“…The main effect of the nonlinearity is the appearance of Langmuir harmonics which are not obtained with the previous linear approaches (Apel, 1967;Manheimer, 1971;Joyce et al, 1971;O'Neil and Winfrey, 1972;Kellogg et al, 1986;Schriver et al, 2000). The electrostatic multiple Langmuir Harmonic (LH) waves in the electron beam instability is a known effect previously observed in laboratory (Apel, 1967), in spacecraft observation (Cairns, 1986), in spaceborne rockets (Kellogg et al, 1986), and in various numerical computer simulations (i.e., Joyce et al, 1971;Kasaba et al, 2001).…”