What's the range on a laser, in terms of how far away is the beam still fairly narrow if it doesn't hit anything? Function of the geometry of the emitter?
Line of thought is that aiming a 100GW laser at a small piece of silicon probably makes it very hot, so periodically hitting very small probes with laser from far away could be a power supply as well as propulsion. If you can still hit the things from far away enough.
Making the probes very light is a convincing answer to the problem of accelerating masses to speeds useful for interstellar flight and we can get quite a lot of machinery in a piece of silicon.
It's vaguely plausible that a chip could absorb energy from a far away laser emitter, store some of it, do some arithmetic, emit energy from something like LEDs positioned on the surface and use that to fine tune position or communicate with other chips in the swarm. Can imagine that working well enough for science fiction, might be implementable in reality.
For a Gaussian laser beam, a good metric is the Rayleigh distance, which is the distance where the beam diverges to sqrt(2) of it's initial beam size (waist) [1].
It is proportional to the square of the beam waist and inversely proportional to the wavelength.
For a 1m beam at a 1um wavelength, that is about 3e6m or 3000km.
Therefore larger beam diameters and longer wavelengths reduces divergence.
There's also other beam shapes that are "non-diffracting" which can maintain their original beam profile over an initial distance, such as a Bessel beam [2].
I don't believe that Bessel beam is a workaround for the diffraction limit in the far-field. That diffraction limit is a universal law for any optical system with a finite-size aperture (i.e. the size of the focusing mirror array). To the extent you're approximating a Bessel beam in the real, physical world, we're still stuck with finite apertures, so it's the same law.
I agree. It would depend on the definition of "far-field" in this example, even for a quasi-Bessel beam there is a near region that maybe useful for this example given a large enough aperture.
This paper [1] demonstrates the reduced power loss of a Bessel beam compared to a Gaussian for various target distances. For targeting GEO, a Bessel beam can be 75% the size of a Gaussian for the same halving of power-loss.
In reality, I think a Gaussian beam is fine - and much simpler to engineer.
Thanks for the link. What I'm getting is we think emitting light that doesn't spread out over distance can be done with unbounded power, thus we can probably aspire to make ones that cross greater distances by spending more power on the creation and a degree of inventing new materials. Sound about right to you?
I think for the any initial project, we'll have to resort to 1km scale laser arrays. These would allow for a beam with a low dispersion so there can be a good initial acceleration.
After a few hundred AU, the probes should be close to the target velocity
On a whim I looked up whether magnets or electric fields can refract light, and while they generally can't, strong electric charges can:
Edit: there's probably no way to make an electric field strong enough on the macro scale to bend light, unless it passes by a black hole or magnetar, because the radius of the bending grows by 2nd power of charge but shrinks by the 4th power of distance from charge. But I'll leave my work here in case anyone is curious.
Equation 48:
delta y = -E*(a^2)*(Q^2)
-----------------
80*pi*(m^4)*(b^4)
E = 1 for parallel or (7/4)^2 for perpendicular?
a = 137.036 (fine structure constant)
m = 9.11e-31? (mass of electron? mass equivalent of electric field by E=mc^2?)
Q = quantity of charge in coulombs
b = smallest distance of light from point charge, or radius of light cone
Unfortunately the math is not written well IMHO, and it doesn't have any numeric examples, so the reader is forced to understand the entire paper before drawing conclusions.
It's conceivable that a strong charge placed millions of kilometers away could bend the laser light into a column again, although it might have to have an electric field close to the strength of an atom's, or 10^21 V/m. The breakdown voltage of space is 3x10^6 V/m, so it might require a black hole or high power to concentrate enough charge in one place, for example by using a ring of electron guns aimed at their center to simulate a focussed point charge.
But the bending is towards the charge and grows by Q^2, while falling by b^4. If m is the mass of the electron, then it's all multiplied by about 10^128, which suggests that a small charge would cause a large bend. Or if it's the mass equivalent, then a 1eV field might have an equivalent mass of (1.6x10-19 J)/(c^2) which is about 1/(10^36) or a multiplier of 10^144 ! But that doesn't sound right, so maybe someone can clarify it for us?
Edit: found another paper for calculating the bending angle of light in a nonuniform electric field (like near a point charge):
As an example, for Z = 100, b = 10*lambda*e we get the bending angle theta = 3.4 × 10−8 radian for an x-ray of wavelength 5*lambda*e.
Probably a larger "impact parameter b, over which distance the bending occurs mostly" requires a proportionately larger electric field or point charge.
Edit: another paper calculating the bending of light in nonuniform electric fields near black holes:
Equation 18:
delta y = -(E)(a^2)*(Q^2)*(lambda^4)
--------------------------
640*pi*e0*hbar*c*(b^4)
E = 8 for parallel or 14 for perpendicular (substituted E for a to not conflict with alpha a)?
a = -1 (doesn't say, but uses -1 in other examples)
Q = quantity of charge in coulombs
lambda = 2.426e−12 = hbar/mc = the Compton length of the electron
e0 = 9e9 = permitivity of free space
hbar = 1.055e-34 = reduced Planck's constant
c = 3e8 = speed of light
b = smallest distance of light from point charge, or radius of light cone
It grows by ((Q^2)*(lambda^4))/((e0*hbar*c)*(b^4))
The top lambda^4 term works out to 10^-48 but the bottom e0*hbar\*c term works out to about 2.85e-16 so the formula only works for very small bend distance b.
Line of thought is that aiming a 100GW laser at a small piece of silicon probably makes it very hot, so periodically hitting very small probes with laser from far away could be a power supply as well as propulsion. If you can still hit the things from far away enough.
Making the probes very light is a convincing answer to the problem of accelerating masses to speeds useful for interstellar flight and we can get quite a lot of machinery in a piece of silicon.
It's vaguely plausible that a chip could absorb energy from a far away laser emitter, store some of it, do some arithmetic, emit energy from something like LEDs positioned on the surface and use that to fine tune position or communicate with other chips in the swarm. Can imagine that working well enough for science fiction, might be implementable in reality.