Although solar sails were making their way into the aerospace journals in the late 1950s, Robert Forward was the first scientist to consider using laser beams rather than sunlight to drive a space sail. That concept, which György Marx picked up on in his 1966 paper, opened the door to interstellar mission concepts. Late in life in an unpublished memoir, Forward recalled reading about Theodore Maiman’s work on lasers at Hughes Research Laboratories, and realizing that this was a way to create a starship. His 1962 article (citation below) laid out the idea for the journal Missiles and Rockets and was later reprinted in Science Digest. Marx surely knew the Forward article and his subsequent paper in Nature probed how to achieve this goal.

Image: One of the great figures of interstellar studies, Robert Forward among many other things introduced and explored the principles of beamed propulsion. Credit: UAH Library Robert L. Forward Collection.

Marx was at that time a professor of theoretical physics at Roland Eötvös University in Budapest. He was plugged into the difficulties of interstellar flight through Les Shepherd’s work in Britain, and he cites the latter’s Realities of Space Travel (1957) in the paper as one of many sources highlighting the depth of the problem. His paper “Interstellar Vehicle Propelled by Terrestrial Laser Beam” is a mere two pages built largely around equations, reporting on the “commonly accepted view that, apart from the technical difficulties involved, the laws of conservation of energy and momentum forbid the visiting of other planetary systems in the human lifespan.”

Marx had already explored energy issues for interstellar flight in a 1960 paper for Astronautica Acta (as it was then known) and a second for the same journal in 1963 (citations below). But the idea of laser beaming offered the physicist a glimmer of hope. In the 1966 paper, he cites the advantages of beamed sailing vs conventional rocket propulsion. The paper argues that “a vehicle can be accelerated almost to the speed of light if an emitter on the Earth can accurately project light onto its mirror.”

The ideal focusing mechanism would be the laser, and it is here that he runs into trouble. For Marx worried about the size of the transmitter aperture, which determines the size and initial beam diameter that will emerge. Remember we’re in the Robert Forward era of maxed out engineering, when the idea was simply to establish what was possible even if it required building capabilities far beyond those of the present day. So here’s what Marx comes up with, the best concept he thought feasible:

…the technical conditions are extremely challenging. A range of operation of 0.1 light year would require a coherently radiating surface of the order of 1 km2 which emits hard X-rays, and the vehicle would need an X-ray mirror with an effective cross-sectional area of several km2.

Marx talks about the absorbed energy of his sail ‘mirror’ radiating out isotropically into space, and here we run into serious problems. I took my questions to Jim Benford, CEO of Microwave Sciences and author of High Power Microwaves, a standard text which is about to go into its fourth edition at CRC Press. Jim is also a regular contributor to Centauri Dreams. And he was quick to point out that X-rays reflect from conducting surfaces in ways that defeat Marx’s purpose.

Image: György Marx in his office. Credit: REAL-I, the Image File Collection of the Academic Library.

As Jim told me, incoming X-rays reflect only at very low grazing angles. The efficiency of energy transfer is at stake here. Here’s a bit more of what he said, using one of the most important formulae in all of modern physics:

X-ray photons have far more energy than visible light or microwaves. Remember the relation E=hν, where E is the energy of the photon, h is Planck’s constant, ν the frequency. X-ray photons have energies about a thousand times that of visible light, a million times that of microwaves. If they come in normal to the surface [i.e., striking the sail head on], they ionize atoms, damaging the lattice of the material.

X-ray telescopes, as a matter of fact, work through a series of grazing incidence reflectors. In other words, we can’t direct Marx’s fantastic X-ray beam toward our sail without seriously damaging it, not unless we are willing to bring the beam to it at such a low angle that the intrinsic power of the beam is largely lost. Benford again:

There’s no way to accelerate a sail with X-rays. The cross-section of the sail must be at a slight angle to the beam, not perpendicular to it, for the X-rays to reflect. That’s hugely inefficient. Grazing incidence means that only the slight transverse component of the photon velocity vector is reversed, leaving the far larger axial component almost unchanged. Little energy is transferred to the inclined sail, and that drives it sideways to the beam, not antiparallel to it, as reflected photons do when they incident normally. So the sail is accelerated very little in the direction of the X-ray beam.

This is the coup de grâce for the X-ray sail. It’s interesting to see what Robert Forward thought of Marx’s idea. Here he is, writing in a 1984 paper called “Roundtrip Interstellar Travel Using Laser-Pushed Lightsails,” which is one of the classics of the field:

The concept of laser-pushed interstellar lightsails was reinvented by Marx in 1966. Since Marx was unwilling to consider a laser aperture greater than 1 km2, he was forced to assume the use of hard x-rays in order to obtain the operational ranges needed for interstellar flight. The impossibility of constructing both an x-ray laser and a lightweight sail to reflect those x-rays led to Marx’s highly pessimistic conclusion about the feasibility of the concept. If Marx had been willing to consider a larger transmitter aperture, then his laser frequencies and sail requirements would have been much easier.

J. L. Redding, then at Bishop’s University in Quebec, saw Marx’s paper and responded to it in the same year, offering corrections to Marx’s equations without challenging the X-ray concept. His telling remark that “…one does not need to consider the difficulties of arranging suitable deceleration and landing facilities” refers to what he saw as the overwhelming problems in making a beamed energy propulsion system work at all. Marx had commented on the deceleration problem and Forward would go on to offer a potential solution in his 1984 paper, one so baroque that it deserves a future post of its own.

I should also mention a little referenced paper by W. E. Moeckel, “Propulsion by Impinging Laser Beams,” which ran in the Journal of Spacecraft and Rockets in 1972. Moeckel (working at what was then NASA’s Lewis Research Center in Cleveland) analyzed laser beaming to 100 ton relativistic flyby probes, each of which would require 1012 watts of X-ray energy. Making specific reference to Marx, Moeckel found X-ray beaming promising but did not know if it was feasible. His conclusion would have warmed the hearts of science fiction writers of the time:

…some future generations of mankind, with a somewhat different ordering of priorities than ours and much more available power, could conceivably explore other stars and other solar systems with highly sophisticated unmanned spacecraft capable of relaying information in elapsed times of the order of decades.

If only it worked! Fortunately, we’re not restricted to X-rays when it comes to beamed propulsion.


The early Forward paper is “Pluto-Gateway to the Stars,” Missiles and Rockets 10, 26 ff. (2 April 1962); reprinted in Science Digest 52, 70-75 (August 1962). Forward’s “Roundtrip Interstellar Travel Using Laser-Pushed Lightsails” appeared in the Journal of Spacecraft and Rockets 21 (1984), pp. 187-195 (abstract).

György Marx’s paper on X-ray beaming is “Interstellar Vehicle Propelled by Terrestrial Laser Beam,” which ran in Nature on July 2, 1966 (abstract). His two other interstellar papers are “The mechanical efficiency of interstellar vehicles,” Astronautica Acta 9 (1963) 131–139, and “Über Energieprobleme der Interstellaren Raumfahrt,” Astronautica Acta 6 (1960) 366–372.

The Redding paper in response to Marx has the same title, “Interstellar Vehicle Propelled by Terrestrial Laser Beam,” Nature February 11, 1967 (abstract). W. E. Moeckel’s paper “Propulsion by Impinging Laser Beams” appeared in the Journal of Spacecraft and Rockets Vol. 9 (1972), 942-944 (abstract).

My thanks to Jim Benford, Greg Matloff and Al Jackson for invaluable references and commentary.