Fig. 4 | Scientific Reports

Fig. 4

From: Nonlinear excitation of energetic particle driven geodesic acoustic mode by resonance overlap with Alfvén instability in ASDEX Upgrade

Fig. 4

The resonance overlap illustrated by the energetic particle distribution \(\delta f\) in phase space. The \(\delta f\) in (\(P_\phi ,E\)) phase space for different \(\mu\) values at different times are shown. \(P_\phi\) is normalized to the product of particle charge \(e_{EP}\) and the maximum \(\psi\) at the plasma center. From the top to the bottom, the three rows are plotted at \(t = 0.375~{\textrm{ms}}\), \(0.516~{\textrm{ms}}\) and \(0.656~{\textrm{ms}}\), respectively. From the left to the right, the five columns represent different \(\mu\) values of 1.62, 3.56, 5.51, 7.45 and 9.39 with unit keV/T, respectively. The red color represents positive \(\delta f\) and the blue represents negative \(\delta f\). The solid and dashed black curves represent respectively \(L_{Alv} = 1\) and 0, and the red curve represents \(L_{EGAM} = 1\). The two black dotted lines represent two constant \(E'\) values. The constant \(P_\phi\) lines are not plotted because they are parallel to the vertical axis.

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