Interstellar propulsion by self-focusing radio beams

[Thorondor]

TL;DR: Filament propagation isn't just limited to visible light waves in dense media.  The same physics applies to much lower-frequency radio waves in low density plasma.  So if we point a very powerful radio transmitter at the interstellar medium, the radio waves should self-focus and propagate over very long, possibly interstellar distances.  This effect can be used to propel a spacecraft to near the speed of light.

I imagine many of you here have probably heard of laser filamentation.  Normally, a laser beam diverges as it propagates through space.  For example, you cannot mark a spot on the Moon with a laser pointer.  But when the laser beam becomes sufficiently intense, and it has a medium to propagate in (even air will work), that's no longer true.  Now, the beam remains tightly confined or even becomes tighter as it travels.  This is a nonlinear optical effect known as the Kerr effect.  It occurs because the refractive index of a medium is not constant, but can be affected by a powerful light wave.

It turns out that strong electromagnetic waves can also change the refractive index of a plasma in other ways.  One mechanism is based on the ponderomotive force.  If a laser beam is stronger in the center than at the edges, then electrons get pushed towards the edges of the beam.  That changes the refractive index of the plasma in the center of the beam, causing the beam to focus more tightly.

But the beam doesn't have to be a laser!  Although filament propagation has only ever been observed in intense laser beams in dense plasmas, there's nothing in the physics that requires the beam to be any particular frequency, as long as it's an electromagnetic wave.  Thus, exactly the same physics should apply to much lower-frequency waves in much less dense plasmas.

That brings us to radio waves in the interstellar medium.

Following various papers on laser filament propagation e.g. Akhmanov et al. http://iopscience.iop.org/article/10.1070/PU1968v010n05ABEH005849/meta, Sharma et al. https://aip.scitation.org/doi/pdf/10.1063/1.1605102, we can calculate the critical condition for ponderomotive self-focusing of a Gaussian beam as

r^2 = (c^2 / omega_p^2) * (e^p0 / p0)

where r is the beam radius, c is the speed of light, omega_p is the plasma frequency, and p0 is

p0 = 3/4 * e^2 * E^2 / (6 * kB * T * omega^2 * m_electron)

where e is the electron charge, E is the electric field, kB*T is the plasma temperature, omega is the wave frequency.

All right, let's plug in some numbers, shall we?  In the interstellar medium, T is about 7000 K and the electron density is about 0.05 cm^-3.  Source: http://adsabs.harvard.edu/abs/1997A%26A...324.1105L.  That gives a plasma frequency of about omega_p = 13 kHz.  If we choose omega = 1 MHz and E = 5 V/m, p0 works out to 0.91: https://www.wolframalpha.com/input?i=3%2F4+*+%285+V%2Fm%29%5E2+*+%28electron+charge%29%5E2+%2F+%286+*+Boltzmann+constant+*+7000+K+*+%281+MHz%29%5E2+*+electron+mass%29.  Then the critical radius is about 39 km, giving a total beam power somewhere in the range of 150 MW.

If that's all correct (and it sounds pretty math-y, so it must be right), then we can build a 150 MW radio amplifier, connect it to a suitable antenna, and the beam will self-focus in the interstellar medium.  That's cool, but what could we do with one of these?  Well, consider what happens if we put a large grid of superconducting wires in the path of the beam.  The wires will reflect the radio waves.  Reflection means radiation pressure.  The grid will behave as an enormous, very low-density light sail.  Riding a relatively narrow beam that continuously focuses itself, there would be little to stop the sail from accelerating to near the speed of light.

There are of course a few details that should be addressed.  By the standards of interstellar propulsion proposals, the engineering for the spacecraft would be relatively "straightforward."  A large 150 MW vacuum tube oscillator powered by solar panels, connected to a suitable dish or phased array antenna, would work for the transmitter.  The spacecraft itself would consist mostly of a grid of superconducting wire spaced out by some fraction of the beam wavelength.  For the beam physics, a quick back-of-the-envelope calculation suggests that losses due to collisional damping would be small even over light-year scales.  The directional stability of the beam against variations in plasma density or magnetic field is a concern that needs further consideration, though it's at least somewhat reassuring that filament propagation has been tested in Earth's atmosphere over 70 Rayleigh lengths with the beam profile remaining very steady.  https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.011006.

Overall, what do you think?  Does this seem like a viable idea?

[Phil Stooke]

We'll let you know when you've got it working.

[daedalus1]

What? Interstellar medium is a hard vacuum,  it won't focus any electromagnetic waves.

[Durham Park]

Something vaguely like this has been proposed before but it supplied it's own focusing medium and used lasers.
I've not heard anything about it for a while which is a shame as it was one of the most innovative interstellar propulsion ideas I'd heard of for a while. Most of these techniques make use of ultrafast pulsed lasers whose electric fields are a lot stronger than radio (strong enough to rip electrons off of atoms).

https://ldpdl.engr.tamu.edu/combined-laser-and-particle-beams-for-self-guided-beamed-propulsion/

https://www.nasa.gov/directorates/spacetech/niac/2018_Phase_I_Phase_II/PROCSIMA/

https://www.centauri-dreams.org/2018/04/04/procsima-wedding-two-beam-concepts/

https://www.centauri-dreams.org/2018/04/05/tightening-the-beam-correspondence-on-procsima/

[Thorondor]

What? Interstellar medium is a hard vacuum,  it won't focus any electromagnetic waves.

The interstellar medium is very close to a hard vacuum, but not actually a vacuum.  In our neighborhood, it contains about 10^5 particles, many of them charged, per cubic meter.  That means it is able to interact with electromagnetic waves if the frequency is low enough that the wavelength is a few orders of magnitude larger than the distance between particles.  Like any plasma, it reflects waves below the plasma frequency (which is extremely low due to the low density).  Above the plasma frequency, it no longer reflects waves, but it still has some refractive properties (increasingly weak at higher frequencies) which is what I'm trying to take advantage of here.

[InterestedEngineer]

Cool idea, worth pursuing.  Thanks for the math.

I see one problem:  You have to exit the solar system.  The particle density in the solar system is 10x that of interstellar medium.  What does the maths say about that?

Then you encounter the heliopause, which may distort the filament.  Then beyond the heliopause you get the interstellar densities.

What happens when a filament transits different mediums?

[Thorondor]

Cool idea, worth pursuing.  Thanks for the math.

I see one problem:  You have to exit the solar system.  The particle density in the solar system is 10x that of interstellar medium.  What does the maths say about that?

Then you encounter the heliopause, which may distort the filament.  Then beyond the heliopause you get the interstellar densities.

What happens when a filament transits different mediums?

Good question.  To answer it, we can calculate whether a beam with the same power will self-focus in both plasma regimes, the solar system and the interstellar medium.  Although there is actually a steady gradient of plasma parameters as we travel farther away from the Sun inside the solar system, I will approximate and consider only the solar wind near Earth and the interstellar medium.  I'll use 5 electrons/cm^-3 for the solar wind plasma density near Earth (3 to 10 cm^-3 is given at https://umbra.nascom.nasa.gov/spartan/the_solar_wind.html#:~:text=At%20the%20orbit%20of%20the,of%20approximately%20400%20km%2Fs.).  That gives a plasma frequency of omega_p = 130 kHz (https://www.wolframalpha.com/input?i=sqrt%285+cm%5E-3+*+%28electron+charge%29%5E2+%2F+%28electron+mass+*+epsilon_0%29%29).  That makes sense; the plasma frequency is proportional to the square root of the electron density and the density I just used is roughly 100x greater than the density in the interstellar medium.

The plasma frequency is inversely proportional to the beam radius.  So a higher frequency near Earth means that the beam must be more tightly concentrated here than in the interstellar medium.  That implies a higher field strength E, which factors into p0.  As the beam crosses from one regime to the other, the total beam power is the same; therefore since the power density is proportional to E^2, E^2 will be inversely proportional to the area of the beam which is proportional to r^2.  That tends to increase p0.  On the other hand, the temperature T is also much higher near Earth, which tends to decrease p0.  The solar wind is very non-Maxwellian but as an estimate, I'll model the plasma near Earth as having an effective electron temperature of about 10eV (https://www.pnas.org/doi/10.1073/pnas.1917905117).

So if I start off the beam with E = 25 V/m, then with the assumptions above, p0 = 1.37 and the critical radius r = 4 km.  150 MW is more power than we need to achieve self-focusing in these conditions, so our initial transmit beam will be larger than the critical radius (or we can squeeze more power into a smaller beam by using a higher field strength).  As the beam propagates into regions of space with lower plasma density and temperature, it will spread out a bit and become wider.  But it should remain within the self-focusing regime.

[InterestedEngineer]

  As the beam propagates into regions of space with lower plasma density and temperature, it will spread out a bit and become wider.  But it should remain within the self-focusing regime.

Good, because it's a non-starter if the entire path from near the Sun to past the heliopause can't remain in the self-focusing regime.

How close to the Sun can you get before it no longer self-focuses?  That matters for the power generation aspects - the closer to the Sun, the more efficient solar arrays are.

[daedalus1]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

[laszlo]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

Sounds as if the system needs the equivalent of an assistant cameraman - the guy who keeps the camera focused and the aperture set while the cameraman concentrates on the framing and composition.

[InterestedEngineer]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

Look up how fiber optics work.  Same idea, but the medium isn't specially doped plastic fiber, but the sparse plasma present in space.

[daedalus1]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

Look up how fiber optics work.  Same idea, but the medium isn't specially doped plastic fiber, but the sparse plasma present in space.

I don't see how that's the same analogy.  Fibre optic wall is a fixed cylinder,  but the interstellar plasma is dispersed.

[InterestedEngineer]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

Look up how fiber optics work.  Same idea, but the medium isn't specially doped plastic fiber, but the sparse plasma present in space.

I don't see how that's the same analogy.  Fibre optic wall is a fixed cylinder,  but the interstellar plasma is dispersed.

the heating of the plasma by the radio waves creates its own cylinder.

Maybe think like lightning.

[Asteroza]

Normally something focuses to a fixed point. How does that work with an accelerating starship?

Look up how fiber optics work.  Same idea, but the medium isn't specially doped plastic fiber, but the sparse plasma present in space.

I don't see how that's the same analogy.  Fibre optic wall is a fixed cylinder,  but the interstellar plasma is dispersed.

the heating of the plasma by the radio waves creates its own cylinder.

Maybe think like lightning.

Wait, like those electrolaser setups, but instead of a laser making a plasma tunnel to send an electric charge, doing the reverse?

[daedalus1]

Lighting is definitely not a good analogy it does not go in anywhere near a straight line.

[endlesslimitation]

This is interesting. Really interesting. If it holds up, then this is the holy grail for interstellar travel. And it SOUNDS good. I agree it reminds me a bit of the dual particle photon beam idea (https://ldpdl.engr.tamu.edu/combined-laser-and-particle-beams-for-self-guided-beamed-propulsion/) but I think that previous idea would ultimately still diverge because both the particle and light beams have divergence. In this idea you get around that by dispensing with the particle beam in favor of the ambient medium.

[endlesslimitation]

The one thing I'm wondering about: if you increase the power then the radius increases right? So as you add power you have to add mass to the system in the form of your reflector. Given the areal mass density of your proposed reflector (the superconducting wire mesh) what kind of acceleration could you get for that 150 MW? 

[InterestedEngineer]

The one thing I'm wondering about: if you increase the power then the radius increases right? So as you add power you have to add mass to the system in the form of your reflector. Given the areal mass density of your proposed reflector (the superconducting wire mesh) what kind of acceleration could you get for that 150 MW?

the 150MW is good for a tiny probe.

Solar sailing gives about 125W/uN, so you'll get 1.2N, though that's highly optimistic given the lower frequency of radio waves vs. solar light.

let's say it's 1N.   With a 10,000kg probe (mostly the sail, and at 35km that's highly optimistic), that's an acceleration of 1e-4.

Over a year that will give you 3000m/sec.   not particularly exciting.   It'll take 100 years to get to 1%C.

Somehow need to use that 150MW to do something besides get photon momentum.  Perhaps capturing interstellar matter and accelerating it with the 150MW.

[endlesslimitation]

A basic question: for self focusing to occur does the beam need to have a radius greater than, equal to, or less than the critical radius?

[endlesslimitation]

Over a year that will give you 3000m/sec.   not particularly exciting.   It'll take 100 years to get to 1%C.

But if the acceleration can be sustained at essentially arbitrary distances it's still pretty exciting - only a few generations of exponential growth to total galactic domination!