Figure 2

Frequency analyses of the density and velocity fluctuations. (a) Typical power spectrum densities (PSDs) of \(\tilde{n}_p(t)\) (\(S_n\): blue line) and \(\tilde{v}_e(t)\) (\(S_v\): red line) taken at \((x,z)=(18~{\rm{cm}}, 30~{\rm{cm}})\). The large amplitude fluctuations in \(\tilde{n}_p(t)\) and \(\tilde{v}_e(t)\) can be found at around 40 kHz. (b) The coherence and the real part of the cross spectrum \(\Re [S_{nv}]\) of the \(\tilde{n}_p(t)\) and \(\tilde{v}_e(t)\) signals in (a). Strong correlation between \(\tilde{n}_p(t)\) and \(\tilde{v}_e(t)\) can be confirmed by the coherence and the cross-field inward electron flux induced by the fluctuation and directed to the negative x direction can be identified by \(\Re [S_{nv}]\). (c) The cross-phase between \(\tilde{n}_p(t)\) and \(\tilde{v}_e(t)\) taken at \((x,z)=(18~{\rm{cm}}, 30~{\rm{cm}})\) (red dots) and \((x,z)=(-18~{\rm{cm}}, 30~{\rm{cm}})\) (blue dots), where the yellow-colored region shows that the flux is directed to the positive x direction. The phase around 40 kHz clearly demonstrates that the electron flux is directed to the negative and positive x directions at \(x=18~{\rm{cm}}\) and \(x=-18~{\rm{cm}}\), respectively. (d) x–z profile of the power \(P_n\) of the density fluctuation obtained by integrating \(S_n\) over the frequency. The fluctuation is found to exist at the peripheral region of the plasma flow along the MN.