Abstract
This paper examines the specific features of measuring electrostatic fields in the upper layers of the atmosphere and approaches to developing instrumentation suitable for these measurements.
Full Text
Measurement of Electrostatic Fields in the Upper Layers of the Earth’s Atmosphere
I. M. Imyanitov
1. Introduction
Until now, information on electrostatic fields and, correspondingly, on space charges in the upper layers of the atmosphere has been almost entirely lacking.
Inaccessible to direct measurement at the surface of the Earth, owing to the shielding action of the highly conducting layers of the ionosphere, these fields also cannot be measured by indirect methods. A change in the absorption spectrum in these layers due to the Stark effect, for example, cannot be measured, since the displacement of the lines would in the best case amount to hundredths of an angstrom. Nor can the measurement of the energy or the determination of the trajectories of cosmic particles arriving at the Earth serve to estimate the magnitude of electrostatic fields: this is prevented by the strong influence of the magnetic field and of the processes of formation of secondary particles.
At the same time, information on electric fields and on space charges is urgently needed for solving such problems, essential for the physics of the upper layers of the atmosphere, as the creation of a sufficiently complete theory of auroras, the testing of theories of magnetic storms, the identification of regions where charged particles penetrate into the Earth’s atmosphere, and so on.
It should be noted that, although the experimental facts confirming the existence of electrostatic fields in the upper layers of the atmosphere are very scanty, all the basic theories of auroras (Birkeland and Størmer, Chapman, Ferraro and Martyn, Alfvén) either postulate or assume the existence of these fields. Among the experimental data confirming the presence of significant electric fields in the upper layers of the atmosphere may be included certain measurements of the electrostatic field at the surface of the Earth, associated with processes occurring in the upper layers of the atmosphere. Although it is difficult to establish an unambiguous connection between the two phenomena, since the field at the Earth’s surface can vary under the influence of many factors, systematic observations nevertheless make it possible to establish certain regularities.
Measurements of the intensity of electrostatic fields near the Earth’s surface show, for example, that both the values of this intensity averaged over considerable intervals of time^1 and its instantaneous values (see, for example,^2) may undergo noticeable changes during auroras. This fact confirms the assumption that in the upper layers of the atmosphere there exist large potential differences and space charges.^3,4,5
The possibility of electrification of the Earth and the atmosphere by extraterrestrial sources is also indicated by the work of M. V. Okhodimskaya,^9 who noted anomalies in the annual variation of the field intensity at a mountain station in Alma-Ata, coinciding in time with the Earth’s crossing of the Perseid meteor stream. It should be noted here that at the surface of the Earth there may be
there may be observed changes in the electrostatic field that constitute only a small part of the field changes occurring in the very high layers of the atmosphere. The field reaching the Earth owes its existence to that part of the charges which has not had time to become uniformly distributed over some spherical surface enclosing the atmosphere. At the same time, the field above this surface is formed by all the excess charges that have entered the Earth’s atmosphere. In considering such a simplified model, in which the Earth and the atmosphere are treated as the plates of a spherical capacitor, it should be remembered that, owing to the conductivity of the atmosphere, the field may undergo a considerable “shrinkage,” especially large in the ionospheric region.
Thus, the study of electrostatic fields in the upper layers of the atmosphere will make it possible to decide whether the Earth, together with its atmosphere, is a neutral body in space. The answer to this question is of very great importance for understanding the mechanisms of charge exchange between the Earth and the atmosphere and, consequently, for solving one of the fundamental problems of the science of atmospheric electricity—the explanation of the reason for the preservation of the Earth’s negative charge—as well as for deciding what role extraterrestrial sources of electrification play in the electrical state of the atmosphere and the Earth.
It should be noted that knowledge of the character of the distribution of the field around the Earth will make it possible to draw conclusions about the source of this field. Thus, for example, the existence of a radially symmetric field would indicate that the Earth and the atmosphere as a whole are charged, while the presence of a field increasing in the Earth–Sun direction would indicate the existence of an electrostatic field created by the Sun. The pattern of the field distribution, in particular, should make it possible to decide whether charged or uncharged streams of particles move from the Sun.
Information about the electric field of the Earth (together with its atmosphere) may also prove essential for clarifying the causes of the appearance of fast charged particles in the atmosphere and for identifying the nature of cosmic rays. If this field exists, then the Earth can act as a gigantic linear accelerator of charged particles. Even relatively weak electrostatic fields, with strengths of the order of units or even fractions of a volt per centimeter, can accelerate particles to energies of the order of \(10^9\)–\(10^{10}\) eV.
The possibility of creating artificial Earth satellites, together with the possibility of using high-altitude rockets, has for the first time made it possible to pose the problem of directly measuring electrostatic fields at great heights. The advantages of using artificial satellites for this purpose are obvious, since with their help one can obtain the distribution of electric fields both with altitude and around the entire Earth, and the variation of these fields with time.
It must be stipulated that measurements of fields and volume charges produced by charged particles intruding into the atmosphere should essentially be carried out at heights (80–500 km and even up to \(\sim 1000\) km) at which phenomena caused by these particles occur (for example, aurorae); measurements of the electrostatic fields around the Earth and the atmosphere as a whole, however, should preferably be carried out at the greatest attainable heights (\(\sim 500\)–1000 km and higher), and the value of the materials provided by such investigations will increase as the altitude of satellite flight above the Earth increases.
The use of artificial satellites for measuring electrostatic fields in the upper layers of the atmosphere requires the development of special methodology and apparatus.
In the present work, the features of measurements of electrostatic fields in the upper layers of the atmosphere and ways of creating apparatus suitable for these measurements are considered.
2. MEASUREMENT OF ELECTROSTATIC FIELDS IN SPACE BY MEANS OF AN ISOLATED BODY
The principles of measuring electrostatic fields in space by means of flying apparatus have been set forth by us earlier[^6]. The main difficulties that arise when using a flying apparatus as a probing body are connected with the fact that, first, the flying apparatus itself may have a certain electrostatic charge, whose field is superposed on the measured field; second, the appearance of a conducting body in the field produces, owing to the charges induced on the body, local distortions of the measured electrostatic field; and, third, the appearance of the probing body in space may distort the measured field by changing the distribution of charges in the atmosphere.
The task of the method for measuring the strength of electrostatic fields in the atmosphere is to eliminate the influence of all these factors interfering with the measurement on the measurement results.
The field strength \(E_i\) at some point \(i\) of a conducting body placed at some point in space consists of two parts. One part \((E_i')\) is determined by the magnitude of the strength of the external electrostatic field at the chosen point and by a coefficient \(k_i\), depending on the configuration of the body and its position in the field (assuming that the dimensions of the inhomogeneities of the field are much larger than the dimensions of the body); the other part \((E_i'')\) is determined by the magnitude of the body’s own electrostatic charge \(Q\) and by a coefficient \(p_i\), depending on the shape of the body.
Thus,
\[ E_i = k_i E + p_i Q . \tag{1} \]
It follows from this that if the field strengths \(E_m\) and \(E_n\) are measured at two points of the body \(m\) and \(n\), choosing these points so that they lie in a plane directed along the lines of force of the field, then
\[ E_m = k_m E + p_m Q,\quad E_n = k_n E - p_n Q, \tag{2} \]
i.e., by measuring the field strength at two points of the body, one can independently determine the magnitude of the field strength \(E\) in the atmosphere and the magnitude of the charge \(Q\) of the body.
In the case where the body is symmetrical and, as the points \(m\) and \(n\), symmetric points on the surface of the body are chosen (the case most characteristic for satellites), then \(k_m = k_n = k\) and \(p_m = p_n = p\). In this case:
\[ \begin{aligned} E &= \frac{E_m + E_n}{2k},\\ Q &= \frac{E_m - E_n}{2p}. \end{aligned} \tag{3} \]
Thus, independently of the magnitude \(p\), the field strength of the atmosphere will be proportional to the half-sum of the field strengths measured at the points \(m\) and \(n\) of the body. It is essential to note that changes in the quantities \(p\), if they occur simultaneously at both points of measurement, do not affect the accuracy of determining the electric-field strength. Similar considerations may, of course, be applied in determining the charge of the body.
In the general case, in order to reconstruct the complete vector of the electrostatic field in space (independently of the position of the body), it is necessary to know the field at four points of the body, for each of which four coefficients must be determined, taking into account the action of the three components of the field vector and the body’s own charge. Since errors in determining the individual coefficients are added together when the field is calculated, the accuracy of such measurements will be low.
When measurements are made at points of the body located at the intersection of the electrostatic neutral lines for the corresponding components of the field strength, the number of coefficients to be determined is reduced to eight, and the accuracy of the measurement increases, since each of the components of the field vector is determined independently.
The measurement problem can be simplified by limiting oneself to measurements at two points of the body. In this case only one of the components of the field-strength vector will be measured. For an oriented satellite one may choose the desired component of the field, say the vertical one. For unoriented satellites, in this case the component of the field in the coordinate system associated with the satellite itself will be measured.
The coefficients \(k_i\) and \(p_i\) are determined by measurements on models of the sounding bodies. To determine the coefficients \(k_i\), a model made of conducting material is placed in the field of a plane capacitor and the density of the induced charge is measured at various points of the model; to determine the coefficients \(p_i\), a certain charge of known magnitude is applied to the model and the charge density is measured at selected points of the surface of the model\({}^{7}\).
3. SPECIAL FEATURES OF MEASUREMENTS WHEN THE BODY IS IN A PLASMA
The described method for measuring electrostatic fields is based on the assumption that the change in the distribution of charges in the surrounding medium as a result of the action of the body may be neglected. This assumption, quite justified in the lower layers of the atmosphere, ceases to be valid when the body is in the ionosphere. On the one hand, the high conductivity of the medium in this region leads to the fact that no electrostatic charge can be retained on the body unless there is a sufficiently intense process continuously generating it. On the other hand, the body itself, being in a plasma, must become charged.
A body in a plasma can acquire charge because the fluxes of electrons and positive ions to the body are, generally speaking, not equal, and, consequently, the body will be charged until these fluxes become equal. A body in a plasma can also be charged by the emission of electrons, due to the photoelectric effect, the action of soft X-ray and cosmic radiation, etc. Finally, for satellites flying at high speed, charges induced by the magnetic field on the moving body may affect the measurement results.
Let us consider the charging of a body placed in a plasma, using the usual concepts of Langmuir probe theory. Then, assuming a Maxwellian distribution of particle velocities and equality of the electron \(T_e\) and ion \(T_i\) temperatures (\(T_e = T_i = T\)), as well as equality of the ion and electron concentrations, and taking into account that at altitudes greater than \(300\ \text{km}\) the mean free path of the particles will be much greater than the dimensions of the body, the potential of the body \(V\) may be found from the equation\({}^{8}\)
\[ V = \frac{kT}{e}\ln \frac{I_-}{I_+}, \tag{4} \]
where \(I_-\) and \(I_+\) are the currents produced by electrons and positive ions; \(k\) is Boltzmann’s constant, \(e\) is the charge of the electron. Taking the ion mass to be \(m = 16\) (the mass of atomic oxygen), we obtain
\[ V \simeq 5\,\frac{kT}{e}. \tag{5} \]
Table I gives the expected values of the body potential \(V\) as a function of the ambient temperature \(T\).
Table I
| \(T^\circ\mathrm{K}\) | \(500^\circ\) | \(1000^\circ\) | \(1500^\circ\) | \(2000^\circ\) | \(2500^\circ\) | \(3000^\circ\) | \(3500^\circ\) |
|---|---|---|---|---|---|---|---|
| \(V,\ v\) | 0.22 | 0.44 | 0.67 | 0.89 | 1.12 | 1.34 | 1.56 |
In reality, at the assumed flight altitudes of the satellite one may expect the presence not only of atomic oxygen, but also of molecular nitrogen and other gases. This may affect the value of the coefficient in the last formula. The dependence of the quantity appearing in formula (4) under the logarithm on the ion mass is given by the expression:
\[ \ln \frac{I_-}{I_+} = \ln \sqrt{\frac{m_2}{m_1}}, \]
where \(m_1\) and \(m_2\) are, respectively, the masses of the electron and the ion; therefore the magnitude of the logarithm changes little even when the molecular mass doubles. If it is assumed that the mean effective mass of the molecules at the presumed altitudes of satellite flight will be 28 (the mass of an \(N_2\) molecule), then the coefficient in formula (5) changes by 5%, i.e., this formula may be used with a sufficient degree of accuracy.
To estimate the possible values of the field strength due to the body’s own charge that may be encountered during satellite flight, it is necessary to establish the relation between the potential acquired by the satellite and the field strength at its walls.
The distribution of space charges and fields near an immobile body placed in a plasma can, in a first approximation, be described by equations obtained on the basis of the classical theory of probes (see, for example, \(^{8}\)). Figure 1 gives the form of the distribution of the field and space charge near the wall of the body. Assuming that the mass of the positive ions is \(m_2 = 16\), we obtain for the relation between the field strength \(E\) at the wall and the body potential \(V\) the expression
\[ E = 5.6 \cdot 10^{-5}\sqrt{n_0 V}, \tag{6} \]
where \(n_0\) is the concentration of positive ions in the region where the perturbations introduced by the body no longer have an effect. Thus, the field strength in the vicinity of the body also depends on the ion concentration.
The motion of the body may affect the value of its potential and the field strength. The potential to which elements of any surface perpendicular to the direction of motion become charged (if they are insulated and the thermal velocity of the ions is neglected in comparison with their relative velocity) can be calculated from the expression
\[ V = \frac{kT}{e}\ln\frac{v}{c}, \tag{7} \]
where \(v_-\) is the thermal velocity of the electrons, and \(c\) is the speed of the satellite.
In the case of a satellite, the relative velocity of the positive ions may exceed their thermal velocity (taking the gas temperature in the ionosphere to be \(\sim 1000^\circ\) K) by at least an order of magnitude.
In this case the values of the satellite potential calculated by formula (5), i.e., under the assumption that the latter is motionless, and those calculated by formula (7), which takes into account the motion of the body, will differ very little.
Fig. 1. Distribution of the field strength \(E\) and the potential \(V\) near the wall of a body located in plasma.
The relation between the field strength at the front wall and the potential of the body, in the case of motion of the latter, will be expressed by the dependence
\[ E = 8.5 \cdot 10^{-5} \sqrt{n_0 V}. \tag{8} \]
To determine the field strength at elements of the frontal part of the satellite inclined at some angle \(\alpha\) to the flow, it is necessary to calculate the velocity of the flux of positive ions onto the corresponding element. The component of the satellite velocity along the normal will be equal to \(c \sin \alpha\). Consequently, the satellite will acquire a potential of some intermediate value between those determined by formulas (5) and (7), and all values of the field strength arising as a result of acquiring
satellite will lie between the values determined by formulas (6) and (8). Thus, the motion will have a relatively weak effect on the value of the satellite potential and on the magnitude of the field strength at its walls.
An estimate of the magnitude of the field strength at the walls of satellites (at the flight altitudes presently assumed) leads to values reaching several volts per centimeter.
In measurements of the electric-field strength, it is essential to estimate the thickness \(\delta\) of the disturbed layer. For such an estimate one may use the classical formula of the “\(3/2\)” Langmuir law\(^{8}\). In reality the extent of the disturbed layer may be somewhat larger than follows from Langmuir’s formula, since the latter does not take into account the action of the space charge created by electrons.
Table II gives the value of \(\delta\) (in centimeters) for a plane probe at various concentrations \(n\) of positive ions and temperatures \(T\).
Table II
| \(n,\ \mathrm{cm}^{-3}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) | \(T^\circ\mathrm{K}\) |
|---|---|---|---|---|---|---|---|
| \(n,\ \mathrm{cm}^{-3}\) | 500 | 1000 | 1500 | 2000 | 2500 | 3000 | 3500 |
| \(10^{4}\) | 6.7 | 9.4 | 11.5 | 13.4 | 15.0 | 16.4 | 17.7 |
| \(10^{5}\) | 2.1 | 3.0 | 3.6 | 4.2 | 4.7 | 5.2 | 5.6 |
| \(10^{6}\) | 0.7 | 0.9 | 1.2 | 1.3 | 1.5 | 1.6 | 1.8 |
| \(10^{7}\) | 0.2 | 0.3 | 0.4 | 0.4 | 0.5 | 0.5 | 0.6 |
The solution of the problem of the distribution of space charges in the rear part of a moving body has not yet been obtained. From general considerations it follows\(^{14}\) that behind the body there should form a hollow “bag” of conical shape, since ions will not have time to fill the vacuum formed behind the moving body. On the other hand, electrons may have time to fill this “bag”; however, a negative space charge will then be formed in the “bag,” limiting by its field the number of electrons capable of penetrating inside the “bag.” A quantitative account of these effects, as well as the solution of the problem of the distribution of charges and fields around bodies of complex shape moving in space, constitutes a set of problems that must be solved.
As the concentration of charged particles \(n\) decreases, the thickness of the disturbed layer surrounding the body will increase, and the field distribution around the body will approach ever more closely the field distribution in vacuum. At temperatures of the order of \(1000^\circ\mathrm{K}\), this occurs at charged-particle concentrations \(\sim(10—1)\ \mathrm{cm}^{-3}\). Since, according to Berning’s experiments\(^{10}\), the concentration of charged particles falls sharply at altitudes of 350–400 km, one may expect that the experimental conditions will approach the conditions of measurement in vacuum at altitudes \(\sim 1000\) km.
Other sources of charge imparted to the satellite are also possible. Thus, for example, the results of experiments on measuring the mass spectra of ions carried out with rockets\(^{11}\) force one to assume that in certain regions of the ionosphere the rocket potential relative to the unperturbed plasma reached 20–25 V, the rocket being charged negatively. Such a considerable negative potential cannot arise owing to the charging mechanism considered above; nor can it, naturally, be due to the photoelectric effect, which imparts a positive charge to the body.
Measurements of the satellite’s charge should answer the question of whether photoemission, together with such processes as charging by impacts with meteoritic dust, can lead to a change in the sign of the body’s charge in the plasma from negative to positive.
The magnitude of the field strength at the surface of the satellite may also be affected by charge induction due to the motion of the body in a magnetic field. The potential difference \(\Delta V\) that arises at the ends of a satellite of width \(l \sim 100\ \text{cm}\), moving with velocity \(c \sim 10^6\ \text{cm/sec}\), should not exceed tenths of a volt. Since the magnetic-field strength on the satellite will be measured, and the velocity of the latter is known, the influence of this potential difference \(\Delta V\) on the readings of the instruments can be taken into account. An exact allowance for this quantity, however, is possible only for oriented satellites.
One should note yet another possibility for using data on the field strength created by the satellite’s own charge for studying the physical characteristics of the ionosphere. In those regions of the ionosphere where the body acquires a charge owing to the difference in the magnitudes of the fluxes of positive ions and electrons onto the body, by measuring the field strength at the surface of the body created by the body’s charge, one can estimate the temperature of the atmosphere. As follows from formulas (4) and (6), the relation between the ionospheric temperature \(T\) and the field strength \(E\) at the wall of a stationary body is given by
\[ E = 6.7 \cdot 10^{-8} \sqrt{n_0 T}, \tag{9} \]
i.e., to determine the temperature it is also necessary to measure the ion concentration.
Taking the velocity of the body into account leads to the result that on parts of the body normal to the direction of motion (formula (8)), the relation of the field strength to the temperature will be given by
\[ E = 10.2 \cdot 10^{-8} \sqrt{n_0 T}. \tag{10} \]
Thus, the temperatures determined from formulas (9) and (10) may differ by a factor of two.
Measurements of the ion concentration are complicated by the circumstance\(^{14}\) that the quantity \(\alpha\) measured by the instrument is a function not only of the concentration \(n\) of particles, but also of the potential \(V\) of the satellite.
Comparing the data on the charge \(Q\) and on the concentration \(n\), we thus obtain \(Q = f_1(V,n)\) or \(E = f(V,n) = \varphi(T,n)\), while \(\alpha = \Phi_1(n,V) = \psi_1(n,T)\), or \(n = \Phi(\alpha,V) = \psi(\alpha,T)\). By the method of successive approximations, analyzing the functions \(f\) and \(\Phi\), one can calculate the potential of the satellite and the temperature of the ionosphere, at least on the shadowed part of the orbit.
A substantial refinement of the results obtained can be achieved by carrying out the described measurements jointly with measurements of the ion mass spectrum\(^{12}\). The results of measuring the ion mass spectrum depend on the potential of the probing body. The ion mass spectrum may include only certain discrete values corresponding to the masses of molecular and atomic oxygen, nitrogen, etc. These discrete values appear in measurements of the ion mass spectrum as a series of current peaks on the curve of the dependence of ion mass on retarding potential\(^{11}\). The fact that the probing body has a certain potential with respect to the plasma leads to a shift of all current peaks by the magnitude of this potential. By comparing the value of the potential obtained by means of the method described above with that obtained from the curve of the ion mass spectrum, one can substantially refine the results of measurements both of the potential of the body and of the ion mass spectrum.
It should be noted that there is one more possibility for using the results of measurements of the body potential. According to data obtained from investigations of the ionosphere by radio methods, microinhomogeneities of concentration are observed in the latter, having an extent on the order of 3 km. In these inhomogeneities the value of the ratio of the maximum concentration to the minimum may reach two. Recording the field strength at the surface of the satellite should register oscillations of the corresponding extent. By comparing the measurement data with data on particle concentration, it will be possible to obtain information characterizing the relative changes in particle temperature in these inhomogeneities.
4. PRINCIPLE OF OPERATION OF THE INSTRUMENT MEASURING FIELD STRENGTH, AND FEATURES OF ITS OPERATION IN A CONDUCTING MEDIUM
To carry out measurements of electric-field strength it is necessary to create special apparatus capable of operating under the very difficult conditions arising during the flight of satellites.
Without dwelling on such general characteristics as vibration resistance, operation over a wide temperature range, etc., which any apparatus installed on satellites must possess, let us consider the features of the operation of instruments for measuring electrostatic-field strengths when measurements are made in the ionosphere.
The theory of operation of instruments for measuring electrostatic-field strength (electrostatic fluxmeters) is set forth in work \(^{13}\). An essential part of these instruments is the receiving electrode (the so-called “measuring plate”), placed in the field being measured. The measuring plate, with the aid of a special shielding electrode, is alternately exposed in the field and shielded from it. Thus, at the surface of the measuring plate the constant field being measured is transformed into a pulsating one. The change of field at the measuring plate causes displacement of induced charges and, consequently, the appearance of a current. The magnitude of the current is strictly proportional to the measured electric-field strength. By measuring, in one way or another, the magnitude of this current, one can thereby measure the strength of the electrostatic field.
Without considering the general theory of electrostatic fluxmeters, which was done in the cited work \(^{13}\), let us dwell on the variant most essential for operation in the ionosphere, when the measuring plate may be regarded as loaded by a purely ohmic resistance. In this case the magnitude of the current is measured by the magnitude of the voltage drop produced by the current across a certain (known) load resistance.
A flat measuring plate 1 of area \(S\) (Fig. 2) is connected with the body housing through a resistance \(R\) and is placed in the measured field of strength \(E_A\). The shield 2, moving with velocity
\[ \frac{dS}{dt}=\pm a\quad (a=\mathrm{const}), \]
alternately either exposes plate 1 or shields it from the field \(f\) times per second. Then a voltage arises on the plate
Fig. 2. Schematic diagram of the instrument’s principle of operation.
\[ V=\pm iR=\pm k\frac{E_A S}{4\pi} fR, \tag{11} \]
where \(i\) is the current flowing from the measuring plate, \(k\) is a coefficient, deter-
determined by the configuration and design of the instrument and by its placement in the field. Formula (11) is valid under the assumption that the field at the measuring plate, when the measuring plate is opened and closed by the shield, changes from some value \(kE_A\) to zero. If only the value of the field strength \(E\) at the surface of the instrument is to be measured, then, putting \(E=kE_A\) (see formula (1)), equation (11) can be somewhat simplified:
\[ V=\pm \frac{ES}{4\pi} fR. \tag{12} \]
Thus, a sign-alternating voltage with amplitude value \(V\) will arise across the resistance \(R\). The instants at which the sign of the voltage changes will coincide with the instants at which either exposure or shielding of the measuring plate by the shield ends. Reversal of the direction of the field-strength vector will evidently lead to a phase shift of the current \(i\), or of the voltage \(V\), by \(180^\circ\).
Using formulas (11) or (12), one can estimate the magnitude of the current \(i\) that will flow through the resistance \(R\).
If the field strength at the instrument is \(E=1\ \mathrm{V/cm}\) and the area of the measuring plate is \(S=10\ \mathrm{cm}^2\), and the frequency is \(f=1000\ \mathrm{cps}\) (figures close to those that can be obtained for an actual instrument), then an alternating current of magnitude \(\sim 1\cdot 10^{-9}\ \mathrm{A}\) will flow from the plate. The voltage \(V\), taken from the load resistance, will be proportional to the resistance \(R\) *). For a resistance \(R=10^5\ \Omega\), under the stated conditions the value of \(V\) will be \(10^{-4}\ \mathrm{V}\). A voltage of this magnitude can be amplified relatively simply by means of a tube amplifier and then measured.
The signal at the amplifier output can be increased by increasing the resistance \(R\). In doing so, however, it should be remembered that leakage from the measuring plate through the air can reach a considerable value in the ionosphere; since the resistance \(R\) is shunted by the resistance of this leakage, to improve the accuracy of the measurement it is desirable to choose the smallest possible values of the load resistance.
a) Influence of leakage current on the operation of the instrument
Let us suppose that the measuring plate and the shield are made in the form of similar flat plates representing a number of circular sectors (Fig. 3), with the shielding plate placed at a distance \(d\) from the measuring plate and rotating in a plane parallel to the latter; a leakage current, determined by the concentration of charged particles, their velocity, and the design of the instrument, will flow between the measuring and shielding plates. The action of this leakage current will appear as a shunting of the load resistance. The leakage current will be produced first of all by those ions that are in the space between the measuring and shielding plates. The total number of such ions \(N\) is evidently equal to
Table III
| Ion concentration \(n,\ \mathrm{cm}^{-3}\) | Leakage current \(i_{\mathrm{leak}},\ \mathrm{A}\) |
|---|---|
| \(10^4\) | \(1\cdot 10^{-13}\) |
| \(10^5\) | \(1\cdot 10^{-12}\) |
| \(10^6\) | \(1\cdot 10^{-11}\) |
\[ N=\frac{nSd}{K}, \tag{13} \]
*) Let us recall that the operating regime considered is that of an electrostatic fluxmeter loaded by a purely ohmic resistance, in which the time constant of the measuring plate may be neglected in comparison with the period of shielding or exposure.
where \(n\) is the concentration of ions outside the disturbed zone, and \(K\) is a coefficient taking into account the decrease in the concentration of these ions at the wall of the body.
Fig. 3. Diagram of the sensor device.
\(1\)—shielding plate, \(2\)—measuring plate, \(3\)—guard ring, \(4\)—insulator, \(5\)—grounding brush, \(6\)—electromagnetic generator, \(7\)—motor, \(P_1\)—connector, \(P_2\)—connector.
For an ambient temperature \(T = 1000^\circ\mathrm{K}\), one may take \(K = 8\) (see, for example, [8]). The maximum leakage current that these ions can create is
\[ i_{\mathrm{leak}}=\frac{N}{\tau}=\frac{enSd}{K}\,2f, \tag{14} \]
where \(\tau\) is the time of exposure or shielding of the measuring plate, and \(e\) is the electron charge. The values of the leakage current for various concentrations of ions \(n\), for the case \(S = 10\ \mathrm{cm}^2\), \(d = 0.1\ \mathrm{cm}\), \(f = 1000\ \mathrm{Hz}\), \(K = 8\), are given in Table III. As follows from this table, this current constitutes only a small part of the current through the resistance, and consequently, with the proper choice of design, the leakage current will have little effect on the measurement results.
In estimating the leakage current it was not taken into account that ions from the surrounding space may additionally enter the gap between the measuring and shielding plates, thereby increasing the number of ions that create the leakage current. These ions can enter the gap between the two plates only when the trajectory of the ions deviates from a straight line, which is possible either owing to reflection of ions from various parts of the instrument or owing to collisions with other ions.
The number of ions that have changed their trajectory upon striking parts of the instrument must be very small, since the coefficient of adhesion of ions to the walls is very high and close to unity; one must also bear in mind that those ions take part in creating the leakage current whose charge sign is opposite to the sign of the body’s charge; therefore the coefficient of their adhesion to the body must be still higher than in the case of a neutral body. Hence these ions cannot appreciably affect the magnitude of the leakage current. Ions entering the gap between the plates owing to collisions with other ions will likewise have little effect on the leakage current. The number of particles that have collided, \(\Delta n\), in \(1\ \mathrm{cm}^3\), at an ion concentration in the undisturbed region \(n\), will be determined by the equality
\[ \Delta n = n_0 d S e^{-\frac{L}{d}}, \]
where \(L\) is the free path length of the ions. Since at satellite flight altitudes the value of \(L\) is meters and even tens of meters, while the value \(d\) is, in order of magnitude, no greater than fractions of a centimeter, then
\[ e^{-\frac{L}{d}} \sim e^{-1000} - e^{10000}, \]
i.e., \(\Delta n\) is a negligibly small quantity. Thus, formula (14) makes it possible to estimate with sufficient accuracy the magnitude of the leakage current and, consequently, the error introduced by it into the measurements.
b) Influence on the operation of the instrument of the current to the satellite body
No current should flow to the satellite body in the equilibrium state. However, in addition to cases of disturbance of the equilibrium state for the entire satellite as a whole, it should be kept in mind that operation of the instrument reduces to a continuous disturbance of quasistationary conditions.
In this case, an alternating-sign pulsating current with pulsation frequency also \(f\) will flow through the resistance \(R\). This current will interfere with measurement of the alternating-sign signal current. If an alternating-current amplifier is used in the circuit, the two currents will be shifted by \(90^\circ\). By using synchronous detection in the amplifier circuit, it is possible, within the limits of amplifier linearity, to suppress completely the signal caused by the current to the body. It is therefore possible to carry out measurements of fields at currents to the instrument several times greater than the currents arising at the maximum measured fields. Since the electron concentration at the body is two hundred times less than normal, then at particle concentrations of \(10^4 \div 10^6\ \mathrm{cm}^{-3}\) the current to the measuring instrument will not exceed \(10^{-10} \div 10^{-9}\ \mathrm{A}\).
c) Influence of the distribution of volume-charge density on the operation of the instrument
As already indicated earlier, near a body in the ionosphere there arises a volume charge which, by its field, shields the field of the charged body. The thickness of the layer of this volume charge may be very small, reaching, at particle concentrations of \(10^6—10^7\ \mathrm{cm}^{-3}\), several millimeters.
Under these conditions, the operation of the instrument may be substantially affected by the circumstance that the shielding plate is separated from the measuring plate by some distance \(d\), comparable with the thickness of the space-charge layer. To estimate the measurement error, it is necessary to consider what fraction of the space charge may lie in the gap between the shielding and measuring plates, and how the influence of this space charge will affect the measurement results.
The distribution of potentials and fields at the wall of a body placed in plasma can be calculated on the basis of the classical theory of probes. From the data on this distribution one can calculate, for the zone of thickness \(d\), the fraction of the space charge
\[ \int_0^d \rho\, dz \]
relative to the entire space charge at the wall
\[ \int_0^\infty \rho\, dz . \]
For concentration \(n = 10^6\ \mathrm{cm}^{-3}\) and temperature \(1000^\circ\mathrm{K}\), the value of this fraction is given by Table IV.
Table IV
| \(d,\ \mathrm{cm}\) | 0.1 | 0.2 | 0.3 |
|---|---|---|---|
| Law “3/2” | 0.03 | 0.06 | 0.12 |
(the “3/2” law corresponds to a calculation according to Langmuir’s law).
From the data in the table it is clear that even for relatively low temperatures and high concentrations, a layer of thickness \(0.1 \div 0.3\ \mathrm{cm}\) contains no more than 12% of the total quantity of charges.
Fig. 4. Dependence of the thickness of the disturbed layer on the temperature of the medium.
For higher temperatures and lower concentrations this quantity will be still smaller, as is evident from Fig. 4, in which the dependence \(d=f(T)\) for different concentrations \(n\), calculated according to the “3/2” law, is presented graphically.
It is essential to take into account how the space charge that remains in the gap between the measuring and shielding plates will affect the measurement error. The error in the measurements produced by this charge will have an effect only if, during the shielding of the measuring plate, this charge is preserved and creates a field. The time \(t_p\) for the dissipation of this charge will be determined by the rate of settling of ions on the measuring and shielding plates and will be
\[ t_p=\frac{d}{u_p}, \]
where \(u_p\) is the thermal velocity of the positive ions. If the distance between the measuring and shielding plates is \(d\sim 0.1\ \text{cm}\), then at a temperature \(\sim 1000^\circ\mathrm{K}\), when the ion velocity is \(10^5\ \text{cm/sec}\), the time is \(t_p\sim 10^{-6}\ \text{sec}\). If the process of shielding the plate lasts more than \(10^{-4}\ \text{sec}\), then it may be assumed that the entire space charge in the layer between the two plates dissipates instantaneously and the error introduced into the measurements by the space charge near the body becomes vanishingly small.
For \(d\sim 1\div 2\ \text{mm}\), this error may be neglected.
5. DESCRIPTION OF THE BASIC CIRCUIT OF THE INSTRUMENT
As already indicated above, for measurements it is necessary to have at least two sensors located at diametrically opposite points of the satellite. It is desirable to carry out measurements along the entire orbit in order to take account of latitudinal, meridional, and altitude variations. To measure inhomogeneities in the ionosphere, measurements must be made with sufficiently small inertia; for the indicated dimensions of inhomogeneities the inertia of the instrument should not exceed tenths of a second.
Fig. 5. Block diagram of the instrument. Fig. 6. Diagram of the installation of the apparatus
The block diagram of the instrument is shown in Fig. 5. Two sensors \(D_1\) and \(D_2\) are installed on the satellite in positions 1 and 2, indicated in Fig. 6. In order for the surface of the satellite to be equipotential, it must be electrically conducting. It should be noted that the high conductivity of the atmosphere in the operating altitude range also promotes equalization of the potentials along the surface of the body. Sensors \(D_1\) and \(D_2\) are connected by cables to the measuring unit \(U\) (\(3\) in Fig. 6), located in the satellite cabin (Fig. 5 and Fig. 6).
The measuring unit, in which the amplifiers and the circuits for switching the apparatus on and off and for sensitivity control are located, is connected by cables, respectively, to the input of the telemetric
stations “Tm,” the power-supply unit “P,” and the programming device “Pr.”
Let us consider a possible design scheme for the individual units of the instrument.
a) Sensors
The design scheme of the sensor is shown in Fig. 3. The measuring plate 2 is shielded from the field by means of the shielding plate 1. A guard ring 3 serves to equalize the field near the measuring plate 2.
All three parts are gold-plated in order to reduce the influence of the contact potential difference between them on the readings of the instrument. The measuring plate is attached to the body of the instrument by means of an insulator 4 and is connected to the input of the amplifier by means of the plug connector \(P_1\). To ground the shielding plate 1, brushes 5 are used, sliding along a metal ring mounted on the shaft.
To create the synchronous voltage feeding the synchronous detector at the output of the instrument, an electromagnetic generator 6 is used, which is structurally part of the direct-current electric motor 7 rotating the shielding plate. The voltage to the synchronous detector and the supply of the motor are delivered by a cable connected by means of connector \(P_2\).
The distance from the measuring plate to the shield is \(d \sim 2\) mm. This distance, as follows from the considerations given above, should be made as small as possible, since decreasing \(d\) leads to a reduction in the shunting action of the ionosphere, errors due to the distribution of volume charge near the wall, etc. However, a limit to reducing \(d\) is imposed by the influence of the interference arising from the contact potential difference between the measuring and shielding plates. The influence of this potential difference, which is not constant in magnitude, grows linearly as the distance between the two plates is decreased.
In order to reduce the amount of ionized air passing between the measuring and shielding plates, a ring mounted on the guard ring is used. This ring is not shown in Fig. 3.
b) Amplifiers
The purpose of the amplifier in the circuit is to linearly amplify the signal appearing at the output of the sensors, to detect it, and to extract the phase of the measured voltage in order to determine the sign of the field strength at the surface of the body.
In order to reduce the shunting effect of the medium, the input resistance of the amplifier should not exceed 50–100 kΩ. In the circuit, an input resistance of \(\sim 10\) kΩ may be used. Across such a resistance, in a field of strength \(1\) V/cm (and it may be expected that the measured field strengths will not exceed \(2\) V/cm), with the indicated sensor parameters, a voltage of magnitude \(\sim 50\) μV will be produced. This means that the amplifier must make it possible to measure reliably signals of magnitude \(0.5\) μV. Amplification of such small signals in the low-frequency region requires the creation of an amplifier possessing considerable noise immunity.
On the basis of the characteristics of existing parts, materials, and power sources, one may expect that it will be possible to create apparatus having the necessary minimum weights and volumes.
References
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