DIPARTIMENTO DI FISICA

1. Intermittency in solar wind induced electric field DIPARTIMENTODIFISICA Luca Sorriso-Valvo Vincenzo Carbone Sezione di Cosenza Roberto Bruno

2. INTRODUCTION We analyse PDFs of the solar wind induced electric fielde=-vxb We show that the induced electric field is characterized by intermittency. Breech et al. (JGR, 2003) reported on PDFs of the interplanetary induced electric field, using the NSSDC Omnitape database, including 30 years of hourly averaged spacecraft measurements of solar wind fields PDFs of the induced electric field from their data show exponential tails

3. BACKGROUND • Data used by Breech et al. include: • 1hour averages • different solar activity levels • fast and slow solar wind (and interfaces between them). • Exponential tails for field components has been previously investigated theoretically and using numerical data. • If velocity and magnetic field components have gaussian PDFs, and satisfy some hypothesis about their correlations • -ez=vxby-vybx, P(vi)=P(bi)= gaussian + {hp. on corr.} • P(ez) = exponential tails • Milano et al., PRE 65, 026310, 2002

4. SIMULATIONS DNS of the 2-dimensional MagnetoHydroDynamics equations z=v ± B/(4pr)1/2are the Elsasser variables, 2n=n h, F external forcing, P*total pressure Pseudo-spectral method, resolution 1024² induced electric field PDF Re ~ 1600 data: 2×107 pts The currentj exponential tails simulations: H. Politano & A. Pouquet,

5. SOLAR WIND DATA • data: ~ 104 pts, sampling time: 81 sec • velocity and magnetic field  e=-vxb • Separation in fast and slow streams Fast wind Slow wind Helios 2spacecraft: in situ measurements • We thus define: • fast streams with v0 > 550 km/sec • slow streams with v0 < 450 km/sec

6. PDFs of the field components We compute the PDFs of the components and the magnitudes of the fields (v, b and e) in the SE frame (x || V0) using the standardized variables:

7. x y z magnitude fast wind slow wind velocity x magnetic field = induced electric field almost gaussian PDFs! the only case presenting exponential tails... (not true in the x|| B0 frame)

8. Comments... • Our results are quite different from those by Breech et al. • Possible reasons for measured PDFs differences: • the different time resolution • the mixing of fast and slow wind, as well as the non-steady interstream regions, in OMNITAPE data • the widely diffrent solar activity in OMNITAPE data • The mixing of different physical conditions could be responsible for the exponential tails found by Breech et al. • Possible reasons for differences with respect to theoretical and numerical results: • violation of conditions about correlations, anisotropy…

9. INTERMITTENCY We study the intermittency of the induced electric field. Look at the Flatness of the field increments at different scales t. The gaussian reference value is F=3. F>3 indicates rising tails of the PDFs. The growth of F toward the small scales is the signature of intermittency. fast wind slow wind Flatness

10. INTERMITTENCY by PDFs fast wind slow wind x y x y Small scale: stretched exponential Inertial range: raising tails Large scale: nearly Gaussian

11. A multifractal model for PDFs According to multifractal models, the P(df) at scaletis obtained as superposition of Gaussians, each one: • ...describing the statistics in different regions of space • ...with different variance  • ...opportunely weighted : We must choose a model for the weight of each gaussian in the convolution. For example: Log-normal distribution of the variances  Castaing et al., Phys. D 46, 177 (1990) • l²= 0, L(s)is ad-function centered ins0computing the convolution, the resultingP(df)at scaletis Gaussian • As l²increases, L(s)is wider  more and more Gaussians of different width are summed  the tails ofP(df)become higher

12. Relevant parameters of the model The parameter ² is found to behave as a power-law of the scale and its scaling properties can be used to characterize the shape of the PDFs • l²max, the maximum value of the parameter l² within its scaling range, representing the non-gaussianity of the PDF • b, the ‘slope’ of the power-law, representing the efficiency of the non-linear cascade

13. wind l²max b wind l²max b fast 0.67±0.04 0.29±0.03 fast 0.74±0.04 0.06±0.02 slow 0.79±0.03 0.12±0.02 slow 0.86±0.03 0.09±0.01 field l²max b vfast 0.51±0.04 0.44±0.05 vslow 0.37±0.03 0.20±0.04 bfast 0.88±0.04 0.19±0.02 bslow 0.73±0.04 0.18±0.03 Results for the induced electric field Results for v and b Results for e components y x

14. CONCLUSIONS • From the analysis of the Helios 2 solar wind time series, we find that the induced electric field components have quasi-Gaussian probability distribution function for both fast and slow wind. • The model presented by Milano et al.is not reliable to reproduce the solar wind induced electric field features as observed from Helios 2 data. • This could be due to the presence of correlations between the field components, which are more complex than cross-helicity type. • The induced electric field is shown to be intermittent through the analysis and modeling of the field increments PDFs. • Intermittency could in fact be a candidate responsible for long-range correlations characterizing the solar wind fields.