341. Nuclear fusion – energy of the future: video of the day
Save This Post as PDFA nice quantum flapdoodle promo video about thermonuclear fusion by the Max Planck Institute of Plasma Physics (as usual, physics behind the video is extremely nice while actors are pathetic).
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340. Thermonuclear fusion: some basic facts about thermonuclear reactions
When I wrote Ten open problems in physics, the ultimate plan behind the post was that I first list those problems and then discuss every single one of them to some details – just to learn something new and relevant about each of the problems would already be enough fun for me to consider this idea seriously. As I said before, discussing important open problems is a) fun, b) it makes physics interesting and c) it makes it also relevant.
Somehow, the plan got crippled (I am lazy), and so far I was only able to discuss the only problem in the list to some extent – the problem of turbulence. Although I did not finish with turbulence yet, let me switch to something else: problem N 7 in the list – thermonuclear fusion and recall…
Some basic facts about thermonuclear reactions
Thermonuclear reactions are reactions between light atomic nuclei that proceed at very high temperatures, 
K. Wikipedia has a great article about nuclear fusion, and it would be stupid to reproduce it here, so I’ll try to be as original as possible in the given context 
Thermonuclear reactions belong to the class of processes (actually, relatively rare) where nuclei overcome Coulomb repulsion and get close enough in order for weak interactions to cease to be negligible.
In practice, the latter means that once the Coulomb interaction gets overcomed, the system basically falls into the deep potential well on the picture above and gets restructured with subsequent (kinetic) energy release.
Weakly bound nuclei get transformed into strongly bound ones. Since nuclei with the largest binding energy per nucleon are located in the middle part of the Mendeleev table, the most typical thermonuclear reactions are fusions of lighter nuclei with production of heavier ones. Such reactions as 
(decay of light nuclei with production of heavier ones) are also possible in Nature, though.
In Nature, the Coulomb barrier gets usually overcomed in two ways (correspondingly, we will classify thermonuclear reactions as A-reactions and B-reactions).
In the first case, the basic idea is to lower the Coulomb barrier in order to overcome it. The potential can be deformed for example due to high pressure (this naturally happens in really dense stars with 
), screening of the Coulomb field of the proton by captured negatively charged muon living on the Bohr orbit (so called muon catalisis) etc. etc. This is what is called cold fusion – since you don’t need to keep kintic energy of the nuclei too high in order to start the fusion.
In the second case, the (undeformed) Coulomb barrier can be overcomed by very high kinetic energy of nuclei (for example, you collide these nuclei on LHC or a much less powerful device) or high temperature (essentially, the same story since temperature is a characteristic kinetic energy of particle in plasma) etc. etc. This is a non-elegant, unsportsman-like way to start thermonuclear fusion but that’s how it typically happens in stars like our Sun.
Sometimes, it seems that we find reactions which belong to neither type A nor B, like in the effect observed by Fleischmann and Pons in 1989 The work of those two guys is considered pseudoscience nowadays but – who knows… according to Wikipedia
“Triple tracks” in a CR-39 plastic radiation detector claimed as evidence for neutron emission from palladium deuteride, suggestive of a deuterium-tritium reaction. On 22-25 March 2009, the American Chemical Society held a four-day symposium on “New Energy Technology”, in conjunction with the 20th anniversary of the announcement of cold fusion. At the conference, researchers with the U.S. Navy’s Space and Naval Warfare Systems Center (SPAWAR) reported detection of energetic neutrons in a palladium-deuterium co-deposition cell using CR-39, a result previously published in Die Naturwissenschaften.
By the way, if we have an expert here on NEQNET reading my post, can please comment on those experiments?
So, why one should be interested to learn about thermonuclear fusion? There are several reasons: a) as I said above, thermonuclear fusion is the main mechanism of the energy release in stars and Sun in particular, b) it does seem that thermonuclear synthesis is the way of the future for the global economics – it is cheap once we learn how to control it and it should make Greenpeace happy.
Next time I am going to talk about rates of thermonuclear reactions and will try to keep the level of the discussion basic.
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339. Twistors: getting more formal
After discussing (or rather musing about) generalities related to twistor formalism, let me now get a bit more formal – I hope it will finally help you to understand what I was talking about in the previous posts
As was mentioned before, the twistor space corresponding to 4-dimensional real Minkowski spacetime is a complex projective space 
– that is, by definition we introduce complex coordinates 
such that 
and the points 
and 
are identified for arbitrary 
.
It is possible to describe lines in by a pair 
, 
for any . The set of these straight lines therefore depends on four complex parameters. Conformal structure in twistor space is defined by the condition that the distance between any straight line 
crossing a given line 
and the line itself is zero (therefore the line belongs to the light cone with origin somewhere in ).
Let us consider a real hypersurface (called Hermitian quadric) given by the equation
.
It divides the twistor space into two parts: the form 
is positive in one part and negative in the other. The set 
of all straight lines belonging to this Hermitian quadric depends only on 4 real parameters and therefore represents conformal compactification of Minkowski space. Cones of all lines from the set that cross the given line are just light cones. If we want to get the usual Minkowski space, we need to choose a particular line 
(for example, 
, 
) and remove all the lines belonging to the set 
from the twistor space.
That’s how 4-dimensional flat space with Minkowski signature is embedded into the twistor space … Euclidean space (
) can be embedded into as follows. Consider a set of straight lines connecting points and 
. All these lines either do not intersect or coincide. This way we can divide into classes of non-intersecting lines or introduce fibration in other words.
Finally, let us talk a bit about various symmetries associated with twistor space and various embeddings discussed above. First of all, the group of projective transformations of space is 
. It has a subgroup 
which conserves the quadric above. It therefore induces the group of conformal transformations of Minkowski space. If we want to keep the line defined above fixed, the corresponding subgroup of the group is nothing but Poincare group of Minkowski space. Finally, if we fix one more line not crossing , we will get Lorentz group.
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338. Before the Big Bang: video of the day
BBC News’ Stephen Sackur interviews Sir Roger Penrose about cyclic universe theory and the problem of initial state.
The quality is not terrific, but the interview itself is fun. By the way, do you know why Penrose is uncomfortable with inflationary paradigm?
P.S. As Lubos pointed out, this is just a part of the full interview, the whole interview (20+ min) can be found on the BBC www site.
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337. Twistors and non-linear differential equations. Curved spacetime
Let my continue our micro-discussion of twistors. Last time I explained how using the language of twistors allows to express solutions of the linear differential equations (massless free fields propagating in the flat spacetime) in a different way – not too deep to really call it a result.
As it turns out, twistors also help dealing with non-linear differential equations. For example, Ward and Sir Michael Atiyah have used the language of twistors to construct self-dual solutions of the Yang-Mills equations – instantons. I guess I don’t need to explain how much instantons are important for the quantum Yang-Mills theory – they are non-trivial topological configurations of the Y.-M. field that extremize the Y.-M. action and (which is much more important) give contribution into the overall Y.-M. partition function of non-zero measure.
Instantons – solutions of the self-duality equation – defined in the 4-dimensional Euclidean space turn out to correspond to complex vector bundles in twistor space. This fact allowed Atiyah, Hitchin, Drinfeld and Manin to find all possible instanton solutions for the Y.-M.
Another direction of research where twistor formalism proved to be useful was finding new solutions of the Einstein equations. The point is that instead of Minkowski space we can of course consider general curved spacetime. While 4-dimensional Minkowski spacetime corresponds to the set of straight lines in the 6-dimensional complex space, it is natural to expect that generic curved spacetime should naturally correspond to the set of curved lines in the same complex space. Of course, as usual, reality is more complicated than the first naive guess about it. Not all curved manifolds can be realized as sets of curves in the twistor space, but only those which satisfy to vacuum Einstein equations and additional conformal condition of autoduality (autodual part of the Weyl tensor is equal to zero). Such manifolds indeed correspond to sets of curves in a curved twistor space, and the language of twistors allowed us to find many self-dual solutions of the Einstein equations.
Next time, let me discuss a couple of examples which will hopefully make all this twistor ideology clear.
Some basic literature
1. Yu. Manin, Gauge field theory and complex geometry. A very strong book about complex geometry, holomorphic bundle theory and some physical applications.
2. R. Penrose, W. Rindler, Spinors and Space-Time, Vol. 1. In this volume authors discuss twistor space corresponding to Minkowski space and free massless fields.
3. R. Penrose, W. Rindler, Spinors and Space-Time, Vol. 2. Here, the authors describe twistor description of curved spacetimes and also discuss many physical applications.
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