Tandem Mirror Approach to Magnetic Fusion

Tandem Mirror Approach to Magnetic Fusion SIMPLE MIRROR David E. Baldwin, Livermore (Lawrence Livermore National Laboratory) The concept of containing a plasma long enough for thermonuclear fusion to take place, by means of a straight magnetic field in which the reacting particles describe substantially circular paths, was amongst the first to be explored. In its simplest form, the reacting volume consists of a cylindrical tube inside a solenoid, into which ions are injected tangentially, there to become trapped. Some longitudinal mo tion is however inevitable as a result of scattering and it was quickly perceived that a simple solenoid would need to be kilo metres in length for ions to be trapped for a useful length of time. It was logical then to try to close the ends magnetically by a high field mirror that would reflect the majority of the ions back into the reacting volume. However the more one tried to "cork the bottle" by increasing the reflectivity, the more unstable the plasma became. Interest in the technique waned, and research concen trated on the various forms of toroidal con figuration. While it is still probable that the first demonstration of thermonuclear fusion with magnetic confinement will be achiev ed in a tokamac device, it has become recognized over the past five years that magnetic mirror confinement offers the best long term alternative. Active research aimed at optimising such a system is being carried out in Japan, the USA and the USSR although does not seem to have at tracted a great deal of attention yet in western Europe. This resurgence of interest in the mirror approach arises from a combination of ex perimental and theoretical results. Until 1975, efforts to contain a plasma for ap preciable periods had been frustated by RF noise in the plasma which increased the loss from the bottle to unacceptable levels. In 1975, however, in the 2XIIB experiment at the Lawrence Livermore National Labo ratory (LLNL), USA, it was demonstrated that this phenomenon could be controlled. Shortly afterwards, at Novosibirsk, USSR, and at LLNL, the development of the ambipolar trap, or tandem mirror configura tion (TM), opened the way towards a much improved mode for plasma confinement based on the mirror principle. Initial tests of this concept at LLNL and elsewhere have confirmed the promise of the original ex pectations. 4 The following summarizes the physics properties of three generations of mirror devices: the single-cell mirror machine, the original TM concept, and the TM modified by thermal barriers. With this final feature, which is soon to be tested experimentally, the TM becomes a viable candidate for a fusion power plant. SINGLE-CELL MIRRORS TM confinement based on the single-cell mirror machine is shown in Fig. 1. It will be evident immediately that the magnetic geo metry is "open” in the sense that magnetic lines leave the confinement volume, which can be contrasted with the "closed" geo metries of tokamaks and stellerators, in which the magnetic lines lie on closed sur faces within the plasma volume. In simple mirror machines, Fig. 1(a), the strength of a solenoidal magnetic field B = | B| is increased at the ends, forming the mirrors that reflect ions having a suffi cient pitch angle, cos'1 (v · B/vB), or magnetic moment to energy ratio, back towards the middle. Ions with a pitch angle less then a certain minimum are lost along the axis. For ions to be confined over a useful period they must be reflected backwards and forwards for up to 106 times. This is only possible if the magnetic moment p = V2 / 2B is approximately constant (adiabatically invariant), otherwise there will be axial losses due to pitch angle scat tering. Under most conditions, the electrons in the plasma are scattered more rapidly than the ions and so are lost at a higher rate. This results in the plasma becoming positively charged until the potential becomes typically four to five times the electron temperature Te.(In plasma physics it is normal to speak of the electrostatic potential of the plasma in terms of the potential energy of the particles expressed in eV. Similarly, temperature is used as an expression of energy from the relation E = kBT.) At this point, the electrons become electrostatically held by the ions which are themselves confined adiabatical ly by the magnetic field. This binding of the electrons to the ions greatly reduces the electron heat loss that would otherwise oc cur along the open field lines. It should be noted nevertheless, that those electrons that are lost as the ions are lost, have energies five to six times T. MINIMUM-B MIRROR Fig. 1—Two types of single-cell mirror machine with (shaded) their confined plasmas. In both, |B| is maximum at the ends; in the simple mirror, |B| decreases radially, whereas in the minimum B, it increases. A measure of the rate of ion loss through scattering, and so the rate at which ions need to be replaced to maintain the plasma density, is given by the average time taken for particles to be scattered after multiple collisions through 90°, i.e. from an ideally confined trajectory to a total loss situation. This time τii is given by: where the mean energy is Ei and the parti cle density ni. Ions of energy below a certain minimum, despite the confining field, are expelled by the positive potential, which means that mirrors cannot be fuelled by the ionization and subsequent heating of cold gas within the mirror volume. They must be fuelled by energetic atoms, whereas other types of fusion device might be ignited (i.e. fuelled by cold gas and heated by charged reaction products). In experiments, the injection of beams of energetic neutral atoms normal to, which then become ionized, has proved a suc cessful means of filling with ions having confined pitch angles. Such a process however requires a substantial injection of power. Calculations indicate that, as a result, the power amplification factor Q, that could be obtained in a single mirror reactor, would barely exceed unity, and would be too low to be of economic in terest. Instabilities This picture of classical confinement in mirrors, by no means reveals the whole story. Problems of stability of the con figuration to both low-frequency, longwavelength modes and to high-frequency, short-wavelength micro-instabilities have dominated research in almost all mirror ex Although it is now recognized that the periments to date. Indeed, the experimen mirror configurations described so far can tal milestones of the programme can be not achieve sufficient confinement to act measured in terms of the success achieved as reactors in themselves, the characteris tic positive potentials of the plasma and the in controlling instabilities. In simple mirrors, because the magnetic ability to hold high plasma pressure are field decreases from the centre line out, in profitably employed in the tandem con other words, the volume of tubes of equal figuration. magnetic flux increas (...truncated)