1. -1- Solar wind turbulence from radio occultation data Chashei, I.V. Lebedev Physical Institute, Moscow, Russia Efimov, A.I., Institute of Radio Engineering & Electronics, Moscow, Russia Bird, M.K. Radio Astronomical Institute, Univ. Bonn, Bonn, Germany

2. -2- TURBULENCE  Turbulence is a permanent property of the solar wind.  Fluctuations spectra of B, N, V… cover many decades in wavenumbers / frequencies.  Formed flow R > 20 R S, in situ + radiooccultation data.  Acceleration region: R < 10 R S, no in situ data.  Below we concentrate mainly on Galileo and Ulysses spacecraft data.

3. -3- GEOMETRY OF CORONAL RADIO OCCULTATION EXPERIMENT

4. -4- OBSERVATIONAL DATA  SPACECRAFT GALILEO (1994-2002) AND ULYSSES (1991-1997)  HIGH STABILITY RADIO SIGNALS AT S-BAND (2295 МHz)  GROUND BASED NASA-DSN TRACKING STATIONS: –GOLDSTONE (DSS 14) –CANBERRA (DSS 43) –MADRID (DSS 63)  MEASUREMENTS OF FREQUENCY FLUCTUATIONS  SAMPLING RATE: 1 Hz  RECORDS AT INDIVIDUAL STATIONS → – TEMPORAL POWER SPECTRA OF FREQUENCY FLUCTUATIONS  CROSS CORRELATION OF OVERLAPPING RECORDS → – VELOCITY OF THE DENSITY IRREGULARITIES  SOLAR OFFSET R: 7 R  < R < 80 R 

5. -5- EXAMPLE (ULYSSES) OF FREQUENCY FLUCTUATION RECORD

6. -6- TEMPORAL POWER SPECTRA OF THE FREQUENCY FLUCTUATIONS  Typical temporal spectra are power law  Power law interval is bounded by the frequency of the turbulence outer scale at low frequencies and the noise level at high frequencies  Power law spectral index of the temporal frequency fluctuation spectrum  is related to the power law index of the 3D spatial turbulence spectrum р by the equation  = р-3

7. -7- FREQUENCY FLUCTUATION POWER SPECTRA: SOME EXAMPLES

8. -8- CROSS-CORRELATION FUNCTION: FREQUENCY FLUCTUATIONS

9. -9- ) RADIAL EVOLUTION OF THE SPECTRAL INDEX (LOW HELIOLATITUDES)

10. -10- RADIAL EVOLUTION OF THE SPECTRAL INDEX (HIGH HELIOLATITUDES, R = 22-30 R  )

11. -11- FRACTIONAL LEVEL OF DENSITY VARIANCE ( SLOW SOLAR WIND, GALILEO)

12. -12- DENSITY TURBULENCE OUTER SCALE

13. -13- DENSITY TURBULENCE OUTER SCALE Radial dependence approximation L 0 ( R ) = A ( R / R S ) m with A = 0.24 R S and m = 0.8, very close to linear.

14. -14- RESULTS  A change of the turbulence regime occurs at the transition from the acceleration region to the region of the developed solar wind. (Also, Woo & Armstrong, 1979)  FR fluctuations measurements in the acceleration regions shows that flat flicker type spectra with p=3 are also typical for magnetic field fluctuations (Chashei, Efimov, Bird et al., 2000). Recently (Chashei, Shishov & Altyntsev) the evidences were found from the analysis of angular structure of the sources of microwave subsecond pulses for such spectra in the lower corona.  The heliocentric distance of this change of turbulence regime is greater for the fast solar wind than for the slow solar wind during the period of low solar activity.

15. -15- RESULTS  The fractional density fluctuations tend to increase slowly with increasing heliocentric distance.  Turbulence outer scale increases approximately linear with increase of heliocentric distance in the range 10R S < R < 80 R S.  Galileo data (1994-2002): no changes of slow wind turbulence during the solar activity cycle.

16. -16- TURBULENCE MODEL (acceleration region)  The source of turbulence is a spectrum of Alfvén waves (magnetic field fluctuations), propagating away from the Sun.  Slow and fast magnetosonic waves are generated locally via nonlinear interactions with Alfvén waves. Density fluctuations are dominated by slow magnetosonic waves.  Turbulence is weak in the solar wind acceleration region (R < 20 R  ).  The fractional level of turbulent energy increases with increasing heliocentric distance.  Temporal power spectra are flat (  = 0,  р = 3.0). No cascading of turbulence energy from the turbulence outer scale to smaller scales.

17. -17- TURBULENCE MODEL (change in turbulence regime)  The turbulence power spectrum of the developed solar wind in the inertial spectral range is defined by nonlinear cascading processes. Source of turbulence energy – l.f. (outer scale) Alfven waves. Nonlinear generation of magnetosonic waves (density fluctuations) (Spangler &Spitler, Ph. Pl., 2004). Spectra: –Kolmogorov (p=11/3) or –Iroshnikov-Kraichnan (p=7/2) spectra.  The change in turbulence regime is caused by the increase of fractional turbulence level (and increase of fractional level of fast magnetosonic waves compared with slow magnetosonic waves).  The more distant transition for the fast solar wind may be explained by the lower value of the plasma parameter  = 4  P/B 2, i.е. by stronger ambient magnetic fields above the coronal holes.

18. -18- TURBULENCE MODEL (outer scale)  Data are related to the region of formed solar wind flow.  Model : W k =C 1 k -n at k k 0 ; linear (WKB) propagation of Alfven waves at k k 0 (Kolmogorov, Kraichnan, 4-waves interactions); equal linear and nonlinear increments at k=k 0 ; k 0 (R, n, m). LF spectrum can be assumed as flicker spectrum with n=1 (Helios =>Denscat, Beinroth & Neubauer, 1983; Ulysses => Hourbury & Balogh, 2001).  Comparison of the models with observational data: best agreement at n=1 is found for the Kraichnan turbulence.

19. -19- CONCLUSIONS  Turbulence regimes in the acceleration region and in the formed solar wind are strongly different.  Sufficiently good agreement between the observational data and the model.