Nuclear fusion probabilities are extremely small! In a typical Dragon experiment where we fire radioactive nuclei at a gas target, sometimes only 1 in every 10,000,000,000,000 particles undergo a fusion reaction. Thus, in order to collect a handful of reaction products in order to tell how such a reaction would occur in a stellar environment, one needs to fire a hell of a lot of particles at the gas target; in this case at least 1,000,000,000,000,000 (ten to the 15th power, or 1 x 10^15) of them. Now, you can either do this by producing a low intensity beam of these radioactive nuclei, and run for a very, very long time in order to get this large number, or you can create a very intense beam and run for a shorter timescale. Since time is finite and expensive (we share beam time with other experiments, like any large science lab) and intensity is difficult to achieve more often than not a compromise is reached and a typical Dragon experiment may last 3-4 weeks of continuous running (yes we do nightshifts) with radioactive beam intensities of between 1 x 10^7 and 1 x 10^9 particles per second.
Artists impression of a Classical Nova, where a compact White Dwarf star receives transferred hydrogen-rich material from a less-evolved orbiting companion which has expanded into its Red Giant phase. The material provides fuel and the conditions necessary to initiate a thermonuclear explosion on the White Dwarf surface, leading to the synthesis of some heavier types of nuclei and the ejection of material into space.
How does such an experiment work? Well first we must describe what occurs in the particular type of nuclear fusion reaction we are interested in. (Warning: some complicated concepts approaching…)
Inside a stellar plasma, nuclei are moving fast, at typical velocities of around 0.1% the speed of light in stars like our sun, and up to a couple of percent the speed of light for hotter scenarios like x-ray bursters. The particles do not all have the same velocity, but instead exhibit what is known as a Maxwell-Boltzmann, or thermalized distribution, indicating that the ensemble of particles have reached thermal equilibrium. Thus, two individual particles may approach one another at a range of different relative velocities, or kinetic energies, and in the simplest cases the probability that they will fuse is dependent on this relative velocity for two reasons: firstly, these particles behave in some ways like waves, and have a characteristic wavelength relative to the other particle which is dependent on the velocity – the lower the velocity, the bigger the wavelength, and the higher the probability of interaction since the wavelength defines a kind of geometric area of overlap between the approaching particles (think of firing a billiard ball at a marble, and then at another billard ball – the latter will be easier to hit); the second effect is that of the repulsive electrostatic field between similarly charged particles (we are assuming the particles are charged), giving rise to the opposite effect – the probability drops off exponentially at low approach energies (velocities). This is called the penetrability. However, things are made more complicated by the presence of quantized ‘energy levels’ in the final nucleus (the one that is made by fusion) that exhibit themselves as ‘resonances’ in the probability, or regions at a specific energy where the probability of fusion suddenly skyrockets to values much higher that if considering penetrability alone (for purists I defer a complex discussion of ‘direct capture’ to bound final states for now).
The DRAGON recoil spectrometer for astrophysics, TRIUMF
Ok, I hope you got that – it’s a little complex – but the point is there are these ‘resonances’, and we are currently incapable of coming up with a precise enough theory of atomic nuclei that can predict both the strength and position of all these resonances at stellar energies (because a theory of nuclei with more than a few nucleons from first principles is extremely difficult due to the many-body nature of the problem). Therefore, we must measure the strength and energy of the resonances in the laboratory in order to determine the total, energy-dependent fusion probability.
Good. That is the hard bit over now. So, how do we measure the strength of these little resonances using our radioactive beam and a gas target? Well, we start with our beam, which for the purposes of discussion we’ll assume is made up of particles of all the same velocity. They are fired at Dragon’s famous ‘windowless’ gas target, which means that the beam particles, traveling in vacuum, suddenly meet a region of gas at constant pressure, pass through it, then leave into a region of vacuum again without passing through any thin ‘windows’ to confine the gas. This is achieved by using powerful pumps (the kind used on big ships) to quickly recirculate the escaping gas back into the central target region, maintaining a constant pressure there. As our particles pass through the gas, they lose energy due to many small collisions with electrons in the gas, so that the average velocity of particles leaving the gas target will be a bit lower than the original velocity. The beam energy (velocity) is chosen, so that the resonance that we want to measure the strength of occurs at an energy that corresponds to an energy somewhere between the original beam energy and the exist energy of the particles after the target (let’s assume we roughly know where a resonance is). When a beam particle, on its way through the gas, passes through the resonance energy, the probability of reaction shoots up and some of these particles will fuse. Most beam particles will NOT fuse, however, and pass straight through. That is why I gave the number above of only 1 in every 10,000,000,000,000 particles fuse.
From here on the physics is simple: conservation of linear momentum ensures the heaver fusion product, or ‘recoil’, has the same momentum as the original beam particle had (since the gas is effectively at rest relative to the beam). This is until the recoil, which has been ‘excited’ into a particular quantum state by the collision, emits a high-energy photon, or gamma ray. This gamma ray, because it is massless, results in only a small ‘kick’ being given to the recoil, in any direction, with the result that the recoils are confined to a thin conical range of directions around the original beam direction. In order to know that fusion has taken place, we could measure the gamma rays using some sort of detector. This we do using an array of crystals of ‘BGO’ (Bismuth Germanate), which almost completely surround the gas region, and give us an electrical signal when a gamma ray interacts with them. However, many gamma rays come from all directions from natural background radiation, and especially from the radioactive beam itself which results in the intense emission of gamma rays. Thus looking for some particular gamma rays in a forest of others is not the best way to go – we need to also detect the recoil particle. This is where the ‘needle in a haystack’ analogy comes in. To detect one recoil particle in every 10,000,000,000,000 beam particles, the ‘needle’ in the ‘haystack’, we need a pretty good filter. The recoil particles have the same momentum on average as the beam particles, so the main way to tell them apart is by mass, the recoils being around 1 atomic mass unit heavier. Therefore we pass them through the ‘Dragon’, the recoil ‘spectrometer’, which consists of a series of electric and magnetic fields designed to filter out the beam particles and leave only the recoils.
The main filtering occurs in a section called an electric dipole, a kind of constant electric field between two electrodes, in the case some 200,000 volts in strength, which causes the slightly heavier recoil particle to be bent in a circular path with a slightly smaller radius than the lighter beam particles (this is because the bending angle is greater the lower the velocity), therefore the lighter beam particles are ‘underbent’, and usually end up being stopped by a plate while the heavier recoils keep on going.
The recoils can then be detected in a series of instruments which measure their speed, energy, and atomic charge, much like in the discussions of particle physics in previous posts only using specialized nuclear physics instrumentation for the lower energy regime. If we choose to accept only particles which come within a given time window of a gamma ray detected at the BGO array, we have what we call a ‘coincidence’ and this rejects nearly all background events. Thus, by counting the recoil particles at the end of the Dragon, and knowing how many particles we injected, we measure the ‘strength’ of the particular resonance in that reaction. We would do this for all known resonances in the reaction (at different energies) and add up their contributions to get a number for the total reaction rate as a function of temperature. This is the number that is given to the astrophysical modelers who would then investigate how this affects a particular scenario like a classical nova explosion. Usually an individual rate can really change quite drastically the final conditions of the star (e.g. the material it ejects into space) and this is why it is important to measure these nuclear reaction.
So that was quite the essay, but I hope it provides enough background that when I begin to talk about running experiments (which will occur in a few weeks’ time) people will have a decent idea of what the point in all this is! I will in future try to imbed a short movie clip into the post, as well as add some pictures of Dragon. Until next time…cheers!
