### Interstellar ramjet

The Bussard ramjet is a theoretical method of spacecraft propulsion proposed in 1960 by the physicist Robert W. Bussard, popularized by Poul Anderson's novel Tau Zero, Larry Niven in his Known Space series of books, Vernor Vinge in his Zones of Thought series, and referred to by Carl Sagan in the television series and book Cosmos.

Bussard proposed a ramjet variant of a fusion rocket capable of reasonable interstellar spaceflight, using enormous electromagnetic fields (ranging from kilometers to many thousands of kilometers in diameter) as a ram scoop to collect and compress hydrogen from the interstellar medium. High speeds force the reactive mass into a progressively constricted magnetic field, compressing it until thermonuclear fusion occurs. The magnetic field then directs the energy as rocket exhaust opposite to the intended direction of travel, thereby accelerating the vessel.

## Design discussion

A major problem with using rocket propulsion to reach the velocities required for interstellar flight is the enormous amounts of fuel required. Since that fuel must itself be accelerated, this results in an approximately exponential increase in mass as a function of velocity change at non-relativistic speeds, tending to infinity as it approaches the speed of light. In principle, the Bussard ramjet avoids this problem by not carrying fuel with it. An ideal ramjet design could in principle accelerate indefinitely until its mechanism failed. Ignoring drag, a ship driven by such an engine could theoretically accelerate arbitrarily close to the speed of light, and would be a very effective interstellar spacecraft. In practice, since the force of drag produced by collecting the interstellar medium increases approximately as its speed squared at non-relativistic speeds and tends to infinity as it approaches the speed of light (taking all measurements from the ship's perspective), any such ramjet would have a limiting speed where the drag equals thrust. To produce positive thrust, the fusion reactor must be capable of producing fusion while still giving the incident ions a net rearward acceleration (relative to the ship).

An object's velocity can be calculated by summing over time the acceleration supplied (ignoring the effects of special relativity, which would quickly become significant at useful interstellar accelerations). If a ramjet could accelerate at 10 m/s2, slightly more than one Earth gravity, it would attain 77% of light velocity within a year.[1] However, if the ramjet has an average acceleration of 0.1 m/s2, then it needs 100 years to go as fast, and so on.

The top speed of a ramjet-driven spaceship depends on five things:

1. The rate at which mass is collected from space by the ion scoop.
2. The ramjet's exhaust velocity, and the net thrust level obtained from the exhaust jet. The generated thrust can be calculated as the mass of ions expelled per second multiplied by the ramjet exhaust velocity (Ve), adjusted for relativistic effects.
3. The drag produced by collecting the interstellar medium, which will be a function of velocity.
4. The thrust to mass ratio of the ramjet, which is: A = thrust divided mass (N/kg = m/s2) adjusted for relativistic effects.
5. How long the ramjet is actually able to remain under thrust before it breaks down.

The collected propellant can be used as reaction mass in a plasma rocket engine, ion rocket engine, or even in an antimatter-matter annihilation powered rocket engine. Interstellar space contains an average of 10−21 kg of mass per cubic meter of space, primarily in the form of non-ionized and ionized hydrogen, with smaller amounts of helium, and no significant amounts of other gases. This means that the ramjet scoop must sweep 1021 cubic meters of space (approximately the volume of the Earth) to collect one kilogram of hydrogen.

A large energy source adds more mass to the ramjet system, and this makes it harder to accelerate. Therefore, the specific power, (A) of the ramjet's energy source is crucial. The specific power A is the number of joules of energy the starship's reactor generates per kilogram of its mass. This depends on the ramjet fuel's energy density, and on the specific design of the ramjet's nuclear power reactors.

The obvious fuel source, the one proposed by Bussard, is fusion of hydrogen, the most common component of interstellar gas. Unfortunately, the proton-proton fusion rate is close to zero for this purpose: protons in the Sun on average survive for a billion years or more before reacting. Accordingly, an interstellar ramjet would have to be powered by other nuclear reactions, but the required isotopes are rare in the interstellar medium. A fusion reactor used to power a ramjet starship might be a steady state magnetic fusion reactor based on the following nuclear fusion reactions. 2H + 2H → 3He + 1n0 + 4 MeV, or 2H + 3H4He + 1n0 + 17.8 MeV.

This problem was solved, in principle, according to Dr. Bussard by use of the stellar CNO cycle in which carbon is used as a catalyst to burn hydrogen via the strong nuclear reaction.[2] This cycle occurs in the sun (<4%) and is dominant in higher mass stars. The power improvement over the slow PPI chain is by a factor of 1016.

Bussard ramjet designs that use the collected hydrogen only as reaction mass are sometimes referred to as ram-augmented interplanetary or interstellar rockets (RAIR)[1] to distinguish them from the designs that use the collected hydrogen as fuel.

The mass of the ion ram scoop must be minimized on an interstellar ramjet. The size of the scoop is large enough that the scoop cannot be solid. This is best accomplished by using an electromagnetic field, or alternatively using an electrostatic field to build the ion ram scoop. Such an ion scoop will use electromagnetic funnels, or electrostatic fields to collect ionized hydrogen gas from space for use as propellant by ramjet propulsion systems (since much of the hydrogen is not ionized, some versions of a scoop propose ionizing the hydrogen, perhaps with a laser, ahead of the ship.) An electric field can electrostatically attract the positive ions, and thus draw them inside a ramjet engine. The electromagnetic funnel would bend the ions into helical spirals around the magnetic field lines to scoop up the ions via the starship's motion through space. Ionized particles moving in spirals produce an energy loss, and hence drag; the scoop must be designed to both minimize the circular motion of the particles and simultaneously maximize the collection. Likewise, if the hydrogen is heated during collection, thermal radiation will represent an energy loss, and hence also drag; so an effective scoop must collect and compress the hydrogen without significant heating. A magnetohydrodynamic generator drawing power from the exhaust could power the scoop.

The collection-radius of such an ionic ramscoop is the distance from the ramjet at which the ramscoop's electric field is greater than the galactic electric field of 1.6×10−19 V/m, or the ramscoop's electromagnetic field is greater than the natural galactic magnetic field of 0.1 nanotesla (1×10−6 gauss). The strength of the ramscoop collection field would decline proportionately to 1/d3 in distance from the ramscoop generator.

## Feasibility

Since the time of Bussard's original proposal, it has been discovered that the region surrounding the sun has a much lower density of interstellar hydrogen than was believed at that time (see Local Interstellar Cloud). T. A. Heppenheimer analyzed Bussard's original suggestion of fusing protons, but found the bremsstrahlung losses from compressing protons to fusion densities was greater than the power that could be produced by a factor of about 1 billion, thus indicating that the proposed version of the Bussard ramjet was infeasible.[3] However Daniel P. Whitmire's 1975 analysis[2] indicates that a ramjet may achieve net power via the CNO cycle, which produces fusion at a much higher rate (~1016 times higher) than the proton-proton chain.

Robert Zubrin and Dana Andrews analyzed one hypothetical version of the Bussard ramscoop and ramjet design in 1985. They determined that their version of the ramjet would be unable to accelerate into the solar wind. However, in their calculations they assumed that:

1. The exhaust velocity of their interplanetary ion propulsion ramjet could not exceed 100,000 m/s (100 km/s);
2. The largest available energy source could be a 500 kilowatt nuclear fission reactor.

In the Zubrin/Andrews interplanetary ramjet design, they calculated that the drag force d/dt(mv1) equals the mass of the scooped ions collected per second multiplied by the velocity of the scooped ions within the solar system relative to the ramscoop. The velocity of the (scooped) collected ions from the solar wind was assumed to be 500,000 m/s.

The exhaust velocity of the ions when expelled by the ramjet was assumed not to exceed 100,000 m/s. The thrust of the ramjet d/dt(mv2) was equal to the mass of ions expelled per second multiplied by 100,000 meters per second. In the Zubrin/Andrews design of 1985, this resulted in the condition that d/dt(mv1) > d/dt(mv2). This condition resulted in the drag force exceeding the thrust of the hypothetical ramjet in the Zubrin/Andrews version of the design.

Consider also the case of a vessel leaving a star system, or heading to the outer planets. In this case, the force produced by the solar wind is beneficial. Since the values for drag are based on relative velocity, using the scoop as a form of electromagnetic sail will provide additional thrust as long as the vessel is traveling at less than 500,000 m/s away from a star. While interstellar matter is relatively scarce, this abundance of high-energy ions in the neighborhood of stars has potential for initial acceleration and braking on arrival.

The key condition that determines whether or not an interstellar ramjet will accelerate forward in the direction of its thrust is that the thrust of the ramjet must exceed drag that results from scooping up ions from space. Or, as discussed above, the condition d/dt(mv2) > d/dt(mv1) must be true.

• d/dt(mv1) is the drag force experienced by the ramjet during its actual operation; d/dt(mv1) is the mass of collected propellant per unit time times the velocity of the scooped ions relative to the ramjet starship.
• d/dt(mv2) is the thrust produced by the ramjet; d/dt(mv2) is the mass of the collected ramjet propellant per unit time multiplied by the exhaust velocity at which it is expelled from the Ramjet engine to generate thrust.

### Example

For example, a ramjet might collect 1 gram of incoming ions per second from interstellar space beyond the heliopause, at a velocity of 50 km/s relative to the ramjet driven spacecraft. In this case d/dt(mv1) is (0.001 kg/s) (50,000 m/s), yielding a drag force of 50 newtons.

If the gram of ions is then accelerated to 500,000 m/s then d/dt(mv2) is (0.001 kg/s) (500,000 m/s) = 500 N.

Therefore, -50 newtons + 500 newtons yields a net force forward of 450 newtons.

The typical velocity of the solar wind within the solar system is 500 km/s. The typical velocity of the interstellar wind is 50 km/s beyond the heliopause. In the solar system, if the exhaust velocity of the ramjet exceeds 500 km/s there will be a net thrust that will accelerate the ramjet. Figures here assume the spacecraft is traveling towards the sun (since the solar wind is directional), under the worst conditions for thrust.

If the example were set in the solar system, the drag force, d/dt(mv1), would be about (0.001 kg/s) (500,000 m/s), or 500 newton.

If the exhaust velocity of the ramjet were 1,000,000 m/s then d/dt(mv2) = (0.001 kg/s) (1,000,000 m/s) = 1000 N of thrust, and -500 newtons + 1000 newtons = net thrust of 500 newtons to accelerate the ramjet forward.

If the Zubrin/Andrews assumption were correct then d/dt(mv1) = 500 N, and d/dt(mv2) = 100 N, and the drag forces would exceed the thrust of the ramjet. Under those conditions, the ramjet would likely only function along vectors perpendicular to the solar wind.

## Related inventions

### Magnetic sail

The calculations (by Robert Zubrin and an associate) inspired the idea of a magnetic parachute or sail. This could be important for interstellar travel because it means that deceleration at the destination can be performed with a magnetic parachute rather than a rocket.

### Electrostatic ion scoop

One possible modification of the ramjet design is to use an electrostatic ion scoop, instead of an electromagnetic ion scoop to achieve the ion collection from space. In an electrostatic scoop a negative electric field on a forward grid electrostatically attracts the positive charged ions present in interstellar space and thus draws them into the ramjet engines. This can be a 100% electrostatic scoop in which an electromagnetic field is not used at all. There will be no converging electromagnetic field lines that can potentially generate drag effects by scooping the ions from interstellar space if this pure electrostatic approach is used. The scooped ions will however have an electric field-induced velocity when they are drawn inside of the ion ramjet engine. So long as the velocity of the ramjet engine exhaust jet is greater than the electric field-induced velocity of the incoming scooped ions there can be a net force in the direction of the ramjet's flight that will accelerate the spacecraft.

Furthermore, the net potential difference of the galactic electric field in interstellar space is only 1.6×10−19 volt. The effective ion collection radius of an electrostatic ion ram scoop will be the range at which the ramscoop electric field has a greater potential difference from the galactic electric field. This potential difference declines proportionately to 1/d² for distance d from the source of the ram scoop electric field.

### Pre-seeded trajectory

Several of the obvious technical difficulties with the Bussard Ramjet can be overcome by prelaunching fuel along the spacecraft's trajectory[4] using something like a magnetic rail-gun.

The advantages of this system include

• Pre-launching only ionized fusion fuel so that either magnetic or electrostatic scoops can more easily funnel the fuel into the engine. The drawback is this will cause the fuel to disperse due to electrostatic repulsion.
• Pre-launching the fuel on a trajectory so that the fuel velocity vector will closely match the expected velocity vector of the spacecraft at that point in its trajectory. This will minimize the "drag" forces generated by the collection of fuel.
• Pre-launching optimized isotope ratios for the fusion engines on the spacecraft. A conventional Bussard ramjet will mostly collect hydrogen with an atomic weight of 1. This isotope is harder to fuse than either the deuterium or tritium isotopes of hydrogen. By launching the ideal ratio of hydrogen isotopes for the fusion engine in the spacecraft one can optimize the performance of the fusion engine.
• Although the pre-launching fuel for the ramjet negates one advantage of the Bussard design (collection of fuel as it moves through the interstellar medium) it retains the advantage of not having to accelerate the mass of the fuel and the mass of the rocket at the same time.
• The prelaunched fuel would provide some visibility into the interstellar medium – thus alerting the trailing spacecraft of unseen hazards (e.g. brown dwarf stars).

The major disadvantages of this system include:

• The spacecraft could not deviate from the precalculated trajectory unless it was critical to do so. Any such deviation would separate the spacecraft from its fuel supply and leave it with only a minimal ability to return to its original trajectory.
• Pre-launched fuel for deceleration at the destination star would not be available unless launched many decades in advance of the spacecraft launch. However, other systems (such as the Magnetic sails) could be used for this purpose.
• It would be very difficult to perform a round-trip with this system unless materials and time are allocated to building another fuel launch mechanism at the destination star.

## References

• The original paper is : Robert Bussard, “Galactic Matter and Interstellar Flight,” Astronautica Acta Vol. 6 (1960), pp. 179–94