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abstract:
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The author discusses the meaning of coherent instabilities and illustrates the techniques that can be used to study this problem. He considers a particle and introduces the equations of motion for the case of longitudinal and transverse coherent oscillations. An expression for the longitudinal and transverse coherent is derived forces. There forces are then used in the Vlasov equations to obtain a dispersion relation and define the limiting conditions for stability. The longitudinal and transverse stabilities are discussed. (25 References).
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