Apparent enhancement of electron temperature in the wake of spherical probe in a flowing plasma

Planet. Space Sci. 1974, Vol. 22, pp. 873 to 878. Pergamon Press. Printed in Northern Ireland

RESEARCH NOTES

APPARENT WAKE

ENHANCEMENT OF A SPHERICAL

OF ELECTRON

TEMPERATURE

PROBE IN A FLOWING

IN THE

PLASMA

(Received in final form 13 November 1973) Abstract--An apparent enhancement of electron temperature has been observed in the wake of a conducting sphere in a flowing laboratory plasma, using as a probe a segment of the sphere itself. It is considered to be due to the negative potential well that is present in the wake, and which causes the velocity distribution of the electrons collected on the rear hemisphere to be non-Maxwellian. This interpretation of the phenomenon has been checked by numerical simulation. Recently Samir and Wrenn (1972) have published experimental evidence of an apparent electron temperature increase in the wake of an ionospheric satellite. We have observed this effect with a conducting spherical probe in a flowing laboratory plasma, and propose an explanation, which we have confirmed by numerical simulation. Our experiments were performed in a large plasma wind tunnel at the Office National d'Etudes et de Recherches Aerospatiales, which has been adapted for simulation of the ionospheric plasma (Pigache, 1971). The plasma was obtained, in the form of a diverging beam, from a source of the Kaufman type (Le Vaguerese and Pigache, 1971). The neutral gas pressure was kept sufficiently low ( ~ 10-* torr) that the plasma flow was almost collisionless. The probe was placed on the axis of the beam, at a distance of about 3'5 m from the source. Here the plasma density was uniform, to within 4-10 per cent, out to distances of 50 cm from the axis. The plasma density and the beam velocity could be varied independently, the former from 103 to 10e cm -3 and the latter from 10 to 30 km/sec. Argon ions were used, however, rather than those of the natural atmospheric gases. The electron temperature also could be varied over a wide range, the lowest value attainable being about 300°K. The probe was a sphere 3 cm in diameter, with a segment of its surface insulated from the rest (Fig. 1). The circumference of this segment was a circle that subtended an angle of 60 ° at the centre of the sphere. The two parts could be connected together so as to form an ordinary spherical probe, or alternatively the segment alone could be used as the probe, with the rest of the sphere held at the same potential and acting as a 'guard ring'. This second mode of operation was used for measuring the distribution of the collected current over the surface of the sphere. The probe was supported on a fibre-glass rod 10 cm long and 0.5 cm in diameter; by turning this rod around its axis, the orientation of the segment with respect to the direction of flow of the plasma could be varied. The currents collected both on the segment alone and on the complete sphere were measured, as functions of the applied potential, for different orientations. Considerable precautions had to be taken in respect of the state of the surface of the probe, before reproducible current/voltage characteristics could be obtained and the effect of interest observed. The probe was made of sintered graphite. Its surface was prepared by first polishing to optical quality, then cleaning with ultrasonics in a freon bath, and finally heating to 500-600°C in a vacuum for about 2 hr. After cooling, it was finished by spraying a thin layer of colloidal graphite on to it. For this amorphous material thework functionis uniformto withina few tens ofmillivolts (Trendelenburgetal., 1970; Godard, 1971). Nevertheless, the surface retained a layer of absorbed gas which caused the probe characteristics to exhibit 'hysteresis'. We found that this layer could be removed by electron bombardment, as Smith (1972) has reported. For this purpose, it sufficed to bias the probe to +200 V in the presence of a plasma beam, the electron density of which--as measured by the same probe at low potentials--was about 10ecm -3. The electron current to the biased probe, which was about 5 mA, was not sufficient to heat the surface appreciably. Hence the energetic electrons must have acted on the adsorbed gas molecules directly, by ionizing them and breaking their bonds with the surface. After about 10 min of this treatment, tbe hysteresis disappeared and the characteristics became reproducible (Fig. 2). Throughout each experiment, in which the current/voltage characteristic was measured for several different orientations of the probe, care was taken to check that the hysteresis did not reappear, and also that the plasma conditions (including plasma potential) remained constant. At the end of the experiment, the probe was returned to its initial orientation, and a check was made that the initial characteristic could be reproduced within the limits of experimental error. 873

~)'~t

R E S E A R C H NOTES n su la l i o n J

4:_ ::i:-.i,!.:

'

- ....

...... <2

Spherical

segment

FIe. l. CONSTRUCTION OF THE PROBE. ( I

! (13OO*K}-- = = : = ~ =Before bombordmenf

4 t

, ~, ,, ,~* ,After bornbcrdment 4 mn (200v)

(500"K}

A f t e r bombardment 9mn (200V)

)

t

I I o-eA

I 02v

, z : -; ~ s d ; ~

v

FIG. 2. EFFECT OF SURFACE CLEANING BY ELECTRON BOMBARDMENTON THE PROBE CHARACTERISTICS.

The experiments were performed using plasma beams in which the mean ion flow velocity was 10 2 km/sec. This velocity was fixed by adjusting the accelerating potential applied to the grid of the source; the theoretical dependence of the ion velocity on the accelerating potential had been checked in some previous experiments (Le Vaguerese and Pigache, 1971). The ions being of argon, the corresponding energy per ion was about 21 eV. In the direction parallel to the axis of the beam, the width of the energy distribution for the ions, measured between points where this function was equal to half its maximum value, was about 4 eV. Figure 3 shows a typical example of the characteristics observed at various values of the orientation angle 0 (see Fig. 1). The ordinate is the current I flowing from the probe into the plasma; it is plotted both for the entire sphere, and for the segment alone. The abscissa is the potential V of the probe with respect to the wall of the vacuum chamber. The arrow marks the plasma potential Yp, which was assumed to correspond to the condition of maximum slope dI[d V of the characteristic of the segment when oriented forwards; this slope was determined automatically by means of an electronic device. Note that, for negative probe-plasma potentials of a few hundred millivolts, which are of course small compared to the energy of the ions, the positive ion current is thoroughly saturated. In Fig. 4, the data from Fig. 3 regarding the current collected on the segment have been replotted in a slightly different way. The ordinate is the electron current I,, which is the difference between the m~sured current I and the positive ion current I+; the latter has been assumed to equal its saturation value, regardless of the probe potential in the range considered. The abscissa is the potential V, = V -- V~ of the probe with respect to the plasma. Note in Fig. 3 that the total current for 0 = 90 ° differs from that for 0 = 0 °

R E S E A R C H NOTES Complefe

I

875 sphere

,

~Segment 8=0 =

/ / / / /o=,oo '111t,,'" I ///

0

OI

0"2

voV

0'3

0'4

FIG. 3. TYPICAL CHARACTERISTICS FOR A CLEAN PROBE" TOTAL CURRENT POTENTIAL V(V).

I(mA) v s PROBE-WALL

/?____o=90. I,e 2

j

/ -

/,,.~--8-- 18o*

/

//

--// //

o

I

I

I

0-1

0"2

0.3

Plasma potential FIG. 4. SAME DATA AS IN FIG. 3: ELECTRON CURRENT I, VS PROBE--PLASMA POTENTIAL Vs. at large negative potentials, due to the difference in the ion saturation currents, whereas the curves of electron current in Fig. 4 are almost the same for these two orientations. It appears from these data that when the probe-plasma potential is positive, the electron current is distributed non-uniformly over the sphere: for II, = + 5 0 mV, the current collected on the segment when it is facing directly forwards into the oncoming plasma beam (0 = 0 °) is less than half the value observed when it is facing directly backwards into the wake behind the sphere (0 = 180°). This non-uniformity persists through plasma potential and into the electron retardation region, though it becomes progressively

~, ,~

RESEARCH NOTES

less marked as the probe-plasma potential goes increasingly negative. Finally, for negative probe--plasma potentials in excess of about 100 mV, the distribution of electron current over the sphere is uniform wkhin the limits of experimental error. Clearly, if electron temperatures are calculated naively from the slopes of plots of In 1, vs the probeplasma potential V,, at values of V, that are only slightly negative, then a higher value will be found when the segment is facing backwards than when it is facing forwards. For the entire sphere, the apparent temperature may be expected to lie about half-way between these two values. Table 1 shows the apparent electron temperatures obtained in this way under three different sets of plasma conditions. The errors in these values, due to the scatter of the experimental points on the characteristics, are about ± 10°K. When the segment is facing backwards, the apparent temperature is hard to specify, since a semi-logarithmic plot of the characteristic is not straight at low negative values of 17,. Nevertheless we have selected a representative value for this part of the characteristic, and in all three cases it is higher than the value observed with the segment facing forwards. TABLE 1 Electron density N (m -3) 5.1011 4.1011 2"4. I0 ~°

Plasma conditions Thermal energy kTde (meV) 40 23 54

Apparent electron temperature (°K) Debye length 2~ (ram)

0 = 0°

0 = 180 °

Complete sphere

2.1 1.8 11

460 270 630

495 330 660

520 300 790

In our opinion, this result is not evidence of a true enhancement of electron temperature, but rather is an effect of the negative potential well that is present in the wake (Liu, 1969). Electrons that approach the probe from the rear, directly along the axis of the wake, are repelled by the well if their energy does not exceed its depth. This repulsion is experienced also by electrons that approach the probe at acute angles to the wake, though it becomes progressively weaker as this angle increases, since the trajectories then avoid the deepest parts of the well. Hence the negative potential well partly shields the rear surface of the probe from incident electrons of the lowest energies. When the probe-plasma potential is positive or only slightly negative, most of the electrons that are collected on the front surface have such low energies, and this is why fewer electrons are collected in the rear. On the other hand, when the probe-plasma potential is more negative than the bottom of the potential well, the electrons that have enough energy to reach the probe are also able to cross the well, so the collected current density is uniform over the surface. Thus the reduction in the slope of the curve I,(V,) at small negative values of V,, that is observed when the segment faces into the wake, is due to the non-Maxwellian form of the distribution function of the collected electrons, rather than to the collection of electrons having a Maxwellian distribution at an enhanced temperature; Samir and Wrenn (1972) had surmised that this might be the case. According to this interpretation of the phenomenon, the electron temperature measured with the segment facing towards the oncoming plasma beam is correct. The Debye lengths and electron thermal energies listed in Table I have been calculated on this basis. The unexpectedly high values of the apparent electron temperature on the complete sphere, in two out of the three cases, remain unexplained. They may be due to residual surface contamination, or to the perturbation caused by the support rod. These discrepancies bear witness to the difficulty of knowing what the systematic errors in the electron temperature measurements may be. Even when the characteristics are free from hysteresis, such errors may still be present (Thomas and Battle, 1970); one cause of them may be variations of work function across the probe surface. Thus two different conducting surfaces, used as probes in the same plasma, can yield discrepant electron temperatures. Hence we feel that greater significance should be attached to the measurements made by the same probe--the circular segment--in the forward and backward orientations: even though the absolute values of the electron temperature may be in error, the difference between the values obtained in these two orientations is certainly significant. We have checked our interpretation by numerical simulation of the phenomenon, First the potential distribution in the plasma around the sphere is calculated using the programme by Call (1969), which is slightly unrealistic in that it neglects the thermal motion of the ions and obtains the electron density by means of the Boltzmann factor. Then the distribution of electron flux over the sphere is calculated using a programme that we have developed from one written by Fournier (I 971) for the case of a cylinder. Strictly speaking, since the electron density distribution implied by this second step of the calculation is different from that obtained at the first step, there should be a third step in which the potential distribution is recalculated, and finally these second and third steps should be repeated until they converge to a self-consistent joint distribution of electron density and potential; however, we have not performed this iteration, because

R E S E A R C H NOTES

877 +0--0*

R=IOXo

de

•~0=180°l

I

-2'5

.

I

-2

I

-1'5

I

-I

1

-0'5

I

0

0

FIG. 5. NUMERICAL SIMULATION RESULTS FOR R/2D = 10: ELECTRON CURRENT ]e PER UNIT AREA (ARBITRARY UNITS) VS NORMALIZED PROBE-PLASMA POTENTIAL ~m.

it is too costly in computer time. Hence our simulation is not entirely realistic nor self-consistent, but nevertheless we believe that it cannot be seriously in error. We have performed it for a spherical probe in a flowing plasma under conditions similar to those in our experiments: argon ions flowing at 10km/sec; probe radius equal to 10 Debye lengths. The results appear in Fig. 5. The ordinate is the surface electron current density J', (in arbitrary units) at various orientations, while the abscissa is the normalized probeplasma potential $, = eVo[kT,, where e is the magnitude of the elementary charge, k is Boltzmann's constant, and T, is the electron temperature. The general similarity of these first theoretical results to those from the experiments is evident, and it confirms the correctness of our interpretation of the apparent enhancement of electron temperature in the wake of a spherical probe in a flowing plasma. Further work, both experimental and theoretical, is being done in order to improve the agreement, and the results will be presented in a future publication.

Acknowledgments--We wish to express our thanks for stimulating discussions with Dr. U. Samir of the Department of Environmental Sciences of the University of Tel-Aviv, and also with Dr. J. Taillet and Dr. G. Fournier of the Office National d'Etudes et de Rechercbes Aerospatiales. The assistance of the technical staff of the O.N.E.R.A. in the operation of the plasma wind tunnel and of Mr. P. Gille with the programming also is acknowledged gratefully. We thank the anonymous referee for his helpful comments. This research was sponsored by the Centre National d'Etudes Spatiales. J. M. ILLIANO L. R. O. STOREY

Groupe de Recherches Ionosph~riques du Centre National de la Recherche Scientifique, 45 Orl~ans-la-Source, France

.<7;~

R E S E A R C H NOTES REFERENCES

CALL, S. M. (1969). Report No. 46, Plasma Laboratory, Columbia University. Fovm',~F,, G. (1971). Th6se de Docteur 6s Sciences, Universit6 de Paris-Sud. GODARD, R. (1971). Th6se de Doctorat de 3 6me Cycle, Universit6 de Paris-Sud. LE VAGUERESE,P. and PIGACHE,O. Revue Phys. aFpt 6, 325. LIu, V. C. (1969). Space Sci. Rev. 9, 423. PIOACHE, D. (1971). A.I.A.A. 4th Fluid and Plasma Dynamics Conference, Paper No. 71-608. SAMm, U. and WRENN, G. L. (1972). Planet. Space Sci. 20, 899. SMITH, D. (1972). Planet. Space Sci. 20, 1717. THOMAS, T. L. and BATTLE, F. L. (1970). J. appl. Phys. 41, 3429. TRENDELENBURG, E. A., FrrroN, B., PAGE, D. E. and PEDERSEN, A. (1970). ELDO/ESRO Sci. 7~ch.

Rev. 2, I.

Planet. SpaceSci. 1974, Vol. 22, pp. 878 to 879. PergamonPress. Printedin Northern Ireland

COMMENT THE

ON:

MARTIAN

"THE

PHOTOLYTIC

ATMOSPHERE" AND

STABILITY

OF

B Y R. C. W H I T T E N

J. S. S I M S

(Received 22 October 1973) Abstract--It is pointed out that the models given contain internal contradictions: they produce more Os than they destroy by factors of I00 or more. Whitten and Sims (1973) (WS) present two models of the photolysis and recombination of COs that are claimed to be in balance. Such a result is in direct conflict with earlier models by McElroy and Hunten (1970) and McElroy and McConnell (1971) which used the same chemistry as the first model of WS, but even larger values for the rate coefficient of CO+O

÷ M--~COs+M.

(4)

The downward velocity of 2 cm see-x used by WS should be nearly equivalent to an eddy-diffusion coefficient of 2 × 106 cm* see-1 (for a mixing length equal to the scale height). Thus, earlier models, with eddy coefficients of 5 × l0 s cm 2 sec-1, actually have faster downward transport than WS. Nevertheless, they do not mention the discrepancy. Oxidation of CO is only half the problem for a dry CO, atmosphere; the other half, earlier discussed by Donahue (1968), is that reaction of O with itself produces O4 much faster than it can be destroyed. It is shown here that neither model of WS achieves a balance for Os, which is produced about a hundred times faster than it is lost. In the WS models, the sources of Os are O+ O+ M--~Os+ M

(5)

O -'~ O s - ÷ Os + Ov

(7)

Reaction on dust in their second model is negligible in comparison. With the densities and rate coefficients given by WS, the Os production rates are as shown in Table 1. Loss is almost entirely by photolysis in the Herzberg continuum, reaction (8b) of WS, since shorter wavelengths are removed by COs. The numbers are rough, based as they are on densities scaled from figures; but the discrepancy is so large as to leave no TABLE I. Os PRODUCTIONAND LOSS (molecules cm -s see-0 Reaction

Fig. 1

Fig. 2

O+ O+ M

l q i l013

O + O~

6.6

10 ~2

4"4 × 10 n 4.4 x l0 is

6 .": I0 ~°

6 × I0 ~°

O~ + hv