Friday, August 14, 2009

The Other Chandrasekhar Limit

As a schoolboy in India, one couldn't help knowing of the Chandrasekhar mass limit. I distinctly remember being challenge-quizzed by fellow schoolmates about it - as early as the sixth grade. That an Indian-born astrophysicist had discovered a fundamental limit - the stellar mass, that, if exceeded in a white dwarf, could lead to gravitational collapse - was something every Indian schoolboy in the 1970s seemed to know (at least in the schools I went to!). Later, in high school, I remember doing an elementary calculation, and later still, at college and university, more detailed calculations were done. Chandrasekhar himself became an idol of sorts, and his benign gaze, from a picture portrait framed on the wall above my desk, was deeply inspiring in the last two years of my university career. In the very last year - 1983-84, he was also awarded the Nobel Prize in Physics, for, it turned out, the very work he had done, as a nineteen-year old, in calculating his Mass Limit. [This seemed to ignore his work of a lifetime since, which did not sit at all well with him - but be that as it may for now, it can be the subject of several blog posts.]

That, apart from Subrahmanyan Chandrasekhar, there were other Indian physicists named Chandrasekhar as well, I also knew. One of them, who also shared his first initial, was Sivaramakrishna Chandrasekhar, a liquid crystals specialist, who was at the Raman Research Institute in Bangalore (which I visited often as an undergraduate, since my family happened to live near by). [The two were actually first cousins, both also being nephews of C.V. Raman.]

But it was Professor B.S. Chandrasekhar, (Bellur Sivaramiah Chandrasekhar) formerly of Case Western Reserve University and now at the Walther Meissner Institut at Munich – like me, a Delhi University alumnus (M.Sc. 1949) and a Rhodes Scholar as well - passing through some 35 years before me - for whom another Chandrasekhar limit is named. In 1962 (the year of my birth) he wrote a paper in the very first issue of the journal Applied Physics Letters: A Note on the Maximum Critical Field of High-field Superconductors. This paper defined a natural upper limit on the ambient Magnetic Field which, if exceeded, causes a complete loss of superconductivity. Independently, the idea was also suggested by A.M. Clogston, and has ever since then been known as the Chandrasekhar-Clogston (Field) Limit.

For reasons I cannot fathom, this limit on the upper critical field of superconductors has not received the type of (er ahem) critical acclaim that the first Chandrasekhar Limit received - not even noticed in the Delhi University Physics Department, of which Prof. B.S. Chandrasekhar, is a distinguished alumnus! He was felicitated for a lifetime of work in superconductivity and condensed matter physics, with a special award at the American Physical Society March Meeting in Indianapolis in 1992 (where I was fortunate to be present). I remember seeing him from afar but being too intimidated to approach him directly and introduce myself!

Professor B.S. Chandrasekhar has continued to work on superconductivity, and still does, at the Walther Meissner Institut (the Institute is of course named for the discoverer of the famous Meissner Effect - which describes the exclusion of magnetic flux from the interior of a superconductor below its critical temperature). He has worked on the critical field of Niobium, and on magnetic fields created by superconducting solenoids. As it happens, the magnetic fields required by the ITER tokamak - both the central solenoid and the toroidal field - are created by superconducting Niobium-Tin alloy - of which some 750 tons (seven hundred fifty tons) of wire, 200 km (two hundred kilometers) long will be required. Thus, considerations following from the Chandrasekhar-Clogston Limit are relevant to ITER design and operation. What is really interesting is that the other Chandrasekhar - Subrahmanyan Chandrasekhar - worked on the theory of fusion - especially laser fusion (or inertial fusion) - using the pressure of light to push two hydrogen atoms close enough that they fuse. (This is not the approach at ITER, which is a magnetic fusion reactor). Prof. B.S. Chandrasekhar has also written a popular book, Why Things Are The Way They Are.

Today, the Chandrasekhar-Clogston limit occurs most often in the physics literature in descriptions of work relating to spin-polarized fermionic atomic fluids - which display both superfluidity through a BCS-like pairing, as well as a Bose-Einstein Condensation (BEC) after dimerization (which makes them bosons) at ultra-low temperatures. A group at the University of Trento (Italy) and, appropriately, the Walther Meissner Institut (where Prof. Dr. B.S. Chandrasekhar is a 'Permanent Guest') is active in the field. The Chandrasekhar-Clogston limit appears in that context as a critical value of the ratio of up-and-down spin polarizations in a dilute fermionic atom gas, and determines phase separation of the dilute gas into a superfluid phase and a 'normal phase'.

Whether and how the two Chandrasekhar limits, in speaking of different aspects of a gas of fermions (dilute in one case, and degenerate in another) are actually (or at all) related are interesting questions I might explore in a subsequent blog post.

Wednesday, August 5, 2009

Fusion Through a Hydrogen Economy Prism

Fusion has long suffered from the unfortunate impression of being a technology that is always 'thirty years into the future'. Reality has always been more complicated, even if sometimes the impression seems to ring true. Since nuclear fusion has been understood for longer than nuclear fission, the seeming lack of progress in commercializing fusion has appeared especially frustrating. While technical issues certainly remain to be addressed, the lack of a compelling future scenario within which nuclear fusion could be seen as a 'natural' energy solution has also been a barrier in the techno-scientific as well as policy discourse surrounding fusion.

If seen merely as an attempt to extract energy by fusing deuterium and tritium atoms (in the simplest conception), fusion appears less compelling than when seen as a natural part of a future carbon-free hydrogen economy. Deuterium (D) and tritium (T), after all, are isotopes of hydrogen, and the energy they yield on fusion is usefully seen as nuclear hydrogen energy. But what if the heat yielded by the neutrons in D-T fusion were further used in thermochemical schemes to create molecular hydrogen, from which chemical or electrochemical hydrogen energy could be extracted? If this is successfully done, the transportation sector of the future could well come to be powered indirectly by fusion.

I sketch out and elaborate this vision for a fusion-driven hydrogen economy of the future in my paper Nuclear Hydrogen Production: Re-examining the Fusion Option. I discuss more generally a vision for a Fusion Island (first sketched out by Nuttall & Glowacki), in which a complete hydrogen economy is envisaged - a scheme which uses all the isotopes of hydrogen (protium, deuterium, tritium) in all forms of matter (solid, liquid, gas, plasma). I discuss the new perspective in which fusion appears when seen through such a hydrogen economy prism, the policy implications thereof, and the likely present-day economic actors who might find such a vision of the future hydrogen economy sufficiently compelling to begin more actively participating in and funding fusion R&D today. Such a new perspective on fusion also sees both fusion and fission as complements instead of substitutes, and offers novel possibilities such as fusion breeders of fission fuels, as well as, for example, fusion-fission hybrids, and fission breeders of fusion fuels.

Update Presidential Science Adviser John Holdren, giving the Rose Lecture at MIT on 25 October 2010, discussed the role of fusion and fission in providing future energy options that would mitigate climate change. He mentioned that both fission and fusion represent energy sources with 'nearly inexhaustible' fuel supplies, and though the fusion fuel supply was 'much more inexhaustible' (paraphrasing), that was not much of an advantage over fission since fission was 'quite inexhaustible already'! However, he also stressed that he personally was in favor of funding fusion R&D, since the number of such 'nearly inexhaustible' fuel options was so small. However, this funding could only be sustained if the overall funding pie for energy R&D of all kinds was increased. Here's the video of part of his talk where he discusses this issue:

Dr. Holdren also presents a number of quantitative projections for the future of nuclear power that are worth summarizing in brief. The world currently has about 440 nuclear reactors which produce a total of 375 GWe of electrical energy, constituting about 13% of world total electricity supply, a percentage that is declining even as new plants are being built - since other sources of supply are growing faster in the aggregate. He feels that in the next 90 years, that is, out to the year 2100, the world total supply of nuclear power would fall considerably short of the 3500 GWe total that some analysts have hoped for [and which would have been an order of magnitude larger than current capacity].

He feels, however, that by the year 2050, a rough quintupling of current supply, to about 1700 GWe could happen. However, I found the most remarkable figure in his talk to be the estimate of Remaining Ultimately Recoverable Uranium (RURU) as 100 Million tons, based on a recent MIT study. What this means is that a once-through fuel cycle option using natural or lightly enriched uranium will remain competitive, and that reprocessing and breeding options may not need to be commercialized for several decades yet. Of course, the issue of how this recoverable uranium is actually distributed throughout the world, as well as how widely the technology of extraction will become available, remains. Different countries who feel uranium-constrained may still very well choose to pursue fuel cycle options that include reprocessing and breeding technologies.