Statistics of Langmuir wave amplitudes observed inside Saturn's foreshock by the Cassini spacecraft

We present the first systematic study of Langmuir wave amplitudes in Saturn's foreshock using the Cassini Radio and Plasma Wave Science/Wideband Receiver measurements. We analyzed all foreshock crossings from June 2004 to December 2009 using an automatic method to identify Langmuir waves. Using this method, almost 3 x 10(5) waveform intervals of typical duration of about a minute were selected. For each selected waveform interval the position of the satellite inside the foreshock was calculated using an adaptive bow shock model, which was parametrized by the observed magnetic field and plasma data. We determined the wave amplitudes for all waveform intervals, and we found that the probability density function amplitudes follow a lognormal distribution with a power law tail. A nonlinear fit for this tail gives a power law exponent of -1.37 0.01. The distribution of amplitudes as a function of the depth in the foreshock shows the onset of the waves near the upstream boundary with its maximum slightly shifted inside the foreshock (approximate to 1R(S)). The amplitudes then fall off with increasing depth in the downstream region. Our results are in agreement with previous observations and roughly follow the generally accepted stochastic growth theory mechanism for the foreshock region, with an exception at the highest observed amplitudes. The estimated energy density ratio W for largest amplitudes does not exceed 10(-2), suggesting that modulational instability is not relevant for a large majority of waves. The decay instability can be important for the stronger electrostatic waves in Saturn's foreshock, as was previously reported for multiple solar system planets.