2. Paired velocity distributions in the solar wind Vasenin Y.M., Minkova N.R. Tomsk State University Russia STIMM-2 Sinaia, Romania, June 12-16, 2007

3. Plasma flows (including solar wind) are traditionally described by one- particle velocity distributions for electrons and ions. Thus motion of each plasma species is modeled separately and Coulomb interactions of particles are considered in approximation of a mean polarization field ψ and collision integrals I: (1) Observed large scale fluctuations of solar plasma density suggest to consider strong interparticle interactions in quasineutral two-component plasma by applying two-particle velocity distribution : (2) Introduction The two-particle kinetic models of the solar wind are presented in the paper (for different approximations of plasma polarization field). The derived analytical dependences for plasma flow density and speed are compared to observational data.

4. The kinetic equation for a steady spherically symmetrical flow of collisionless quasineutral electron-proton plasma (magnetic field influence is neglected): (3) where k=e, p refers to electron and proton, r,θ,φ – spherical coordinates; φ’, ψ’ denote radial gradients of the Sun’s gravitational potential φ(r) and plasma polarization potential ψ(r) The assumed bi-maxwellian distribution at the exobase r 0 (T 0e =T 0p =T 0: ) yield the solution for f at r>r 0 (Fig.1): (4) that is defined over the phase domain D : (5) Where. A monotone potential of particles is assumed. Two-particle kinetic model and the first integrals of the kinetic equation (3) (conservation laws)

5. Figure 1. Evolution of the velocity distribution function f (4),(5) along the heliocentric distance axis r in projection on the proton velocity space and the definition domain of f (5) (scales are relative,, eψ≈m p φ/2)

6. The integration of f over the domain D and u re u rp f 2 over the domain D → of escaping particles yield respectively squares of number density N 2 and flux Nu 2 of a plasma flow because plasma is assumed to be steady (zero flux of ballistic particles), quasineutral (N e =N p ), and currentless (Nu e =Nu p ): where The analytical dependence for the flow speed U=Nu/N reproduces the terminal value that is consistent with observations of in-ecliptic solar wind (under assumption eψ 0 =m p φ 0 /2) : The derived stationary dependences N(r), Nu(r), U(r) exist if the considered monotone polarization potential have values within the following domain: The corresponding radial dependences of solar wind density and speed covers rather narrow domains of values. The theoretical results N * (r), U * (r) calculated for the equilibrium potential eψ=m p φ/2 deliver respectively the upper and lower estimations for the considered model: N(r)≤N * (r), U(r)≤U * (r). The Fig.2 demonstrates the estimators N * and U * in comparing to observational data as well as to an one-particle kinetic and a fluid models formulated for similar assumptions. Density and speed

7. Figure 2. The empirical dependence of the solar wind number density (dotted line - Rubtsov, et.all 1987) and the theoretical dependence N * (solid line). The theoretical speed dependence U * (solid line) and the observational data (Yakubov, 1997). The dotted line – Hartle-Barence hydrodymanic two-fluids model (Hundhausen, 1976); dash-dotted line – one-particle kinetic model (Lemaire, Pierrard, 2003 – r 0 =5R s ). NUMBER DENSITY AND SPEED OF THE SOLAR WIND

8. Solar wind acceleration The analyze of the analytical results shows that the total density N~r -2 decreases at r>>r 0 slower than the density of ballistic particles N bal ~r -2.5. Thus the part of ballistic particles (that do not contribute the flux and serve as a ballast) reduces and the flow speed increases by approaching to the terminal bulk velocity of escaping particles. Neutral model The two-particle model is considered also in the neutral approximation that can be interpreted as the statistics of dynamic electron-proton pairs: This model does not depend on the polarization potential and produces upper estimations for U(r) derived in the frame of the model presented above (respectively blue solid and dashed lines on the Fig.3). The results of the neutral model are also consistent with observations. Figure 3.

9. Conclusions Thus the presented two-particle kinetic approach reproduces the observed solar wind acceleration that is provided by energy of thermal motion of particles at the exobase where plasma is assumed to be equilibrium. The analytical dependences of density and speed are consistent with observational data for the in-ecliptic solar wind and allow to suggest the explanation of solar wind acceleration. References 1.Hundhausen A.J. 1976 Coronal expansion and solar wind. Moscow, Mir. 2.Lemaire J.F., Pierrard V. Conference Proceedings, 2003, 663. Rarefied gas dynamics. 23th International symposium. P.857-964. 3.Koehnlein W 1996 Solar Phys. 169 P.209-213. 4.Rubtsov S. N., Yakovlev O. I. and Efimov A. I. 1987 Space Research. 25, 2. P.251. 5.Yakubov V. P. 1997 Doppler Superlargebase Interferometery. Tomsk, Vodoley 6.Vasenin Y.M., Minkova N.R, Shamin A.V. 2003 AIP Conference Proceedings. 669 P.516-519 7.Vasenin Y. M., N.R. Minkova 2003 J. of Physics A: Mathematical and General, 36 P. 6215. THANK YOU FOR YOUR ATTENTION!