By Ronald C. Davidson
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I n this case, E q s . (1), (3), (56), and (58) constitute a closed one-dimensional description of t h e electron fluid in t h e electrostatic a p p r o x i m a t i o n . 2 The Single-Water-Bag Model T h e " w a t e r - b a g " model has received considerable attention in t h e literature in relation to plasma, stellar, and b e a m - p l a s m a p r o b l e m s [6 13-19]. It is interesting to note t h a t t h e closed m o m e n t description afforded by E q s . (1), (3), (56), and (58) is equivalent to t h e single-waterb a g m o d e l  in a kinetic (Vlasov) description of t h e electrons.
W . T a r n , / . Plasma Phys. 4 , 109 (1970). O n t h e B r e a k i n g of L a r g e A m p l i t u d e P l a s m a Oscillations, T . P . Coffey, Phys. Fluids 1 4 , 1402 (1971). 4. 1 Introduction I n this chapter, we consider circumstances in w h i c h t h e resonant interaction between waves and particles plays a significant role in t h e nonlinear evolution of t h e system. T h e analysis is electrostatic, o n e dimensional, and in t h e absence of external magnetic field. F u r t h e r m o r e , t h e plasma is described within t h e framework of t h e Vlasov-Poisson equations.