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Intermittency in solar wind induced electric
field
DIPARTIMENTO DI FISICA
Luca Sorriso-Valvo
Vincenzo Carbone
Sezione di Cosenza
Roberto Bruno
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INTRODUCTION
We analyse PDFs of the solar wind induced
electric field e-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
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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
• -ezvxby-vybx, P(vi)P(bi) gaussian hp. on
  corr.
• P(ez) exponential tails
• Milano et al., PRE 65, 026310, 2002

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SIMULATIONS
DNS of the 2-dimensional MagnetoHydroDynamics
equations
z? v B/(4pr)1/2 are the Elsasser variables,
2n? n ? h, F? external forcing, P total
pressure
Pseudo-spectral method, resolution 1024²
induced electric field PDF
Re 1600
data 2107 pts
The current j
exponential tails
simulations H. Politano A. Pouquet,
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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 2 spacecraft in situ measurements

• We thus define
• fast streams with v0 gt 550 km/sec
• slow streams with v0 lt 450 km/sec

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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
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x
magnitude
z
y
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)
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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

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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 F3. Fgt3 indicates rising tails of the PDFs.
The growth of F toward the small scales is the
signature of intermittency.
fast wind
slow wind
Flatness
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INTERMITTENCY by PDFs
fast wind
slow wind
x
y
x
y
Small scale stretched exponential
Inertial range raising tails
Large scale nearly Gaussian
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A multifractal model for PDFs
According to multifractal models, the P(df) at
scale t is 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 a d-function centered in s0 ?
  computing the convolution, the resulting P(df) at
  scale t is Gaussian

• As l² increases, L(s) is wider ? more and more
  Gaussians of different width are summed ? the
  tails of P(df) become higher

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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

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Results for the induced electric field
Results for v and b
Results for e components
y
x
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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.