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

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

Region of study

Figure 1

Figure 2

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.

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

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

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

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].

(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

Monte Carlo simulation

ResultsResults

HH++ ions temperature ions temperature

HH+ + ion velocity distributionion velocity distribution

OO++ ions temperature ions temperature

OO+ + ion velocity distributionion velocity distribution

0

2

4

6

8

10

0.1 1 10 100

T(H+) [eV]

Alt

itu

de

[RE

]

RCC Model

Bouhram Model

Barghouthi Model

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

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

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++::

RCC ModelRCC Model106106 eVeV

Bouhram ModelBouhram Model88 eVeV

Barghouthi ModelBarghouthi Model202202 eVeV

ObservationsObservations200200 eVeV

* *for Ofor O++: :

22 - -The TemperaturesThe Temperatures. .

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.

..

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.