# Re: Problems with beaming

```Hi Timothy,

Sorry this has taken so long, but work before pleasure...

I did not mean to stir up such a hornet's nest with my comments (not
objections) but I will try to respond as best I may. Rex has already
addressed several of the issues you questioned, and I think Steve had some
input too. Plase forgive me if I am redundant.

At 08:58 PM 4/6/96 +0100, you wrote:

>Yes, but lasers keep a tight beam and thus their diametre (cross-section)
>does not increase with distance and the energy-density (per surface) stays
>the same.
>So I don't see a problem here.

No lasers, do not keep a tight beam, only compared to incoherent light can
the laser beam (or maser) be described as tight. While I will admit that the
inverse square rule primarily applies to SUNLIGHT, there is still some
attenuation even with a laser. I don't have the equations or the figures to
give an exact or even estimated amount. All I can do is assure you that
across 10 to 11 light years, you will lose a SIGNIFICANT amount of your
initial power. This is an inherent design limitation of the MARS plan. I was
simply trying to wake somebody up to make them examine more closely a point
I felt they had missed. (It seems to have worked.)

My point was that ALL of the currently stated plans have design limitations,
many or most of which are being ignored in our enthusiasm.

>The criterion of Rayleigh states that two wavelengths l and l+dl are just
>resolved in the n-th spectral order when the maximum of one spectral-line
>falls upon the first minimum of the other.
>I don't see what resolvement has to do with beaming power, could you explain
>what I missed?
>(What formula did you use?)

RAYLEIGH'S CRITERIA:

Where
theta=diffraction limited beam convergence angle
r=separation between light source, S, and sail
ds=sail diameter

The beam of radiation just fills the sail, thus minimizing energy that
bypasses the sail. For a diffraction limited radiation source
(monochromatic) and theta a small angle, Rayleigh's Criterion that
determines the required diameter of the radiation transmitter is:

sin(theta)~theta=1.22*lambda/d

where lambda is the radiation wavelength and d is the diameter of the
optical system that collimates the beam. The larger the transmitter and the
smaller the wavelength, the sharper the beam collimation. But for
interstellar distances, by geometry:

sin(theta)~theta=ds/2r

Therefore,

ds/2r=1.22*lambda/d.

The distance at which the beam will just fill the sail is then:

r=ds*d/2.44*lambda

If radiation is not to be wasted in "bypass" as the sail travels away from
the radiation transmitter, either the sail must unfurl (expand) with time,
the transmitter must grow in aperture, or both must be large enough at the
outset to be good for all ranges during the mission.

Okay, now that the math is out of the way, what does it all mean?

Simply put, the problem is not the same one every one has been discussing here.
FIRST, the beam WILL NOT be wider than the sail for any practical mission
and to do so is WASTEFUL.

SECOND, for reasons previously discussed, the power requirements for beamed
propulsion are EXORBITANT so lets not be wasting any energy in "bypass".

THIRD, there is an absolute upper limit at which beamed propulsion becomes
unfeasible due to the required aperture size. I think every one would agree
that a 400 km aperture is impressive even with phased array technology, that
being the aperture required for yellow light (a solar pumped laser) and a
mission to TC.

Note that a maser would require a larger aperture or array than the yellow
light laser, so this discussion applies equally to both pure solar sails,
laser driven sails, and the MARS design.

'Lest I be thought overly pessimistic, I don't believe ANY of these
limitations are insuperable. I think that given current technology we could
do this. Given known and expected advances, I am sure we could do this.
However, this also applies to each of the other currently proposed methods.

Lee Parker

P.S. Rex, do you happen to have a formula for the attenuation of power in a
laser? With your previous associations with SDI I hope you might. I can't
seem to find ANYTHING in my references.
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+  Weave a circle 'round him thrice, and close your eyes with holy dread...   +
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