Nonlinear Waves in a Finite Plasma

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We have studied both theoretically and experimentally nonlinear phenomena in a finite plasma without magnetic fields, and the following results are obtained.1. We examined the characteristics of the ion acoustic wave reflected by the boundary. The main results are as follows :(i) The particles trapped in the sheath formed around a negatively biased grid play an important role in the wave reflection.(ii) When an ion acoustic solution propagates into the sheath, the reflected wave becomes a solution for the large amplitude, and an ion acoustic wave for the small amplitude, respectively.(iii) The experiments on the reflection of ion waves are carried out using the DP machine. It is found that ions play an important role in the reflection, and the reflection coefficient does not depend on the frequency for the beam modes and it is decreasing function of frequency for the ion acousti wave.2. We attempted the suppression of the ion-ion instability by an external field and found that the threshold value at which the instability is suppressed depends on the frequency of the external field.3. We observed the mode transition of the electron beam-plasma instability : from the beam mode to the beam Langmuir mode.4. We succeeded in the excitation of the subharmonics of the beam mode. The subharmonics may be excited by period doubling.These results will contribute to the development of nonlinear phenomena in plasmas.