Mean free path values in wave-particle interactions&#160; of the solar wind with the Venus ionosphere&#160;
Authors: Pérez-de-Tejada Hector 
Published: July 2024

Issues related to the fluid dynamic behavior of the solar wind as a continuum gas emitted from the sun have led to an increasing number of phenomena related to its motion, and distribution through the solar system. Among them it has been necessary to provide a source that justifies the continuum response of its particles as they expand from the sun with continuously decreasing densities.&#160; As such, it is convenient to point out that their ability to interact among them through particle-particle collisions strongly decreases as they move away from the sun. As a result, conditions without that quality should be rapidly encountered thus diminishing the manner in which the solar wind behaves as a continuum. Different from reaching planetary magnetic fields conditions are encountered whre the solar wind interacts with non-magnetic planets (Venus, Mars)..&#160; In such case the solar wind conducts a turbulent stochastic interaction that force strong oscillations ( P&#233;rez-de-Tejada, 2024). Such conditions have not been resolved and require further analysis with calculations of parameters that are involved in the interaction process. In the data analysis presented below we will derive values for the mean free path of wave-particle interactions implied by the transport coefficients that are suitable to turbulent plasmas.&#160;While there have been adequate efforts to examine plasma motion produced by instabilities in the complex mixture of solar wind and planetary ion particles there are issues that have not yet been suitably considered. In particular, the effects of dissipative phenomena to their motion together with the manner in which they transfer statistical properties have not been properly explored. Interest in this respect was advanced by Liepmann and Roshko (1967) who proposed a technique adequate to the kinetic theory of gases and that can be applied to examine the conditions in the solar wind interaction with planetary ionospheres.A correlation between a suitable wave-particle interaction mean free path value &#955; and the kinematic viscosity and thermal conduction coefficients &#957; and k in a gas was derived by Liepmann and Roshko (1967) by using dissipation processes in the gas kinetic equations:&#160;&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#957; = vT &#955; &#160;&#160;for viscous dissipation &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(1)&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; &#160;&#160;&#160;&#160;&#160;&#160;&#160;vT &#955; = &#945; k/&#961;cp for thermal dissipation&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; &#160;&#160;&#160;&#160;&#160;&#160;&#160;(2)where &#961; and cp are the fluid density and its specific heat at constant pressure, and that were later employed by P&#233;rez-de-Tejada (2024) in an analysis of the solar wind interaction with the Venus ionosphere that led to estimate &#955; values in terms of the &#957; and k coefficients. &#160;A complementary analysis of that calculation will be conducted to explore the implications of considering varying values of the thermal speed vT of the solar wind and those of the kinetic viscosity coefficient &#957;. In particular, it can be noted in equation (1) that the &#955; value is inversely corelated to the thermal speed vT (60 km/s&#8211;100 km/s) of the solar wind in the Venus ionosheath where there are strong magnetic field fluctuations and that are available from the Mariner 5 spacecraft plasma data reproduced in Figure 1. In addition, by using the &#957; = 3 105 km2/s value of the kinematic viscosity coefficient derived from the momentum equation of the solar wind within a viscous boundary layer at and downstream from the Venus ionosphere (P&#233;rez-de-Tejada, 1999) it is possible to estimate from equation (1) that &#955; is in the 103 - 104 km range that is comparable to the (~ 6 103 km) scale size of the Venus wake. In addition to evidence of the strong magnetic field fluctuations indicated in the Venus inner ionosheath in Figure 1 there is further support for such variations from the plasma measurements reported in the plasma data of the Venera spacecraft. In this case there is evidence that the plasma temperature and the bulk flow speed experience distinct and frequent variations between labels 2 and 3 in the Venus inner wake which are reminiscent of those shown in Figure 1. As a result, the flow behavior reveals turbulent conditions that are peculiar of the solar wind as it streams around the Venus ionosphere. The &#955; values derived above are indicative of the mean free path values that are required to justify that behavior. In particular, smaller &#955; values should be expected in the inner regions of the ionosphere where vT shows larger values that lead to more notable turbulent conditions. &#160;Figure 1. (lower panel) Trajectory of the Mariner 5 spacecraft projected in cylindrical coordinates in its flyby past Venus. The labels 1 through 5 along the trajectory mark important events in the plasma properties (a bow shock is identified at features 1 and 5), the intermediate plasma transition occurs at features 2 and 4). (upper panel) Magnetic field intensity and its latitudinal and azimuthal orientation, together with the plasma properties (thermal speed, density and bulk speed) that were measured around Venus (Bridge et al., 1967). &#160;&#160;On the other hand, larger &#955; values could also be obtained far away from the interaction region where smaller thermal speeds are available in terms of the same &#957; value used by P&#233;rez-de-Tejada (2024).&#160; For example, if vT = 10km/s had been revealed in Figure 1, and we had applied the same &#957; = 3 105 km2/s value of the kinematic viscosity coefficient, equation (1) would now have led to &#955; &#8776; 2 104 km which is larger than the width of the interaction region. A description of this variation was depicted by P&#233;rez-de-Tejada (2024) to illustrate the manner in which &#955; varies as a function of vT for the &#957; = 3 105 km2/s value derived before. As a whole it is expected that &#955; &#8805; 103 km with small values expected in the Venus inner ionosheath where vT is larger. &#160;&#160;Liepmann J, and A. Roshko, Elements of Gasdynamics, John Wiley, 1967 (p.372); P&#233;rez-de-Tejada, H., ApJ, 525, L65, 1999; Wave-particle interactions in Astrophysical plasmas, Galaxies, 2024 (In Press); Bridge et al., Science,158, 1669, 1967.&#160;P&#233;rez-de-Tejada, H., Vortex structures in planetary plasma wakes, Cambridge Scholars Pub. ISBN (10):1-5275-0110-8, 2023.&#160;