Extreme Airy rings

[Keith Lofstrom]

Early versions of SBSP assumed a simple, uniform power
transmitter disk (with appropriate phasing) focused on a
rectenna that captures the central power lobe and the first
Airy ring, confining the second and third Airy rings within
a keepout fence, and ignoring the other rings.

Sadly, the world's troubles begin beyond the rectenna fence.

After learning how to compute the J1 Bessel function,
I computed 2000 more Airy rings - the outer rings perhaps
wider than the Earth, down in the nW/m². Assuming
centerline power is 230 W/m², the 25th ring is more than
1mW/m², and the 265th Airy ring is greater than 1μW/m².

A 300K black body is 4pW/GHz of noise. Good room-
temperature receivers are 20pW/GHz of noise. Cryo
temperature receivers for radio astronomy are much
better than that.

We plan to have MANY powersats up there, and the distant
Airy rings of all those will overlap and make interference
patterns. Sometimes the amplitudes of many SSPS will
overlap constructively, producing power spikes many times
the sum of the averages.

The SSPS themselves will move a bit, in and out and
sideways; while the beam will be (hopefully) nailed to the
rectenna, the rings will shift radially as the SSPS moves
inwards and outwards. Multiple SSPS interference patterns
will add/cancel rapidly as different SSPS follow different
orbits. Beyond the rectenna, and the "focus" (ahem) of
our attention, chaos may ensue.

The interference patterns will be very dynamic, possibly
modulating at kilohertz rates if many SSPS move
significantly in relation to each other over the course
of their 24 hour /almost/ circular orbits. Those orbits
are perturbed by lunar and solar tidal effects, and the
spherical harmonics (Legendre functions) of the Earth's
imperfect gravitational field, which tends to make GEOsats
"roll downhill" towards a couple of stable longitudes.

Most importantly, the above assumes a uniform grid of
radiators at the SSPS transmit antenna, In Real Life,
some of the transmit elements will fail, and all will have
engineering tolerances for position, planarity, and power
level. Those variations cause "Strehl scatter", like the
tiny imperfections of a telescope mirror.

Harmonics, synthesis jitter, Imperfect orientation,
self-shielding, mechanical vibration, tidal effects on
the transmission surface, and many imperfections make
the Airy disk assumption too optimistic regards off-axis
interference power. An erroneous assumption that pervades
our work is a belief that a larger transmit disk requires
a smaller rectenna, when in fact the projected "image"
from a larger transmit disk can be "shaped" to produce a
same-sized top-hat rectenna image, but with more uniform
illumination and a steeper dropoff at the edges. Just as
a larger camera lens has more degrees of freedom, which
can be optimized for many different image qualities, not
just a single-point focus.

To better quantify these effects with an improved computer
model, it would help to develop an approximate "strawman"
model for the transmitter panel on the SSPS, and an array
of approximate orbital positions, so the interference and
interactions can be simulated and quantified.

After I am provided with a "canonical" SSPS specification,
both in shape (and no, I can't do complex shapes), and for
for orientation and position variation, I will clean up
my C code and share it with the list.

Warning, my spaghetti C is barfogenic; please read with an
empty stomach, or a painter's tarp over your keyboard. :-)

Keith L.

P.S.: years ago, my friend Dana W. was onsite radio engineer
for the Arecibo radio observatory. I frequently swap emails
with him. If some rich folk have money to burn, perhaps they
can purchase the broken antenna and radio infrastructure,
and repurpose it for SBSP transmit or rectenna experiments.

P.P.S.: Other wealthy friends have a villa in Caguas,
Puerto Rico. They care about sailing, not SBSP or radio
astronomy, but they might have fun measuring radio signals
in the middle of the Caribbean or the Pacific, with no
onboard electrical noise sources besides the measurement
equipment itself. In Caguas, they live minutes away from
La Casa de los Tornillos, "the house of screws", a fastener
and hardware store with an outdoor counter and stools for
tinkering. Not relevant to SBSP, but very relevant to
the hardware nerd culture SBSP (and we) emerged from.

--
Keith Lofstrom kei...@keithl.com

[Keith Henson]

On Sun, Jan 8, 2023 at 3:26 PM Keith Lofstrom <kei...@kl-ic.com> wrote:
>
> Early versions of SBSP assumed a simple, uniform power
> transmitter disk (with appropriate phasing) focused on a
> rectenna that captures the central power lobe and the first
> Airy ring, confining the second and third Airy rings within
> a keepout fence, and ignoring the other rings.

My vague memory of this was that the transmitter profile was Gaussian.
Sure enough, down at the bottom of page 29 here:

https://web.archive.org/web/20180715064419/http://space.nss.org/media/SSP-DOE-1978-space-solar-power-Reference-System-Report.pdf

"The lO-decibel Gaussian taper has the best overall performance of the
optimized illumination functions after considering the maximum power
density constraints in the transmit array and rectenna."

That might help. As I recall it put more power on the rectenna and
less outside.

KeithH
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[Roger Arnold]

I'm sure there was literature around that time that posited an untapered transmitter aperture with a "top hat" profile. But as Keith H "vaguely recalled" -- and then confirmed -- the transmitter aperture for Boeing's reference design was tapered. It was a truncated gaussian profile, with the cutoff 10 db down from the peak. 

One of the things I did when I was kibbitzing on the design was to write a simple Basic program to compute the beam profile from the aperture profile. A true Gaussian profile is impossible to implement; it tapers to infinity. The 10 db cutoff that the SPS team went with was a practical compromise. The abrupt transition from finite to zero at the edge of the transmitter put a significant amount of energy into the far field, but only 1% as much as abrupt transition from full power to zero would have. I wanted to see if I could improve on that with a profile that tapered more smoothly to zero at the edge. I took the FFT of a square wave, threw away the high frequency components, took the inverse FFT of that, and truncated the inverse FFT at its first null. The result, as I recall, was good, but not noticeably better than the truncated Gaussian profile that the SPS team had used.

To view this discussion on the web visit https://groups.google.com/d/msgid/power-satellite-economics/CAPiwVB6Xo6ePh%3DuY1KQBwfwiHt4bmNACnBPRufjNK_USyM%2BJQA%40mail.gmail.com.

[James M. (Mike) Snead]

My thanks to Keith for this information. It highlights the serious engineering work that remains to achieve acceptable operational SSP system designs and associated safety considerations.

This also highlights to me why a substantial human spacefaring presence will be needed both during development as well as during construction and operation. Thousands of platforms will need to be properly maintained and operated to remain within established safety parameters. This will not happen by only sitting at a desk on the Earth.

It would be nice to have an informative, well-illustrated video discussing this information so that it is better understandable by non-electrical engineers.

This shows why we now need a pro-SSP technical organization to identify and focus on such considerations.

Mike Snead