University of Kansas

Cassini Studies

DRAFT

A Two-Dimensional Multifluid MHD Model of Titan's Plasma Environment

T. E. Cravens, C. J. Lindgren, and S. A. Ledvina

Appendix

Collision Terms for Quasi-Multi-Fluid MHD Equations

A.1 Collision Terms for Continuity Equations

The net source term for the continuity equation for species s can be expressed as S_s = R_s - L_s, where R_s is the primary plus chemical production rate and L_s is the chemical loss rate. The primary production rates (R_s0) were shown in Figure 2 for the three species. At higher altitudes these production rates are just proportional to the density of the relevant neutral species.

No chemical production is assumed for the light species, but chemical losses occur due to ion-neutral reactions with the medium and heavy mass neutrals and due to dissociative recombination with electrons. Denote the light, medium, and heavy ion species as L+, M+, and H+ and the neutrals as L, M, H. The light ion chemistry (and reaction rate coefficients) are:

L⁺ + M ---> M⁺ + L	k_LM	(A1)
L⁺ + H ---> H⁺ + L	k_LH	(A2)
L⁺ + e ---> light neutrals	a_L	(A3)

Some more medium species chemistry is:

M⁺ + M ---> H⁺ + L	k_MM	(A4)
M⁺ + e ---> neutrals	a_M	(A5)

Some further heavy species chemistry is:

H⁺ + e ---> neutrals

(A6)

The dissociative recombination rates were representative values from Keller et al. [1992]: a_s = a_s0 (300 / T_e)^1/2 with a_L0 = 3.3 x 10^-7 cm³ s^-1, a_H0 = 7 x 10^-7 cm³ s^-1, and a_H0 = 6.4 x 10^-7 cm³ s^-1. The ion-neutral rate coefficients were chosen to improve the relative abundances of the ion species in comparison with Keller et al.: k_LM = 2 x 10^-10 cm³ s^-1, k_MM = 1 x 10^-10 cm³ s^-1, and k_LH = 3 x 10^-10 cm³ s^-1.

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REFERENCES

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Last modified January 28, 2004

Tizby Hunt-Ward
tizby@ku.edu