Electrostatic fluctuations at short scales in the solar-wind turbulent cascade.

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Electrostatic fluctuations at short scales in the
solar-wind turbulent cascade.
Francesco Valentini Dipartimento di Fisica and
CNISM, Università della Calabria,
Italy francesco.valentini_at_fis.unical.it

• In collaboration with
• D. Perrone and P. Veltri, Università della
  Calabria
• F. Califano and F. Pegoraro, Università di Pisa

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Outline

• Vlasov simulations of solar wind turbulence
  electrostatic activity at short spatial lengths,
  consisting of waves with phase speed close to the
  thermal velocity of protons (ion-bulk waves)
• The ion-bulk waves, electrostatic oscillations
  driven by particle trapping effects the
  Vlasov-Yukawa model
• Dispersion relation of the ion-bulk waves
  analogies with non-neutral plasmas
• Numerical Vlasov-Yukawa simulations the
  excitation of the ion-bulk waves can be obtained
  even at low values of the electron to ion
  temperature ratio (relevant for space plasmas)
• The late time evolution generation of long lived
  soliton-like waveform
• Conclusions

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Electrostatic activity at short wavelengths
Ion-Acoustic waves
Valentini et al., PRL 2008 Valentini and Veltri,
PRL 2009
Fourier spectrum of the electric energy
New branch of waves
The proton distribution function

• Diffusive longitudinal plateau
• F. Kennel and F. Engelmann Phys. Fluids 9, 2377
  (1966)
• - M. Heuer and E. Marsch J. Geophys. Res. 112,
  A03102 (2007)

Ion-Bulk waves at phase speed close to
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The ion-bulk waves
Valentini et al., in press in PRL
Boltzmanian electrons
Vlasov Yukawa (VY) model
Proton distribution function
Debye length
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Plasma dielectric function
Weak damping or amplification
We assume a plateau of vanishing velocity width
in the proton velocity distribution that suppress
wave damping
Ion-acoustic waves
See, for example, Valentini et al., PoP 2006 and
Johnston et al. , PoP 2009
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Ion-bulk wave dispersion relation
No solutions are recovered for
From thumb to tear drop for an non-neutral
electron plasma
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Numerical simulations
The system dynamics is investigated in terms of
the electron to proton temperature ratio
External driver electric field (applied ONLY to
the Vlasov equation for protons)
See, for example, Valentini et al., PoP 2006 and
Johnston et al. , PoP 2009
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Numerical results
Resonance curve
IA
IBk
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Proton distribution function
During the driving process we observe the
generation of trapped proton populations and of
unstable regions with positive velocity slope
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Proton distribution function
Generation of wavepackets locked in the phase
space votices, in the spatial region of positive
velocity slope LOCAL SECONDARY INSTABILITY
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Bump-on-tail like instability
We evaluate the imaginary part of the wave
frequency using the distribution function from
the simulations
The bump is not on the tail of the distribution
but the theory works very well
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Late time evolution
Secondary vortex merging and very long lived
soliton-like waveform
Mangeney et al., 1999 Isolated electrostatic
structures (data from WIND)
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Summary and conclusions

• We have demonstrated the existence of a new
  branch of electrostatic waves with acoutic-like
  dispersion and sustained by trapping effects
• These waves have phase speed comparable to the
  proton thermal velocity and can be excited even
  at low values of the electron to ion temperature
  ratio
• Our numerical results can represent a new
  interpretation of the electrostatic noise
  recovered in the high frequency region of the
  turbulent spectra in the solar wind

THANK YOU!