Instability of plasma waves during relaxation of 2D turbulent flows*

We observe strong excitation of novel low-frequency $z$-dependent plasma waves $(m_{\theta } =0,k_{z} =1)$, occurring during the nominally 2D relaxation of turbulent initial conditions (10 $-$100 interacting vortices) in strongly magnetized electron columns. This initial relaxation often results in ``2D vortex crystal'' states [1, 2]. Here we describe experiments showing the concomitant growth of ill-understood low-frequency plasma waves, probably due to ``leakage'' of 2D turbulent potential energy into $z$-dependent fluctuations. With plasma injection, the lowest regular $T$rivelpiece-$G$ould mode $(m_{\theta } =0,k_{z} =1)$ is observed at $f_{TG} (t)\approx 2.8$MHz and exponential decay time $\tau_{TG} \sim 1$msec. Also, we observe rapid exponential growth of a novel low-frequency mode with $f_{LF} (t)\approx 0.3$MHz, nominally also with $m_{\theta } =0,k_{z} =1$. In a few milliseconds (several tens of rotation times at $B=$10kG), the \textit{LF}-mode becomes highly nonlinear, developing up to a dozen temporal harmonics. When a \textit{LF}-harmonic resonates with the decaying \textit{TG}-mode, \textit{LF}-mode energy is transferred into the \textit{TG}-mode, and both modes remain at moderate amplitudes until the 2D turbulent relaxation abates (hundreds of rotation times). The ill-understood $f_{LF} $ is \textit{independent} of $B$, even though the growth and duration times follow scale as $B^{\mathrm{1}}$ from the 2D flows. \\[4pt] [1] K.S. Fine \textit{et al}., PRL \textbf{75}, 3277 (1995).\\[0pt] [2] D.Z. Jin and D.H.E. Dubin, PRL \textbf{80}, 4434 (1998).