Presentation on theme: "A parametric study of frequency sweep rate of chorus wave packets E. Macúšova (1), O. Santolík (1,2), P. Décrèau (3), D. A. Gurnett (4), J. S. Pickett."— Presentation transcript:
A parametric study of frequency sweep rate of chorus wave packets E. Macúšova (1), O. Santolík (1,2), P. Décrèau (3), D. A. Gurnett (4), J. S. Pickett (4), D. Nunn (5), A. G. Demekhov (6), E. E. Titova (7) (1) Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, (2) IAP/CAS, Prague, Czech Republic, (3) LPCE/CNRS, Orleans, France, (4) University of Iowa, IA, USA, (5) ECS, Southampton University, UK, (6) Institute of Applied Physics, Nizhny Novgorod, Russia, (7) Polar Geophysics Institute, Apatity, Russia. Whistler-mode chorus consists of intense electromagnetic wave packets generated by a nonlinear mechanism. Source region of chorus emission is localized close to the geomagnetic equatorial plane. Chorus wave packets are discrete time-frequency structures in a frequency range from a few hundreds of Hz to several kHz changing their frequency at time scale from a few tenths of seconds to a few seconds. Our investigation is based on multipoint measurements of the wideband (WBD) plasma wave instruments on board the four Cluster spacecraft. We investigate the sweep rate of the emission frequency as a function of the plasma density in the equatorial plane measured by the WHISPER active sounder and we then compare it with theoretical and simulation results. A model based on the Backward Wave Oscillator (BWO) theory, a numerical simulation using Vlasov Hybrid Simulation (VHS) code and also our experimental results give an increasing sweep rate for a decreasing background plasma density. INTRODUCTION Table 1. The first column shows processed cases, the second column contains average electron densities, the third column shows median values of frequency sweep of risers, the fourth column contains number of processed risers events, the fifth column contains median values of frequency sweep of fallers and the last column contains the number of fallers for each case. We have investigated the sweep rate of the chorus emission frequency as a function of the cold plasma density in the equatorial plane near L = 4.2 – 4.6 R E The theoretical scaling based on the BWO theory and also numerical simulations predict increasing sweep rate of chorus elements for decreasing cold plasma density. Preliminary results of our study seem to be consistent with these predictions. The duration of the processed wave packets varied between 30 and 500 ms. In the future we would like to investigate the sweep rate as a function of wave amplitude. Figure 2a-e: Examples of histograms of the sweep rate of individual chorus elements (events are sorted from the lowest electron density to the highest) measured on following days. 2a) on December 06, 2003. The average electron density during the time interval (14:30 - 15:00 UT) was around 9 particles per cc and Kp index was 3 0 and the L = 4.6R E ( L = Mc’Ilwain’s parameter). During this day occurred mostly risers. 2b) on January 20, 2004 during the time interval (19:25-19:30 UT) the average electron density was 11 cm −3, Kp index was 4 + and 3 − and the L value was 4.3 R E. We observe mostly fallers. 2c) on November 19, 2001 from 12:00 to 12:45 UT the average electron density was about 12 cm−3, L value was 4.4 R E and the Kp index was 3 +. 2d) From 13:56 UT to 14:20 UT on March 25, 2002 the Kp index was 2 0, the electron density was about 27 cm −3. On this even we observe only risers close to L= 4.5R E. 2e) on October 21, 2001 during the processed time interval (23:15 - 23:35 UT) at L = 4.2R E the geomagnetic activity was very high, with the Kp index 8 −. The average electron density was about 192 cm −3. 2e 2b 2c 2a2d Figure 6 CONCLUSIONS REFERENCES Nunn et al.(2005), A parametric study of the numerical simulations of triggered VLF emissions, Annales Geophysicae, Volume 23, Issue 12, pp.3655-3666, 2005. Trakhtengerts et al.(2004), Interpretation of Cluster data on chorus emissions using the backward wave oscillator model, Physics of Plasmas, Volume 11, Issue 4, pp. 1345-1351, 2004. Figure 5. Each point characterizes the median value of the sweep rate for one of all processed time intervals of all chorus events versus the average value of electron density. The error bars describe quantiles: Q 16/100 and Q 84/100. Red dashed lines represent results from the numerical simulation Nunn et al. (2005) and the green dash-dot line represents theoretical scaling (see Fig.6) based on the BWO model of Trakhtengerts et al. (2004). We fit median values of the sweep rate of the measured risers with the theoretical model using a least squares method. Figure 3a-b: Probability density function of the duration of chorus elements measured a) on December 6, 2003 and b) on October 21, 2001. 3a3b Figure 6. Each point and error bar represents the same as in the Figure 5. Red dashed lines - the numerical simulation as in Figure 5. Green dash-dot line describes linear fit of theoretical scaling based on the model of Trakhtengerts et al. (2004) with input parameters: log (N e ), logarithm of median of risers and measurements errors ((logQ 16/100 -logQ 84/100 )/2). Blue dash-dot line is linear fit with input parameters: log (N e ), logarithm of geometrical average of Q 16/100 and Q 84/100 and uncertainties (log(Q 84/100 - median value of risers)) Figure 1. Example of chorus elements measured on board of Cluster satellites on December 22, 2001 by the wideband (WBD) plasma wave instrument. Spacecraft position is given on the bottom: UT-universal time; λ m -magnetic dipole latitude; R E - Earth radius; MLT-magnetic local time.