بسم الله الرحمن الرحيم prof. imad a. barghouthi department of physics, al - quds...
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الرحيم الرحمن الله بسم
Prof. Imad A. Barghouthi
Department of physics, Al - Quds university Jerusalem - Palestine
Second Physics Conference – 20077 & 8 May, 2007
An-Najah National UniversityNablus - Palestine
Comparison of wave – particle interaction models for H+ and O+ Comparison of wave – particle interaction models for H+ and O+ ions outflow at high altitudes equatorward ions outflow at high altitudes equatorward
of the cusp with observations:of the cusp with observations: The Barghouthi modelThe Barghouthi model
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OutlineOutline 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, fs (vs, rs ,t) . The velocity distribution function is defined such that fs(vs ,rs, t) dvsdrs represents the
number of particles of species s which at time t have velocities between vs and vs+ dvs, and positions between rs
and rs+drs. The changing of the distribution function with respect to time (changing of vs, rs ) because of the net effect
of many external forces can be described Boltzmann equation:
)].1
([.t
ff
cm
ef
t
f ssvss
s
sss
s
BvEgv
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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;
(1) 1
v
fvD
vvt
f
WPI
(2)
22
2
3
3
2
2
vknAnKdd
m
qD n
n
(3) ,2
1,,
2
1 221
222
221 kEJkE
v
JvkEJA Rn
n
Lnn
(4) )(4
2
2
2
xE
m
qD
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To improveTo improve the altitude dependence of the diffusion coefficientthe altitude dependence of the diffusion coefficient..
BarghouthiBarghouthi, [1997] and , [1997] and Barghouthi et al.,Barghouthi et al., [1998] processed the [1998] processed the
data collected by PWI on board the DE-1 space craft; they data collected by PWI on board the DE-1 space craft; they obtained the following expressions for in the region obtained the following expressions for in the region
equatorward of the cuspequatorward of the cusp..
(5)
.Ofor ,sec)(1094.6
.Hfor ,sec)(1045.4
)(323.135
3295.77
cmRr
cmRr
rD
E
E
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However, the adoption of this altitude dependent However, the adoption of this altitude dependent diffusion coefficient and similar ones such as the adopted diffusion coefficient and similar ones such as the adopted by by Crew et alCrew et al., [1990], ., [1990], Barghouthi Barghouthi [1997], and [1997], and Barghouthi Barghouthi et al.et al., [1998] results in unrealistically high ion , [1998] results in unrealistically high ion temperatures at high altitudes and did not produced the temperatures at high altitudes and did not produced the above observations of non-Maxwellian features at middle above observations of non-Maxwellian features at middle (4 (4 RREE) and high ( 8 ) and high ( 8 RREE) altitudes, such as H) altitudes, such as H+ + and Oand O+ + ion ion
toroids and Htoroids and H+ + and Oand O++ ions temperature. The description ions temperature. The description of these non-Maxwellian features requires a velocity of these non-Maxwellian features requires a velocity dependent diffusion rate as suggested by dependent diffusion rate as suggested by Retterer et alRetterer et al., ., [1994].[1994].
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(1) RCC model: based on the work of (1) RCC model: based on the work of Crew and ChangCrew and Chang, , [1985]; [1985]; ChangChang [1993], [1993], Retterer et alRetterer et al., [1987a, b, 1994].., [1987a, b, 1994].
(6)
14
1)(),(
ovv
ovv
rDvrD
) ) 22 ( (Bouhram model: based on the work of Bouhram model: based on the work of Bouhram et Bouhram et alal., [2004]., [2004]..
(7) )(),( 20
i
vkJrDvrD
(3) Barghouthi model: based on the work of (3) Barghouthi model: based on the work of BarghouthiBarghouthi, [1997], , [1997], Barghouthi et al.Barghouthi et al., [998], and , [998], and Barghouthi and AtoutBarghouthi and Atout, [2006]., [2006].
(9)
1for
1for 1
)(),(3-
ii
i
vk
vk
vk
rDvrD
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Monte Carlo simulation
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ResultsResults
HH++ ions temperature ions temperature
HH+ + ion velocity distributionion velocity distribution
OO++ ions temperature ions temperature
OO+ + ion velocity distributionion velocity distribution
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0
2
4
6
8
10
0.1 1 10 100
T(H+) [eV]
Alt
itu
de
[RE
]
RCC Model
Bouhram Model
Barghouthi Model
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0
2
4
6
8
10
0.1 1 10 100 1000
T(O+) [eV]
Alt
itu
de
[R
E]
RCC Model
Bouhram Model
Barghouthi Model
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ComparisonComparison
Comparison with Huddelston et al., (2000) observations at Comparison with Huddelston et al., (2000) observations at 24000 km in the equatorward region of the cusp:24000 km in the equatorward region of the cusp:1- the velocity distribution function. 1- the velocity distribution function.
H+
Fig. 15
-2
0
2
4.8 Re
-2
0
2
4.8 Re
-2 0 2
-2
0
2
4.8 Re
-2
0
2
4.8 Re
-2
0
2
4.8 Re
-2 0 2
4.8 Re
O
Observations
RCC Model
Bouhram Model
Barghouthi Model
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2- The Temperatures .2- The Temperatures .
RCC ModelRCC Model6.06.0 eVeV
Bouhram ModelBouhram Model2727 eVeV
Barghouthi ModelBarghouthi Model7474 eVeV
ObservationsObservations7878 eVeV
* *for Hfor H++::
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RCC ModelRCC Model106106 eVeV
Bouhram ModelBouhram Model88 eVeV
Barghouthi ModelBarghouthi Model202202 eVeV
ObservationsObservations200200 eVeV
* *for Ofor O++: :
22 - -The TemperaturesThe Temperatures. .
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Evidences for Barghouthi modelEvidences for Barghouthi model
1) Produces O1) Produces O++ conics at 2 geocentric distance conics at 2 geocentric distance (Winningham and Burch, 1984).(Winningham and Burch, 1984).
2) Consistent with the observations of Arvelius et al., (2005)2) Consistent with the observations of Arvelius et al., (2005)
(i.e. O(i.e. O++ ions have been accelerated from less than 1 keV to more than 1 keV ions have been accelerated from less than 1 keV to more than 1 keV
between 8 and 12 between 8 and 12 . . geocentric distancegeocentric distance ..
3) Consistent with observations of Eklund et al., (1997) (i.e. the existence of 3) Consistent with observations of Eklund et al., (1997) (i.e. the existence of keV OkeV O++ ions at high-altitudes. ions at high-altitudes.
4) Consistent with Bouhram et al. (2004), they have suggested finite 4) Consistent with Bouhram et al. (2004), they have suggested finite perpendicular wavelength of the electromagnetic turbulence.perpendicular wavelength of the electromagnetic turbulence.
5) Consistent with the calculations of Curtis (1985), (i.e. for 80 eV H5) Consistent with the calculations of Curtis (1985), (i.e. for 80 eV H++, v, vthethe= =
101077cm/s.cm/s.
6) Consistent with the estimates of mean particle theory (Chang et al., 1986).6) Consistent with the estimates of mean particle theory (Chang et al., 1986).
7) Consistent with Nilsson et al., (2006), they observed that O7) Consistent with Nilsson et al., (2006), they observed that O++ ions drift velocity ions drift velocity is ~ 60 km/s at 7 geocentric distance.is ~ 60 km/s at 7 geocentric distance.
..
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ConclusionConclusion
The different forms of velocity diffusion coefficientThe different forms of velocity diffusion coefficient
RCC modelRCC model
Bouhram modelBouhram model
Barghouthi modelBarghouthi model
++
Monte Carlo simulationMonte Carlo simulation
ProduceProduce
O+ and H+ ions temperatures and velocity distributionsO+ and H+ ions temperatures and velocity distributions
AtAt
high altitudes in the equatorward region of the cusp.high altitudes in the equatorward region of the cusp.
The results of these models have been compared with the corresponding The results of these models have been compared with the corresponding observations of observations of HuddlestonHuddleston et al.et al. [2000]. [2000].
As a result of comparisonAs a result of comparison
we have found an excellent agreement between the observationswe have found an excellent agreement between the observations
and the Monte Carlo calculations obtained by and the Monte Carlo calculations obtained by
Barghouthi model.Barghouthi model.
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