Cylindrical Langmuir probe to measure artificially induced variations of vehicle potential in ionospher

Bettinger, R. T.

English

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I A FIRST ORDER TECHNIQUE FOR THE MEASUREMENT OF 
VEHICLE POTENTIAL IN THE IONOSPHERE I 
I RICHARD T. 8EilINGER 
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A FIRST ORDER TECHNIQUE FOR TEE MEASUREMENT OF 
VEEICLE POTENTIAL IN THE IONOSPHERE* 
Richard T. Bettinger 
Center for Atmospheric and Space Physics 
Department of Physics and Astronomy 
University of Maryland 
College Park, Maryland 
7 
August 1965 
* 
Presented to the Western Meeting of the American Geophysical Union, 
Dallas, September 1965. 
Supported by the National Aeronautics and Space Administration Grant 
NGR-21-002-057. 
ABSTRACT 
Under certain conditions, the potential of vehicles immersed 
in the ionospheric plasma can become very large. 
the presence of on-board equipment (dc sweeps, etc.) often gives 
rise to significant variations in this potential. 
small diameter, cylindrical Langmuir probe is suggested as a means 
of measuring the arificially induced variations of potential with 
good accuracy. 
(approximately 1 volt) on the vehicle potential as controlled by 
the geophysical parameters. 
In addition, 
The use of a 
This technique will also provide crude information 
ACKNOWLEDGMENTS 
The author is  pleased to acknowledge the assistance of 
Professor A. Nagy who made a number of useful suggestions with 
regard t o  the manuscript. This work was supported by NASA Grant 
NGR-21-002-057. * 
A FIRST ORDER TECHNIQUE FOR TE HEASUBEHENT OF FEHXCLE POTENTIAL 
I N  THE IONOSPHERE 
The moarur-nt of ionorpheric properties by means of 
- situ prober usually leads t o  the requirement for knowledge of the 
vehicle potential. 
which all conntituents are completely thermalized at 1-t by rpecies, 
this potential ir anall, of the order of 4KT, (typically leas than 
1 volt). The potential of vehicles in the ionorphere is often not 
in accordance with this simple picture however, generally aeruming 
valuer of from 1 to 3 volt8 when belw the F maximum, and occarionally 
displaying much higher excuriione. 
function of ruch on-board paramoterr as external probe rweepr; of 
motioxml paramotorr, much ar volocity and orientation with rorpoct 
to tho volocity vmctor; .ad of tha magnetic field and tho run voctor 
oriontation#. 
neipligiblo valuo cllad ir ronritivrly dependent on tho large numbor of 
interrolatod parmters. 
rator which aro rolatod to the motional activity of the vohiclo, 
oxtoma1 m o p  p r o g r w ,  otc. 
In a well-behaved plasma, that is, one in 
This value ie alro a renritive 
Thw, in genoral, the vehicle potential har a non- 
In particular, It $8 varyins with time at 
Tho rapid tiw variation in the vohicle potont1.l ha@ boan 
largrly ipnorad by many iav.rti~rtorr but thio can load to rigaiflcaut 
errotr. 
probo (to plamu) volt-. chrracterirtic of bipolar L a n p l r  probor of 
varlour a r m  ratior and rmblont condition#. It io evidont that for an 
aroa ratio, of ray 300, an approciable portion o f  tho 8ppli.d rwop 
appoarr u "vohlclo potatgal bounce" .ad th8t tho probo potonti.1 i 8  
For IXU~. IDCO, Pigo. 1 and 2 rhow tho appliod volt4r vorrur 
la 
I 
FIGURE 1 
D 
B 

appreciably less than that applied. 
versus applied voltage, the resultant slope may be interpreted in terms 
of the electron temperature. The distortion in the applied sweep cume 
will cause us to over-estimate the temperature, but the error may or may 
not be serious depending upon the specifics of the situation. 
other hand, (as has been pointed out by Nagyl) attempts to measure the 
~ e h i c l a  potential in terms of the point at which the curve departs from 
a straight line will be subject to large uncertainties as a result of 
finite measurement errors. 
in the charge density depending upon the specific data analysis techniques 
employed. 
If we should plot log of the current 
On the 
Correspondingly large errors can also appear 
The functions which govern the vehicle potential are many and complex. 
Attempts to calculate this factor2 are highly unrealistic. 
therefore, essential to measure this parameter experimentally and this 
may be best accomplished by means of a unipotential cathode called a 
TEP3. 
aprreciable amounts of heater power ( of the order of watts). Alternatively, 
it is possible to make "first order" measurements of the vehicle potential 
by means of a small diameter Langmuir probe. 
simpler than the TEP and requires considerably less power. 
consists of physically placing the Langmuir probe outside the volume of 
influence of the spacecraft and allowing it to "float". Its potential is 
measured by means of a high impedance voltmeter with a frequency response 
in excess of the highest rate of anticipated time variation in the vehicle 
potential. 
It is, 
While the TEP is a relatively simple device, it does require 
This approach is even 
The technique 
The use of a small diameter Langmuir probe as a voltage reference w a s  
I 
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2 a  
0 
Ib 
UI 
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-0 
;LI 
0 
5 i4 
E P c 
v) 
c rn 
3 c 
PROBE POFTEWIAL 
0 
A < 
0 
I r 
w i 
0 Y u, 
FIGURE 3 
3 
was suggested to us by calculations4 of the equilibrium potential of 
various idealized geometries (see Fig. 3)  in which the potential for 
a sufficiently small diameter was found to be largely uneffected by the 
perturbing element; the high energy electron tail in this case. 
instance, let us consider a cylindrical probe of sufficiently small 
diameter so that the ratio of the sheath radius to the probe radius is 
For 
--- " S f j :  large* PI- mplvI;ng --- the squations of i4ott-Smith and Langmuir', we 
may write % 
i = 2rkNee(2kT/m)' [ 1 + 2) eVp > 2kT, (14 
where r is the probe radius and 
charge concentration, e the electronic charge, k the Boltzmann con- 
stant, T the temperature of the constituent under consideration, m its 
mass, V the potential of the probe with respect to the plasma at infinity. 
If we assume a negative probe potential and a plasma which is thermalized, 
at least by species, then by equating the ion and electron currents and 
assuming no reflections at the surface of the collector, we obtain 
the probe length, Ne is the ambient 
P 
where the indices refer to the ions and the electrons respectively. 
The nondimensional potential is given by 
eV 
,P 
'm kTm (3 )  
4 
Equation (2) contains the % power of the ratio of masses which reflects 
the fact that this is a flux collection process. 
singly charged so that the nondimensional potentials differ only in 
their sign and perhaps in the temperature. 
by graphic techniques or by iteration and, for typical ionospheric 
temperatures of the order of 2000 K, y ie lds  equilibrim -,ztestials of 
less than 1 volt. 
The ions are assumed 
Equation (2) may be solved 
0 
For comparison let us now consider another cylinrical probe 
whose radius is large compared to that of the sheath. 
potential is again negative, the form of the electron current is unchanged 
(Eq. lb), but the ion current now is simply the random current to the 
area of the probe; that is 
If the probe 
Equating the ion and electron currents, we obtain 
The right hand sides of Eqs. 2 and 5 are identical; however, the 
left hand side of Eq. ( 5 )  is independent of potential. This accounts 
for the sensitivity in the equilibrium potential of typical carrier 
vehicles to high energy electrons in the ionosphere. In order to 
illustrate this point we will divide the electron population into two 
groups: one containing the fraction f of the total population, satisfying a 
5 
Maxwellian distribution described by temperature Te2* and the group 
containing l-f electrons at a temperature T . 
relatively small (less than 1%) and the associated temperature is 
relatively high corresponding typically to energies of 5 to 10 
electron volts. 
is of the order of a few t e ~ + , h ~  r?f 2 v o l t .  
The fraction f is e 
The voltage equk-dent of the low energy electrons 
In t h i s  ease we obtain 
When the third term of ( 6 )  is larger than the first then the vehicle 
potential will be nearly completely dominated by the high energy 
component. This condition is satisfied when 
If we assume atomic oxygen as the ion species and 10 electron volts 
as the equivalent temperature of the high energy electrons, transition 
value of the fraction f is approximately .25X. 
first term of equation ( 6 )  then leads to a condition which we might 
term "potential run away". With small probes, however, this behavior 
is considerably modified by the presence of the potential dependent term 
on the left side of Equation (2).  A high energy electron tail will be 
effective in increasing the equilibrium potential of such a probe, but 
the effect is considerably less than the case of a large probe and only 
under very severe conditions less than the case of a large probe and only 
under very severe conditions will the high energy electron component 
dominate the behavior of the equilibrium potential. 
The constancy of the 
6 
A number of other factors can affect the equilibrium potential, 
of course. 
solar radiation, but its contribution can be approximated as a constant 
term added to the ion current. This term is not generally of numerical 
impcmtance except at extreme altitudes (greater than 500KM). The 
photo-electric current acts t n  reduce the large xegati;-e qi i i l ibr ium 
potentials by effectively increasing the first term of Equation(6) 
(the ion current contribution). 
the equilibrium potential in the "rhermal" range (OW ~1.0) but it 
must become very large, of the order of the random current of the 
electrons, in order to generate positive vehicle potentials. 
condition is not generally satisfied. 
One of these is the photo-electric current resulting from 
It can be very effective in keeping 
V 
This 
Vehicle velocity and aspect with respect to this velocity are 
other impoztant factors which need to be considered in these calculations. 
The vehicle velocities are typically small compared to the electron 
thermal velocities but of the order of, or large, compared to the ion 
thermal motions. This generally has the effect of increasing the ion 
current by an amount dependent upon the specifics of the situation. 
As with photo-electrons, its most important effect in the present context 
is to increase the critical value of the fraction of high energy electrons 
given by Equation (7).  
Although both the photoelectric and vehicle velocity effects can 
be very impartant in determining the value of the equilibrium potential 
in a given situation, they will not alter our basic conclusion; a small 
diameter Langrnuir probe will maintain a relatively low equilibrium 
7 
potential which may be used as a reference. 
Several obvious practical considerations need to be satisfied. 
First, the probe needs to be physically located outside of the 
effective sheath of the main vehicle. 
which may be handled in several ways, one of which is indicated 
schematically in Figure 4. 
place the probe outside the sheath of the main vehicle, is maintained 
at the probe potential by means of a unity gain amplifier. 
amplifier introduces our second limitation. 
be large enough so that the loading of the amplifier is not serious; 
that is, the current drown by the detector must be small when compared 
to that of Equation (1). 
cylindrical over spherical geometry since one dimension is largely 
unrestrained. 
voltage induced by the earths field. 
This presents a support problem 
A guard electrode, of sufficient length to 
The 
The size of the probe must 
This is the main reason for selecting 
In practice the length of the probe is limited by the 
The proposed approach may be used to measure the variations of the 
vehicle potential induced by on-board systems with excellent accuracy. 
Since its sensitivity is inherently low, it will also supply first 
order information on "geophysically induced" potential variations. 
it may be used to provide a continuous on-board reference of the plasma 
potential. 
Thus 
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1 FIGURE 4 
REFERENCES 
1. A. F. Nagy and A. Z. Faruqi, "Ionospheric Electron Density and 
Body Potential Measurements by a Cylindrical Probe", U. of 
Michigan, College of Engineering Report 05671-44 (1964). 
2. W. C. Knudsen and G. W. Sharp, "Simultaneous Ion and Electron 
Temperature Results from a Satellite-Borne Ion Trap in a Polar 
Orbit", Transactions of the AGU 46, 1 (1965). 
3.  R. T. Bettinger, "An In Situ Probe System for the Measurement of 
Ionospheric Parameters", in Interactions of Space Vehicles with 
an Ionized Atmosphere, ed. S. F. Singer, (Pergamon Press, London) 
1965, in press. 
4 .  R. T. Bettinger, "Offset Voltages of Langmuir Probes in the 
Ionosphere", Rev. of Sci. Inst. 36, 630 (1965). 
5. H. M. Mott-Smith and I. Langmuir, "The Theory of Collectors in 
Gaseous Discharges", Phys. Rev. 28, 727 (1926). 


A First Order Technique for the Measurement of Vehicle Potential in the Ionosphere

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