Physics
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmsm11c..08c&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #SM11C-08
Physics
2407 Auroral Ionosphere (2704), 2471 Plasma Waves And Instabilities (2772), 2706 Cusp, 7857 Stochastic Phenomena (3235, 3265, 4475), 7867 Wave/Particle Interactions (2483, 6984)
Scientific paper
Plasma waves in space are almost invariably bursty and widely variable in amplitude, motivating statistical approaches such as stochastic growth theory. Recent wave experiments on rockets moving through Earth's auroral regions, as well as the STEREO and Wind spacecraft, have sufficient time resolution to measure the waveform as well as the envelope field. Typically, however, experiments measure the envelope field averaged over long times compared with the wave period. Four sets of new contributions are presented. First, analytic theory is used to predict the distribution of waveform fields for a single mode with known distribution of envelope fields. The distribution P(log Ew) of waveform fields Ew is shown to be proportional to the rectified field Ewa with a ≍ 1.0 for a number of special cases of the distribution P(log Ee) of envelope field Ee. This form arises due to P(log Ew) being proportional to an integral over P(log Ee) that has a square-root singularity in Ee2. Numerical calculations confirm and extend this prediction to wide range of envelope distributions. Second, ensembles of stochastically-driven waves are simulated and the distributions P(log Ew) and P(log Ee) calculated. While small differences exist between the case of a single mode and multiple modes, it is found in general that the results are independent of the product of the wave frequency and decorrelation time. Of importance here is that the distributions P(log Ew) are found to be power-law with index ≍ 1.0 at low Ew, consistent with the analytic prediction. Moreover, the envelope distribution is found to be well fit by the form P(log Ee) ∝ Ee2 exp(- Ee2 / Eth2). This form applies to one- dimensional thermal waves and now, unexpectedly, also to waves driven stochastically near marginal stability. Third, initial calculations show that averaging (boxcar and sliding averages, whether linear or logarithmic) over multiple wave periods leads to both the envelope and waveform distributions being well fitted by lognormal distributions. Fourth, initial comparisons are made with Langmuir-like waves observed in Earth's cusp region by the TRICE rocket. It appears that the foregoing analytic and numerical calculations explain semi-quantitatively the power-law form and index near 1.0 for the waveform distribution of unaveraged fields, the functional form of the envelope distribution of unaveraged fields, and the transition of the waveform and envelope distributions towards lognormal forms with averaging over multiple wave periods. The waves appear consistent with stochastic growth. The theory and simulation results extend stochastic growth theory to measurements on timescales less than or close to the wave period.
Cairns Iver H.
Kletzing Craig A.
LaBelle James
Li Baowen
Robinson Adam P.
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