Classifying Starships

One way to classify starships is by the sources they use for energy and momentum.  Does the vessel generate energy internally, or does is it supplied after launch or extracted from the environment?  Does the vessel carry its own reaction mass?  This table illustrates different approaches that illustrate different answers to these questions.

Approach	Energy Source	Reaction mass	Example[s]
I/I	Internal	Internal	Classical rocket; Project Orion.
E/E	External	External	Bussard Ramjet using fusion of ISM to accelerate remnants of drive gas away; beamed power used to accelerate ISM
E/I	External	Internal	Energy beamed to vessel is used to accelerate on-board reaction mass to relativistic velocities
I/E	Internal	External	Internal power source (antimatter?) used to accelerate ISM reaction mass to relativistic velocities.
E/mixed	Internal	E/acceleration,I/deceleration	Beamed light pressure on sails to accelerate. To decelerate break into two mirrors and first bounces light back to second slowing it down.

All of these approaches look like they could be feasible (for our somewhat warped view of feasibility) and in future posts we may contemplate the technologies that would favor one over the other. There is some balancing between carrying the energy supply/reaction mass versus the mechanisms to acquire these from the environment or from Earth-based transmissions.

Feasibility of magnetic field

In our last post we found that we need to generate fields of the order of 1.5 x 10^-6 Tesla to move particles around the way we want to. Is this feasible? Let's consider a simple wire loop with a 1 mm² cross-section and in a 200 km radius circle. The volume of material in such a loop would be 1^-6m² x π x 400x10³ m = 1 m³. For unit density the mass is just a ton. For the best current superconductors that critical current density is 10³ to 10⁴ A/mm². Superconducitivity should be easy to achieve since we can run at just a few Kelvin. So let's say we can run 3000 A in the loop. This page let's us plug in the radius and current values and indicates that the resultant magnetic field at the center of the loop will be about 10^-8Tesla. So we're not quite there. If we use 150 coils we get our desired magnetic field at the cost of 150 tons of mass. This is a significant fraction of our mass budget, but not out of line with what we might expect for a major element of the propulsion system. It seems feasible to generate the magnetic fields we want without pushing current technologies too hard.

So we can generate the scale magnetic fields we need to collect the interstellar medium for fuel or reaction mass. Actually designing such a system is a very different thing. Of course we can only affect the ionized component of the medium. The neutral fraction will be unaffected by magnetic or electric fields. Our location in the Local Bubble is fortunate since it means that we can control most of the matter we will pass through.

One implication might be that travel through different regions on the Galaxy may require very different mechanisms with journey's through regions dominated by neutral matter using an entirely different approach than where the ISM is mostly ionized.

Moving matter

A few posts ago we noted that if we want to use the interstellar medium, then to get a mass comparable to our ship we'll need to excavate a tube roughly 200 km in diameter during our voyage. Presumably we'll need to move material from the outside of that cone to some central structure. A physical funnel would be far too heavy, so we'll need to use electric and magnetic fields. Can we do this with reasonable values for these fields?

Our vessel is moving through space and needs to move material 200 km from the edge of our tube to our processing facility in the center. How long do we have to do that? The ship is moving past the interstellar medium at some velocity V_ship in the range from 0 to about 0.2 c. Let's characterize the length of the ship, including the apparatus we have to move the matter by some length L_ship. This is likely comparable to the width. If so we have about

    Δt = Lship/vship

to move. If we look at accelerations we need to get

    1/2 a Δt2 = Lship (where we are assuming the width and length of the ship are comparable).

So

    1/2 a (Lship/vship)2 == Lship

Or

    a = 2 vship2 / Lship

The material we want to move are the protons of ionized hydrogen. Their acceleration in a magnetic field is given by

    a = q/m v X B

where q and m are the charge and mass of the proton and v and B are the vector values of the particle velocity and the magnetic field. Here we're only interested in the magnitudes we can just write this as

    a = q/m vshipB

where we've assumed that the nearly relativistic velocity of the ship is much larger than the thermal or bulk motions of the ISM. [For a 10⁶ Kelvin ISM, the thermal velocity of the protons is just a bit over 100 km/s.] Even for a medium at a temperature of 10⁶ K, this should be true except at the very beginning and end of the trip.

We can use these two equations to get an estimate our our needed magnetic field.

    2 vship2 / Lship = q/m vshipB

or

   B = m/q vship / Lship

In MKS units the ratio m/q is about 10^-8. If we pick 0.1c as our average velocity and 200 km for the size we get

   B = 10-8 3x107 / 2x105 Tesla = 1.5x10-6 T.

The response to the electric field depends upon the gradient of that field, but we need to impart an acceleration on protons sufficient to get them moving as fast as the ship. That means the electric field must impart about 1/2 mv² energy in the particles within L. But if v_ship is about 0.1c that implies that we need to impart about 1/2 m(.1c)² or about 1/200 of the mass energy of the proton. Protons have the same charge as electrons (apart from the sign) so we need to give protons a kick of 1/200 of their mass which is about 10⁹GeV. Here an electron volt is just the energy that a particular with the charge of an electron gains across a volts electric field. So we need a 1 GeV/200 or 5 MeV voltage differece between the edge of our tube and the the processing apparatus. That's about 5 megavolts/200,000m or just about 25 volts/m.

Solar Power

If we are looking for where we can find the 1 Terawatt of power we need for our mission, we probably need look no further than the big fusion reactor in the center of the Solar system. The Solar Constant, the power per unit area emitted by the Sun as measured at the Earth's radius is about 1.3 kilowatt per square meter. Equivalently we get better than a Gigawatt per square kilometer, so a fully efficient collector could be as small as a square 30 kilometers on a side.

Of course there's no reason why we need to build the collector at the Earth's orbit: the closer we get to the Sun the smaller we can make it. The linear size of our structure goes down directly with the distance from the Sun. If we go into about Mercury's radius we can only need about 100 square kilometers or a square 10 km on a side.

So we need only very modest structures to collect solar power and since it's already in the form of electromagnetic radiation we can build mirrors to concentrate and direct it where we want.

What's in the neighborhood?

The content of the interstellar medium in the solar neighborhood is surprisingly poorly understood. It is thought that the Sun in in a Local Bubble of higher temperature and lower density than elsewhere nearby in the Galaxy. The bubble is the result of supernovae going off in the last few million years, or perhaps recent star formation. One recent article suggests that most of the Local Bubble is filled with about 40,000 m^-3ionized atoms with an admixture of 10,000 m^-3 on non-ionized material. To first order we can just assume that this material is all hydrogen. If so that means each for each square meter of cross-section of our ship we'll have about

    s = D ρ = 1017 x 50,000 m-2 = 5x1021atoms m-2

This isn't very much. A single meter of air has about 10²⁷ atoms, so over the entire journey we'll only run through the equivalent of about 5 microns of atmosphere....

It also seems likely to be a bad assumption that the interstellar medium is uniform on any particular scale. We know of lots of small bubbles with a bit more neutral gas and higher densities, but we should probably be visualizing this as a chaotic environment with lots of fluctuations on all scales.

That lack of intervening matter good news and bad news. Friction won't be much of a problem: if our cross section of the main ship is a few hundred meters we're not goring to run into more than a gram or so of matter on the way. If we are hoping to use interstellar material for fuel or reaction mass we need to look over a large area. E.g., how large an area do we need to collect over to get a mass comparable to our ship. One gram of hydrogen is about 6 x 10²³ atoms and our ship masses 1000 tons or a billion grams. So the area we need to collect over is

    A = 6x1032 / 5x1021 = 1011 m2 = 105km2

If we collect in an area of a circle then

    π r2 = 105km2

So we need to collect all of the material within a radius of about 200 km of the center of the ship. Here the fact that most of the matter is ionized could be a big help. In principle at least, we can use magnetic fields to interact with the medium and move it around.

Power with a push

A couple of posts ago we noted that we'd probably need something on the order of 1 Terawatt of power to accelerate the ship. If we get beam this power from the solar system, e.g., using masers or lasers we'll get a bit of momentum with it as well. If we just absorb the power then the force on the ship is

    F = P/c

where P is the power of the beam and c is the speed of light. For 1 Terawatt we get

    F = 1012 / 3x108 Newtons = 3000 Newtons

This about 1% of the total force needed to accelerate our vessel. So if we just ramp up the power a bit we can push our ship this way. We get an extra factor of two if we reflect the incoming beam rather than absorbing it.

However while this works nicely accelerating our ship, without a comparable beam at our destination it won't work to slow down. So for an established interstellar pathway this might be something to consider, but it's not going to do the trick for exploration. We can use the beam to speed up, but we'll need something else to slow down.

One approach here is to have sent a dummy mirror out in front of our vessel simply to reflect the beam back. The dummy mirror needs a mass comparable to the vessel and thus doubles all of the energy requirements, but we might be able to use it as a probe to explore a further star system since it will end up travelling at a good fraction of c.

How much force?

A couple of posts ago we calculated that the constant acceleration mission would have an acceleration of about 0.04 m s^-2.  If our vessel is wholly payload then this means that we need a force of only about 0.04 x 10⁶ newtons to push the spacecraft.  This is a total of 2.4x10⁵ newtons.  This is comparable to the force exerted by a reasonably large elevator.  It's about 0.1% of the force of a Saturn V rocket The long duration of the flight means that the average force required is quite modest.  Of course if we have a large fuel supply to carry along, the force needed goes up with it. We may also choose a mission profile with much higher accelerations during early and late phases of the mission to minimize the velocity needed.