Strongly Driven Frequency-Sweeping Events in Plasmas

A generic model of a kinetic plasma formed from a source and sink is presented which without instability would form a strongly unstable state due to a single mode. Instead, the resulting wave-particle resonant interaction maintains the distribution near a marginally stable state through the continual production of fast frequency-sweeping modes that sweep unidirectionally (upward in our case) throughout the energy-inverted region of the distribution function. The energy of these modes can be channeled to the background plasma through wave dissipation and, in our particular example, one quarter of the injected energy is available to be channeled.

Figure 1

Field mode spectrum ${\tilde{E}}_1(\omega ,t)$ from generic model simulation exhibits nonperturbative frequency sweeping: $\delta \omega \propto \delta t$. The logarithmic gray scale has range [0.001, 0.08].

Figure 2

A snapshot of $f_0(v)$ at $t=9750$ (solid line) and $F_0(v)$ (dashed line). The arrows show the phase velocities of the modes present at this time, all of which are increasing.

Figure 3

A snapshot of $f(x,v)$ also at $t=9750$. Several islands are visible in this plot; over time their phase velocities increase, corresponding to an increase in the frequency of the associated modes.

Figure 4

The long time average $\overline{f_0}(v)$ (the solid line) is observed to be approximately linear across the wide region ($v_1$, $v_2$) where it differs from $F_0(v)$ (the dotted line). The dashed line shows the marginal stability distribution $F(v)$ predicted by the theory described in the text.

Figure 5

Analysis of a single structure. Simulation (solid line) and theory (dashed line) show good agreement for both phase velocity and mode amplitude.