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

```At 11:57 PM 10/30/96, DotarSojat@aol.com wrote:
>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.

I read that as about 10,000,000 kilometers, or 32 light secounds.  Not a
lot of slack over interstellar distences.  A sligh sail problem could have
you well out of that pretty quickly.

>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.

Hum, I would have expected interfearence and lensing to have a greater
effect then that.  This is good news.

>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.

Probably true.  The problem is in the budget not the tech.  ;)

>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
>
>   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.)

We had, long ago, been discusing small automated scout craft to be sent
ahead of the main ship to look for debries and stuff.  They could also
scout out the beam boarders and report to the main ship.  Being smaller
they could have a better sail to weight ratio, which would make them less
vulnerable to low power levels at the fringe.

>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

A thermal engine processing e18th of power?  <gulp>

Good work up Rex.  We might want to pull a lot of this stuff into a web
page for the site.

Kelly

----------------------------------------------------------------------
Kelly Starks                    Phone: (219) 429-7066    Fax: (219) 429-6859
Sr. Systems Engineer                                     Mail Stop: 10-39
Hughes defense Communications
1010 Production Road, Fort Wayne, IN 46808-4106
Email:  kgstar@most.fw.hac.com
----------------------------------------------------------------------

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