Related Techniques in Thermonuclear Research

Among the aspects of thermonuclear plasma research and accelerator technology which have common techniques and problems is the problem of injection which in the case of accelerators is guided by limitations imposed by Liouville theorem. This limitation is being more and more fully appreciated in the problem of assembling a thermonuclear plasma. There are various examples of how this limitation on injection comes into play in the case of some plasma devices. There is an interesting analogy between the topology of phase space for particle accelerators and the topology of coordinate space for lines of force in a plasma containment device such as a toroidal stellarator. There are integral, 1/2 integral, 1/3 integral, and 1/4 integral, etc. resonances which can be stimulated by magnetic field errors in plasma confining devices and which would cause the flux plot topology to break up into rings of islands for a case where the flux plot has shear. The size of the islands depends upon the type of the multipole field forming the flux plot. Although stellarators are made with twisted or helical multipole windings wound around the major circumferential, they can also be made by sectored multipole magnets rotated between focusing and de-focusing positions as in an accelerator. For the quadrupole case, the transfer matrices include only exponentials with real expotents and no sines and cosines such as are found in the accelerator analogy. K. R.