Lightsails: Safe Passage After All?

by Paul Gilster on April 16, 2012

Despite my best intentions, I still haven’t put my hands on the exchange between Robert Forward and Ian Crawford on lightsails that ran back in 1986 in JBIS, nor have I managed to come up with the source of the ‘lightsail on arrival’ illustration I mentioned last week. This was the one showing a battered and torn sail docked in what I assume was a repair facility at the end of its long journey, and the effects of passage through the interstellar medium were all too obvious. It was a great image and I was frustrated about not being able to find the magazine it was published in, but an email from James Early quickly changed my mood.

As opposed to the missing image that nagged at my memory, this was a case of having missed something perfectly obvious in the first place. I didn’t know about the paper Jim did with Richard London on lightsails and the interstellar medium — it was published in the Journal of Spacecraft and Rockets back in 2000, but somehow I didn’t find it in the research for my Centauri Dreams book back then. It’s a welcome addition to the literature, one Jim went on to present to the 100 Year Starship Symposium in Orlando last fall. Jim tells me the presentation tracks the earlier paper, and I’ll draw today from the more recent paper as we look at lightsail concepts.

Defining the Sail

Although Robert Forward came up with sail ideas that pushed as high as 30 percent of the speed of light (and in the case of Starwisp, even higher), Early and London are content with 0.1 c, which provides technical challenges aplenty but at least diminishes the enormous energy costs of still faster missions, and certainly mitigates the problem of damage from dust and gas along the way. Lightsails will be slow to accelerate, given that the light absorbed by the sail creates a thermal limit on the maximum laser power usable. In short, we can’t heat the sail beyond a certain point, and that gives us a maximum acceleration, so our sail may take a tenth of a light year to get up to cruise velocity. It’s noteworthy that the sail does not have to be deployed during cruise itself, but deceleration at the target star, depending on the methods used, may demand redeployment.

Geoffrey Landis’ work on the different types of sails that are feasible seems to be the standard. Landis divides sails into three broad categories:

  • Extremely thin, low-density metal sails. Forward proposed using aluminum in his paper on a round-trip mission to Epsilon Eridani, but beryllium seems to be the material of choice.
  • Heat-resistant thin metal sails made from niobium or tantalum. These offer higher temperatures and power densities.
  • Dielectric thin films at one-quarter wavelength thickness for the laser light. Dielectric materials are poor conductors of electricity but can support electrostatic fields, as in a capacitor. These materials offer excellent reflectivity, requiring thicker sails, but the materials make for low absorption and offer good thermal performance, so higher accelerations are possible.

Early and London use beryllium sails as their reference point, these being the best characterized design at this stage of sail study, and assume a sail 20 nm thick.

The Sail and the Medium

In terms of the interstellar medium the sail will encounter, the authors say this:

Local interstellar dust properties can be estimated from dust impact rates on spacecraft in the outer solar system and by dust interaction with starlight. The mean particle masses seen by the Galileo and Ulysses spacecraft were 2×10-12 and 1×10-12g, respectively. A 10-12g dust grain has a diameter of approximately 1 µm. The median grain size is smaller because the mean is dominated by larger grains. The Ulysses saw a mass density of 7.5×10-27g cm-3. A sail accelerating over a distance of 0.1 light years would encounter 700 dust grains/cm2 at this density. The surface of any vehicle that traveled 10 light years would encounter 700 dust grains/mm2. If a significant fraction of the particle energy is deposited in the impacted surface in either case, the result would be catastrophic.

The question then becomes, just how much of the particle’s energy will be deposited on the sail? The unknowns are all too obvious, but the paper adds that neither of the Voyagers saw dust grains larger than 1 μm at distances beyond 50 AU, while a 1999 study on interstellar dust grain distributions found a flat distribution from 10-14 to 10-12 g with some grains as large as 10-11 g. Noting that a 10-12 dust grain has a diameter of about 1-μm, the authors use a 1-μm diameter grain for their impact calculations.

The results are intriguing because they show little damage to the sail. Catastrophe averted:

At the high velocities of interstellar travel, dust grains and atoms of interstellar gas will pass through thin foils with very little loss of energy. There will be negligible damage from collisions between the nuclei of atoms. In the case of dust particles, most of the damage will be due to heating of the electrons in the thin foil. Even this damage will be limited to an area approximately the size of the dust particle due to the extremely fast, one-dimensional ambipolar diffusion explosion of the heated section of the foil. The total fraction of the sail surface damaged by dust collisions will be negligible.

The torn and battered lightsail in its dock, as seen in my remembered illustration, may then be unlikely, depending on cruise speed and, of course, on the local medium it passes through. Sail materials also turn out to offer excellent shielding for the critical payload behind the sail:

Interstellar vehicles require protection from impacts by dust and interstellar gas on the deep structures of the vehicle. The deployment of a thin foil in front of the vehicle provides a low mass, effective system for conversion of dust grains or neutral gas atoms into free electrons and ions. These charged particles can then be easily deflected away from the vehicle with electrostatic shields.

And because the topic has come up recently in discussions here, let me add this bit about interstellar gas and its effects on the lightsail:

The mass density of interstellar gas is approximately one hundred times that of interstellar dust particles though this ratio varies significantly in different regions of space. The impact of this gas on interstellar vehicles can cause local material damage and generate more penetrating photon radiation. If this gas is ionized, it can be easily deflected before it strikes the vehicle’s surface. Any neutral atom striking even the thin foil discussed in this paper will pass through the foil and emerge as an ion and free electron. Electrostatic or magnetic shields can then deflect these charged particles away from the vehicle.

Ramifications for Sail Design

All of these findings have a bearing on the kind of sail we use. The thin beryllium sail appears effective as a shield for the payload, with a high melting point and, the authors conclude, the ability to be increased in thickness if necessary without increasing the area damaged by dust grains. Ultra-thin foils of tantalum or niobium offer higher temperature possibilities, allowing us to increase the laser power applied to the sail and thus the acceleration. But Early and London believe that the higher atomic mass of these sails would make them more susceptible to damage. Even so, “…the level of damage to thin laser lightsails appears to be quite small; therefore the design of these sails should not be strongly influenced by dust collision concerns.”

The third type of sail, the thicker dielectric sail, is more problematic, suffering more damage from heated dust grains because of its greater thickness, and the authors argue that these sail materials need to be subjected to a more complete analysis of the blast wave dynamics they will be subjected to. All in all, though, velocities of 0.1 c yield little damage to a thin beryllium sail, and thin shields of similar materials can ionize dust as well as neutral interstellar gas atoms, allowing the ions to be deflected and the interstellar vehicle protected.

These are encouraging results, but the size of the problem is daunting, and I keep coming back to something Jean Schneider said in the exchange with Ian Crawford discussed here last Friday:

“The question is what probability of collision is acceptable. If a collision is lethal, this probability must be extremely close to zero for a several hundred billion € mission.”

The original paper on this work is Early, J.T., and London, R.A., “Dust Grain Damage to Interstellar Laser-Pushed Lightsail,” Journal of Spacecraft and Rockets, July-Aug. 2000, Vol. 37, No. 4, pp. 526-531. JBIS is planning to publish selected papers from the 100 Year Starship Symposium and I assume this is one of them. When this revised paper runs, I’ll post the complete citation.

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Eniac April 16, 2012 at 11:13

The impact of this gas on interstellar vehicles can cause local material damage and generate more penetrating photon radiation.

How much damage? A micrometer thick sail will be “in tatters” after an interstellar trip if each gas atom knocks out just a single sail atom. Is it being claimed that a 10-100 MeV proton going through a thin foil will normally not displace even a single atom? This seems too good to be true to me. I would like to see it explicitly claimed and supported with a physical argument of some sort.

Michael April 16, 2012 at 12:38

When the dust has vapourised itself and the sail the ionised gases may now be available to push the sail forward as they can now interact much better with the laser pointed at it, in effect it may be useful. Further a very small hole will have very little effect so long as it is of a certain size to the light wavelength pushing it. Think of a microwave oven door.

Jim Early April 16, 2012 at 18:27

Eniac, think of this as a traditional Rutherford scattering experiment (he used alpha particles and gold foils). At 0.1c a proton is about 5 Mev. It only interacts weakly with the charges in the foil, and this weak interaction of multiple small angle scatterings leads to the electron heating discussed in the paper. Only collisions with a nucleus results in large angle scattering. If we assume a cross-section of one barn (10-24 cm2), then the chance of scattering while going through a 20nm foil is 10-7. After traveling 10 ly only 10-5 of the foil atoms have been impacted.

Joy April 16, 2012 at 18:52

The great thing about light sails, is that post IKAROS, we can now consider the technology to have been demonstrated, at least in a primitive form. Concerns about the fate of sails accelerated to significant fractions of c by space based terawatt lasers are remote at this point, as we have not even experimented with space based communications lasers.

Sails, IMO, are the answer to the burning question, What if self financing space industrialization is not possible, what could humanity accomplish with an energy budget stalled near the current value?

Light sails, not laser driven, but unfurled after a close solar pass, could enable slow interstellar passages, with the light sail also used for deceleration at the destination. In this case the sails would be furled during the cruise phase and erosion is not a problem. Designing cybernetic systems and biological systems for cruises of thousands of years is not a trivial challenge, but at least this approach is not demanding of exorbitant energy and resources from the starfaring culture.

Here’s hoping that Japan’s >200% public debt/GDP ratio and post disaster economic calamity doesn’t interfere with launching the follow on to IKAROS.

Rob Henry April 16, 2012 at 22:14

Jim, Rutherford’s experiment might have shown that protons and alpha particles have a very low cross-sectional area, and relativistic collisions might be good at striping electrons, but to my mind it is the combination that is troubling. Are we to believe that neutral particles are striped of their electrons so rapidly that they have no time for even one initial interaction and by such gentle process as to not result in the displacement of even a single sail atom?

Christopher Phoenix April 16, 2012 at 23:06

@Joy

Sails, IMO, are the answer to the burning question, What if self financing space industrialization is not possible, what could humanity accomplish with an energy budget stalled near the current value?

Not much. When you think about the things humans and aliens are capable of in science fiction, you realize that with enough energy, we could do many of those things. Do you want to accelerate a starship to a significant fraction of C? With a dauntingly large amount of energy, this is possible. Do you want pocket-sized ray-guns? With a battery capable of storing a couple dozen megajoules, you could create lethal pocket heat-rays. Do you want to build space cities? If you can obtain the energy and resources needed to build and maintain the city, it is possible.

If energy budgets don’t rise at all, there will be no space development at all. Even solar sail starships are highly unlikely in such a future, as solar sail starships imply a space based infrastructure capable of constructing massive lightsails and self-sustaining habitats. If you can build all this, why not a solar power satellite? Why not a million solar power satellites built by self-replicating machines with the intelligence of insects? Next thing you know, a Kardashev Type-2 society has sprung up. Either humans go forward to become an interstellar civilization that has harnessed the power of stars, or we fall back and eventually disappear.

I have a question for the engineer types around here- how do you suggest I should portray a lightsail in art? As I understand it, such a sail must be very, very large in relation to its payload. Would the payload even be visible if the whole sail is seen? I’ve seen some illustrations of lightsails that show such a tiny lightsail attached to such a massive spaceship the thing would probably accelerate at an inch per second per century, and I certainly don’t want to make that error. Any ideas?

Eniac April 17, 2012 at 9:25

Jim & Rob, Rutherford scattering does not usually take recoil into account. What we need to know is the cross-section for a proton that will provide more than a few eV of energy to the sail atom. Not sure how to do that. Anyone seen it done?

Jim Early April 17, 2012 at 10:03

Rob, There will be two types of interaction. The proton hitting a nucleus is a strong interaction involving short range forces and results in large angle scattering. The short range or small cross-section for these reactions make them very rare but non-zero. So about 10 out of a million foil atoms will be scattered out of the foil by these gas collisions during the 10 ly voyage. There will be far more long range, weaker electrostatic interactions between the charged particles. The electrons in a dust particle were heated to 1. kev, far above their ionization potential. Similarly the single electron in a hydrogen atom will be gently bumped by many long range collisions until it has an energy far above its ionization energy. The passage of the electron and proton of the hydrogen atom will also heat some electrons in the foil. However this energy should quickly be spread among many more electrons and likely doesn’t lead to long term damage. There will likely be some optical/xray radiation generated as well as general heating as a result of this electron heating.

ljk April 17, 2012 at 10:47

Christopher – Rick Sternbach has created a number of memorable pieces of artwork of various starships, including sails.

Start with this page and scroll down, then check out his other examples here:

http://www.ricksternbach.com/spaceart.html

Alex Tolley April 17, 2012 at 11:00

@ C Phoenix

The POV could be close to the payload looking out on to the more distant sail.
Essentially the same type of POV if you want to depict human scale against a landscape or other megastructure, such as a city.

Ron S April 17, 2012 at 11:20

Christopher: “…how do you suggest I should portray a lightsail in art? As I understand it, such a sail must be very, very large in relation to its payload. Would the payload even be visible if the whole sail is seen?”

I’m no artist but I have a few ideas. First, it’s a matter of perspective. If the payload is indeed small in size (or, really, in mass) relative to the sail, all you need to do is get in close. Near to the center payload you have the opportunity to show details of the payload (actual spacecraft) and the hub of the sail super-structure. The sail itself will seem to be a vast artificial field that stretched from horizon to horizon.

Another possibly interesting perspective is from the outer edge of the sail.

You could extend the payload somewhat so that there is even some living space or machinery structure integrated with the “spokes” that support the sail segments.

If the payload is sufficiently high in mass, you can show a 3D tensional structure such as an axial member and an array of stays (like a sail on a ship) that maintains the sail’s integrity and shape.

I’m sure there are other ideas.

Rob Henry April 17, 2012 at 16:46

Thanks Jim, I actually had no idea that Rutherford’s experiment demonstrated strong interactions directly, rather than electromagnetic repulsion by a unit that was merely held together by strong interactions. But if that is the case, my back-of-the-envelope calculations indicate that you are using the wrong model. Wikipedia puts strong interactions starting around 3 femtometres, and 2 protons would need to approach each other with an order of magnitude more kinetic energy than they have here to get that close, let alone a proton and heavier nucleus.

Also Eniac has a frightening point in that these experiments are not generally designed to detect each case where a nucleus speeding through a high tensile chemical imparts just a few eV on a neighbour, which is all it would take to disrupt bonding locally. That could have huge long-term consequences

I would feel much happier if these assertions over sail endurance were backed directly by relevant experimentation.

Rob Henry April 17, 2012 at 16:53

Bother and sorry Jim, I misread your earlier post. Forget the first paragraph of my last post.

Jim Early April 17, 2012 at 17:57

The nice thing about this problem is that it can be experimentally demonstrated in a rather modest physics lab. All one needs is a few cm2 of thin foils, a 3kev electron beam, a 5Mev proton beam (ok, not such a small lab), and a short pulse (ps) laser. The electron and proton beams should be able to simulate the total gas exposure for a 10 ly trip in a reasonable time. When a dust particle passed through a foil at 0.1c, it heats the electrons in 0.03ps and leaves the nuclei cold. That is also what a short pulse laser does. One can then experimentally observe the resulting damage to the foil. One will not have the same momentum transfer, but the heating is effectively identicle.

Peterh April 17, 2012 at 19:27

A laser driving a light sale is sure to have some spill around the edges of the sail. What effect would this have on dust and gas in the ship’s path? How much less would the ship likely encounter on account of the laser sweeping ahead?

Christopher Phoenix April 19, 2012 at 2:20

@Alex Tolley & Ron S

Thanks for the ideas!! I had been thinking along those lines as well- if the sail is big, I must show how big the sail is. A relatively small ship in the center of a vast, blindly bright “field” of incredibly thin material is an interesting idea…. hmmm.. must try that sometime. A three-dimension structure of glittering, diamondoid cables holding vast reflective sails in shape would be quite interesting.

Focusing on the payload and leaving the sail in the background is a great idea. That approach would work with the Sark 1 interstellar ark, since the sail forms a “parachute” in front of the actual starship habitat. Sark-1 offers some interesting opportunities for showing the craft making its close pass to Sol or decelerating near an alien sun.

If I try a laser-pushed lightsail, I will show the star of origin being colored by the color of the laser instead appealing to artistic license and showing the beam glowing in the vacuum of space.

ljk, thanks for the link- indeed, Rick Sternbach made some fine images. I especially like the sailing to Mars one- he showed the small scale of the payload and the large size of the sails by showing one ship’s habitat in the foreground and another ship’s sail the background.

Eniac April 19, 2012 at 8:04

Jim: Sure, it would be nice to do the experiment in an accelerator, but it would be much easier to determine the cross section for atom dislocation theoretically, and no more than Rutherford math would be required.

You sound like you have done or seen it, but you do not give specifics. So let me give it a try (pulls out tattered envelope and starts scribbling on back):

From Rutherford we have the relation between the deflection angle theta and the impact parameter b given as:

theta = 2 arctan ( Z1 Z2 e^2 / 4pi eps0 m v^2 b)

which reduces for small angles and the situation here to

theta = Z e^2 / 4 pi eps0 E b.

Z is the atomic numbers of the sail nuclei, e the elementary charge and E the energy of the incoming proton (say: E ~ 5 MeV).

We are looking for the impact parameter which will result in a few eV transferred to the stationary nucleus, which is roughly 10^-6 of the energy of the incoming proton. From conservation of momentum, the nucleus will be pushed to the side with a velocity of m_n v_n = theta m_p v, yielding an energy of E_n = m_n v_n^2 = theta^2 (m_p/m_n) E .

Thus, the solution we seek is the impact parameter that makes theta^2 (m_p/m_n) ~10^-6, and we get this as follows:

theta0 = 10^-3 sqrt(m_n/m_p) For carbon: theta0 ~ 3*10^-3

b = Z e^2 / 4 pi eps0 E theta0 ~ Z * 0.1 nm (for E = 5 MeV)

So, for carbon, I get an impact parameter of 0.6 nm, which is dangerously close to the interatomic distance. This would mean any foil would be dispersed long before it could travel even a small fraction of a lightyear. The 5 MeV I have assumed correspond to less than 0.1 c, if I am not mistaken. Obviously, this does not agree with your work by several orders of magnitude, so most likely I have made a mistake. Perhaps you could show your numbers and we can track down together where the difference lies?

Paul D. April 19, 2012 at 12:15

A resonant plasma sail may be much more resistant to damage than a sail made of some solid material.

The idea here would be to confine ions in a magnetic container. The ions would be chosen to have a spectral line at which they have a very high scattering cross section. Singly ionized alkali earth elements may be suitable. A laser tuned (after doppler shift) to this resonance would prodice photons that would be scattered off the ions.

This has a number of advantages: (1) resonant scattering cross sections can be enormous, even after thermal broadening, (2) the sail is already vaporized and ionized, so its can tolerate a great deal of heating, (3) if the laser is tuned slightly off resonance, it can actually cool the plasma.

The sail would scatter photons at a variety of angles, so it wouldn’t produce as much thrust as a classical reflective sail. Also, the confinement time of the ions would have to be long enough and losses to scattering off interstellar gas low enough.

Eniac April 21, 2012 at 15:04

All in all, though, velocities of 0.1 c yield little damage to a thin beryllium sail, and thin shields of similar materials can ionize dust as well as neutral interstellar gas atoms, allowing the ions to be deflected and the interstellar vehicle protected.

If the cross-section for interstellar gas erosion is anywhere like I have estimated, serious doubt must be cast on this statement. Has anyone had further thoughts?

Eniac April 24, 2012 at 23:22

Is the answer to the title question then, “No”, after all? It looks like Jim Early has gone elsewhere. I would think if he had seen a flaw in my calculation he would have commented on it. Any way we could ask him, Paul?

The most concrete he has gotten here on the question is “If we assume a cross-section of one barn”, which is not much, and it does not seem to agree with he Rutherford scattering math I showed. Perhaps the 2000 paper has more? is there a link?

Paul Gilster April 25, 2012 at 8:23

Eniac, I’ve written to Jim and we may get an answer shortly.

Florian Marquardt January 1, 2013 at 15:32

Eniac,

with regard to your calculation from April 19, 2012:

You estimated the critical impact parameter b for a proton to deposit about an electron Volt of energy into a nucleus of the sail while zipping through the sail and being deflected slightly via the Coulomb force. Here is the formula you used (and with which I agree, at least as an estimate):

b = Z e^2 / 4 pi eps0 E theta0

However, if I simply insert numbers into this formula, I do not get your numerical estimate

b~ Z * 0.1 nm (for E = 5 MeV)

but rather [with theta0=3e-3, as you assumed]:

b~ Z * 10^-13 m

which is a thousand times smaller than your estimate. This would greatly change things, because the fraction of protons hitting the nucleus within that distance would then correspondingly decrease by a factor of a million.

Any thoughts? Did I misunderstand something?

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