Subject: Space-tech Digest #120 Contents: Magsails (tension, etc) (13 msgs) ------------------------------------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ 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 ------------------------------ End of Space-tech Digest #120 *******************