Indian Journal of Radio & Space Physics Vol. 28, February 1999, pp . .36-42

Field aligned current and parallel electric field between magnetosphere and ionosphere of Mars

S A Haider, S P Seth* & K S Raina

Physical Research Laboratory, Ahmedabad 380 009

Received 2 September 1998; revised received II December 1998

A ~ t cady ~ta(c kinetic model is used to estimate the electron current density at different potential differences between the ll1ag ncto~phere and ionosphere of Mars. For this calculation it is assumed that Mars has a weak dipole magnetosphere whose plasma sheet is connected to the ionosphere along the magnetic field lines. The total electron flux of 5 . 79x I0~ cm-2

S- I i~ cal cu lated in the Marti an magnetosphere corresponding to the downward current density of 1.0x I0-{i A/m2 at zero potential dillercnce. The maximum flux of thermal electrons escaping towards the plasma sheet of Mars at zero current density is c il cul ated to he 3.0x I OX cm-2

S- I. At zero current density the precipitating flux of plasma sheet electrons is approxilllately equal to max imum escape flux of thermal electrons. The calculated results are found to be in reasonable agreel11cnt with the experimcntal data obtained from Hyperboli c Ret arding Potential Analyzer (HARP) experiment onboard PIHlhos-2 .

I Introduction The solar wind interacti on with Mars is hi ghly

cont rove rsial mainl y beca use of insufficient data. The measure lllcni s from Mars-2,-3 and -5 have been used to prov ide evidence that Mars has an intrinsic magnet ic fi eld wit h a d i pole moment 1.1 in the range of 1.:iO-2 .2x IOI :igauss em' and that the field can be effective obstacle to the so lar wind . Relati vely large obstac le height and lack of ionopause-like signatures in the pla\ ma de.nsity 1 have also been considered to support thi s argument. Recent results from Phobos-2 encoutller indicate that Mars should have hybrid magnetosphen.:: ~ whic h is the combination of intrinsic magnet ic field emanating from the pole of a weak dipole and Venu s- like draped interplanetary fi eldS suppl y ng in the ne ighbourhood of the magnetic eq uat or.

The case for direct interacti on of so lar wind wi th Mars has been di scussed by Luhmann et a l .f> They pointed out that Mars' ionosphere is weak and solar wind pressure exceeds the ionospheric pressure most of the time. The situat ion is thus similar to solar maximum of Venus ionosphere under hi gh solar wind pressure. Shinagawa and Cravens7 have proposed an one-dimensional magneto-hydrodynamic model of the Martian ionosphere and concluded that Mars"

*Perillall cllll y at Bhavan' s R A Colkge of Science, Ahmedabad .1ilO OOl)

intrinsic magnetic fi eld is very small which does not playa major ro le in so lar wind interaction . On the other hand Lundin et {(I . R, I) and Barabash et al. 10 have found striking similarities between ionospheric outflows from Mar'S and Earth. Lammer and Bauer l

t

used an intrinsic magnetosphere for the transportation of ionospheric ions from the days ide cusp region to the plasma sheet of Mars. [n the present study also an intrinsic magnet ic fi eld has been used to calculate polar wind flux and densities I2.13 at Mars. This ca lculati on suggests that physical process of ions escap ing from the ionosphere of Mars and Earth at high latitude should be the same inspite of small Martian magnetosphere compared to that of Earth .

The magnetospheric plasma is essentiall y colli sion less. In such a plasma, the parallel electric fi eld free ly accelerate particles along the magnetic field lines between the ionosphere and pla'sma sheet. The e lectron s and ions are accelerated in opposite directions giving rise to a current along the n1agnetic fi eld lines. The elect rons make the dominant contribution to net e lectric current because the mobility of the ion is lower than the mobility of the electrons. In thi s paper, a kinetic model is used to calculate the parallel electric current carried by elect rons along the intri nsic magnetic fi eld lines connecting- the ni ghttime ionosphere of Mars with the plasmasheet. The va lidit y of this model rests upon the assumption that the sca le of magnetic fi e ld gradients

"

HAIDER 1'/ ,,/. CU RR ENT & ELECTRIC FIELD IN MAGNETOSPHERE-IONOSPHERE OF MARS 37

is much smaller than the particle gyro-radius, so that the guiding centre approximation is valid l2 as is generall y the case throughout .the magnetosphere of Mars. To obtain parallel current along the magnetic field line the Maxwellian steady state solution for electrons was used for the ionosphere and plasma sheet. The electron temperature in the plasma sheet 1.\ 15 of Mars is about 106 K and the density vari esx

.13 from - 0.1 to 10 el.cm-'; so the mean free

path is about 1010 cm. However, the mean free path fa ll s to the order of 107 cm at the exobase where maximum electron temperature is about 2000 K ana h . h . d d . 16-1 R . I 01 I -, Th t e IlIg tSI e enslty IS - . e .cm . . us, we

can describe elec tron motion along the Martian fi eld line by means of co lli sion less Boltzmann equation.

2 Calculation Foll owing Kn ight l9 and Lemaire and Scherer20 the

parallel current density of electron is calcul ated between the ionosphere and plasma sheet of Mars. The formul a of the electron current density used in the calcul ati on is given below:

+ BE ]exP( - x) Bs

. .. (I)

where, t = Ts/TE, n (the rati o of electron densities) = N,y'NE, x = e (<1>E - <1>s)/ KTE, K the Boltzmann constant , e the electronic charge, B the magnetic field intensity between the ionosphere and plasma sheet, m the mass of the electron, x the dimensionless potential difference, I the rati o of electron temperatures, <1> the electric potenti al and T and N are the electron temperature and density, respecti vely. The subscripts Sand E on the temperature, density, potential and magneti c fi eld terms refer to their values on the bases of plasma sheet and exosphere, respectively. The electron flu x at any point on the magnetic fi eld line of Mars can be calcul ated from Eq. ( I) as N e. Rosenbauer e l al.21 have reported approx imate area of plasma sheet region varyi ng from 15000 km to 15235 km with its di ameter of two Mars radi i. In the present

calculation we have taken the height at the bases of exosphere and plasma sheet at about 200 km 'and 15000 km, respectively .

For Eq. ( I ), the magnetic field is calcu}ated using the following relations:

B, = -2j.l cos8/ / + BT sin 8cos<l> (2)

(3)

(4)

where, 8 is the colatitude, r the radial distance and <I> the longitude measured from midnight meridian. The parameters j.l and BT are the magnetic moment and current sheet fi eld , respectively. The Martian magnetic moment and current sheet field are taken22

as 1.39x lO12 Tm' and 5 nT, respectively . For this calculati on two assumptions were made :

(i) Mars has weak dipole magnetosphere which wi II be modified by magnetospheric currents fl owing around it , and

(ii ) The directi on of solar wind is perpendi:;ular to the dipole axis (which is colinear with the axis of planetary rotation) and parallel to Mars-Sun line.

The parameters r, 8 and $ , as a function of distance s along the magnetic fi eld lines, are calculated by the following numerical solutions:

dr = B / B ds '

· . . (6)

· . . (7)

d<l> = _I_ (B / B) ds r sinS <I>

· .. (8)

Using Eq. (5) the intensity of the magnetic fi eld at the exobase (200 km) is obtained to be 60 nT, while in the plasma sheet at -1 5000 km, it is found to be 6 nT.

The electron density (NE) and temperature (7s) at the bases of nightti me exospherel5.18 and plasma

38 I DIAN J RAD IO & SPACE PHYS, FEBRUARY 1999

sheet 14 of Mars are taken to be 1.0x IO·~ cm -J and 1.0 x lOll K, respec ti vely. The electron density in the

plasma sheet varies from 0.1 to 10.0 cm-J (Ref. 8) . The calculations are made at Ns = 0.1, 1.0, 5.0 and 10.0 cm-J

. The pl asma temperature in the exosphere of Mars IS uncertain because of insufficient measurements in the ionosphere and magnetosphere. The ion temperature profiles measured by Viking I ·and 2 in the daytime exosphere of Mars are highly vari abl e. ~ 1 . ~4 At the exobase it varies from 2500 K to

30000 K . Singhal and Whitten25 calculated exospheric e lec tron temperature of about 700 K in the nighttime Martian ionosphere . Shinagawa and Cravens7 have reported that calc ulated electron temperature profi les of Chen et a/.26 and Rohrbaugh ef a t . n for the day time are more consistent with the measured va lue. Boughe r ef al. 2R used thi s electron temperature having h=2S00 K at th.e exobase for the calcu lation of the night;;ide neutra l density of Mars.

J<) • f d24 I Fox- IIlcorporated the va lues 0 measure e ectron temperature for her ionospheric calcul at ion (Her electron temperature profile is simil ar to that calculated by Rohrbaugh ef a/

27) . The upper limit of

ni ghtt ime exospheri c plasma temperature l 2 has been reported to be ~ 2300 K by Hai der l

2. In the present paper, ca lcu lations are made at different exospheric elec tron temperatures, i.e . at h =SOO, 1000, 1500 and 2000 K .

-~ ...... (/)

z w o ......

1.2)(16~

~ :3oX166

a: a: => u

o

1=500

3 Results and discussion During in situ measurements onboard Phobos-2

Martian orbiter, the large electron fluxes were measured by Hyperbolic Retarding Potential Analyzer (HARP) experiment l4 in the magnetotai l lobes and in the plasma sheet. The main population of these electron fluxes were found to be isotropic except in the high energy ta il of the spectra. The total electron fluxes in the magnetotail lobes and plasma sheet of Mars were estimated l5 to be 4.0x 103 cm-2

S- I and _108 cm- 2

S- I, respective ly. Thus, the ~um of these e lec tron fluxes of -·S.OxI08 cm-2

S- I was measured in the Martian magnetosphere. Although ~ome of these e lec trons were found moving towards Mars , yet it is not clear what magnitude of the·se electron fluxes actually do precipitate into the atmosphere . In earlier studies I5

..'o.J I, we had assumed th~t tota l e lectron flux observed e ither in the magnetotail lobes or pl asma sheet reac hes at the top of Martian atmosphere. Thi s assu mption can be verified froT'9 the calcu lated results of electron current densit ies ~hown in Figs 1-5 at different values of Il and t . In Figs 1-5 the electric potential and current are given in the un its of Khle and NE e (KTdm)l l2 , respective ly. These uni ts give the potential and e lectron current in volt and ampere/m2

,

respective ly. It is fo und that the current densities are increasi ng with exospheric temperatures from TE = SOOK, 1000K, ISOOK and 2000K for electron

-4 n = IXIO

POTENTIAL DIFFERENCE. V

ril! . I - Pilritllt.:l l! lt.:c tri c current densi ty as a functi on of the electric poten ti al difference hetween the ionosphere and plasma sheet of Mars for 11 = 1.0x I 0-4

HAIDER el a f. : CURRENT & ELECTRIC FIELD rN MAGNETOSPHERE-IONOSPHERE OF MA RS

Ne "-<l: ->-~

(f)

z w 0

~ z w a::: a::: ::> u

1.2XI05

1=500

0

-3.0XI06

102

->­r-(/)

z w o r-

1.2XI05

9.0XI08

6.0XI08

o

~ -3.0XI06

0::: 0::: :::> U -6.0XI06

-1.2XIO!l

101 Ie? 10'

-3 n=IXIO

POTENTIAL DIFFERENCE. V

Fig. 2-Same as in Fig. I, but fo r n= 1.0x I 0-.1

-3 n '5XIO

POTENTIAL DIFFERENCE, V

Fi g. 3-Same as in Fig. I, but for n=S .Ox I 0-.1

39

40 INDIAN J RADI O & SPACE PHYS, FEBRUARY 1999

NE "-<l . >-..... UJ Z W 0

..... Z w a:: a:: :::> u

12XI05

6.0X106

- 60XI06

- 1.2XI05

- l.exlo 5

-2.4XI0 5

-30X105

102

t~500

10 ' 100

10'

-2 n = I X 10

POTENTIAL DIFFERENCE, V

Fig. 4-Same as in Fig. I, but for 11= 1.0x I 0-2

,= 500

-2AXIO!l

-4 n = I X 10

POTENTIAL DIFFERENCE, V

Fig. 5-Same as in Fig. l, but for different values of nand 1=500

prec lpitatlllg onto the Martian ionosphere. At low plasma sheet density the large currents are flowing towards Marti an ionosphere. For large plasma sheet density , most of the elec trons were found going away from Mars.

From Eg. ( I), it is seen that for no potential difference (x=O), J 'I ex: ( I-ll ...) t) . For thi s condition, the

field aligned current is posItive, i.e. the current is flowing towards the ionosphere of Mars. A't this limit the precipitating flux of plasma sheet electrons is approximately equal 10 S.79x 108

. cm-2 S-I

corresponding to the parallel electric CutTent density of I .Ox I 0-6 Alm2

• This is in close agreement with the total elec tron flux of -5.0>: 108 cm-2

S- l measured by

HA IDER el at. : CU RRENT & ELECTRIC FIELD IN MAGNETOSPHERE-IONOSPHERE OF MARS 4 1

HARP ex periment in the Martian magnetosphere. This also confirms the earlier assumption IS that total elec t. un flu x measured by thi s experiment is precipitating into Martian atmosphere. For infinite potential difference (x=oo), J II ex: -11-Yt(BEIBs). Therefore, the electron current will be negative, i.e. it will be fl owin g towards the pl asma sheet from Martian ionosphere . For negati 've current , the parallel current densit y increases with potenti al difference reac hing a maximum va lue dependent upon fl . The max ima is obtained when the magnitude of potential difference is sufficientl y large, i.e. neariy all electrons incident upon the top of the region of potential va riati ons al ong the field lines are accelerated so as to be within the atmospheric loss cone. Due to these two boundary conditi ons the null current is obtained. At thi s limit the prec ipitating flu x of the plasma sheet electron is approx imately equal to the maximum escape flu x of thermal electrons. The maximum escape flu x of thermal electrons at 2000 K is obtained to be ].Ox IOx cm-2

S- I from Eq. ( I) as given by Haider. ' 2 Th is is in good agreement with the electron flu x measured by HARP experiment in the pl asma sheet of Mars. The null point va ries with different va lues of 1/ and f . It increases with smaller values of t . The va lue of f is always greater than unity. Therefore, as long as .I( Bs I Bd < I and x « BE tl Bs we can ex pand and truncate the ex ponential in Eq. ( I) which gives dependence of parallel current density to ( I +x )t' - , « 1/ I. Later it increases linearly like - Il I( I +xlr) unti I the second approx imation x«

BEllBs IS no longer va lid where upon the currents are saturated ~l pidl y .

The parallel electri c field due to electrons trave lling on the magnetic field line between the ionos phere and the plasma sheet can be calculateQ

'E ll sin g the potential difference as <D E - cDs = - J Elld.'·,

':5 where, r E and rs are the heights on the bases of exospht' re amI pl asma sheet, respecti ve ly. The values of r E and 1\ are reported2 U 2 to be about 200 km and 15000 km, respecti ve ly. In earlier studi es I2

.13 the ion

density distributi ons and loca l quasi-neutrality conditi on of exospheri c plasma have been discussed. In these studies the parallel elect ric field di stributions for electrons and ions (CO/ , 0+, O2+, and NO+) on the magnet ic fi eld lines of Mar.s were calculated. The electric potenti al distribution $(r), or the parallel

electric fi eld EII= -V"$(r) will generally lead to an electron density NE and a scale height HE which differ from the total ion density I i Ni and the ion scale height Hi. As a consequence, an unrealistic electric space charge density would ex ist in the whole exosphere of Mars. Indeed, the parallel electric field in the plasma determines the electron and ion density gradients or scale height along the mag!1etic field lines. At each altitude, there will be a unique value of Ell such that V' lI l1e=V'1I I, Ni and Ne=Ii Ni. This electric fi eld decreases ' 2 with altitude and is approximately equal to 1.0 IlV/m in the Martian magneto~phere . The parallel electric field carried by electrons at zero current is also ca lculated to be 1.0 IlV/m at the exobase using the potential difference $E - IPs < 1.0 V.

4 Summary and conclusion A steady state kinetic model is used to calculate the

parallel electron current density at different potenti al differences in the exosphere of Mars. For th is

calculation, it is assumed that the ionosphere of Mars

is connected to the plasma sheet through the weak

dipole magnetic field lines. It is found that for zero

potential difference the field aligned current is

pos itive fl owing towards the ionosphere of Mars. At

thi s limit the precipitating flux of plasma sheet electrons is approximately equal to 5.79x 108 cm-2

S-I

corresponding to the parall el electric current density

of 1.0x 106 Nm2 Thi s is in close agreement with the total electron flu x of 5.0x 108 cm-2

S- I measured by

HARP experiment in the Martian magnetosphere. For

infinite potenti al difference. the electron current will

be negati ve flowing towards the plasma sheet from

the ionosphere of Mars. At zero current density, the

prec ipitating flux of plasma sheet electrons IS

approximately equal to maximum escape flux of

thermal electron s. The maximum escape flux of thermal electrons at exospheric electron temperature 2000 K is obtained as 3.0x 108 cm-2

S- I, matching well

with the electron flux measured by HARP experiment

in the plasma sheet of Mars. This suggests that the physical processes of electrons' escape and their precipitation between the ionosphere and magnetosphere of Mars could be the same as it was observed in the magnetosphere of Earth .

42 IND IA N J RADIO & SPACE PHYS, FEBRUARY 1999

Acknowledgements The authors are grateful to Prof. R Sridharan and

Prof. A C Das for thei r help and encouragement in preparing thi s paper.

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