# The Bussard Ramjet

## The Driving Need for Relativistic Space Travel

 Fig. 1: The ramjet system (in red) before and after an increment of interstellar gas (blue) is used to power a fusion reaction. The factor a is related to how much of the interstellar gas can be converted to energy via fusion, and the factor K is related to the efficiency of the conversion to kinetic energy. This figure is a simplified schematic of one found in Bussard. [3] (Source: J. McCullough)

Humanity has spent a great deal of time grappling with the technologies needed for successful space travel. Placing satellites in orbit, setting foot on the moon, and sending probes across our solar backyard have each required immense feats of engineering. The fastest spacecraft to be flown as of this writing is the Parker Solar Probe, which will reach a peak heliocentric velocity of nearly 190 km/s. Say that we were to naively assume this velocity was sustainable. (It sits at the perihelion of a closed orbit, fewer than nine solar radii from the surface of the sun , meaning that the fastest and closest approach relies heavily on the sun's gravity. [1]) Suppose we wanted to reach our nearest stellar neighbor, Proxima Centauri, sitting 4.24 lightyears away. [2] It would therefore take

 4.24 × 3.0 × 105 km s-1 × 3600 s h-1 × 24 h d-1 × 365 d 190 km s-1 × 3600 s h-1 × 24 h d-1 × 365 d y-1 = 6.74 × 103 y

This is a loose calculation of our fastest, modern day expectation of space travel. Not only is this far beyond the reach of a human life, this threatens the lifetime of a great deal of technology as well! If we wanted to reach Proxima Centauri in a human lifetime, say 80 years, we would need an average velocity of

 4.24 × 3.0 × 105 km s-1 × 3600 s h-1 × 24 h d-1 × 365 d 80 y × 365 d y-1 × 24 h d-1 × 3600 s h-1 = 1.59 × 105 km s-1

This is a little over 5% of the speed of light! For timely interstellar travel, we therefore require much faster velocities than we currently have been able to reach. It is also helpful to think of this in terms of acceleration rather than velocity - positively accelerating for half of the trip and negatively accelerating for the second half. Constant velocities lead to larger proper times than constant accelerations do, which would be the amount of time a traveller on board would have to wait before arriving at their destination.

One such proposed propulsion system was dubbed the Bussard Ramjet after its proposer, Robert W. Bussard in 1960. It relies on nuclear fusion of hydrogen found in the interstellar medium (ISM). That is, the fuel needed to power the nuclear reactor is scooped from the low density matter that lies between stars. I will describe the initial design, modifications that have been proposed to improve it, and lastly I will discuss the major issues that would currently prevent its implementation.

## The Bussard Ramjet: As Written

The interstellar ramjet is dubbed so because it bears an analogy to atmospheric jets that utilize supersonic flight to generate compressive shocks using the material around the jet and the fast speed of the vehicle to do the work of compressing the air, rather than an onboard compressor. [3] The vehicle can be lighter because it does not have to carry the oxidizer (air) or the compressor. In the case of the Bussard Ramjet, the vehicle would require no onboard fuel, which allows it to be lighter, and allows it to generate a constant acceleration at low velocities, as the mass of the vehicle itself does not change as onboard fuel is burned away (as in a rocket). A simple schematic of the system is shown in Fig. 1.

The interstellar medium, on average has about 1 atom per cubic centimeter. The real distribution of matter is a bit different, with hydrogen gas clumping up in the galactic disk into clouds, meaning the density may be as high as 50 atoms/cm3 in wide stretches more than tens of parsecs across. [3] Bussard relied on the proton-proton fusion chain, which has two hydrogen nuclei (protons) colliding at high velocities (meaning very high temperatures) to create Deuterium, a positron, an electron neutrino, and energy. These products are also fused with more Hydrogen, resulting in a final product of Helium. [4] The full chain reaction follows from the equation

 4 1H → 4He + 2 e+ + 2 νe + (26.73 MeV)

where the energy is released kinetically in the reaction products. It should be fairly evident that p-p fusion, as seen in our sun, requires very high temperatures (collision speeds) to take place, and that the mechanical challenges of achieving this with diffuse, ionized hydrogen would be significant.

## The Bussard Ramjet: As Modified

 Fig. 2: An approximate idealized performance curve of the proton-ramjet with achievable distance in light-years plotted against travel time. The solid line represents a constant 1 g acceleration, and the blue lines are optimistic interpretations of the minimum mass theorem for structural materials explored in Fishback's thesis. This figure is simplified from a similar one seen in Fishback. [6] (Source: J. McCullough)

Not long after Bussard's paper, Whitmire proposed using the CNO cycle in place of the p-p chain. This requires a carbon catalyst on board, but speeds up the reaction by as many as 18 orders of magnitude over the slowest link in the p-p chain. [5] Since the "scooping" of hydrogen was meant to be done with magnetic fields, he also proposed a way to ionize hydrogen in front of the ramjet to allow it to work in non-HII (neutral or even molecular hydrogen) regions using stripper foil placed over the intake area, rather than an ionizing laser.

Additionally, Fishback tackled the beginnings of the problem with momentum transfer and structural stresses on the scoop, and how this impacts the maximum velocities attainable by the vehicle. [6] While he looked primarily at the expression required for the magnetic field of the scoop, he did begin to explore the tensile stresses acceptable within this structure, as seen in Fig. 2. While diamond appears to be the best choice explored in this paper, more recent investigations suggest graphene would be a better choice due to its high performing tensile stress properties. [7] Overall, the theoretically attainable Lorentz factors, or the length/time contraction seen due to relativistic travel, for such a ramjet go as high as 10,000. [7] That is to say, that a larger achievable Lorentz factor corresponds to a longer achievable distance under constant acceleration.

Lastly, a more modern addition to the conversation was added in 2022, with Schattschneider and Jackson revisiting the magnetic scoop proposal by Fishback and finding via simulations that the magnetic solenoids for such a ramjet would be excessively long with requisite masses of more than a kiloton. [8] Additionally the design was found to have overestimated the potential acceleration it would be able to attain, as well as underestimated the difficulty of engineering the magnetic source. [8]

## Fatal Flaws

With this discussion in mind, there is not yet any degree of specificity on design or structure for such a ramjet. The scoop sizes being discussed here are quite large, on the order of tens of miles. [5] This as well as the velocities being aimed for bring up a number of technical questions that have not yet been answered. The material strengths involved, the extensive need for cooling, the potential for inflow turbulence, the mechanism of momentum transfer between the interstellar medium and the vehicle, as well as the vehicle and the exhaust - each of these poses an enormous difficulty. Most of the papers cited here have acknowledged this as a difficulty for future engineers, but nevertheless the challenges are extensive. Presently, this leaves us with only the most theoretical model of how such a spacecraft would work, as just one of many concepts put forward in the realm of interstellar travel.

© Jamie McCullough. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] N. J. Fox et al., "The Solar Probe Plus Mission: Humanity's First Visit to Our Star," Space Sci. Rev. 204, 7 (2016).

[2] X. Luri et al., "Gaia Data Release 2," Astron. Astrophys. 616, A9 (2018).

[3] R. W. Bussard, "Galactic Matter and Interstellar Flight," Acta Astronaut. 6, 179 (1960).

[4] B. W. Carroll, An Introduction to Modern Astrophysics, 2nd Ed. (Cambridge University Press, 2017), pp 309-313

[5] D. P. Whitmire, "Relativistic Spaceflight and the Catalytic Nuclear Ramjet," Acta Astronaut. 2, 497 (1975).

[6] J. F. Fishback, "Relativistic Interstellar Space Flight," Acta Astronaut. 15, 25 (1969).

[7] A. A. Jackson IV, "Three Interstellar Ramjets," Lunar and Planetary Institute, 2016.

[8] P. Schattschneider and A. A. Jackson, "The Fishback Ramjet Revisited," Acta Astronaut. 191, 227 (2022).