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

1. Electrostatic fluctuations at short scales in the solar-wind turbulent cascade. Francesco Valentini Dipartimento di Fisica and CNISM, Università della Calabria, Italy francesco.valentini@fis.unical.it • In collaboration with: • D. Perrone and P. Veltri, Università della Calabria • F. Califano and F. Pegoraro, Università di Pisa

2. 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 Vienna WPI - Valentini

3. Electrostatic activity at short wavelengths Ion-Acoustic waves Valentiniet 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 Vienna WPI - Valentini

4. The ion-bulk waves Valentiniet al., in press in PRL Boltzmanian electrons Vlasov – Yukawa (VY) model Proton distribution function Debye length Vienna WPI - Valentini

5. 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, forexample, Valentinietal., PoP 2006 and Johnstonet al. , PoP 2009 Vienna WPI - Valentini

6. Ion-bulk wave dispersion relation No solutions are recovered for From thumb to tear drop for an non-neutral electron plasma:

7. 10.00 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, forexample, Valentinietal., PoP 2006 and Johnstonet al. , PoP 2009 Vienna WPI - Valentini

8. Time evolution of three electric field Fourier components m=1,4,6 Numerical results Resonance curve IA IBk Vienna WPI - Valentini

9. Proton distribution function During the driving process we observe the generation of trapped proton populations and of unstable regions with positive velocity slope Vienna WPI - Valentini

10. Proton distribution function Generation of wavepackets locked in the phase space votices, in the spatial region of positive velocity slope LOCAL SECONDARY INSTABILITY Vienna WPI - Valentini

11. 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 Vienna WPI - Valentini

12. Late time evolution Secondary vortex merging and very long lived soliton-like waveform Mangeney et al., 1999: Isolated electrostatic structures (data from WIND)

13. 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! Vienna WPI - Valentini