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بسم الله الرحمن الرحيم Prof. Imad A. Barghouthi Department of physics, Al - Quds university Jerusalem - Palestine Second Physics Conference – 2007 7 & 8 May, 2007 An-Najah National University Nablus - Palestine Comparison of wave – particle interaction models for H+ and O+ ions outflow at high altitudes equatorward of the cusp with observations: The Barghouthi model The Barghouthi model

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Outline Region of study Statement of the problem Boltzmann equation Monte Carlo simulation Wave-particle interaction Results Comparison Conclusion

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Region of study Figure 1

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Figure 2

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Statement of the problem Several mechanisms of wave-particle interactions [Chang and Coppi, 1981; Chang et al., 1986; Retterer et al., 1987a, b, 1994; Crew et al., 1990; Barghouthi, 1997; Barghouthi et al., 1998; Barghouthi and Atout, 2006, Bouhram et al., 2003a, b, 2004] have been suggested for investigating the energization of keV H + and O + ions in polar region, and to explain the non-Maxwellian features of ions outflows at high altitudes and high latitudes. In this presentation, we are interested to compare between the simulation results of three wave-particle interactions models with observations, and to choose the best model that produce acceptable simulation results when compared to the corresponding observations.

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Boltzmann Equation In dealing with gas mixtures it is convenient to describe each species in the mixture by a separate velocity distribution function, f s (v s, r s,t). The velocity distribution function is defined such that f s (v s,r s, t) dv s dr s represents the number of particles of species s which at time t have velocities between v s and v s + dv s, and positions between r s and r s +dr s. The changing of the distribution function with respect to time (changing of v s, r s ) because of the net effect of many external forces can be described Boltzmann equation:

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Wave Particle interaction The effect of wave-particle interactions can be represented by particle diffusion in the velocity space [Retterer et al., 1987]; that is;

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To improve the altitude dependence of the diffusion coefficient. the altitude dependence of the diffusion coefficient. Barghouthi, [1997] and Barghouthi et al., [1998] processed the data collected by PWI on board the DE-1 space craft; they obtained the following expressions for in the region equatorward of the cusp. Barghouthi, [1997] and Barghouthi et al., [1998] processed the data collected by PWI on board the DE-1 space craft; they obtained the following expressions for in the region equatorward of the cusp.

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However, the adoption of this altitude dependent diffusion coefficient and similar ones such as the adopted by Crew et al., [1990], Barghouthi [1997], and Barghouthi et al., [1998] results in unrealistically high ion temperatures at high altitudes and did not produced the above observations of non-Maxwellian features at middle (4 R E ) and high ( 8 R E ) altitudes, such as H + and O + ion toroids and H + and O + ions temperature. The description of these non-Maxwellian features requires a velocity dependent diffusion rate as suggested by Retterer et al., [1994]. However, the adoption of this altitude dependent diffusion coefficient and similar ones such as the adopted by Crew et al., [1990], Barghouthi [1997], and Barghouthi et al., [1998] results in unrealistically high ion temperatures at high altitudes and did not produced the above observations of non-Maxwellian features at middle (4 R E ) and high ( 8 R E ) altitudes, such as H + and O + ion toroids and H + and O + ions temperature. The description of these non-Maxwellian features requires a velocity dependent diffusion rate as suggested by Retterer et al., [1994].

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(1) RCC model: based on the work of Crew and Chang, [1985]; Chang [1993], Retterer et al., [1987a, b, 1994]. (1) RCC model: based on the work of Crew and Chang, [1985]; Chang [1993], Retterer et al., [1987a, b, 1994]. (2) Bouhram model: based on the work of Bouhram et al., [2004]. (2) Bouhram model: based on the work of Bouhram et al., [2004]. (3) Barghouthi model: based on the work of Barghouthi, [1997], Barghouthi et al., [998], and Barghouthi and Atout, [2006]. (3) Barghouthi model: based on the work of Barghouthi, [1997], Barghouthi et al., [998], and Barghouthi and Atout, [2006].

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Monte Carlo simulation

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Results Results H + ions temperature H + ion velocity distribution O + ions temperature O + ion velocity distribution

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Comparison Comparison with Huddelston et al., (2000) observations at 24000 km in the equatorward region of the cusp: 1- the velocity distribution function. H + Fig. 15 Observations RCC Model Bouhram Model Barghouthi Model

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2- The Temperatures. 6.0 eV RCC Model 27 eV Bouhram Model 74 eV Barghouthi Model 78 eV Observations * for H + :

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106 eV RCC Model 8 eV Bouhram Model 202 eV Barghouthi Model 200 eV Observations * for O + : 2- The Temperatures.

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Evidences for Barghouthi model 1) Produces O + conics at 2 geocentric distance (Winningham and Burch, 1984). 2) Consistent with the observations of Arvelius et al., (2005) (i.e. O + ions have been accelerated from less than 1 keV to more than 1 keV (i.e. O + ions have been accelerated from less than 1 keV to more than 1 keV between 8 and 12. geocentric distance. between 8 and 12. geocentric distance. 3) Consistent with observations of Eklund et al., (1997) (i.e. the existence of keV O + ions at high-altitudes. 4) Consistent with Bouhram et al. (2004), they have suggested finite perpendicular wavelength of the electromagnetic turbulence. 5) Consistent with the calculations of Curtis (1985), (i.e. for 80 eV H +, v the = 10 7 cm/s. 6) Consistent with the estimates of mean particle theory (Chang et al., 1986). 7) Consistent with Nilsson et al., (2006), they observed that O + ions drift velocity is ~ 60 km/s at 7 geocentric distance..

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Conclusion The different forms of velocity diffusion coefficient The different forms of velocity diffusion coefficient RCC model Bouhram model Barghouthi model + Monte Carlo simulation Produce O+ and H+ ions temperatures and velocity distributions At high altitudes in the equatorward region of the cusp. The results of these models have been compared with the corresponding observations of Huddleston et al. [2000]. As a result of comparison we have found an excellent agreement between the observations and the Monte Carlo calculations obtained by Barghouthi model.

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