The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so it can be taken as a generalized method.
The trapping of neutrals from a fast atom beam impinging on an electron-cyclotron-plasma target is studied. The electron-cyclotron plasma is assumed to be fed by an influx of molecular hydrogen. Radial attenuation of the feed gas and the H° formed by its dissociation is considered in detail. Both the addition of neutrals and depletion of the target by charge exchange with the beam are also taken into account, as is reflux from nearby walls. Given a sufficiently high target density ( £ , 1 0 u protons/cm 3 ), a sufficiently low background density, and a 0.01-1.0 A neutral beam, it is calculated that 1 0 u -1 0 u protons/cm 3 can be accumulated with a trapping efficiency of several per cent. * Research sponsored by the USAEC under contract with the Union Carbide Corporation. 1 The Imp experiment will consist of an electron-cyclotronheated plasma created by 8.8 and 5.5 mm heating in a mirrorquadrupole well with B m j n # = 9-19 kG. Hydrogen neutrals of 10-20 keV energy will be injected. This experiment is being constructed at Oak Ridge National Laboratory, Oak Ridge, Tenn., USA.
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