# starship-design: Beam properties, control, etc.

```Hi all

On 10/24, Kelly wrote:

>Questions:
>How much range deviation can you tolerate?  Since the beam is
>being aimed at a ship you can't see in real time.  You'ld have to
>expect it would drift ahead or behind the exact focus spot.  How
>much slack is allowed?
>
>What is the lateral deviation of the beam?  I.E. whats the power
>per m^2 in the center vs the edge of the focused spot?  The diff-
>erences would distort the sail and alter the ships course and
>acceleration.
>
>As mentioned above, how precicely can we measure the possition of
>an object floating in space?  Assuming each microwave emmiter
>platform has laser ranging info to each/some of the others.  Can
>you get the nessisary possitional accuracy?  (Within a couple
>MM?)  Note you don't need to control the position that accurate-
>ly, just know what it is so you can compensate for it.

On 10/24, Zenon wrote:

>However, if the platform moves along the Sun-centered orbit, its
>velocity is of the order of tens of kilometers a second..., hence
>it must compensate for its change of position with appropriate
>change of orientation, and the latter must be VERY accurate...

On 10/26, Timothy wrote:

>I'd rather turn things around, not let the emitter follows the
>ship, but let the ship follows the emitted beam.
>The beaming station makes a "focussed" (as far as interference
>allows) an beams it straight forward (in the direction of Tau
>Ceti.)
>In this case not the velocity of the orbiting station is impor-
>tant, but it's acceleration (to the center of gravity), which is
>rather low. Low enough for the starship to compensate and change
>its direction.

On 10/28, Zenon wrote:

>That is, the ship must go along the helical curve with the radius
>equal the radius of the beaming station orbit (assuming the plane
>of the orbit is perpendicular to the direction of Tau Ceti), or
>along a sinusoid with amplitude equal to the diameter of the
>orbit (assuming the direction to Tau Ceti lies within the plane
>of the orbit).
>
>...
>
>However, I wonder if the jiggle of the direction of the beam due
>to "directional noise" can be compensated in this way...

On 10/28, Timothy wrote:

>What if
> lambda = 500 nm = 5E-7 m, (Blueish green)
> R = 10 ly = 9.46E16 m
> Ds = 300 km = 3E5 m
>...
>300 and 385 kilometer diameters don't seem like a headache...

In recapitulation, questions/observations above address issues of
1. Depth of focus
2. Power distribution in beam spot
3. Antenna figure sensing/control
4. Pointing control
a. Direction: to ship or to destination
b. Orbital motion of antenna platform
c. "Jitter"
5. Sail/ship guidance
6. Effects of reduced wavelength

While I normally prefer to keep my contribution to helping define
the tools available to calculate performance (with some example
results), I may be able to help here with some facts/opinions.

So, in the order itemized above:

1. Depth of focus

Assume the beam from a 2.31E6-km-diameter microwave antenna is
focused to a sail (beam-spot) diameter of 100 km at a distance of
1 lt-yr.  At the distance from the focus that the beam cross-sec-
tion has grown from the area at the focus by 10 percent (power per
unit area reduced by about 10 percent), say, the radius of the
beam has grown by 100 km * [sqrt(1.1) - 1]/2, or about 2.4 km.
The distance from the focus for that growth is (2.4/2.31E6) *
1 lt-yr, or approximately 1E-6 lt-yr.

So, the sail/ship has to stay within about 1.E-6 lt-yr of the
focus to keep the power from dropping off by more than 10 percent.

2. Power distribution in beam spot

If the sail/ship is in the near field of the beam-forming
aperture, then the radial power distribution is given by Fresnel
diffraction: the envelope of the intensity across the spot is
"flat" (the profile is rectangular), with alternating narrow con-
centric rings of dark and light.  As the sail approaches the
boundary to the far field, the radial distribution of intensity
morphs into the approximately-Gaussian profile of the Fraunhofer
diffraction pattern.  I wouldn't want to undertake the calculation
of the actual power distribution at any arbitrary range.  Assuming
it's flat for our purposes is probably adequate.

3. Antenna figure sensing/control

I don't have any detailed information at my fingertips in this
area, but what superficial information I do have indicates that
this problem should not be a show-stopper.  (A lot of work has
been done on phased arrays of both antennas and mirror segments;
some of it pertains to fine beam steering, also.)  I believe this
problem is of far lesser import than achieving the required large
sizes of antennas/mirrors.

4. Pointing compensations
a. Direction: to ship or to destination

I believe Timothy has made the case for pointing the beam at the
destination star quite well.  Let the sail/ship steer to stay in
the beam (see below).

b. Orbital motion of antenna platform

As Timothy calculates in his 10/29 note for a beaming station in
Solar orbit at the distance of the Earth, the maximum lateral
acceleration to follow a helical or sinusoidal interstellar path
of that amplitude and period would be about 6E-4 gs.  This means
that the sail must control its attitude (tilt) through not much
more than about 1E-3 radians to follow the desired path.

c. "Jitter"

One of the losses to be considered in depositing a lethal fluence
from a laser weapon on a target is the effect of fairly-high-fre-
quency, small-amplitude oscillatory motions of the beam axis about
the desired direction, called  "jitter" (Zenon's "jiggles," or
"directional noise").  The frequencies are generally higher than
about 100Hz, and the amplitudes, with today's technology, are less
than a microradian.  This motion is the result of such things as
correction cycles and mechanical vibrations.  This is a random
process that lends itself to averaging.  The intensity at any
point on the spot is given by folding together the beam profile
and a time-average of the deflection vs time of the beam direc-
tion.  On the other hand, with extremely large antenna/mirror
arrays, the frequency may be so low that deflections could be
measured in real time.  These measurements could be introduced as
correction inputs to an electronic fine-pointing-control (element-
phasing) system for the array.

5. Sail/ship guidance

The sail/ship can have outriggers beyond the edge of the sail to
sense the edge of the beam and provide steering-correction inputs
to adjust the tilt of the sail to stay at the radial center of the
beam.

The acceleration of the sail/ship will depend on its distance from
the focus.  (Operating in the near field has some advantages).  A
computer simulation of the sail/ship's motion based on a power
level reduced by a safety factor from that at the focus can be
made to provide a projected safe position of the sail/ship at any
time.

If the focus is placed behind the projected safe position of the
sail/ship during the actual flight, any lag in acceleration of the
sail below the "safe" level will drop it back closer to the focus
where the power is greater.  The higher power there will drive it
forward again toward the safe position, in a stable control
condition at a power level between full (at the focus) and "safe."

(I think I might have described this better if I had first written
the control equation and observed its effects in a simulation.)

6. Effects of reduced wavelength (some already covered by Timothy/
Kelly/Kevin)

While reducing the wavelength of the radiation in the beam to that
of blue-green light allows the required aperture to be reduced
to "only" 385 km, the "antenna" becomes a mirror.  A mirror has
the problem (among others) of maintaining its reflectivity over
long periods in the presence of hazards of the space environment
such as micrometeoroid erosion.

In partial answer to Timothy's question of 10/29 regarding effic-
iency of lasers, I seem to recall efficiencies of about 30
percent, 10 percent and 5 percent for chemical, solid-state and
gas-dynamic lasers, respectively.  (There's nothing in the Grolier
Encyclopedia about the efficiencies of different lasers, except a
mention that CO2 electric lasers have efficiencies in the 15-30
percent range; I don't have any references for any other lasers
than chemical lasers, the favorite of weapons developers.)

Conversion of light energy to electrical energy at any reasonable
efficiency probably involves a thermodynamic cycle.  (Heat engines
are about twice as efficient as the best solar cells.)

Rex

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