Published In: Advances in Space Research, Vol. 31, No. 5, Pp. 1217-1222, 2003

Published in: Advances in Space Research, Vol. 31, No. 5, pp. 1217-1222, 2003

ON THE SPACECRAFT PHOTO-EMISSION EFFICIENCY IN INNER MAGNETOSPHERE

V. Afonin

Space Research Institute (IKI) Russian Acad. Sci, ,Profsoyuznaya 84/32,117997 GSP-7 Moscow,Russia,

ABSTRACT

The emission of photoelectrons from the surface of a satellite in conditions of low density plasma plays crucial role for the spacecraft structure potential, which sets up on the value defined by condition of the currents balance – at steady state conditions total current to the satellite body should be zero. It is commonly believed that in high- latitude inner magnetosphere at altitudes exceeding ~1RE the spacecraft potential Usat is always positive. On the other side, two experiments at Interball-2 have shown (Smirnova et al., 2002) that its potential was predominantly negative. One of possible reasons may be lowered photo emission efficiency in the Interball-2 case. As largest photo-emitting part of Interball-2 structure were flat solar panels, the photo-emission for flat model of a satellite have been calculated for variety of the satellite parameters, including the negative spacecraft potential, and ambient conditions using close-to-real model of electric field distribution around the satellite body. Results of modeling are presented. The largest impact on spacecraft potential comes from the presence of the ambient magnetic field, its orientation, and the size of spacecraft body. In particular, it is shown that in some cases large input to the photoemission efficiency arises from collection of photoelectrons by backward surface of the satellite.

INTRODUCTION

The spacecraft potential is a key parameter in measurements of low-energy plasma and in large extent is defined by photoemission from the satellite surfaces. The purpose of this paper is to analyze photoemission ability of satellites. We consider following factors, affecting the photoelectron emission efficiency, (Jph0 is the photocurrent at zero spacecraft potential, <…> means averaging over the satellite surface), the spacecraft potential, Usat, the size of a satellite, and the magnetic field. Magnetic effect on photoemission was mentioned by Grard et al., 1973, where they noted that the particle tend to escape along the magnetic field lines, and this effect should be particularly marked in outer magneto-sphere where the gyroradius of 1 eV electrons is of the order of 10-30 m. To our knowledge, the only paper dealing with magnetic field and size effect on photo-emission is by Veselov and Buzulukova [2001]; the authors considered only central point of one, sun-illuminated, hemisphere and used not quite correct model of electric field distribution around the satellite. In present paper we use more realistic model of electric field and consider photoelectron collection by both illuminated and shadowed satellite sides.

SATELLITE AND ELECTRIC FIELD

Models and Calculations We have calculated 3-D trajectories of photoelectrons emitted Fig. 1. Electric field around a plane from the surface of a 2D model satellite for plasma conditions of satellite.

1 Interball-2 high-altitude polar passes in Northern outer magnetosphere. Satellite Model. The specific feature of Interball-2 satellite is rather large solar plane panels, constituting the major area defining the photocurrent to the satellite. Thus in the present calculations the satellite was assumed to be flat disk with radius Rsat, both sides of which are conductive. We use Cartesian coordinates with Z-axis along the normal to the satellite surface, Fig. 1. The satellite is sun illuminated at the face side from +Z direction. Trajectories of photoelectrons were calculated from Newton’s law for a charged particle in electric and magnetic fields

medVe(R)/dt = qe(E(R) + [Ve(R) x B]), (1) Fig. 2. Sequence of trajectories for photoelectrons with energy E0=4.0 eV emerging at location R0=(15m, where me and qe are the mass and charge of the electron, R = (x,y,z) is the radius vector of a point in the space, 0, 0) of large, Rsat=30 m, plane satellite with azimuth = 20 and elevations stepped by 3 between 0 and Ve(R) is the velocity of the particle, E(R) is the electric      field strength, and B = (Bm, , ) is the ambient 180 for positive satellite (Usat=+3 V, upper panel) geomagnetic field. The magnetic field was assumed to be and negative satellite (Usat=-3 eV, lower panel). constant with arbitrary direction and its vector was Magnetic field is absent. Note that in case of attractive specified by the magnitude Bm and two angles – the satellite some trajectories end at the back side of the azimuth  and elevation . satellite. Electric field E(R) around a satellite depends on the satellite surface potential Usat, its geometrical form and the ambient plasma parameters. At any point of the satellite surface, including edges and backside E(R) = E0 x n, where n is normal to the satellite surface. Close to the face and back surfaces the field is directed along the normal n and decreases with Z-coordinate. In XY-plane at edges and further away the field vector E is in the XY-plane and aligned with the radius-vector R. At large distances R>>Rsat the field is also aligned with vector R. Weakening the electric field with distance from the satellite surface was taken in commonly accepted form of Debye screening. As the accurate calculation of E(R) is rather complicated, we adopted simplified model of electric field distribution around the plane satellite. The whole space was separated into three regions: - two near regions, consisting of two hemispheres with radius Rsat covering both face and back sides of the plane satellite, where electric field is Z-axis aligned (directed along the normal n to the surfaces) E(R) = E0 x exp(R/D) x n (2) - and far region outside, where electric field is radius-aligned E(R) = E0 x exp(R/D) x R/R. (3) The latter region includes edges of the satellite and (3) properly defines E(R) at the edges and away in XY-plane. Resulting model electric field distribution around the satellite is shown in Figure 1. The upper panel shows E- field in Z=0 plane and lower in X=0 plane (in Y=0 plane the pattern is identical). Each arrow shows direction and magnitude of the field (point marks the end of a vector). As is seen, this model is close to real distribution, except of small local regions close to the satellite edges at the boundary of near and far regions. In the following we assume that photo electrons emerge with a given initial energy E0 and isotropic distribution over directions – the azimuth  and elevations  [Grard et al., 1973]. It is assumed also, that the photoyield does not change with photon angle of incidence, which leads to a small underestimate of photoemission [Grard et al., 1973]. The effective photoemission area for a flat satellite is its illuminated cross-section Rsat2. Example of trajectory calculations for no magnetic field case and positively and negatively charged satellites are shown in Figure 2.

SATELLITE POTENTIAL, SIZE AND GEOMETRY FACTORS

In this section we shall consider the case with no magnetic field. Qualitatively, positively charged satellite, Us>0, attracts photo electrons and Usat value defines the attracting ability, forcing photo electrons back to the surface of SC and thus reduces the photoelectron current, Iph. Negative satellite, Us<0, repels photo-electrons and helps them to run away, thus contributing to Iph. The criterium of photo electron escape is its initial energy:

2 E0  Us for positive satellite (4) and E0  0 for negative satellite. (5) Conditions (4) and (5) are used when considering the satellite (or probe) photocurrent and explicitly or tacitly were used in numerous analyses of satellite equilibrium potential. In case of small satellite (Rsat<< Rdeb) a good approximation is a point. In this case, the electric field is radial, the single criterium of photoelectron escape is its initial energy, and photoemission is controlled by (4) and (5). If a satellite body is not a point, i.e., its size has finite dimensions, the condition for particle escape is more complicated; in this case the cos() effect appears and the particle behavior depends on many factors – elevation , size of the satellite and structure of electric field around the satellite. The particle escapes according to condition (4) only if it is emitted at  =90. At lower elevations it may return to the satellite surface even when E0  Us (due

Fig. 3. Photoelectron with an initial energy E0=3 eV, emerging at elevation 45, returns back at Usat2.4 V.

Fig. 4. Usc=+3.0 V. E0=3.5 eV . Series of trajectories for different elevations (see labels near curves). Photoelectrons are emitted at the center of flat satellite, R0=(0,0,0) and escaped at 20    13 and   60, returned to face at 12 0 and 60    33 and reach the back side at 32    17 . The photoemission efficiency for this point on the satellite surface Jph/Jph0 = 0.444. to the cos law). Example is shown in Figure 3. Photoelectron emerging with small elevations, less than some critical value, < c, will be forced back to the SC surface and will be lost immediately. At higher elevations photoelectron passes the edge and may either escape or reach the back side of the satellite. This is illustrated in Figure 4 that shows a series trajectories for different elevations at the right and an azimuth-elevation map (AE-map) at the left, displaying areas in angle space with the same type of trajectories, emerging at specified point. The AE-map was obtained by computing trajectory for each

Fig. 5. Attractive satellite Usc=+2.0 V, E0=2.0 eV, assumed usually as not-emitting. Calculated effective photoemittivity is 0.576.

3 5x5 cell in azimuth-elevation space and each trajectory was grayscale coded as “gone” if the particle escapes (white), or either “face-collected” (black) or “back- collected” (gray color) otherwise. When going from =0 to =90 the particles will be “face-collected’, “gone”, “back-collected”, again “face- collected”, and finally “gone” again. Another example is shown in Figure 5 for photoelectron energy E0=2.0 eV and the attractive satellite potential Us=+2.0 V, lowest sufficient to catch all emitted photoelectrons; thus we should expect that the photocurrent should be zero. Upper left plot represents the satellite face surface divided into square bins with Rs/10 side. For each of such bin AE-maps have been calculated and color coded Fig. 6. Fraction of escaping photo-electrons, according to the scale shown at the right. In the center of the emerging at the center, R0=(0,0,0), of positively satellite, labeled as “e”, the photoemission efficiency is as charged plane satellite, Usc=+3.0 V, with different expected, Jph/Jph0=0. A series of trajectories starting at energies versus satellite size in absence of the (0,0,0) point is shown in insert (e). Here we have only two magnetic field. trajectory types – “face-collected” or “back-collected”. When moving from the center to edges of the satellite surface the photoemmitivity increases and reaches up to 70% at some edge locations. A number of trajectories, originating at the left edge location, labeled as “b” and stepped by elevation, are shown in insert (b); in this case all types of trajectories are present, including “quasi-trapped” type, when a particle before being gone away, makes one or more full orbits around the satellite like around an attractive center; this is confirmed by patchiness of AE-map for “b” point (c). The insert (d) illustrates the geometric effect. The trajectory (1) starts at the leftmost point (labeled as “b”), other two start at about 1/3Rsat and close to the edge of the satellite in X+ direction. First and third trajectories are of “gone” away type and the second is “face-collected”. The size effect for positively charged satellite is illustrated in Figure 6. When the particle initial energy exceeds the satellite potential the condition (4) is applicable only for small (Rsat< 0.5 m, Rdeb > Rsat), i.e, we have the “point” approximation, For larger satellites the photoemittivity at first rapidly decreases with Rsat and comes to a “saturation” value, magnitude of which depends on the particle energy and the satellite potential. Step-like behavior of curves is due to discrete values of parameters in calculations.

MAGNETIC FIELD EFFECT

Magnetic field bends trajectories of photoelectrons and in most cases decreases the photoemission from the satellite surface. Table 1 lists results of calculation of effective photoemission in the presence of magnetic field as a function of satellite size for fixed Usat=+1 V and energy of emitted photoelectrons E0=2 eV. This energy is close to maximum of energy distribution of photoelectrons. Effective photoemission was obtained by averaging photoemission ratios Jph/Jph0, derived from AE- maps calculated for all bins in the satellite surface, over the Table 1. Photoelectron efficiency for Eph=2.0 eV whole satellite surface. Therefore, these data may be used for and Usat=+1 V as a function of the satellite size rough estimates for real situations. and the magnetic field. Rdeb=300 cm. The average Effect of magnetic field is clearly visible. First column value of selected cells is 0.182. for B=0 illustrates the “size”-effect and add more information B, nT 0 1000 2000 5000 to previous section. Other columns display effect of emission Rsat, m depression by magnetic field, which is most pronounced for 0.5 1.000 0.726 0.449 large satellites. 1.0 0.996 0.616 0.372 0.234 Combined effect of magnetic field and satellite potential 2.0 0.973 0.469 0.246 0.132 may be seen in Table 2 and Figure 7 for rather large satellite 3.0 0.953 0.366 0.189 0.093 Rsat = 5 m and the photoelectron energy E0=2 eV, close to the 5.0 0.914 0.251 0.140 0.057 most probable energy Eph. Again, effect of magnetic field is 10.0 0.831 0.152 0.075 0.029 visible from comparison with column B=0. Magnetic field 20.0 0.731 0.081 0.038 0.015 50.0 0.626 0.038 0.016 0.07 effect overcomes even negative Usat, as photoelectron 100.0 0.591 0.017 efficiency at negative potentials drops by 2-5 fold. 200.0 0.563 0.009

4 Table 2. Photoelectron efficiency for Eph=2.0 eV and Rsat= 5 m as a function of the satellite potential and magnetic field. Rdeb=300 cm. B, nT 0 1000 2000 5000 Usat, V -10.0 1.000 0.885 0.853 0.492 -5.0 1.000 0.877 0.837 0.319 -3.0 1.000 0.869 0.722 0.251 -2.0 1.000 0.852 0.634 0.218 -1.0 1.000 0.792 0.527 0.186 0.0 1.000 0.652 0.393 0.153 +1.0 0.914 0.251 0.140 0.057 +2.0 0.262 0.013 0.005 0.003 +3.0 0.057 Fig. 7. Combined effect of magnetic field and satellite +5.0 0.000 potential for rather large satellite, Rsat = 5 m, and the photoelectron energy E0=2 eV, close to the most probable energy. Distribution of photoemitivity over the surface of large (Rsat = 5 m) positively charged spacecraft, Usat = + 1 V, for photoelectron energy E0=2 eV and different magnetic field magnitudes is shown in Figure 8. Effective photoemission drops from 0.914 at B=0 to 0.057 at B=5000 nT Note that at B=5000 nT a large not-emittive spot appears in the center of the satellite and photoelectrons are emitted only from close-to-edge areas. Left map for B=0 is for comparison and shows slight decrease in photoemittivity to 0.914 evidencing that for satellite with Rsat = 5 m, what is close to the Interball-2 case, size effect overcomes attractive potential +1 V. Unexpectedly, similar effect is observed for negative satellite even for Usat= -10 V. Upper part of Figure 9 shows distribution of photoemitivity over l large (Rsat=5 m) with negative potential Usat = -10 V for photo-electron energy E0=2 eV. Left map for B=0 is put for comparison and shows 100 % emmittivity. In the case of B=5000 nT, what is characteristic for Interball-2 at HRE, we again see in the middle of the satellite the white spot – zero emittivity. Trajectories for white spot at B=5000 are shown in lower part of this figure. The particles emerge at the middle of white spot, location R0=(0,400,0) cm, at azimuth angle = 5 and elevations  are stepped by 5between 5 and 90 and their trajectories in Z-Y plane are marked as (1). Trajectories (2) and (3) are for Usc=0 V and +10 V respectively and are drawn for comparison. In the presence of magnetic field at some set of parameters the particles returning to the surface are collected mainly by shadowed rather than illuminated side of flat satellite. The number of shadow-side collected photoelectrons may exceed that of illuminated side by up to four-fold, (Figure 10, the ratio B/F=3.86).

Fig. 8. Distribution of photoemitivity over large (Rsat=5 m) positively charged spacecraft, Usat = + 1 V, for photoelectron energy E0=2 eV and different magnetic field magnitudes. The effective photoemission drops from 0.914 at B=0 to 0.057 at B=5000 nT.

Fig. 9. Upper panel – same as in Fig. 8 but for negative satellite with Usat = -10 V. Lower panel shows trajectories of electrons emitted in white spot in upper right map.

CONCLUSIONS

(1) Combined size and magnetic field effects may significantly suppress photoemission from a satellite surface.

(2) In outer magnetosphere at altitudes 2-3 RE (Interball-2, POLAR, and CLUSTER orbits) these effects should be taken into account for satellites with sizes Rsat  0.1 m. (3) In above regions in case of small positive potential (+1 V) the suppression may amount to about 0.7-0.5 for Rsat = 0.5 m and to 0.25-0.06 for Rsat = 5 m. Photoemission from an Interball-size satellite at small positive potential (Usat = +1 V) may be suppressed by 3-15 times and by two-fold at rather large negative potential (Usat = -10 V). (4) No photoelectron will escape the large, Rsat  100 m, at altitudes where magnetic field B2000 nT. (5) In presence of magnetic field under some combinations of parameters the particles returning to the satellite surface are collected mostly by shadowed rather than illuminated side of flat satellite. The number of shadow- side collected photoelectrons may exceed that of illuminated-side collected by Fig. 10. Azimuth-elevation map for up to four-fold factor. central point of flat R = 3 m (6) A not-emittive spot may appear on the surface of even slightly attractive satellite. Usat = + 1 V, E0 = 2.0 eV. positively charged satellite of Interball-size (Usat +1 V) at altitudes 1 R E. Similar spot may appears at the surface of Interball-size satellite with rather large negative potential (Usat -10 V).

ACKNOVLEDGEMENT This work was supported in part by INTAS, grant no. 2000-1465.

REFERENCES Grard, R.J.L., Properties of the Satellite Photoelectron Sheath Derived from Photoemission Laboratoty Measurements, , J. Geophys. Res., v. 78, no. 16, pp. 2885-2906, 1973.

6 Smirnova et al., Comparison of Interball-2 Spacecraft Potential from IESP and KM-7 Experiments in High- Latitude Regions of Magnetosphere at Altitudes of 2-3 RE, this issue, 2002. Veselov, M.V and Buzulukova, N.Yu., The Magnetic Field Effect on Photoelectron Current from a Positively Charged Spacecraft, Proc. of 7th Spacecraft Charging Technology Conf., ESA SP-476, p.479, 2001

E-mail addresses of V. Afonin [email protected]

Manuscript received ; revised ; accepted 7