Parametric Instability Driven by Weakly Trapped Particles in Nonlinear Plasma Waves

This Letter describes a new parametric instability mechanism caused by a distribution $f_T$ of particles trapped in the potential wells of a wave train. The mechanism explains a nonlinear instability in Trivelpiece-Gould (TG) waves, and it could also be a destabilizing factor in a range of nearly collisionless nonlinear plasma waves. The theory is compared to particle in cell simulations of TG waves.

Figure 1

PIC simulation showing energy versus position in a TG wave with trapped particles, at two times. (a) ${\omega }_{p}t=0$; (b) ${\omega }_{p}t=400$.

Figure 2

Growth rates in simulations (points) and from Eq. (15) (lines) versus the number of tail particles, for two cases: red, a very nonlinear wave ($\varphi$ shown in Fig. 1) and blue, a less nonlinear wave (see Fig. 3).

Figure 3

(Top) Density, potential, and velocity in the cnoidal wave used for the blue data in Fig. 2. (Bottom) Least-stable fluid eigenmode. Solid lines, real; dashed lines, imaginary.