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Compressibility and scaling in the solar wind as measured by ACE spacecraft

Compressibility and scaling in the solar wind as measured by ACE spacecraft. Bogdan A. Hnat. Collaborators: Sandra C. Chapman and George Rowlands; University of Warwick. Solar wind: Introduction. Stream of supersonic and super-Alfvénic particles originated from the Sun

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Compressibility and scaling in the solar wind as measured by ACE spacecraft

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  1. Compressibility and scaling in the solar wind as measured by ACE spacecraft Bogdan A. Hnat Collaborators: Sandra C. Chapman and George Rowlands; University of Warwick

  2. Solar wind: Introduction • Stream of supersonic and super-Alfvénic particles originated from the Sun • Velocity ~500 km/s, density ~5 cm-3, IMF ~5 nT (at Earth’s orbit) • Consists of electrons, protons (96%), ions (4%) • Exhibits slow and fast components with different properties

  3. Solar wind propagation

  4. Objectives • The main objective of this study was to characterise solar wind fluctuations and develop a stochastic model for their dynamics. • Scaling , if exists, can simplify the description • Some quantities are known to be fractal and are difficult to model (velocity, magnetic field) • We will examine other quantities, such as density (solar wind often assumed to be incompressible) • Which quantities are active and which are passively advected?

  5. Segments: Fluctuations: Length depends on scale Scaling: basic concepts Building blocks Scaling Statistics depends on scale self-similarity

  6. Scaling in ρ and |B| ESS Conditioning: events < 15 σ(τ)

  7. Is density a passive scalar ACE spacecraft data for density and magnetic field Comparison of HD and MHD turbulence simulations B is a passive scalar but density is not Suggests that solar wind plasma is compressible Hnat, Chapman, Rowlands, Phys. Rev. Lett. 94 (2005)

  8. Passive scalar: quantity passively advected in the turbulent velocity field. Passive scalars ∂tT = - (vi ∂i) T + κ ∂i ∂i T (1) • Magnetic field magnitude B is a passive scalar in solar wind [Bershadskyi, PRL 2005] • Incompressible MHD was used to cast equation for B in form (1) • Density should then also be a passive scalar ∂tρ = - (vi ∂i) ρ (2)

  9. Model of the density fluctuations Fluctuations in density are approx. self-similar This result suggests that a Fokker-Planck approach could be used to describe the PDF. Consider following equation and solve for P

  10. Fokker-Planck model Red line: self-similar solution of the F-P equation Result: complete statistical characterization of density fluctuations up to 15 standard deviations Hnat et al., Phys. Rev. E 67 (2003)

  11. Conclusions • Scaling in |B| and ρ are very different • Fluctuations in density are well approximated by the self-similar scaling • F-P approach gives good solutions for PDF dynamics • Density appear to play important role in the ecliptic • Results could be used to develop sub-grid models for solar wind turbulence • Part of the ongoing effort to describe solar wind turbulence

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