1. Multiparticle statistical approach to solar wind modeling Minkova N.R. Tomsk State University Russia STIMM-2 Sinaia, Romania June 12-16, 2007 June 12-16, 2007

2. The two-particle kinetic models [1,2] reproduce the observed acceleration of the in-ecliptic solar wind. At the same time one-particle kinetic models do not provide such acceleration under the same assumptions (Maxwellian distribution at the exobase; quasineutral currentless plasma flow, etc.). How can be interpreted this difference of results? What basic provisions of statistical modeling do provide it? These questions serve as a starting point of investigations presented in the paper. The answers are suggested in the frame of the multiparticle statistical approach [3]. Introduction Fluid models

3. According to the classical statistical approach the mean values of the local number density for the system of N  particles are defined on the base of the additive microscopic local density (for example Klimontovitch 1982, Balescu 1978). In result the particle system is specified by an one-particle probability distribution function. This conception is followed implicitly by the assumption that particles coordinates are distinguishable and therefore resolution scales of instruments are not taken in account. MULTIPARTICLE APPROACH

4. The suggested model is formulated for a flow of particles that is observed with a finite instrumental resolution (respectively particle coordinates are indistinguishable on distances of resolution scales). In this case a flow is specified by a joint probability function that describes chances for N particles to occupy the volume which scale is prescribed by an instrumental resolution. Correspondingly the function is derived on the base of the multiplicative microscopic phase density n N defined as a product of functions - in contrast to the additive form of classical definition (1). The reduced functions define macroscopic parameters of a plasma flow. Remark: The hierarchy of the reduced functions is based on the distribution function that describe the total system of N  particles and is consistent with the Liouville theorem under some assumptions.

5. The multiparticle approach is tested successfully by the following classical problems: density fluctuations in a finite volume occupied by ideal gas (Landau) ideal gas in a gravitation field (Boltzmann distribution of density in latitude) TEST PROBLEMS

6. SOLAR WIND MODEL IN APPROXIMATION OF COLLISIONLESS QUASI-NEUTRAL PLASMA FLOW The suggested multiparticle approach yields the distribution function of probabilities that a probing volume is occupied by N particles. For a steady collisionless spherical flow of quasi-neutral k-component plasma this distribution is polynomial: For the fully ionized hydrogen (two-component) plasma this distribution reduces to a binominal one with the density average: that coincides with the results of the two-particle kinetic model [2] and is consistent with observational data (Koehnlein; Rubtsov;Yakubov - Figure 1, ). The derived relations for solar wind flux and speed U= /N also coincide with the results of the two-particle kinetic model [2] and are consistent with the observational data (Figure 1). The difference between theoretical and observational dependences for plasma density is less then 30% [6,7]. The theoretical values of the solar wind speed are inside the straggling of the related observational data [6,8].

7. Figure 1. The empirical dependence of the solar wind number density (dotted line - Rubtsov) and the theoretical dependence (solid line). The theoretical speed dependence (solid line) and the observa- tional data (Yakubov). The dotted line – Hartle-Barence hydrodymanic two- fluids model; dash-dotted line – one-particle kinetic model (Lemaire,Pierrard). NUMBER DENSITY AND SPEED OF SOLAR WIND

8. CONCLUSIONS The analyze shows that the difference between one- and multi-particle kinetic theories originates from different approaches to modeling of measurable macroscopic parameters. The classical statistical theory operates with distinguishable coordinates of particles and correspondingly plasma parameters are calculated on the base of one-particle probability functions. The multiparticle statistical approach is formulated for description of plasma (gas) flows observed with a finite instrumental resolution what means that particles’ coordinates are indistinguishabe within resolution scales. Plasma parameters are defined in this case by N-particle probability functions. The better agreement of the results (density and speed) produced by the multi- and the two-particle statistical models with the observational data in comparison to one-particle kinetic models (under similar assumptions) can be considered as an argument in favor of the suggested approach.

9. References [1] Vasenin Y. M., Minkova N.R., Shamin A.V. A kinetic model of solar wind // AIP Conference Proceedings. - 2003. V. 669, series Plasma Physics: 11th International Congress on Plasma Physics: ICPP2002. P. 516-519. [2] Vasenin Y.M., Minkova N.R. Two-particle quasineutral kinetic model of collisionless solar wind.// Journal of Physics A. Mathematical and General. - 2003, V.36, Issue 22. P.6215-6220. [3] Minkova N.R. Multiparticle statistical approach to the collisionless solar plasma modeling. // Izvestija vuzof. Physics (Russian Physics Journal).-2004. V.47, No.10 (Special issue on Applied problems of mechanics of continua). P. 73-80. [4] Klimontovitch Yu.L. Statistical physics. – 1982. Мoscow, Nauka. Pp. 22, 31, 595-597. [5] Balescu R. Equilibrium and nonequilibrium statistical mechanics. V.1 - 1978. Moscow, Mir. P.89. [6] Landau L.D., Livshitz E.M. Statistical physics. – 1964. Мoscow, Nauka. Pp. 421-423. [7] Koehnlein W. Solar Physics. - 2000. V. 169. P. 209-213. [8]Rubtsov S. N., Yakovlev O. I. and Efimov A. I. Space Research. –1987. V.25, 2. P.251. [9] Yakubov V. P. Doppler Superlargebase Interferometery.–1997.Tomsk, Vodoley.P.136. Thank you for your attention! nminkova@ftf.tsu.ru nminko@mail.tomsknet.ru