<i>In situ</i> observations of magnetosonic waves modulated by background plasma density

We report in situ observations by the Van Allen Probe mission that magnetosonic (MS) waves are clearly relevant to appear relevant to the background plasma number density. As the satellite moved across dense and tenuous plasma alternatively, MS waves occurred only in lower density region. As the observed protons with \textquoteleftring\textquoteright distributions provide free energy, local linear growth rates are calculated and show that magnetosonic waves can be locally excited in tenuous plasma. With variations of the background plasma density, the temporal variations of local wave growth rates calculated with the observed proton ring distributions, show a remarkable agreement with those of the observed wave amplitude. Therefore, the paper provides a direct proof that background plasma densities can modulate the amplitudes of magnetosonic waves through controlling the wave growth rates.