PUBLICATIONS. Journal of Geophysical Research: Space Physics

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1 PUBLICATIONS Journal of Geophysical Research: Space Physics RESEARCH ARTICLE Special Section: Measurement Techniques in Solar and Space Physics: Particles Key Points: Solar wind electron densities and temperatures measured across the Venus bow shock and within the magnetosheath are presented The shock is a thin layer of plasma 100 to 200 km thick. The highest densities and temperatures recorded occur in this layer Photoelectrons in the ionosphere have a near-maxwellian energy distribution that is defined by a density and temperature Correspondence to: W. C. Knudsen, wcknudsen@msn.com Citation: Knudsen, W. C., D. E. Jones, B. G. Peterson, and C. E. KnadlerJr. (2016), Measurement of solar wind electron density and temperature in the shocked region of Venus and the density and temperature of photoelectrons within the ionosphere of Venus, J. Geophys. Res. Space Physics, 121, , doi: / 2016JA Received 13 FEB 2016 Accepted 24 JUL 2016 Accepted article online 29 JUL 2016 Published online 25 AUG 2016 Measurement of solar wind electron density and temperature in the shocked region of Venus and the density and temperature of photoelectrons within the ionosphere of Venus William C. Knudsen 1, Douglas E. Jones 2,3, Bryan G. Peterson 2, and Charles E. Knadler Jr. 4 1 Saint George, Utah, USA, 2 Department of Physics, Brigham Young University, Provo, Utah, USA, 3 Deceased 20 June 2016, 4 Department of Computer Science, Utah Valley University, Orem, Utah, USA Abstract Presented herein are measurements of the solar wind electron number density and temperature near and within the bow shock of Venus. The measurements were made by the Pioneer Venus mission Orbiter Retarding Potential Analyzer operating in its suprathermal electron mode. The measurements are essentially point measurements. The spacecraft travels approximately 0.8 km during the 0.1 s time interval required to record a single I-V curve. The dual measurement of a density and temperature is obtained from one sweep by least squares fitting a mathematical Maxwellian expression to the I-V curve. The distance between successive measurements is approximately 100 km. In many orbits, when the spacecraft is crossing or traveling within the bow shock, the derived densities and temperatures (high density, high temperature (HDHT)) are large, densities of the order of 100 cm 3 and temperatures of the order of several hundred ev. We interpret these HDHT measurements as measurements in regions where the large, directed kinetic energy of the solar wind ions is being degraded into randomized, more thermal-like energy distributions of the electrons and ions through wave-particle interactions. The HDHT values define the electron energy distribution in the limited energy interval 0 to 50 ev. We assume that the underlying electron flux distributions are flat topped like those measured in the Earth s bow shock. We also report densities and temperatures of EUV produced photoelectron energy distributions measured within the ionosphere. 1. Introduction We report in this paper efforts by the authors to derive solar wind electron number density and temperature from the Orbiter Retarding Potential Analyzer (ORPA) instrument mounted on the NASA Pioneer Venus Orbiter spacecraft. The spacecraft orbited Venus during the period [Fimmel et al., 1995; Russell, 1992]. The ORPA was selected for the Pioneer Venus Orbiter Mission to measure the temperature of ionospheric ions, but it was also designed to measure additional quantities such as the suprathermal electron flux in the nightside ionosphere, thought to be an important source of nightside ionospheric ionization. The original investigators recognized the possibility that solar wind electron density and temperature might be derived from the ORPA and requested that it be commanded into its suprathermal electron mode and assigned any excess spacecraft bandwidth whenever the spacecraft was out of the ionosphere. Occasionally, the ORPA was commanded into the suprathermal mode through periapsis or a portion thereof. Our research efforts reported herein were motivated by the possibility that the Venus bow shock could be defined in more detail than heretofore. The ORPA measurements are essentially point measurements and are separated by only 15 s. The instrument selected for solar wind measurements, the OPA, required 10 min to complete one measurement cycle in which it returned proton density, temperature, and bulk velocity. The ORPA returns 40 measurements of electron density and temperature in 10 min when assigned its maximum band width American Geophysical Union. All Rights Reserved. Both the solar wind electron density and temperature are obtained by least squares fitting a mathematical Maxwellian function to a single I-V sweep consisting of 24 currents and voltages recorded within 0.1 s. The voltage sweep is from 0 to 49 V relative to the spacecraft ground. The time interval of 0.1 s is short enough that the resulting density and temperature measurement may be considered a point measurement with few exceptions. A pattern of four sweeps is repeatedly taken in which the four sweeps are recorded with the instrument looking in four different but constant ecliptic plane directions approximately 90 apart. The four KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7753

2 sweeps are taken over four spin periods of the spacecraft, one sweep per spin period. More details of the instrument and the mathematical function used to fit the I-V curve will be given hereafter. The ORPA was not designed to suppress solar wind protons approaching the instrument with a speed of 400 km/s or to suppress an electron gas with a temperature of hundreds of ev, but the orientation of the instrument axis plus the electronic circuitry design has permitted us to successfully obtain electron densities and temperatures of the solar wind wherever the electron velocity distribution is expected to be Maxwellian. The accuracy with which the ORPA measured electron quantities within the Venus ionosphere was approximately 90% [Miller et al., 1984]. We expect the accuracy of the solar wind electron densities and temperatures to be similar except for errors resulting from neglecting the bulk speed of the solar wind and failure of the electron velocity distribution to be Maxwellian. These two sources of error are discussed, as appropriate, hereafter. Since the authors of this report began their research effort, European Space Agency (ESA) has placed its Venus Express spacecraft into orbit about Venus with periapsis at the North Pole. We anticipate that the ORPA measurements from the Pioneer Mission will be an additional valuable source of information because the Pioneer Venus orbiter was in a substantially different orbit with periapsis close to the equator. The ORPA measurements extend from subsolar, terminator, to antisolar. 2. Some Instrument and Measurement Details To better understand the measurements presented hereafter, we present some instrument and measurement details in this section. The ORPA is a retarding potential instrument which, in the suprathermal electron mode, steps through 48 negative voltages. The voltage steps increase in magnitude quadratically from 0 to 49 V. In its abbreviated mode, which is the mode used for the measurements reported herein, only every other current value was recorded and transmitted to Earth. At the ground laboratory, physical quantities such as electron temperature and number density are obtained by fitting a Maxwellian mathematical expression to the resulting 24 element I-V sweep using a nonlinear least squares computer program [Knudsen, 1966]. How well the measured electron currents fit the calculated Maxwellian currents is revealed by the goodness of fit parameter ϰ 2. Since the ORPA sweep voltage extends only to 50 V, the value of ϰ 2 only reveals the goodness of fit of the electron energy distributions from 0 to approximately 50 ev. It is important to keep this limitation in mind hereafter when some of the derived temperatures are a few hundreds of ev. The sweep voltage steps are separated in time by 2 ms except when an electrometer range change occurs. An extra 2 ms is then required. The sweep time required to define the I-V curve is, accordingly, approximately 100 ms or 0.1 s. The total time required for one complete sweep includes some housekeeping activity and increases the time to approximately 0.12 s. The highest telemetry bit rate assigned to the ORPA permitted one and only one I-V curve to be recorded by the spacecraft telemetry system each 12 s spin period. The ORPA instrument would start a new sweep immediately after completing a previous sweep. Of the approximately 100 sweeps completed in one spin period of the spacecraft, only one is selected on command from the spacecraft for transmittal to Earth. The Pioneer Venus orbiter spacecraft spin axis unit vector ī r was kept perpendicular to the Earth ecliptic plane and directed toward the south ecliptic pole (Figure 1a). The spin period was kept equal to 12 s throughout the mission except for a few orbits. The instrument central axis vector ī n is an inward directed unit vector normal to the instrument grids and lies in a plane containing the spacecraft spin axis. The angle between ī n and ī r is 25. The unit vector ī p is perpendicular to ī r and lies in the plane containing ī n and ī r. The ORPA in the abbreviated solar wind mode sent to Earth four I-V sweeps recorded when the vector ī p pointed in four different but constant longitudinal directions approximately 90 apart (Figure 1b) [Knudsen et al., 1979]. Since only one I-V sweep could be transmitted to Earth per spin period, the four sweeps were selected and transmitted to Earth in four successive spin periods. The pattern was then repeated. The time interval between two successive I-V recordings varied from about 3 s to 15 s. Eight successive time intervals measured from orbit 508 are 3.326, , , , 3.338, , , and s. Near periapsis, the distance covered by the spacecraft during a sweep is typically 0.8 km, and the distance traveled between sweep intervals of 15 s is approximately 100 km. KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7754

3 Figure 1. (a) Schematic drawing of the Pioneer Venus Spacecraft, not to scale, showing spin axis ī r perpendicular to the Earth ecliptic plane and the ORPA sensor axis ī n mounted 25 from the spin axis and in a plane containing the spin axis. The unit vector ī p is in the plane containing both ī r and ī n and is perpendicular to ī r. (b) Diagram illustrating the approximately fixed celestial longitudes at which ī p is pointing when the suprathermal electron sweeps are recorded. It is appropriate at this location in the paper to point out that this pattern of four successive measurements with ī p directed in four different, fixed directions produces a pattern of four different values in the measured electron density and temperature. We derive the electron density and temperature by fitting the I-V curve with a mathematical function that ignores the bulk velocity of the electrons. This neglect introduces errors in the density and temperature the magnitude of which depends on the magnitude and sign of the solar wind velocity component parallel to the vector ī p. Consequently, the derived electron density and temperature vary in magnitude with a pattern of four values when all the measurements are selected for printing. Whether the full pattern of four is visible in a figure depends on the magnitude of the variation, the time scale of the figure, and on our criteria for data selection. When printed, we see four lines with different values, or if printed close together with a line connecting measurements, we see a wide dark line instead of individual KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7755

4 Figure 2. Comparison of the ORPA measured solar wind electron density and temperature with a pseudo total ion density, (n p 1.1), and proton temperature measured by the Pioneer Venus solar wind instrument OPA. The total solar wind ion density must be closely equal to the electron density, but the fraction of the total that is the Helium doubly charged ion can vary. Assuming that the Helium ion concentration is 5% of the total, we compare the ORPA electron density to (n p 1.1). Because the solar wind plasma constituents are collisionless, the electron and ion temperatures can be different. The pseudo total ion density and the electron density track each other closely. The ion temperature and electron density show substantial difference at times. data points. We call this pattern of four different values or solid wide line banding. The correct value is approximately in the center of the band. The mathematical function used to fit the I-V curve and magnitude of measurement errors resulting from neglect of the bulk velocity is presented in Appendix A. We present some of our findings below. 3. Solar Wind Results To provide some confidence that we are measuring the solar wind electron density and temperature with accuracy, we compare in successive orbits, 450 and 451, the electron density and temperature measured by the ORPA with the proton density and temperature measured by the OPA. We have chosen orbit 450 and 451 to display because the ORPA was interrogated at full bandwidth for a substantial portion of both orbits. They were selected without prior knowledge of the measured values. The results are exhibited in Figure 2. The time is indicated in hours relative to periapsis. The dark ORPA densities and temperatures illustrate the effect of banding as described above. The center of the banding is the correct value. To compare the electron density with the proton density measured by the OPA, we have multiplied the OPA proton densities by a factor of 1.1 to account for the absence of the typical 5% Helium doubly ionized ion density present in the solar wind but not recorded by the OPA. The ORPA was interrogated at reduced rates during portions of each orbit where the banding is reduced to a line. The ORPA data were filtered to accept only those measurements for which ϰ 2 was less than or equal to 0.3 and the solar zenith angle of the vector ī n was greater than or equal to 80. The ORPA periapsis measurements from about 1 h to about +2 h have not been printed to improve the clarity of the graphs. No OPA measurements were available during the same KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7756

5 Figure 3. Solar wind electron number density and temperature measured from 3000 s to s in orbit 394. Periapsis is at 0 s. The spacecraft was in the ionosphere from approximately 600 s to +400 s. Except for this ionospheric interval and a short upstream interval between 2800 s and 2600 s, it was in the magnetosheath from 3000 s to s. Small intervals of time with no data indicate time intervals in which the ORPA was not being interrogated by the spacecraft. Also plotted on the same time scale are the ephemeris information, altitude, solar hour, and solar zenith angle (SZA) of the spacecraft in orbit 394. The solar zenith angle is the angle between two unit vectors, the one directed from the center of Venus to the spacecraft and the other directed from the center of Venus to the center of the Sun. The large densities, of the order of 100 cm 3, and high temperatures, several hundreds of ev, may indicate non-maxwellian electron energy distributions and not the density and temperature of a Maxwellian energy distribution (see text). time interval. The width of the variation in ORPA electron density due to banding is about ±3 cm 3 or about ±20%, with center at 15 cm 3 (see Appendix A). We estimate that the banding upstream of the bow shock could be as large as ±25%. We expect the total ion density and the electron density to be equal because of the strong electrostatic force that would exist between small volumes with dissimilar charge density. The spacing between the two densities in Figure 2 need not be precisely constant because the proton fraction of the solar wind ion composition is not constant. The small difference in spacing can be explained provided the helium ion concentration changes sufficiently in magnitude. KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7757

6 Figure 4. Solar wind electron number density and temperature measured from 3000 s to s about periapsis in orbit 400 and corresponding ephemeris information as described in Figure 3. The spacecraft was in the ionosphere from approximately 600 s to +500 s. Except for this ionospheric interval, it was in the magnetosheath from 2500 s to s. In the small time interval, s to s, the spacecraft left the magnetosheath and entered the upstream solar wind. This short time interval in which the spacecraft is outside the magnetosheath supports the suggestion made in the caption of Figure 3 that the spacecraft is skirting the shock surface. No high-density, high-temperature layer was observed in this orbit. At the orbit of Earth the average electron density is 7.1 cm 3 [Hundhausen, 1995]. Assuming the solar wind is flowing outward from the Sun spherically, the average electron density at the orbit of Venus should be 13.6 cm 3. The ORPA density between 7 h and 12 h in orbit 451 is 12 cm 3. The largest value, 23 cm 3, occurs at 12 h. We have not calculated an average for the two orbits, but, eye balling an average, we estimate that it is around 14 cm 3 or 15 cm 3. We suggest that the ORPA densities and temperatures may be considered accurate if the electron energy distribution function being sampled is Maxwellian and we use the average value of the banding. The ORPA electron temperature and the OPA proton temperature are essentially the same at the beginning of orbit 450 and the end of 451. In between the proton temperature drops to about 2 ev, while the electron KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7758

7 Figure 5. Solar wind electron number density and temperature measured from 3000 s to s in orbit 571 and corresponding ephemeris information described in Figure 3. Periapsis is at 0 s. The spacecraft was in the ionosphere from approximately 600 s to +500 s. Except for this ionospheric interval, it was in the magnetosheath from 2400 s to s. Outside these two time intervals, it was in the upstream solar wind near the terminator plane. The high-density, hightemperature values near and in the entry shock region may be reflecting non-maxwellian electron energy distributions and not the density and temperature of a Maxwellian energy distribution. temperature remains about 12 ev. The two temperatures can be different because mean free path lengths of both electrons and ions are of the order of 1 AU, the distance from the Sun to the Earth. We next describe the solar wind features encountered by the Pioneer spacecraft as it traversed the periapsis portion of its orbit from 3000 s to s relative to periapsis time as 0 s. We have chosen two orbits in which the ORPA traveled nearly parallel to the ramp region of the bow shock near the nose of the shock and for which data were obtained throughout most of the periapsis pass. Orbits 394 and 400 are only six orbits (six days) apart, the spacecraft solar zenith angle, SZA, has nearly the same value at periapsis, about 20, and the data should look somewhat similar. They exhibit substantial differences. Figure 3 shows the results obtained for orbit 394. At 3000 s the spacecraft is in the wake of Venus traveling forward toward periapsis. We suggest the spacecraft is in the magnetosheath but close to the foot. At about 2700 s it temporarily slips out of the magnetosheath into the upstream solar wind and then back into the KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7759

8 Figure 6. Solar wind electron densities and temperatures recorded in orbit 157. The high-density, high-temperature values may be reflecting non-maxwellian energy distributions and not the density and temperature of Maxwellian electron energy distributions. magnetosheath. At that time there is a slight dip and return in the density, temperature, and magnetic field B mag (The two following both the density and temperature labels designate that the values pertain to the second of two electron distributions surrounding the spacecraft (see Appendix A)). The scale for B mag /10 (nt) is the same as that for density 2. Continuing toward the nose of the shock but still within the magnetosheath, the density and temperature exhibit essentially no changes in value from 2700 s to about 600 s. At 600 s the density and temperature first decline then the density shows an abrupt increase. The temperature drops to about 10 ev and then slowly decreases with time toward periapsis. This signature is the signature of the spacecraft dropping through the mantle into the ionosphere. At the top of the mantle the spacecraft is within the magnetosheath which is flowing toward the wake. Below the mantle we have the ionosphere. The sharp drop in magnetic field B mag is coincident with the sharp increase in the density and indicates the bottom of the mantle. The density and temperature measurements below the mantle are those of photoelectrons produced in the Venusian atmosphere by solar extreme ultraviolate (EUV) photons. The measured I-V curves of the photoelectrons have the shape of a thermal (Maxwellian) distribution. The ESA satellite has measured the presence of KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7760

9 Figure 7. Solar wind electron densities and temperatures measured across the bow shock in orbit 508 as the spacecraft descended inbound and ascended outbound from periapsis. The shock crossings occurred near the terminator. The spacecraft trajectory is quasi-perpendicular to the shock. The high-density and high-temperature spikes present in the figure may be reflecting the measurement of non-maxwellian energy distributions and not the density and temperature of Maxwellian energy distributions. The first inbound spike is coincident with the ramp in the magnetic field. The second inbound spike appears to be coincident with a second crossing of the magnetic field ramp. electrons with discrete energy of 22 ev consistent with the electrons having been ejected from neutral oxygen by discrete EUV radiation [Coates et al., 2008]. The concentration of these discrete electrons in the total photoelectron distribution is sufficiently small that they do not noticeably distort the I-V curves. When the spacecraft is within the ionosphere, the variation in temperature from measurement to measurement (banding) is noticeably less than it is when the spacecraft is in the magnetosheath. This is due, in part at least, to the much smaller bulk speed of the ionospheric plasma relative to the spacecraft within the ionosphere than that of the solar wind plasma within the magnetosheath. At periapsis the ORPA was not sampled for a few seconds, but, following this interval, as the spacecraft ascends out of periapsis, the same processes occur but in the opposite time sequence. We infer from the behavior of the shocked solar wind density and temperature as the spacecraft ascends outbound above the mantle that the spacecraft is traveling approximately parallel to and within the ramp or overshoot region of the shock. The number density and temperature becomes strongly variable and chaotic. The base value of the density is approximately 40 cm 3, a value that is about 4 times the upstream density. The highest values of the density are of the order of 100 cm 3. The electron temperature is also highly variable and exhibits high values as high as 600 ev. The base of the low-temperature values is approximately 70 ev. We note that the magnetic field B mag is more disturbed in this time interval of chaotic density and temperature measurements than it is prior to periapsis. It is necessary at this point in our presentation to consider the accuracy of the ORPA temperatures equal to several hundreds of ev. In principle, the ORPA can accurately measure temperatures 10 times larger than its sweep voltage range of 49 V provided the energy distribution of the electrons is Maxwellian. The ORPA measures the variation of the electron current for retarding voltages from 0 to 49 V. Our analysis program then calculates the density and temperature of the fitting equation that yields the smallest ϰ 2 fit of the calculated Maxwellian currents to the measured currents. If the measured temperature is equal to or smaller than 25 ev, KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7761

10 Figure 8. Solar wind electron densities and temperatures measured as the ORPA crossed the bow shock both inbound and outbound in orbit 512. Three spikes in density and temperature are observed inbound. The first spike is coincident with the magnetic field ramp. We suggest the two additional spikes occur at two additional excursions of the spacecraft trajectory into or near to the magnetic field ramp. and the ϰ 2 is small, we can be confident that the ORPA had sampled, essentially, the entire Maxwellian distribution and that the measured temperature and density defines it. The upstream densities and temperatures shown in Figure 2 for orbits 450 and 451 above are examples of this condition. As the temperature increases beyond 25 ev, the ORPA will have sampled a smaller portion of the total velocity distribution. If the derived temperature is 50 ev, the ORPA has sampled, approximately, the lower half of the velocity distribution and the lower half is like that of a Maxwellian distribution. If the derived temperature is 500 ev, the ORPA has only sampled a tenth of the lower half of the velocity distribution, and if ϰ 2 is small, we may infer that that small portion of the sampled velocity distribution is the same as that of a Maxwellian distribution with temperature of 500 ev. The remainder of the velocity distribution has not been sampled. We cannot determine what the nature of the remainder of the distribution is like. The foot and ramp region of the Earth s collisionless shock is the region where the large, directed kinetic energy of the protons is degraded into much broader, local, proton and electron velocity distributions which, due to the collisionless condition of the plasma with magnetic and electric fields present, are nonisotropic and non-maxwellian. Burgess [1995] refers to these non-maxwellian velocity distributions as having a kinetic temperature. We will refer to them as having a kinetic velocity distribution. Are the high-density, high-temperature (HDHT) electron energy distributions sampled by the ORPA Maxwellian or kinetic? We cannot infer from the ORPA data what the distributions are like above 50 ev. We do know that the ϰ 2 values of the least squares fit of the Maxwellian function to the measured currents from 0 to 49 ev are less than 0.1 for most of the high-temperature values. This is a very tight fit of the Maxwellian equation to the measured currents between 0 and 49 V and implies that the distribution between 0 and 50 ev is the same as that of a Maxwellian distribution with the derived density and temperature. Because the HDHT are colocated with the magnetic field ramp, we assume that the underlying electron distributions are similar to the flat-topped distributions observed in the Earth s magnetic foot and ramp region [Schwartz et al., 2011]. KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7762

11 Figure 9. Solar wind electron densities and temperatures measured as the ORPA crossed the bow shock inbound in orbit 304. The obstacle to the solar wind at Venus is much different from that at the Earth. At Earth the obstacle is the magnetosphere which holds the shock several Earth diameters away from the Earth. At Venus, the obstacle is the ionopause at altitudes around 300 km at the nose. The nose shock is at about half a Venus radius in altitude. Is it possible that at Venus the shock is collisional, not collisionless? That is, there are binary collisions between the solar wind ions and electrons and the ionospheric electrons and ions within the mantel region. Also, there are binary collisions between the solar wind ions and electrons and the neutral atmospheric atoms that extend through the magnetosheath. Is it possible that there are sufficient collisions to establish Maxwellian electron and ion velocity distributions? We have made a simplified calculation of the mean free path of electrons and ions at the altitudes of the shock crossings where we observe HDHT values, and, although they are greatly reduced below one AU, they are still large, 3 times the diameter of Venus. It appears unlikely that binary collisions between the solar wind electrons and ions with magnetosheath neutrals can establish a Maxwellian energy distribution. We return to a description of our results. Orbit 400 is shown in Figure 4. It is about 0.6 solar hours closer to the subsolar hour 12 o clock than orbit 394 and has a periapsis altitude that is about 20 km higher than that of 394. In both orbits the upstream solar wind density is about 10 cm 3 and the temperature is 20 ev. In orbit 400 the spacecraft appears to again be inside the magnetosheath at 3000 s. At about 600 s the spacecraft passes through the mantle and into the ionosphere. At +500 s it travels upward back through the mantle and into the magnetosheath. The very large, chaotic variability in electron density and temperature evident in the outbound leg of orbit 394 is not present in the outbound leg of orbit 400. However, we do see a small increase in variability in the outbound leg. Perhaps the same processes responsible for the large variation in orbit 394 are present and active in orbit 400 but are less violent or the spacecraft is downstream of the active region. The electron temperature varies from a low of 40 ev to a high of 120 ev. The density varies from a base of 23 cm 3 to a high of 37 cm 3. The ratio of base downstream density to upstream density is 2.3. At approximately 2200 s in orbit 400, the spacecraft exits the magnetosheath and reenters it at 2300 s before finally leaving it at approximately 2600 s. The passage in and out of the upstream solar wind at 2300 s supports KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7763

12 Figure 10. Electron densities and temperatures measured across the bow shock both inbound and outbound in orbit 527. Spikes in temperature and density are coincident with the magnetic field ramp overshoot at the inbound crossing. The temperature and density of the spikes may reflect a measurement of a non-maxwellian velocity distribution and not the values of a Maxwellian distribution. Outbound, no obvious spikes occur. However, the peaks in density and temperature are coincident with the overshoot in magnetic field. the suggestion that the spacecraft is traveling approximately parallel to and near the shock front for a time interval following the passage of the spacecraft through the exit mantle in both orbits 394 and 400. Orbit 571, illustrated in Figure 5, reveals the solar wind features encountered by the Pioneer Venus orbiter spacecraft during a passage through the ionosphere near the Venus terminator. The plane of the orbit is approximately parallel to the terminator plane. The spin period of the spacecraft for orbit 571 was decreased to 6 s, hence, the denser measurements in time visible in orbit 571. Entrance of the spacecraft into the magnetosheath at approximately 2400 s and exit at s is clearly indicated by the electron density, temperature, and magnetic field. Inbound, there are several isolated sweeps in which the density is of the order of 100 cm 3 and temperature is of the order of 400 ev. Outbound, no such sweeps were observed. The spacecraft passage into and out of the ionosphere is clearly indicated by the precipitous drop and rise, respectively, of the magnetic field strength at the bottom of the mantle. The passage is also reflected in the drop in temperature of the solar wind to approximately 10 ev, the temperature of photoelectrons at the top of the ionosphere. Inbound, the top of the mantle is indicated by the lowest density of the solar wind at 750 s and by a change in slope of the temperature. Outbound, passage through the bottom of the mantle is clearly indicated by the rapid rise in magnetic field at about +500 s, but passage through the top of the mantle is not clear. The behavior of the photoelectron density in orbit 571 is different from that of orbits 394 and 400. Inbound to periapsis, the photoelectron density is essentially constant with altitude with a value of approximately 15 cm 3. The spacecraft is continuously within the EUV umbra during this segment of the orbit. Outbound, the spacecraft is still within, near, or at the edge of the UV umbra with a photoelectron density, initially of about 6cm 3. As the spacecraft rises out of the EUV umbra, the density rises to 40 cm 3 at 400 km altitude, about the same density as that in orbit 394 at the same altitude. Outbound, the density decreases abruptly with altitude as the spacecraft enters the bottom of the mantle. At least inbound, the thickness of the mantle is clearly greater at the terminator than at the nose of the shock as evidenced in orbits 394 and 400. KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7764

13 Figure 11. Photoelectron number density versus altitude for the spacecraft within the ionosphere. Inbound the mantle was at a higher altitude than outbound. We include orbit 157 (Figure 6) to show the wide variation in density and temperature observed in both the inbound and outbound portion of the spacecraft passage through the magnetosheath. The ORPA was in an ionospheric measuring mode through periapsis in orbit 157, hence, no data through periapsis. We assume that the spacecraft was traveling within the foot, ramp, or overshoot region of the magnetosheath from 4000 s to 750 s and from s to s. At approximately 2800 s, it passes out of, back into, and back out of the magnetosheath. The variation in density and temperature in orbit 157 is similar to that seen in the outbound portion of orbit 394. This orbit occurred about one Venus year earlier than orbit 394 with periapsis near the subsolar region of the bow shock. Above, we have presented orbits in which the spacecraft skimmed the outer surface of the magnetosheath near its nose. We now present several orbits, 508 (Figure 7), 512 (Figure 8), 304 (Figure 9), and 527 (Figure 10), in which the spacecraft passes more perpendicularly through the bow shock. Periapsis of the orbits is in the wake of Venus with a local solar time near midnight. Inbound the spacecraft crosses the bow shock at solar zenith angles from 66 to 78. And the altitudes of the crossings are from 6400 km to 6770 km. Outbound the spacecraft crossings have solar zenith angles from 85 to 87. These crossing are at a sufficiently large solar zenith angle that the bulk speed of the magnetosheath should have recovered to 75% of its upstream value. Banding of the density and temperature should be visible. There is no outbound crossing shown for orbit 304 because the ORPA was not interrogated during the crossing. The altitudes vary from 7700 to 10,000 km. Data points have been connected by straight lines in these figures. HDHT values, if they occur, appear as spikes, and we will refer to them as spikes. The spikes in orbits 508, 512, 304, and 527 do not exhibit as large a density or temperature as those in orbit 394. We should expect this because a reduced component of the solar wind bulk velocity is normal to the shock plane at the location of these shock crossing. Less kinetic energy of the solar wind bulk velocity is available for forming the shock. We suggest that the spacecraft crosses the bow shock more perpendicular to the shock plane in the outbound crossings than it does in the inbound crossings. There are no spikes as the spacecraft traverses upstream through the magnetosheath toward the shock in orbits 508, 512, and 527. In orbit 508 a spike does occur anomalously about 50 s downstream of the B mag ramp. We say anomalously because in the other shock crossing the spikes occur coincidently with the B mag ramp. It is not obvious that a spike in density occurs at the outbound crossing in orbits 512 and 527. The spike density is in trend with the downstream densities. There is a definite temperature spike in orbit 512. The spacecraft appears to be traveling somewhat parallel to the shock plane in orbit 508. A spike occurs at 1480 s coincident with a small ramp in B mag. After crossing the shock in orbits 512, 304, and 527, the density KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7765

14 first decreases in value then increases to a peak and subsequently decreases. This suggests us that the spacecraft initially descends through the shock and into the magnetosheath for some distance. And then, as it continues along the orbit trajectory, it comes closer to the shock downstream. In orbits 508 and 512, the spacecraft passes through one or more spikes before continuing downstream in the magnetosheath. The density and temperature shock jump values for orbits 508, 512, 304, and 525 are given and discussed in the section 5. Figure 12. Photoelectron temperature versus altitude for the spacecraft within the ionosphere. 4. Photoelectron Results We now discuss the measured photoelectron results. I-V curves obtained within the ionosphere exhibited two straight line portions indicating the coexistence of two Maxwellian electron distributions. The low-voltage, low-temperature steep slope portion N 1 represents the main ionospheric electron population. Following this portion of the I-V curve was a second, shallower sloped portion N 2 that represented the photoelectron distribution. The N 1 electron distribution has the temperature and density values consistent with those measured within the ionosphere by the ORPA and OETP (Orbiter Electron Temperature Probe) during the original mission. The high-temperature distribution N 2 was a surprise until it was realized that it was the manifestation of photoelectrons produced in the sunlit ionosphere by EUV radiation from the Sun. The variation of the current with voltage was consistent with the distribution being essentially thermal (Maxwellian) in character. In Figure 11 the photoelectron densities measured in orbits 394, 400, and 571 are plotted logarithmically along the x axis and the altitude linearly on the y axis. The densities for orbits 394 and 400 are subsolar densities. The densities recorded in Orbit 571 are near-terminator plane densities. We were able to get reliable photoelectron data in orbits 394 and 571 down to about 190 km altitude. Below this altitude the I-V curves were seriously disturbed by ionization produced by the spacecraft impacting CO 2 at a sufficient velocity to ionize them. The ORPA was not interrogated through the central portion of periapsis for orbit 400. The photoelectron density recorded inbound in orbit 571 is approximately 15 cm 3 and exhibits little height variation. The spacecraft solar zenith angle was 103 or greater and was evidently within the EUV umbra. Outbound the density initially is about 7 cm 3 at an altitude of about 200 km and solar zenith angle of 99 and then increases to 50 cm 3 at an altitude of 380 km and solar zenith angle of 96. Outbound the spacecraft is within the EUV umbra at its lowest altitude but climbs out of it as it climbs in altitude and its solar zenith angle drops below 90. The photoelectron temperatures are shown in Figure 12. The temperatures at the top of the ionosphere (bottom of the mantle) are 9 10 ev and decrease to 6 ev at about 200 km altitude, the lowest altitude of measurement. KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7766

15 Figure 13. A conceivable model for the variability of the HDHT values observed in the outbound passage of the spacecraft through the bow shock in orbit 394. A thin, convoluted layer, of the order of 100 to 200 km thickness, is suggested within which the kinetic energy of the directed solar wind ion beam is being degraded into more thermal-like electron velocity distributions through wave-particle processes. 5. Discussion We have stated in section 1 that the measurements can be considered point measurements with few exceptions. Two exceptions occurred just after the initial inbound spike in orbit 508. Examination of their I-V curves revealed current variations inconsistent with the variation expected for a point measurement. During the 0.1 s sweeps either the local plasma was changing rapidly with time or the spacecraft was traveling through a rapid spatial change in plasma density and/or temperature. The measurements from these sweeps were not printed because they had large ϰ 2 values that did not satisfy our criteria for a valid measurement. The occurrence of these two nonpoint I-V curves just after a spike suggests that the spikes represent a measurement of a kinetic electron velocity distribution. The HDHT densities and temperatures derived from the I-V sweeps of the ORPA do not represent the entire velocity distributions of the electrons at that location, assumed to be kinetic. We are unable to determine from our instrument whether the distribution is kinetic or Maxwellian. We suggest that temperatures up to at least 50 ev and their corresponding densities be considered accurate since half of the energy distribution function, 0 to 50 ev, has been sampled in the 50 V sweep range. The HDHT I-V sweeps typically had a small ϰ 2 value, , a very tight fit implying that whatever the distribution was, the low end, 0 to 50 ev, was like that of a Maxwellian distribution. The highest HDHT values in orbits 394 and 157 tend to be isolated with lower values on either side. The ORPA was traveling parallel to the shock plane. This structure suggests that there are randomly isolated volumes of plasma with dimension of the order of 100 to 200 km in size through which the spacecraft is traveling. Alternatively, the spacecraft is traveling through a highly convoluted layer whose thickness is of the order of 100 to 200 km. Figure 13 illustrates such a layer. The spikes shown in orbits 508, 304, 512, and 527 are isolated and also 100 to 200 km in thickness. They occur in or near the B mag ramp. These observations suggest to us that a convoluted layer like that drawn in Figure 13 is more likely to be the correct configuration. Evidently, the degradation of the directed proton kinetic energy into thermal energy is taking place in a thin layer of the order of 100 to 200 km in thickness. The layer thickness is also approximately the Larmor diameter of a proton with 100 ev kinetic energy in a 20 nt magnetic field. It may be instructive to compare the shock jump ratios for the electron densities and temperatures reported herein with the density and temperature jumps predicted by a MHD model for the Earth s bow shock [Spreiter et al., 1966]. The model has an upstream Mach number of 8. At the bow shock the model density jump ratio varies from 3.82 at the subsolar point (0 SZA) to about 3.6 at the terminator (90 SZA). The temperature jump varies from about 22 at the subsolar point to 9 at the terminator. We have not attempted to estimate the upstream Mach numbers pertaining to our results. For orbit 394 we determine a jump ratio for the orbit time of 1000 s, a time when the data exhibit the largest HDHT values. The density data for ±400 s about that time exhibit a lowest value of about 35 cm 3. The low temperatures are clustered around 73 ev. The upstream density, estimated from downstream values at times greater than 2500 s, is 11 cm 3. The MHD model jump ratio at SZA 55, which is the ORPA SZA at 1000 s, is 3.7, KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7767

16 Table 1. Shock Jump Ratios Inbound Outbound Density Temperature Density Temperature ORBIT ED HDHT ED HDHT ED HDHT ED HDHT X X X X a little larger than 3.2. The ORPA travels through the shock at 2500 s at a SZA of 88. The density jump ratio at this location is 2.5. The MHD model value is 3.4. The jump ratio of the HDHT temperatures at 1000 s to the downstream temperatures beyond 2500 s is 600 ev/13 ev or 46 a value larger than the MHD value of 17. If we take an average value of the low electron temperatures correlated with the low-density values, we obtain 73 ev/13 ev or 5.6, a value one third the MHD model value. For orbit 400, which did not have the large HDHT values like orbit 394, we compute a jump ratio using the density values near 2500 s. The upstream density is 10 cm 3 and the downstream density is 27 cm 3 yielding a jump ratio of 2.7. This is the same jump value as that for orbit 394 at the same SZA. We now evaluate the jump ratios for the orbits in which the ORPA crossed the shock more normal to the shock surface. The inbound density and temperature measurement coincident with the B mag ramp in orbit 508 (Figure 8) is a questionable spike. The temperature has the appearance of a spike, but the density value appears to be part of the downstream density trend. To compute an inbound density jump ratio, we have eyeballed a straight line through the center of the downstream density banding between 1800 s and 1500 s. The density at which this straight line intersects the time line of the B mag ramp is the extrapolated density (ED). If there is a spike value at the jump, we ignore it in computing the ED value. We will call densities or temperatures determined in this manner ED values. The jump ratios labeled HDHT are the spike value, density or temperature, divided by the upstream density or temperature, respectively. The ED and HDHT ratios can be very close. Jump ratios for the four orbits are listed in Table 1. For all the inbound orbits, ED is about 3.5, close to the model value. The inbound jump ratios for the spikes, HDHT values, are not much larger except for orbit Conclusions We have successfully measured the electron density and temperature near and within the magnetosheath of Venus where the electron velocity distributions are Maxwellian. Within the magnetic field ramp region our analysis software yields high-density, high-temperature (HDHT) values which do not represent the non- Maxwellian, flat-topped electron distributions assumed to exist there. The HDHT values do describe the I-V current variation between 0 and 50 ev. We infer that the non-maxwellian, assumed flat-topped electron velocity distributions colocated with the magnetic field ramp occur in a continuous but convoluted layer of the order of 100 to 200 km thick. The photoelectron velocity distributions within the ionosphere are essentially Maxwellian in shape and are defined by a density and temperature. Appendix A When we plot log I as ordinate and V as abscissa where I is the electrometer electron current and V is the retarding voltage, we get two straight line portions of an I-V curve which indicates that the I-V curve represents two Maxwellian electron distributions, a low-temperature distribution and a high-temperature distribution. Whenever the spacecraft is exposed to the unattenuated solar EUV radiation and is outside KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7768

17 the ionosphere, it develops a positive potential relative to the solar wind, and a sheath of photoelectrons emitted from the spacecraft surfaces by solar EUV is formed around the spacecraft. The electrons exhibit a near-maxwellian distribution with a temperature of a few ev. This is the low-temperature distribution that the I-V curve exhibits when the spacecraft is upstream of the bow shock within the magnetosheath and outside the Venus umbra. The photoelectrons are assumed to be confined to a sheath that is restricted in dimension. The high-temperature distribution is that of the solar wind, and we analyze only the high-temperature portion of the I-V curve. We do evaluate the effect of the high bulk velocity of the solar wind on the I-V curve hereafter. When the spacecraft is within the ionosphere, the spacecraft develops a negative potential of a volt or two negative and the I-V curve exhibits a low-temperature distribution with temperatures of a few tenths of an ev. This distribution is the thermal distribution of the ionosphere measured extensively by the OETP and ORPA during the mission. The coexisting high-temperature distribution of photoelectrons exhibits an essentially Maxwellian distribution and is the high-temperature distribution when the spacecraft is within the ionosphere. It exhibits, as discussed above, a temperature varying between 10 ev at the ionopause to 6 ev at periapsis altitudes. We consider hereafter what effect the spacecraft velocity relative to the ionospheric plasma might have on the derived temperature and density of the photoelectrons and thermal ionospheric electrons. Because the photoelectrons and thermal ionospheric electrons coexist, we include both distributions in the theoretical expression used to fit the observed I-V curve. We fit the observed I-V curves with equation (A1). I T r ea ¼ N 1fðT 1 ÞþN 2 gt ð 2 ; υþ (A1) f(t 1 ) is the low-temperature Maxwellian distribution and gt ð 2 ; υþ is a Maxwellian distribution with a vector bulk velocity υ. Equation (A1) becomes I T r ea ¼ N v exp v h i 2 b2 1 þ N2 4 exp ð a 2 b 2 Þ 2 1 þ υ i n 2 þ 1 2 erf ð a 2 b 2 Þ (A2) qffiffiffiffiffi 2kT where I is the electrometer current, α ¼ m e, T r is the total grid transparency, v ¼ p 2α ffiffi qffiffiffiffiffiffiffiffiffiffiffi π, N is the electron number density, a ¼ υin evþφ ð Þ α, A is the area of current collector, b ¼ kt, V is the retarding potential, υ is the solar wind bulk velocity (vector), and φ is the spacecraft potential relative to plasma. Equation (A2) differs from that used previously in some of our studies in that it assumes that the hightemperature electron distribution has a bulk velocity large enough to significantly affect the electrometer current. The possibility that it may be significantly affecting the current can be investigated by evaluating the minimum value of r where r is the ratio ν 24 r ¼ υi n The factor multiplying i n υ may have a value ranging 1 to 0 to +1. The absolute value of the factor may be as small as 0 which implies that the bulk velocity of the electrons contributes nothing to the current. For convenience we set the factor to +1. By so doing the value of r will not be less than this value. We now evaluate r for the spacecraft within the ionosphere, the unshocked solar wind, and the shocked solar wind. Near periapsis the spacecraft velocity is directed toward the south ecliptic pole. To the ORPA instrument, the ionospheric photoelectrons will appear to have a bulk velocity directed toward the north ecliptic pole with a speed equal to the spacecraft periapsis speed. The median temperature of the subsolar photoelectrons is about 7 ev as shown above. We assign a value of 9.8 km/s to i n υ. The value of r is for these assumptions equal to 45. The contribution of the Maxwellian term to the current is, at minimum, 45 times larger than that of the bulk velocity term. Consequently, we can safely assume that the densities and temperatures for the photoelectrons derived in this study are not significantly affected by our analyzing our data without including a bulk velocity term. Since we shall also be displaying data obtained in the unshocked and shocked solar wind, we now compute r for these two regions. In the unshocked solar wind a typical electron temperature is 15 ev. We take 400 km/s as a typical solar wind speed and assume that its direction is radially outward from the Sun. With these (A3) KNUDSEN ET AL. ELECTRON MEASUREMENTS AT VENUS SHOCK 7769