Non-Akhiezer-Polovin Model on Plasma Electrostatic Wave and Electron Beam

We study, beyond the well-known Akhiezer-Polovin model, plasma electrostatic wave and unmagnetized electron beam.Our investigation is based on a stricter theory in which a long-lasting misconception about zerotemperature fluid motion equation is removed. Our theory explains some authors' puzzle about why a narrowly focused (charged particles) beam is preserved in the presence of strong space charge forces. The interaction of such a unmagnetized charged particles beam with a plasma electrostatic wave is studied in details and some universal results are revealed. These exact information are crucial to accurate estimation of the quality of a plasma wakefield and hence its performance in acceleration.