Subject: Space-tech Digest #120
Contents:
Magsails (tension, etc) (13 msgs)
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Date: Mon, 27 Apr 1992 04:30 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsails
To: space-tech@cs.cmu.edu
Paul F. Dietz writes:
>
> Gordon suggested coupling energy into the loop inductively...
>
(yes, although what you're proposing is not what I had in mind ...)
>
> This has actually already been tried, with normal materials. A device
> was built at MIT that dumped a massive current pulse into a stationary
> coil. A single turn coil of copper, resting on this, was accelerated
> to 1 km/s in about one centimeter. Melted it, too ...
>
Just to make sure what I had in mind got across correctly: I was proposing
to couple power into the loop *from the spacecraft bus* via a transformer
having a superconducting secondary, through the Josephson-switch equivalent
of a switching full-wave rectifier. This would allow one to ``pump'' current
into the main loop w/out running it through any resistive components, i.e.,
in an (almost) loss-free fashion. I was *not* proposing to supply the main loop
*from the ground*. Nevertheless, it's a neat concept :-) ...
>
> Scaled up, something like this would enable the launcher to
> experience stronger fields, and therefore have weaker currents.
> It could also launch from more convenient locations.
>
Indeed; one could even exploit certain amusing properties of superconductors
in the process.
Let the ground-loop's flux be established while the magsail-loop is *normal*.
Cool the magsail-loop below T_c; the gound-loop's flux linking the magsail-
loop then becomes ``frozen'' --- it can't change. Now: rapidly reverse the
polarity of the ground loop --- preferably via inductive switching to a second
concentric loop of opposite sense, so (almost) no losses occur. Viola!
The magsail springs into the sky!!! 8-D
>But mariners would object when the compasses stopped working. Maybe it could
>be sold as an energy storage device when not being used for launches ...
>
I assume you were being tongue-in-cheek here, and forgot to insert the ":-T."
Nevertheless, just out of curiousity, I've worked out the ratio of magsail-
to-earth's magnetic moments, and they differ by about *eight* orders of
magnitude. Compasses *might* act a little funny around ``Port Bathurst'' ...
but then, they act funny around there *ANYWAY*! ;-). If one really can launch
from somewhere other than the geomagnetic pole using a ground-loop,
*then* they might complain ...
Note, BTW, that a magsail *IS* capable of lifting from places other than
the poles; it's just more complicated, and you get less lift. One needs
to be able to shift the magsail's centre-of-mass away from its ``centre-of-
lift,'' to counterbalance the magnetic torque with a gravity torque.
One needs to be able to do that *anyway*, to balance her on the way up ---
remember: the ``lifting'' configuration is *unstable*, for exactly the same
reason two ``fridge-magnets'' repelling each other are unstable: it's
energetically more favorable for their moments to line up and attract ...
This can be done as Zubrin suggests: by attaching the shrouds via windlasses,
so the cargo-pod can be shifted in the magsail loop-plane, or --- my preferred
approach --- by splitting the loop electrically into (at least) three sectors,
so the ``balancing act'' can be done w/ no moving parts bigger than
Cooper-pairs ... :-T
RE: energy-storage: I suppose one could --- although I don't know how
efficient it'd be ... arrivals and departures might conflict a bit
w/ that role, too ... :-T
> Even more grandiose, one could augment the Earth's magnetic field with
> an equatorial coil. The energy stored in the part of the earth's
> field beyond the atmosphere is only about 30 GW-years (about 200
> megatons TNT), not an impossibly large amount. The coil had better
> be in many segments so that faults didn't cause catastrophe ...
>
If I could build on *that* scale, I'd probably go for a Lofstrom-loop
instead! 8-D O'Course, your proposal may be more ``doable'' w/ current
technology ... ;-)
Gordon D. Pusch
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Date: Mon, 27 Apr 1992 15:32 EDT
From: "GORDON D. PUSCH"
Subject: Magsail tension
To: space-tech@cs.cmu.edu
O.K., I've checked several other references, and everybody seems to agree
on the tension of a single-turn current loop --- even Landau & Lifschitz,
who used exactly the same derivation I did! While it pleases me to be among
such an illustrious company :-T, I am *AMAZED* that such an incredibly
counterintuitive result should have stood for nearly a *century*, w/out
somebody questioning it --- especially since the self-tension of a high-field
magnet is a quantity of such obvious practical importance ...
The only thing I can figure is, L&L mention that this approx to the
inductance is of only *logarithmic* accuracy, i.e., the next term in the
series is proportional to $ 1 / ln( 8 R_m / r_m ) $ (the reciprocal of
the leading log). The log is about 19, so it makes a negligable correction
to the *inductance* ... but it might *not* make a negligable correction to
the *tension* upon differentiation.
Mayhap this problem representeth one of the rare ocassions wherein the
``master'' leadeth himself (and me) down ye olde garden pathe ... :-(
Gordon D. Pusch
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Date: Mon, 27 Apr 92 15:57:13 -0400
From: dietz@cs.rochester.edu
To: PUSCHG@crl.aecl.ca
Subject: Re: Magsail tension
Cc: space-tech@cs.cmu.edu
If you are interested in the tension placed on a conductive loop,
look up the literature on Superconducting Magnetic Energy Storage
loops. They also find the energy stored in a loop of a given
current and cross section goes as R log R. The large stresses
generated are central to the designs, which typically put the
loop down in the bedrock, which takes the stress. Bechtel has done
detailed design studies of a 10 GWh SMES coil. The Japanese
have worked on smaller coils for their Moonlight project, and
SDIO was interested in large SMES coils that, at times of crisis,m
would serve as high power batteries for powering ground based
lasers.
BTW, some interesting recent work on high field magnets has all the stress
taken up by large, outer coils. The inner coils are arranged in such a way
as to make their currents be parallel to the local magnetic field: a force-free
configuration. The outer coils experience lower forces, although the virial
theorem is still satisfied (those outer coils have large volume).
Paul
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Date: Mon, 27 Apr 92 12:01:52 PDT
From: gwh@lurnix.COM (George W Herbert)
To: space-tech@cs.cmu.edu
Subject: Re: Magsail
The _J. Spacecraft_ and another (I believe more recent
J. Propulsion) papers go into a fair amount of detail. The
one cited already is the one that I'm more fammiliar
with, though I don't have a copy on me. I'll try and
grab a copy of it from the UC Berkeley library later
this week, and slowly type it in if people ask nicely 8-)
-george william herbert
gwh@lurnix.com gwh@ocf.berkeley.edu
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Date: Mon, 27 Apr 1992 17:14 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsail
To: gwh@lurnix.COM, space-tech@cs.cmu.edu
X-VMS-To: IN%"gwh@lurnix.COM"
X-VMS-Cc: SPACE-TECH,PUSCHG
Oh, please! Please-please-please-please-please! *pant*pant*pant* *drool* :-)
Seriously, though: my primary area of confusion is how they calculated
their self-tension, and why I get an answer *two orders of magnitude*
off from theirs, using formulas identical to those in classical textbooks.
I'm comfortable with (or at least, not yet worried about :-) everything
else Zubrin states in the _Analog_ article, but *this* aspect is driving
the obsessive-compulsive problem-solver in me up a *WALL* :-(. It'll be
2--4 weeks before our inter-library loan service is likely to cough up copies
of their papers, so I'd be *infinitely* grateful if you could at least
summarize *that* part of their papers. Anything beyond that'd be *gravy* 8-).
Gordon D. Pusch
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Date: Mon, 27 Apr 1992 16:42 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsail tension
To: dietz@cs.rochester.edu, space-tech@cs.cmu.edu
Thanks for the info ... this thing *really* bothers me, though.
My boss is equally puzzled. In the R-goes-to-infinity limit, the Lorentz
force becomes purely radial --- no axial component at all. So where the
heck is the tension *coming* from ??? Granted, this is an unphysical limit
--- the stored energy per unit length goes to infinity, etc. Really, the
whole thing reminds me a lot of the ``self-energy problem'' in clasical
electrodynamics, right down to the logarithmic divergencies. I keep wondering
if there's something fundamentally *wrong* w/the conventional theory of
self-inductance ... :-(
Do you know of any *experimental* verification of the R*log(R) result,
or is this all the result of numerical calculations?
Seems to me, this ``divergent tension'' dispute goes all the way back to
Ampere-Neumann vs. Biot-Savart ... and it hasn't been resolved even yet:
Graneau & Graneau from MIT are *still* managing to get both theoretical
and experimental ``axial Amperian tension'' papers into _Phys. Lett. A_
(in support of their anti-relativity diatribe, no less!!!), interspersed
by a remarkable number of other papers by quite competent physicists which
have either supported or been unable to contradict them ... I do recall
a paper in _Phys. Rev. A_ ca. 1988 claiming to have definitively proved
the equivalence of the Ampere-Neumann and Biot-Savart laws for ideal
current-*filaments*, but I can't remember if it had anything to say about
axial tensions in finite-diameter, *physical* conductors ... :-(
Gordon D. Pusch
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Date: Mon, 27 Apr 92 17:28:24 -0400
From: dietz@cs.rochester.edu
To: space-tech@cs.cmu.edu
Subject: Self-inductance of a coil
According to the AIP Handbook (1972), the self-inductance of
a wire of radius r and relative permeability K_m
bent into a loop of radius a is
L =~ 4 pi a { [1 + r^2 / (8 a^2)] ln (8 a / r)
+ r^2 / (24 a^2)
- 2
+ K_m/4 }
x 10^-7
where r and a are in meters and L is in henries. This formula
is accurate up to a term of order (r/a)^4. The derivative of this
w.r.t. a is:
4 pi { ln (8a/r) - 1 + K_m/4 - (r^2 / 8 a^2) ln (8a/r)
+ r^2 / (12 a^2) } x 10^-7
up to a term of order r^3/a^3. For a ~ 1 cm, r ~ 1 km,
ignoring all but the second term changes the result by less
than 10%. The terms of o(1) are completely negligible.
Paul F. Dietz
dietz@cs.rochester.edu
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Date: Mon, 27 Apr 92 19:06:01 -0400
From: dietz@cs.rochester.edu
To: space-tech@cs.cmu.edu
Subject: Re: Self-inductance of a coil
Ack; that derivative is accurate up to a term of order r^4/a^5.
Paul
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Date: Mon, 27 Apr 92 16:46:34 -0500
From: pgf@srl05.cacs.usl.edu (Phil G. Fraering)
To: gwh@lurnix.com
Cc: space-tech@cs.cmu.edu
Subject: Magsail
Date: Mon, 27 Apr 92 12:01:52 PDT
From: George W Herbert
The _J. Spacecraft_ and another (I believe more recent
J. Propulsion) papers go into a fair amount of detail. The
one cited already is the one that I'm more fammiliar
with, though I don't have a copy on me. I'll try and
grab a copy of it from the UC Berkeley library later
this week, and slowly type it in if people ask nicely 8-)
I wasn't sure that was permitted under current copyright law.
If it is, I volunteer to type it in, and maybe even TeX the
equations (I have a nice little elisp program called calc that
can do a lot of the work of converting to TeX).... (in fact,
this would be a good test of that feature. I've never really
used it before.)
Phil
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Date: Mon, 27 Apr 1992 20:29 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsail tension
To: dietz@cs.rochester.edu, space-tech@cs.cmu.edu
From: Paul F. Dietz
> you said:
>
>> My boss is equally puzzled. In the R-goes-to-infinity limit, the Lorentz
>> force becomes purely radial --- no axial component at all. So where the
>> heck is the tension *coming* from ???
>
> Eh? A radial force (directed out along a radius) will of course
> produce tension a hoop.
>
I expressed myself ambiguously: in the limit that the centre of the loop
``goes to infinity,'' all information that the field was produced by a
*loop* is lost, i.e., the loop degenerates to a *cylinder*; the magnetic
field becomes *cylindricaly symmetric*; the Lorentz force is radial w.r.t.
the *centre of the cylinder*. So with no *axial* (w.r.t. the *cylinder's*
axis!) forces, how can there be any tension?
> Note that the logarithmic divergence is easily understood: the magnetic
> field at distance r from an infinite linear conductor goes as 1/r.
> Therefore, the magnetic energy goes as integral ( 2wr / B^2 ) dr,
> which diverges as ln r ...
>
I am in perfect agreement. The question is: is it valid to conclude that
the *mechanical tension* in the loop is equal to the derivative of the
*electrical stored-energy* w.r.t. the circumference? This is what L&L
(and I) assumed: is it **correct**? I would be *MUCH* more comfortable
if I could find a proof that L&L's expression is equivalent to the
Sophmore-physics answer that:
$
T = 2 \pi R_m f_r
$
where $f_r$ is the integral of the Lorentz force over the cross-section,
i.e., the net radial (w.r.t. the loop-centre) force per unit circumference.
> Of course, in the case of the loop, you cut off the integration
> at the wire radius at one end and the loop radius at the other
> (up to a constant), so you expect a term of on the order of r ln(a/r)
> to show up ...
>
It is precicely the subtleties of this ``cut-off'' procedure that are
worrying me ... I am begining to suspect that this is one of the cases
where it is **NOT** permissable to interchange the limit and the integral ...
Gordon D. Pusch
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Date: Mon, 27 Apr 92 20:05:52 EDT
From: John Roberts
Disclaimer: Opinions expressed are those of the sender
and do not reflect NIST policy or agreement.
To: space-tech@cs.cmu.edu
Subject: Re: Magsails
>Date: Mon, 27 Apr 1992 04:30 EDT
>From: "GORDON D. PUSCH"
>Subject: Re: Magsails
>To: space-tech@cs.cmu.edu
>Indeed; one could even exploit certain amusing properties of superconductors
>in the process.
>Let the ground-loop's flux be established while the magsail-loop is *normal*.
>Cool the magsail-loop below T_c; the gound-loop's flux linking the magsail-
>loop then becomes ``frozen'' --- it can't change.
Based on my recent reading of things I didn't really understand in
Encyclopaedia Brittanica, I'm not sure type II superconductors can be relied
on to do this. I believe the high-temperature superconductors discovered
thus far are all type II.
>Now: rapidly reverse the
>polarity of the ground loop --- preferably via inductive switching to a second
>concentric loop of opposite sense, so (almost) no losses occur. Viola!
>The magsail springs into the sky!!! 8-D
Since the energy present is represented by the magnetic field of the original
polarity, that might be rather difficult - sort of like reversing the direction
of your car by bouncing it off a stone wall. :-)
John Roberts
roberts@cmr.ncsl.nist.gov
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End of Space-tech Digest #120
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