out? Will we one day see deep space swarms of Cubesat-sized (and smaller) craft exploring the outer planets?


Musings on Fusion and the Interstellar Ramjet

Proton-proton fusion produces 99 percent of the Sun’s energy, in a process that begins with two hydrogen nuclei and ends with one helium nucleus, releasing energy along the way. We’d love to exploit the fusion process to create energy for our own directed uses, which is what Robert Bussard was thinking about with his interstellar ramjet when he published the idea in 1960. Such a ship might deploy electromagnetic fields thousands of kilometers in diameter to scoop up atoms from the interstellar medium, using them as reaction mass for the fusion that would drive it.

Carl Sagan was a great enthusiast for the concept, and would describe it vividly in the book he wrote with Russian astronomer and astrophysicist Iosif S. Shklovskii. In Intelligent Life in the Universe (1966), the authors discuss a journey that takes advantage of time dilation, allowing a lightspeed-hugging starship powered by these methods to reach galactic center in a mere 21 years of ship-time; i.e., time as perceived by the crew, while of course tens of thousands of years are going by back on Earth. If you also hear echoes of Poul Anderson’s Tau Zero here, you’re exactly on target.

Shklovskii and Sagan assume proton-proton fusion as the reaction, as Bussard originally did, but Thomas Heppenheimer was able to show in 1978 that it would take more power to compress the protons gathered from the interstellar medium than the reaction would produce. Ramscoops are tricky, and this is just one of their problems — gathering interstellar materials is another, dependent as it is on the density of the gases where the starship travels. Drag is yet another issue, making interstellar ramjets a segue into magsail deceleration rather than starship-enabling speed, though it’s a segue I’ll follow up on another occasion.

But the fusion itself is still interesting. If Bussard assumed proton-proton, it wouldn’t be long before Daniel Whitmire was able to show that a different reaction could produce far more power. The Carbon Nitrogen Oxygen cycle (CNO cycle) came to mind this morning because of word that the team working on the Borexino experiment in the Laboratori Nazionali del Gran Sasso (Italy), which studies the Sun’s fusion reactions through the neutrinos it produces, has been able to identify the CNO cycle as a small component of the Sun’s production of energy.

Image: The Borexino research team has succeeded in detecting neutrinos from the sun’s second fusion process, the Carbon Nitrogen Oxygen cycle (CNO cycle) for the first time. Credit: Borexino Collaboration.

That’s interesting in itself and confirms work by Hans Bethe and Carl Friedrich von Weizsäcker from the 1930s, the first experimental confirmation of their independent investigations. But I cycle back to Bussard’s ramjet. The Carbon Nitrogen Oxygen cycle involves four hydrogen nuclei combining to form a helium nucleus using carbon, nitrogen and oxygen as catalysts and intermediate products in the reaction. Maybe ‘catalysts’ isn’t the right word — I was reminded by reading Adam Crowl’s thoughts on the matter some years back that we’re not talking about chemical catalysis and should perhaps refer to all this simply as ‘nuclear chemistry.’

What boggles the mind about the CNO cycle, which I’ve read is the dominant energy source in stars more than 1.3 times more massive than the Sun, is the degree of energy unlocked by it, far exceeding uncatalyzed proton/proton fusion. And it would take something highly energetic to work on Bussard’s ramscoop, for Whitmire’s 1975 paper showed that a proton-proton reactor built in the fashion originally suggested by Bussard would need a scoop 7,000 kilometers across to make the reaction work.

Isn’t that odd? You would think that a reaction that powers the Sun would be perfectly sufficient to drive the Bussard ramjet, but it turns out that the rate of proton-proton fusion is too low. Looking back through my materials on the problem, I find that the Sun produces less than 1 watt per cubic meter when averaged over its whole volume, which means that the energy produced in a light bulb filament is more powerful. Whitmire realized that the Sun’s vast energy output could occur because of its size. Making equally massive starships is out of the question.

It turns out that Whitmire and Centauri Dreams regular Al Jackson were friends at the University of Texas back in the 1970s, and I’ll remind you of Al’s reminiscence of Whitmire that can be found here — it was actually Al who introduced the Bussard ramscoop idea to Whitmire. Bussard would write to Whitmire that his 1975 paper offered a solution to the proton-proton fusion problem and would “become an enduring classic in this field.”

If you know your science fiction, you’ll recall that Greg Benford uses the CNO cycle in his 1984 novel Across the Sea of Suns, where he gives a poetic description of the process at work as perceived by his protagonist via the ultimate in futuristic telepresence:

He watches plumes of carbon nuclei striking the swarms of protons, wedding them to form the heavier hydrogen nuclei. The torrent swirls and screams at Nigel’s skin and in his sensors he sees and feels and tastes the lumpy, sluggish nitrogen as it finds a fresh incoming proton and with the fleshy smack of fusion the two stick, they hold, they wobble like raindrops — falling together — merging — ballooning into a new nucleus, heavier still: oxygen.

But the green pinpoints of oxygen are unstable. These fragile forms split instantly. Jets of new particles spew through the surrounding glow — neutrinos, ruddy photons of light, and slower, darker, there come the heavy daughters of the marriage: a swollen, burnt-gold cloud. A wobbling, heavier isotope of nitrogen….

Ahead he sees the violet points of nitrogen and hears them crack into carbon plus an alpha particle. So in the end the long cascade gives forth the carbon that catalyzed it, carbon that will begin again its life in the whistling blizzard of protons coming in from the forward maw of the ship.

And there you are: Carbon – Nitrogen – Oxygen in a cycle that makes starship fusion work. And all of this reminiscing suggested by the results of an experiment deep below the the Italian Gran Sasso massif which has turned up evidence for the CNO cycle within the Sun, a small but ongoing component of its output. If you want to read more on what turned up at Borexino, the paper is The Borexino Collaboration, “Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun,” Nature 587 (2020), 577-582 (abstract). The Whitmire paper is “Relativistic Spaceflight and the Catalytic Nuclear Ramjet,” Acta Astronautica 2 (1975), pp. 497-509 (abstract).