= Waterbag distribution
{title2=$f_0(v)=n\mathbf1_{|v|<V}/(2V)$}
A <phase-space distribution function> constant inside a prescribed region and zero outside. The one-dimensional example in the title has a <velocity plateau> and distributional derivatives at its edges. Its simple kinetic response can support undamped collective modes, illustrating why absence of growing modes does not imply <Landau damping>. For electrons with fixed ions, $\epsilon(\omega,k)=1-\omega_p^2/(\omega^2-k^2V^2)$, so collective roots lie outside the populated <velocity> interval.
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