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 , published in 1960, inspired a generation of science fiction authors; the most celebrated is probably Poul Anderson with the novel Tau Zero . The plot is supposedly based on an article by Carl Sagan  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“ .
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 .
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 . 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 .
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 . 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 . 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 , (ß?)M from . ?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 .
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  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  found some numerical errors in . Apart from that, Fishback used an optimistically biased (ß?)c. Closer scrutiny, in particular the use of a more realistic rocket equation , 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 .
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.
 Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.
 Poul Anderson: Tau Zero. Doubleday 1970.
 Carl Sagan: Direct contact among galactic civilizations by relativistic inter-stellar space flight, Planetary and Space Science 11 (1963) 485-498.
 Eugen Sänger: Zur Mechanik der Photonen-Strahlantriebe. Oldenbourg 1956.
 John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.
 Claude Semay, Bernard Silvestre-Brac: The equation of motion of an interstellar Bussard ramjet. European Journal of Physics 26 (1) (2005) 75-83.
 Anthony R. Martin: Structural limitations on interstellar space flight. Astronautica Acta 16 (6) (1971) 353-357.
 Peter Schattschneider: The EXODUS Incident. Springer 2021,
ISBN: 978-3-030-70018-8. https://www.springer.com/de/book/9783030700188#aboutBook