PUBLICATIONS. Journal of Geophysical Research: Space Physics. DC and low-frequency double probe electric field measurements in space

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1 PUBLICATIONS Journal of Geophysical Research: Space Physics RESEARCH ARTICLE Special Section: Measurement Techniques in Solar and Space Physics: Fields DC and low-frequency double probe electric field measurements in space F. S. Mozer 1 1 Physics Department and Space Sciences Laboratory, University of California, Berkeley, California, USA Key Points: It is explained how and why the double probe electric field experiment works Electric field data analysis techniques are described Methods for improving the electric field measurement are described Correspondence to: F. S. Mozer, forrest.mozer@gmail.com Citation: Mozer, F. S. (2016), DC and low-frequency double probe electric field measurements in space, J. Geophys. Res. Space Physics, 121, 10,942 10,953, doi: / 2016JA Received 16 MAY 2016 Accepted 27 OCT 2016 Accepted article online 29 OCT 2016 Published online 17 NOV The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. Abstract The double probe technique for measuring DC and low-frequency electric fields in space plasmas is described with an emphasis on uncertainties in the measurements, data analysis techniques, and methods for improving the electric field measurements in future missions. 1. Introduction Electric fields in space plasmas have been directly measured as potential differences between two separated conductors divided by their separation in what is called the double probe technique. They have been indirectly measured by tracing electron drift trajectories via the electron drift technique of Paschmann et al. [1998] and from plasma flows, barium cloud releases [Haerendel et al., 1967] retarding potential analyzers, ion drift meters [Hanson and Heelis, 1975], and the first moment of plasma distribution functions. Each of these techniques has its relative strengths and weaknesses. Plasma flows measure only perpendicular electric fields and only when the additional terms in the generalized Ohm s law are negligible, which is not the case in some of the most interesting regions of space. The electron drift instrument provides only perpendicular electric fields and only when the magnetic field magnitude is in the appropriate range and is constant on the time scale of the electron gyroperiod. The double probe technique also has limitations which are discussed in this paper as part of the description of the measurement technique. Before this discussion, it is noted that the double probe technique has produced numerous successes such as discovery of the low-altitude auroral acceleration region and its electrostatic shocks, observation of electric fields in symmetric and asymmetric magnetic field reconnection, provision of statistical maps of electric potentials in the magnetosphere, direct observation of electric fields parallel to the magnetic field line, measurements of very large amplitude and oblique whistlers, mapping of Poynting flux along auroral field lines, discovery of time domain structures and their acceleration and precipitation of electrons. In addition, the potential of the biased electric field sensors (discussed below) provides an estimate of the plasma density that is routinely used in analyses of other data. The difference between low- and high-frequency double probe E field measurements may be considered by reference to the equivalent circuit of a single electric field sensor in Figure 1. In this figure, the plasma is connected to the sensor (the black sphere) through a parallel R 1 C 1 circuit where R 1 is the sheath impedance (discussed below) that ranges between 10 7 and ohm, depending on the current bias to the sensor, and where C 1 is approximately the free space capacitance of the sensor (~10 pfd). Likewise, R 2 represents the input resistance of the electronics and the leakage resistance ( ohm if a high input impedance preamplifier is mounted on a clean surface), and C 2 is the preamp input capacitance plus the stray capacitance (a few pfd if the circuit is properly designed and laid-out). Near DC, the input circuit is dominated by R 1 and R 2, so the requirement is that R 2 >> R 1 in order that the input signal is not attenuated by the resistor divider network. At low frequencies, the voltage of a sensor is affected by its low-frequency stray currents, photoemission or work function differences, asymmetries associated with the magnetic field direction or fields and currents from the spacecraft, etc. If these currents were identical on each of two opposing sensors, the spurious potentials associated with them would cancel when the potential difference between the sensor pair is measured. If they are different, these asymmetries produce a spurious electric field that makes measurements at DC and low frequencies more difficult. At higher frequencies ( several hundred Hertz) the capacitive impedance is small compared to the resistive impedance, and the input signal is attenuated by the capacitor divider effect, which can be significant. More importantly, due to the capacitive coupling at these higher frequencies, differences of DC or low-frequency currents to opposing sensors do not matter, so the E field measurement is easier and more accurate. It is the measurement at DC and low frequencies (where the resistive coupling dominates) that is the subject of this paper. And, to simplify the discussion, it is assumed MOZER E FIELD MEASUREMENTS 10,942

2 Figure 1. Equivalent circuit diagram of the connection between the plasma and the equipment that measures the electric field. that the measurements are in sunlight (so the photoemission current plays an important role), in the Earth s magnetosphere (which sets the ranges of the plasma density and other parameters), the satellite is spinning about a single axis, and the Debye length is comparable to or larger than the boom dimensions. (In the opposite limit of a very short Debye length, much of the following discussion is irrelevant.) The first successful double probe electric field measurement in space was made on a French sounding rocket launched from Andenes, Norway, on 17 October 1966 [Mozer and Bruston, 1967]. Figure 2 (top) shows the French launch crew preparing the rocket for launch, and Figure 2 (bottom) shows the celebration by the French crew plus one American when the real-time data showed that electric fields were actually measured. Since that first measurement, double probe electric field measurements have been flown on numerous rockets, more than 100 balloons, and on a few dozen satellites, including S3-2, S3-3, DE-2, ISEE-1, CRRES, Polar, Viking, Freja, FAST, the four Cluster spacecraft, the five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, the two Van Allen Probes, C/NOFS, and the four Magnetospheric Multiscale satellites. Figure 2. (top) Photo of the sounding rocket flown from Andenes, Norway, on 23 October 1966 to make the first double probe measurement of electric fields in space. (bottom) A scene from the party held when it was realized that electric fields were actually measured. 2. Measurement Design In the double probe technique, the three-component electric field is measured as the potential differences between three orthogonal pairs of separated sensors divided by their separation distances. Thus, the electric field has components V 12 /L 12, V 34 /L 34, and V 56 /L 56 where V 12 is the potential MOZER E FIELD MEASUREMENTS 10,943

3 difference between sensors 1 and 2 whose separation is L 12. V 12 and V 34 are measured in the spacecraft spin plane, and V 56 is measured along the spin axis. Measurement of the potential difference between two separated sensors with the required accuracy is difficult because the expected potential differences might be as small as 10 millivolts, while differences in the work functions of the sensors, photoemission differences between the sensors, and asymmetries with respect to the spacecraft, the plasma flow, or the magnetic field direction, can all result in error potentials that are orders of magnitude larger. These facts lead to the following requirements on the electric field measurement: 1. L 12,L 34, and L 56 must be as large as possible, and the spacecraft should be as small as possible. On spinning spacecraft L 12 and L 34 can be ~100 m by use of wire booms that are held radial by centrifugal force. However, L 56 is forced to be as much as an order of magnitude smaller, depending on the spacecraft design, due to the moment-of-inertia limitations associated with stable rotation about the 56 axis. As discussed below, the effective parameter associated with the boom is its length divided by the radius of the spacecraft. 2. The surfaces of the conductor pairs must have uniform and identical work functions. This minimizes error voltages due to contact potentials. The most successful surfaces that have been flown are carbon suspensions (aquadag). 3. The sensor pairs must experience identical sunlight and all other perturbations, and the photoemissions of the sensor pairs must be uniform and identical. If the sensors are asymmetric with respect to the direction of the Sun, they can experience a rotation-dependent spurious voltage signal because the sunlight on the sensors varies with the spin phase. In this case, the sensors must be spheres such that, at any spin phase, the opposite spheres of a pair experience the same sunlight. 4. The satellite perigee should be above about 1000 km if possible. This prevents atomic oxygen from forming a surface layer that reduces the photoemission of the spheres, as happened on ISEE, THEMIS, and VAP (large photoemissions are desirable as the following discussion shows, even though the double probe instrument works well with smaller photo currents and at lower altitudes). 5. The input electronics must have a high input impedance (>10 11 ohm) and low leakage ( 0.1 na). This is required to prevent error voltages due to currents flowing in the electronic circuits. 6. A high level of cleanliness in fabrication and assembly is required in order to minimize leakage currents through contaminated surfaces. On some occasions, this leakage current has been a major source of error in the E field measurement. As may be clear from the above discussion, the difference currents to a sphere pair, ΔI, causes the largest error in the electric field measurement. ΔI produces an error voltage Δv =(dv/di)δi, where dv/di is called the sheath impedance. In the following discussion, this sheath impedance is examined with the goal of minimizing it by driving bias currents to the spherical sensors. A note about notation: through this article, the lower case voltage, v, is the potential difference between the surface of interest and the nearby plasma. Such voltages cannot be measured. Alternatively, upper case voltages, V, are potential differences between two bodies and these can be measured. Thus, for example, V 12 = V 1 V 2, where V 1 = v 1 v sc and v sc is the potential of the spacecraft with respect to the nearby plasma. A body immersed in a plasma charges to the potential, v, until the sum of all currents to the body is zero, at which point it is in equilibrium. In sunlight in the Earth s magnetosphere, the body charges to a positive equilibrium potential because the photoemission, I ph, is greater than the plasma electron current, I e. Neglecting currents such as those due to focusing, ions, secondary emission, etc., but including an imposed current or leakage current, I, this equilibrium condition is I e þ I ph þ I ¼ 0 (1) where I e ¼ 4πr 2 neðkt e =2πm e Þ 1=2 and Iph ¼ πr 2 i ph exp ev=kt ph and r is the radius of the body of interest, i ph is the photoemission per unit area of the body, T e is the temperature of the assumed Maxwellian plasma electron spectrum, T ph is the temperature of the assumed exponential photoemission spectrum, and v is the positive potential that the body reaches with respect to the nearby plasma in order to collect back enough low energy electrons to satisfy equation (1). These three MOZER E FIELD MEASUREMENTS 10,944

4 Figure 3. Graphical illustrations of the current balance to an electric field sensor [Pedersen et al., 1998]. equations can be solved for v and its derivative with respect to I in order to obtain the sheath impedance [Fahleson, 1968] dv=di ¼ kt ph =ei j e þ Ij (2) For kt ph ~ 10 ev and for a large bias current, I = 100 na, dv/di ~10 8 ohms, and a leakage current of 1 na produces an error voltage of 100 mv or ~10 mv/m in the axial electric field component. This is large compared to the smallest electric field that is desired to be measured. Thus, current asymmetries between opposite sphere pairs must be much less than 1 na for a successful measurement. It is again noted that, if each sphere of an opposite pair has the same error current, the error cancels when taking potential differences. This is why a very high level of symmetry between two opposite spheres is required such that any effect on one sphere is identical to that on the opposite sphere and, as a result, the effect cancels when taking potential differences. Equation (2) also shows that it is desirable for the spheres to have large photoemissions because the current I e + I must be essentially balanced by the photoemission. The same conclusions may be reached by the graphical analysis of Figure 3a, which offers a more intuitive understanding of what happens. In this figure, the sign of the current to the sphere is positive. It is plotted versus the potential, v, of the sphere with respect to the nearby plasma. For v < 0, photoelectrons are accelerated away from the body so they all escape to make a constant positive current to the sphere at all negative voltages. As v becomes increasingly positive, more of the low energy photoelectrons are attracted back to the sphere so the escaping photoelectron current decreases as the positive voltage on the sphere increases. For positive voltages, the plasma electrons are accelerated to the sphere so the plasma electron current to the sphere is negative and constant. For v < 0, the plasma electrons are decelerated as they reach the sphere so the plasma current decreases with increasingly negative potentials on the sphere. In Figure 3a no other currents are considered, so the equilibrium is reached when the positive photoelectron current to the sphere is equal to the negative plasma current, at the location in the figure where the voltage on the sphere is called its floating potential. At this location di/dv is small so the sheath impedance, dv/di, is large. In Figure 3b, an additional, constant, negative current to the sphere, called the bias current, is added. This causes the location of the equilibrium, at which the sum of the three currents is zero, to shift toward zero voltage, and this decreases dv/di by orders of magnitude, which makes the measurement significantly less sensitive to differences of current to the opposite sphere pairs. The optimal bias current is that which makes the equilibrium potential on the sphere positive and close to zero. If the bias current is too large, the equilibrium voltage shifts to and the electronics saturate. The effects of both too big and too little bias current are revealed in the slow sweep (sweep steps comparable in duration to the spin period such that the changes can be clearly seen) calibration runs that are periodically made in space to set the bias current. (They are periodically run because the photoemission depends on the sensor surface properties, which vary, depending on the spacecraft orbit and the plasma.) Because there are two surfaces near each sphere (the guard and the usher, whose roles are described below) whose potentials MOZER E FIELD MEASUREMENTS 10,945

5 Figure 4. Illustration of the slow sweeps of bias current to a sensor and two voltages that surround it. Such sweeps are made to obtain the optimal operating currents and voltages. For this example, the spacecraft was located on the nightside, premidnight, inner magnetosphere. However, because the photoemission is constant and the electron thermal current is small compared to the photoemission at any location in the magnetosphere, results like those illustrated are obtained anywhere in the magnetosphere. may be adjusted to minimize electron transfer to and from the sphere to the wire boom that holds it, the slow sweeps of Figure 4 run the full range of bias currents, and guard and usher voltages. In this figure, all 625 combinations of bias current from 80 to +10 na, and guard and usher voltages from 10 to +10 volts are sampled in order to select, from among these 625 possibilities, the optimal parameters for the instrument. An example of one sweep of the bias current, at the guard voltage of 5 volts and the usher voltage near zero, is shown in Figure 5. During this sweep, the electronics were saturated for very large negative bias currents (near the beginning of the plot) because the equilibrium voltage on the sphere was very negative, making the amplitude of the spin periodic sine wave in the bottom panel of the figure large, and totally unreliable. As the bias current approached 40 na, the spheres came out of saturation and small electric fields were measured. As the bias current further increased toward zero, the spin periodic electric field amplitude increased because the sheath impedance increased and the ΔI current differences between the two opposite spheres produced a growing error electric field. Thus, in this example, the optimal bias current was about 30 na, which is much smaller than typical because the spacecraft perigee altitude was below 1000 km and atomic oxygen contaminated the sphere surfaces. If the perigee had been above 1000 km, this contamination would not have occurred and the bias current would have been a factor of 5 larger, which would have increased the range of acceptable bias currents and decreased the sheath impedance. For the case of Figure 5, any bias current between about 50 and 20 na would suffice for a good measurement because the electric field amplitude is small and constant over this interval. Because of this spread of allowable values, the bias current is generally set to a constant value over the entire orbit because the plasma thermal current throughout the orbit, being generally much smaller than the bias current, does not influence the sheath impedance of equation (2) over the orbit. It is also noted that guard and usher surfaces have been components of most electric field instruments that have been flown, including ISEE, CRRES, Polar, Viking, Freja, THEMIS, Van Allen Probes, and others. 3. Data Reduction and Analysis The techniques summarized below have been applied to analyses of electric field data from many spacecraft, resulting in production of archives of analyzed data on missions such as Polar ( edu/tgo.html) or Cluster ( Discard Bad Data Because the booms that hold the separated pairs of spheres in the spacecraft spin plane are wires that are held radial by centrifugal forces, the separations between opposite spheres in the spin plane can be ~100 m, while the sizes of the on-axis rigid booms are an order of magnitude smaller due to moment-of- MOZER E FIELD MEASUREMENTS 10,946

6 Figure 5. Blowup of one bias current sweep from the data of Figure 4. For this example, the spacecraft was located on the nightside, premidnight, inner magnetosphere. However, because the photoemission is constant and the electron thermal current is small compared to the photoemission at any location in the magnetosphere, results like those illustrated are obtained anywhere in the magnetosphere. inertia and weight limitations. The data quality for the spin plane measurements is considerably better than that for the on-axis measurements because their signals are larger and the perturbations due to the spacecraft are much smaller. For this reason, the following discussion of spin plane wire boom measurements must be separated from the later discussion of on-axis electric field data. The four spheres in the spin plane are labeled 1, 2, 3, and 4, and the electric field measurements are V 12 /L 12 =(V 1 V 2 )/L 12 and V 34 /L 34 =(V 3 V 4 )/ L 34, where V 1 = v 1 v sc. The first step in the analysis of double probe electric field data is to discard bad data. An example of such data is shown in the raw electric field plots of Figure 6, in which the two panels are sine waves associated with the spin plane detectors rotating in the approximately constant electric field. During the first half of the plotted interval, the signals are reasonable-looking sine waves because higher harmonics in the signal are small but, in the second half, small horizontal distortions in the sine waves appear. These distorted sine waves are caused by a wake effect associated with cold flowing ions having a temperature less than the spacecraft potential [Engwall et al., 2006]. As illustrated in Figure 7, such ions are deflected by the spacecraft potential to create an ion void in the antiflow direction. This produces a local electric field that is well measured but that is not associated with plasma processes in open space. In such cases, the data must be corrected or discarded until such time that the spacecraft potential or the flow speed decreases. In the design of electric field instruments, this effect is minimized by having longer booms and a smaller spacecraft. The necessity for avoidance of bad data raises the question of how one can recognize bad data from good. Techniques such as comparing the measured E B/B 2 with plasma flow velocities are useful, but any disagreements may be the result of errors in the magnetic field or the flow velocity or due to neglected terms in the generalized Ohm s law, and not in the electric field. For this reason, the technique described below may be used to evaluate the electric field data quality because it depends only on the direct electric field measurements and no other data or assumptions. For good data, the signals from opposite spheres should be anticorrelated (if one sphere is positive, the opposite sphere should be negative). Consider V 1 = v 1 v sc (these quantities are defined in the paragraph before MOZER E FIELD MEASUREMENTS 10,947

7 Figure 6. Raw electric field data measured in the spacecraft spin plane during a time when the data are good (first half of the interval) and when the data are disturbed due to the wake effect of a cold flowing ion stream (second half of the interval). For this example, Cluster was located in the nightside inner magnetosphere where cold flowing ions are often observed. equation (1)). Comparisons of V 1 with V 2 contain a part that should be anticorrelated (v 1 and v 2 ) and a part that should be correlated (v sc ). To avoid this mixture of correlated and uncorrelated data, one may compare dv 1 with dv 2, where dv 1 = V 1 (V 3 + V 4 )/2 = v 1 (v 3 + v 4 )/2 and dv 2 = V 2 (V 3 + V 4 )/2 = v 2 (v 3 + v 4 )/2. Because (v 3 + v 4 )/2 is essentially equal to the potential of the plasma at the position of the spacecraft and because dv 1 and dv 2 do not contain the potential of the spacecraft, dv 1 and dv 2 should be anticorrelated for good measurements. This result is illustrated in Figure 8, where the three panels compare the potential measurements of the three pairs of orthogonal spheres. In this figure, dv 1 and dv 2 as well as dv 3 and dv 4 are clearly anticorrelated (the top two panels), while dv 5 and dv 6 are not (the bottom panel). Thus, it is concluded that the spin plane measurements with the long wire booms produced good electric field data while the on-axis measurements, with the much shorter booms, did not make good measurements at DC and low frequencies. These measurements were made in the dayside magnetosphere, but such results occur frequently in all magnetospheric regions and on all three-axis double probe electric field measurements made to date. Methods for improving this measurement in future missions are discussed below Correct the Good Data Figure 9 (top) is V12, one component of the raw electric field in the Cluster spin plane. It shows good sine waves at the spin frequency plus small spikes that appear twice per spin period. These spikes arise when each sphere passes into the spacecraft shadow or the spacecraft wake once per spin period. (These spikes serve to provide information on vehicle attitude and give confidence of the proper operation of the instrument.) The spikes must be removed in the course of the data analysis. In addition, the mean level of the sine wave differs from zero because of offsets in the electronics, etc. Figure 9 (bottom) illustrates two corrections of this raw data, the first of which is to remove the DC offset in the sine wave such that the average amplitude of the sine wave is zero. The second correction is to multiply the data by the shorting factor that has a typical value of ~1.2. This factor arises because the wire boom extends through the equipotential contours of the external electric field to distort these contours such that the potentials at the spheres are less than they would be in the absence of the spacecraft. This effect was first estimated analytically by U. Fahleson [1968] who showed MOZER E FIELD MEASUREMENTS 10,948

8 Figure 7. Illustration of the ion void that can be created on the antiflow side of a satellite by a cold ion beam that is deflected by the positive potential of the spacecraft. (a) The electron kinetic energy is much greater than its temperature and both are much greater than the spacecraft potential, so the ion beam is not deflected by the spacecraft and the wake behind the spacecraft is nearly uncharged. (b) The spacecraft potential is large compared to the electron kinetic energy and temperature, so the ion beam is deflected by the spacecraft potential to create an ion void in the antiflow direction and a spurious but real electric field that is measured by the electric field detector and that must be removed [Engwall et al., 2006]. that it depends on boom length, geometry of surfaces near the sphere, and plasma parameters such as the Debye length. Subsequent measurements on spacecraft with boom lengths from 6 m to 130 m, flying through the magnetosphere and into the solar wind, have observed shorting factors between about 1.05 and 2. This effect was first investigated on ISEE along with the spurious sunward electric field discussed below [Mozer et al., 1978]. Another correction of good electric field data is to remove a spurious sunward electric field that arises from the asymmetry associated with the photoelectrons from the sunward sphere escaping into free space while those from the antisunward sphere escape more readily by moving along the attracting potential of the wire booms. This makes the antisunward sphere more positive than the sunward sphere, which produces the sunward electric field illustrated in Figure 10. Figure 10 (left column) illustrate the sunward and dawn-dusk spin period averaged electric fields measured by spheres 1 and 2 in the top two panels and measured by spheres 3 and 4 in the bottom two panels. It is seen that the dawn-dusk field was small (the y component), while the sunward field in each measurement (the x component) was ~1 mv/m. In Figure 10 (right column), this sunward offset was removed to produce electric fields that were much less than 1 mv/m. The procedure for determining the magnitude of the sunward offset is to find a quiet region near the time of interest where E y ~ 0 and the magnetic field and the plasma are quiescent. The value of E x at this time is an estimate of the offset. Confidence in this offset estimate is then obtained by repeating this procedure very many times and finding the offset to be approximately constant (~1 mv/m for this satellite). 4. Improving the Spin Axis E Field Measurement As illustrated in Figure 8 (bottom), DC and low-frequency measurements of the spin axis electric field component have been challenging on all spacecraft. In this section, two methods for improving this measurement are discussed, the first method being to make improvements in the existing technique and the second method being to develop a radically new technique for measuring this component Improving the Existing Technique The goal of a good measurement of the on-axis component of the electric field should drive the spacecraft and mission design from the outset. For example, within the constraints of carrying the desired payload, the spacecraft should look more like a pancake than a sphere in order to maximize the moment of inertia in the spin plane and allow a stable spacecraft with longer axial booms. While obtaining a favorable shape is desirable, minimizing the spacecraft size is even more important. Because the potential, v, at a sensor arising from the potential, v o, of a spacecraft having radius R o is v = v o R o /L, where L is the boom length, the figure of merit of a boom system is the boom length divided by the spacecraft dimension. Thus, making the spacecraft smaller is as important as making the boom larger. Making R o /L small also minimizes wake effects such as those discussed in Figures 6 and 7. The Polar spacecraft had one of the more successful axial electric field MOZER E FIELD MEASUREMENTS 10,949

9 Figure 8. Comparisons of potentials of the three pairs of electric field spheres. (top and middle) The measurements were made by the sensors in the spin plane, and the anticorrelation of the data between opposing spheres shows that good electric field measurements were made. (bottom) The data from the two sensors along the spin axis are not anticorrelated, so this component of the electric field was not well measured. measurements, and its figure of merit was about four. With proper design of both the spacecraft and the booms, this quantity could increase by more than a factor of 5, which would make it approach the figure of merit of successful wire boom measurements on many spacecraft. In order to obtain and maintain the highest level of symmetry between the pair of on-axis sensors, the spacecraft spin axis should be perpendicular to the Sun-Earth line in order that the solar radiation is equal on the two sensors. This requirement defines a plane in which the spin axis must be located. Within this plane the spin axis should be perpendicular to the expected direction of the magnetic field in the spatial region of interest to optimize symmetry with respect to the magnetic field. The length of the spin axis booms is limited by the requirement that the moment of inertia in the spin plane exceeds that along the spin axis in order that the stable spin direction be along the axial booms. To maximize the spin plane moment of inertia, the heaviest spacecraft components should be mounted at its periphery and advantage should be taken of the moments of inertial of the wire booms. The effective moment of inertia of a wire boom is proportional to the radial location of its hinge point to the spacecraft. Normally, this hinge point is at the radius of the satellite, but it can be increased by running the wire down the center of a root stacer that expands into a rigid boom whose length adds to the hinge point of the wire boom. (A stacer is a coiled spring that pops up and expands into a rigid, hollow boom. It is the structure that has generally been used as the on-axis boom.) An illustration of an improved geometry of the boom systems is given in Figure 11, where the spacecraft is to the left of each panel and the main part of each boom is at the potential of the spacecraft. For the wire boom in Figure 11 (top), the sensor is a sphere held radially away from the amplifier by a fine wire. The purpose of the fine wire is to separate the sphere from surfaces that are at the potential of the spacecraft. The amplifier is in a box, called the usher, whose surface potential, v u, is held at a ground-commanded DC voltage relative to the potential of the sphere (see Figures 4 and 5). On the spacecraft side of the usher is another surface, called the guard, whose potential, v g, is also held at a ground-commanded DC voltage relative to the potential MOZER E FIELD MEASUREMENTS 10,950

10 Figure 9. Measurement of a spin plane component of the electric field, illustrating the shadow spikes produced as each sphere rotated into and out of the spacecraft shadow and the (top) corrections that are made to the data to (bottom) obtain the data. For this example, the Cluster spacecraft was located on the dayside in the solar wind, but spin dependent perturbations were observed throughout the orbit on this and virtually every satellite. of the sphere. In many previous flights the dimensions of the guard and usher surfaces have been the order of a centimeter. This results in the potential of the spacecraft, on the inner wire boom, being only a short distance from the sensor, so the sensor becomes sensitive to spacecraft perturbations. In the improved design illustrated in Figure 11 (top), the guard surface is as long as possible in order to physically separate the sensor from the spacecraft potential. An upper limit to this distance is given by the fact that the photoelectrons emitted by the guard surface must be collected by the spacecraft without greatly perturbing the spacecraft potential. A comment with regard to driving the usher and guard at the potential of the sphere is that this can produce a high-frequency oscillation under certain plasma conditions unless the circuit that provides the sensor potential to the guard and usher includes a low-pass filter that eliminates the Figure 10. Illustrating the correction of Polar satellite data for the spurious sunward directed electric field that is caused by the antisunward sensor losing more photoelectrons than does the sunward sensor. For this observation, Polar was located in the dayside magnetosphere. However, this sunward offset is caused by a geometric effect so it occurs throughout the orbit of this and most other satellites. MOZER E FIELD MEASUREMENTS 10,951

11 Figure 11. The geometries of an improved design for the (top) spin plane and (bottom) axial electric field sensors. high-frequency signals from the sphere which, otherwise, could initiate the positive feedback that drives the oscillation. An improved, on-axis, rigid boom design is illustrated in Figure 11 (bottom). Because the sensor is a wire whip that is fully illuminated by sunlight at any phase of the spacecraft spin (because the Sun-Earth line is perpendicular to the spacecraft spin axis) a spherical sensor is not required. This decreases the tip mass and, therefore, the moment of inertia of the axial boom system such that longer booms become feasible. For axial as well as radial boom systems that have been flown, the guard is small so the spacecraft potential extends along to boom to a short distance from the sensor. In the improved design, the length of the guard element would be as great as feasible. Analyses indicate that, with the improvements in the system design described above, successful threecomponent measurements of the DC and low-frequency electric field would be made. Such data are required to study and understand the small, parallel, low-frequency electric fields associated with magnetic field reconnection and other physical processes. Figure 12. A nonrotating spacecraft that carries two orthogonal spinning plates that provide the three orthogonal components of the electric field from long spinning wires. This design, as well as egg beaters and helicopters, has counter-rotating components that do not overlap and tangle. MOZER E FIELD MEASUREMENTS 10,952

12 4.2. A New Approach for Accurate Measurements of All Three Components of the Electric Field The ideal way to obtain all three components of the electric field would be to be measure each component with long wire booms that are held radial by centrifugal forces associated with their rotation. Such measurements require spin tables on the spacecraft as is illustrated in Figure 12. Spin tables have successfully flown and operated on the Polar satellite for about a dozen years, and they have also flown on commercial and military vehicles. So the technology of spin tables is flight proven. The stability of a nonrotating satellite having two spin tables, such as the example in Figure 12, has been studied [Mao et al., 2015] with the conclusion that a stable configuration can be obtained and maintained. In Figure 12, the stable configuration has the Sun shining on the far side of the satellite and the two counter-rotating and synchronized spin tables are mounted in 90 planes relative to each other. Each spin table houses four wire booms that make an instantaneous measurement of the two components of electric field in each of the two spin planes, so four measurements of the three-component vector electric field are obtained. Four red wire booms and two green magnetometer booms are mounted on the leftmost spin table along with plasma detectors. Similar detectors on the other spin table are colored black. Because of the two spin tables, improved measurements of the electric field as well as the magnetic field and plasma can be made. The two-spin table configuration is called Grotifer because a rotifer is a millimeter-size insect with very many antennas, so this concept looks like a Giant rotifer or Grotifer. The Grotifer technology is tested and analyzed, so next great step forward in space physics may come from flying this concept. Acknowledgments The early understanding of double probe electric field measurements benefitted greatly from the work of Ulf Fahleson, Arne Pedersen, and John Wygant. Determining the stability of wire boom systems and convincing NASA of this stability is due to the work of David Pankow who, along with Bob Weitzmann and Paul Turin, has designed all of the mechanical systems for boom deployment that have been flown by the Berkeley group. Jack Vernetti and Winston Teitler are thanked for developing the software used for electric field data analyses. Because this paper describes an instrument design, it contains no data that is subject to the AGU data policy. References Engwall, E., A. I. Eriksson, and J. Forest (2006), Wake formation behind positively charged spacecraft in flowing tenuous plasmas, Phys. Plasmas, 13, 062,904, doi: / Fahleson, U. (1968), Theory of electric field measurements conducted in the magnetosphere with electric probes, Space Sci. Rev., 7, , doi: /bf Haerendel, G., R. Lust, and E. Rieger (1967), Motion of artificial ion clouds in upper atmosphere, Planet. Spa. Sci., 15, 1, doi: / (67) Hanson, W. B., and R. A. Heelis (1975), Techniques for measuring bulk gas motions from satellites, Space Sci. Instrum., 1, 493. Mao, Y.-T., D. Auslander, D. Pankow, K. Vega, F.S. Mozer and P. Turin (2015), Modeling and control design for a new spacecraft concept for measuring particles and fields with unprecedented resolution and accuracy, AIAA Modeling and Simulation Technologies Conference, AIAA Sci Tech, , doi: / Mozer, F. S., and P. Bruston (1967), Electric field measurements in the auroral ionosphere, J. Geophys. Res., 72, , doi: / JZ072i003p Mozer, F. S., R. B. Torbert, U. V. Fahleson, L. G. Falthammar, A. Gonfalone, and A. Pedersen (1978), Measurements of quasi-static and lowfrequency electric fields with spherical double probes on the ISEE-1 spacecraft, IEEE Trans. Geosci. Electron., GE-16, , doi: / TGE Paschmann, G., C. E. McIlwain, J. M. Quinn, R. B. Torbert, and E. C. Whipple (1998), The electron drift technique for measuring electric and magnetic fields, measurement techniques in space plasmas: Fields, Geophys. Monogr., 103. Pedersen, A., F. S. Mozer, and G. Gustafsson (1998), Electric field measurements in a tenuous plasma with spherical double probes, in Measurement Techniques in Space Plasmas Fields, edited by R. F. Pfaff, J. E. Borovsky, and D. T. Young, pp. 1 12, AGU Geophysical Monograph, Wash. MOZER E FIELD MEASUREMENTS 10,953