Tropospheric New Particle Formation and the Role of Ions

The Suprathermal Electron (STE) instrument, part of the IMPACT investigation on both spacecraft of NASA’s STEREO mission, is designed to measure electrons from ～2 to ～100 keV. This is the primary energy range for impulsive electron/³He-rich energetic particle events that are the most frequently occurring transient particle emissions from the Sun, for the electrons that generate solar type III radio emission, for the shock accelerated electrons that produce type II radio emission, and for the superhalo electrons (whose origin is unknown) that are present in the interplanetary medium even during the quietest times. These electrons are ideal for tracing heliospheric magnetic field lines back to their source regions on the Sun and for determining field line lengths, thus probing the structure of interplanetary coronal mass ejections (ICMEs) and of the ambient inner heliosphere. STE utilizes arrays of small, passively cooled thin window silicon semiconductor detectors, coupled to state-of-the-art pulse-reset front-end electronics, to detect electrons down to ～2 keV with about 2 orders of magnitude increase in sensitivity over previous sensors at energies below ～20 keV. STE provides energy resolution of ΔE/E～10–25% and the angular resolution of ～20° over two oppositely directed ～80°×80° fields of view centered on the nominal Parker spiral field direction.     

The Electron and ion Plasma Experiment for Fast

The ion and electron plasma experiment on the Fast Auroral Snapshot satellite (FAST) is designed to measure pitch-angle distributions of suprathermal auroral electrons and ions with high sensitivity, wide dynamic range, good energy and angular resolution, and exceptional time resolution. These measurements support the primary scientific goal of the FAST mission to understand the physical processes responsible for auroral particle acceleration and heating, and associated wave-particle interactions. The instrument includes a complement of 8 pairs of `Top Hat' electrostatic analyzer heads with microchannel plate (MCP) electron multipliers and discrete anodes to provide angle resolved measurements. The analyzers are packaged in four instrument stacks, each containing four analyzers. These four stacks are equally spaced around the spacecraft spin plane. Analyzers mounted on opposite sides of the spacecraft operate in pairs such that their individual 180° fields of view combine to give an unobstructed 360° field of view in the spin plane. The earth's magnetic field is within a few degrees of the spin plane during most auroral crossings, so the time resolution for pitch-angle distribution measurements is independent of the spacecraft spin period. Two analyzer pairs serve as electron and ion spectrometers that obtain distributions of 48 energies at 32 angles every 78 ms. Their standard energy ranges are 4 eV to 32 keV for electrons and 3 eV to 24 keV for ions. These sensors also have deflection plates that can track the magnetic field direction within 10° of the spin plane to resolve narrow, magnetic field-aligned beams of electrons and ions. The remaining six analyzer pairs collectively function as an electron spectrograph, resolving distributions with 16 contiguous pitch-angle bins and a selectable trade-off of energy and time resolution. Two examples of possible operating modes are a maximum time resolution mode with 16 angles and 6 energies every 1.63 ms, or a maximum energy resolution mode with 16 angles and 48 energies every 13 ms. The instrument electronics include mcp pulse amplifiers and counters, high voltage supplies, command/data interface circuits, and diagnostic test circuits. All data formatting, commanding, timing and operational control of the plasma analyzer instrument are managed by a central instrument data processing unit (IDPU), which controls all of the FAST science instruments. The IDPU creates slower data modes by averaging the high rate measurements collected on the spacecraft. A flexible combination of burst mode data and slower `survey' data are defined by IDPU software tables that can be revised by command uploads. Initial flight results demonstrate successful achievement of all measurement objectives.     

Helium, Oxygen, Proton, and Electron (HOPE) Mass Spectrometer for the Radiation Belt Storm Probes Mission

The HOPE mass spectrometer of the Radiation Belt Storm Probes (RBSP) mission (renamed the Van Allen Probes) is designed to measure the in situ plasma ion and electron fluxes over 4π sr at each RBSP spacecraft within the terrestrial radiation belts. The scientific goal is to understand the underlying physical processes that govern the radiation belt structure and dynamics. Spectral measurements for both ions and electrons are acquired over 1 eV to 50 keV in 36 log-spaced steps at an energy resolution ΔE _FWHM/E≈15 %. The dominant ion species (H⁺, He⁺, and O⁺) of the magnetosphere are identified using foil-based time-of-flight (TOF) mass spectrometry with channel electron multiplier (CEM) detectors. Angular measurements are derived using five polar pixels coplanar with the spacecraft spin axis, and up to 16 azimuthal bins are acquired for each polar pixel over time as the spacecraft spins. Ion and electron measurements are acquired on alternate spacecraft spins. HOPE incorporates several new methods to minimize and monitor the background induced by penetrating particles in the harsh environment of the radiation belts. The absolute efficiencies of detection are continuously monitored, enabling precise, quantitative measurements of electron and ion fluxes and ion species abundances throughout the mission. We describe the engineering approaches for plasma measurements in the radiation belts and present summaries of HOPE measurement strategy and performance.     

The IMPACT Solar Wind Electron Analyzer (SWEA)

SWEA, the solar wind electron analyzers that are part of the IMPACT in situ investigation for the STEREO mission, are described. They are identical on each of the two spacecraft. Both are designed to provide detailed measurements of interplanetary electron distribution functions in the energy range 1～3000 eV and in a 120°×360° solid angle sector. This energy range covers the core or thermal solar wind plasma electrons, and the suprathermal halo electrons including the field-aligned heat flux or strahl used to diagnose the interplanetary magnetic field topology. The potential of each analyzer will be varied in order to maintain their energy resolution for spacecraft potentials comparable to the solar wind thermal electron energies. Calibrations have been performed that show the performance of the devices are in good agreement with calculations and will allow precise diagnostics of all of the interplanetary electron populations at the two STEREO spacecraft locations.     

The Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) NASA Mission-of-Opportunity

Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) is a NASA Explorer Mission-of-Opportunity to stereoscopically image the Earth’s magnetosphere for the first time. TWINS extends our understanding of magnetospheric structure and processes by providing simultaneous Energetic Neutral Atom (ENA) imaging from two widely separated locations. TWINS observes ENAs from 1–100 keV with high angular (～4°×4°) and time (～1-minute) resolution. The TWINS Ly-α monitor measures the geocoronal hydrogen density to aid in ENA analysis while environmental sensors provide contemporaneous measurements of the local charged particle environments. By imaging ENAs with identical instruments from two widely spaced, high-altitude, high-inclination spacecraft, TWINS enables three-dimensional visualization of the large-scale structures and dynamics within the magnetosphere for the first time. This “instrument paper” documents the TWINS design, construction, calibration, and initial results. Finally, the appendix of this paper describes and documents the Southwest Research Institute (SwRI) instrument calibration facility; this facility was used for all TWINS instrument-level calibrations.     

Overview of the New Horizons Science Payload

The New Horizons mission was launched on 2006 January 19, and the spacecraft is heading for a flyby encounter with the Pluto system in the summer of 2015. The challenges associated with sending a spacecraft to Pluto in less than 10 years and performing an ambitious suite of scientific investigations at such large heliocentric distances (>32 AU) are formidable and required the development of lightweight, low power, and highly sensitive instruments. This paper provides an overview of the New Horizons science payload, which is comprised of seven instruments. Alice provides moderate resolution (～3–10 Å FWHM), spatially resolved ultraviolet (～465–1880 Å) spectroscopy, and includes the ability to perform stellar and solar occultation measurements. The Ralph instrument has two components: the Multicolor Visible Imaging Camera (MVIC), which performs panchromatic (400–975 nm) and color imaging in four spectral bands (Blue, Red, CH₄, and NIR) at a moderate spatial resolution of 20 μrad/pixel, and the Linear Etalon Imaging Spectral Array (LEISA), which provides spatially resolved (62 μrad/pixel), near-infrared (1.25–2.5 μm), moderate resolution (λ/δ λ～240–550) spectroscopic mapping capabilities. The Radio Experiment (REX) is a component of the New Horizons telecommunications system that provides both radio (X-band) solar occultation and radiometry capabilities. The Long Range Reconnaissance Imager (LORRI) provides high sensitivity (V<18), high spatial resolution (5 μrad/pixel) panchromatic optical (350–850 nm) imaging capabilities that serve both scientific and optical navigation requirements. The Solar Wind at Pluto (SWAP) instrument measures the density and speed of solar wind particles with a resolution ΔE/E<0.4 for energies between 25 eV and 7.5 keV. The Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI) measures energetic particles (protons and CNO ions) in 12 energy channels spanning 1–1000 keV. Finally, an instrument designed and built by students, the Venetia Burney Student Dust Counter (VB-SDC), uses polarized polyvinylidene fluoride panels to record dust particle impacts during the cruise phases of the mission.     

Origins of Anisotropic 40–300 keV Electron Events Observed at Low and High Latitudes

Using a survey of anisotropic electron events in the energy range of ～40–300 keV observed by HI-SCALE on Ulysses, we have selected several time intervals during 1999 when Ulysses traveled from about 20° S at 5.2 AU (January 1999) to 42° S at 4.2 AU (January 2000). We compare these events with observations at ～1 AU using the nearly identical instrument, EPAM on ACE. In order to study the solar origins of these electrons using the imaging Nançay Radioheliograph, we further restricted the list of events to those in which interplanetary magnetic field lines with origins on the visible solar disk, intersected Ulysses. We find that not all the anisotropic electron events are observed by both spacecraft and there exists a strong dependence on the spacecraft's magnetic connection back to the Sun. We have identified the solar origin for five electron events using radio observations, and correlate these with interplanetary type-III radio emissions using the WIND/WAVES experiment.     

The Solar Wind Around Pluto (SWAP) Instrument Aboard New Horizons

The Solar Wind Around Pluto (SWAP) instrument on New Horizons will measure the interaction between the solar wind and ions created by atmospheric loss from Pluto. These measurements provide a characterization of the total loss rate and allow us to examine the complex plasma interactions at Pluto for the first time. Constrained to fit within minimal resources, SWAP is optimized to make plasma-ion measurements at all rotation angles as the New Horizons spacecraft scans to image Pluto and Charon during the flyby. To meet these unique requirements, we combined a cylindrically symmetric retarding potential analyzer with small deflectors, a top-hat analyzer, and a redundant/coincidence detection scheme. This configuration allows for highly sensitive measurements and a controllable energy passband at all scan angles of the spacecraft.     

The Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI) on the New Horizons Mission

The Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI) comprises the hardware and accompanying science investigation on the New Horizons spacecraft to measure pick-up ions from Pluto’s outgassing atmosphere. To the extent that Pluto retains its characteristics similar to those of a “heavy comet” as detected in stellar occultations since the early 1980s, these measurements will characterize the neutral atmosphere of Pluto while providing a consistency check on the atmospheric escape rate at the encounter epoch with that deduced from the atmospheric structure at lower altitudes by the ALICE, REX, and SWAP experiments on New Horizons. In addition, PEPSSI will characterize any extended ionosphere and solar wind interaction while also characterizing the energetic particle environment of Pluto, Charon, and their associated system. First proposed for development for the Pluto Express mission in September 1993, what became the PEPSSI instrument went through a number of development stages to meet the requirements of such an instrument for a mission to Pluto while minimizing the required spacecraft resources. The PEPSSI instrument provides for measurements of ions (with compositional information) and electrons from 10 s of keV to ～1 MeV in a 160°×12° fan-shaped beam in six sectors for 1.5 kg and ～2.5 W.     

The IBEX-Lo Sensor

The IBEX-Lo sensor covers the low-energy heliospheric neutral atom spectrum from 0.01 to 2 keV. It shares significant energy overlap and an overall design philosophy with the IBEX-Hi sensor. Both sensors are large geometric factor, single pixel cameras that maximize the relatively weak heliospheric neutral signal while effectively eliminating ion, electron, and UV background sources. The IBEX-Lo sensor is divided into four major subsystems. The entrance subsystem includes an annular collimator that collimates neutrals to approximately 7°×7° in three 90° sectors and approximately 3.5°×3.5° in the fourth 90° sector (called the high angular resolution sector). A fraction of the interstellar neutrals and heliospheric neutrals that pass through the collimator are converted to negative ions in the ENA to ion conversion subsystem. The neutrals are converted on a high yield, inert, diamond-like carbon conversion surface. Negative ions from the conversion surface are accelerated into an electrostatic analyzer (ESA), which sets the energy passband for the sensor. Finally, negative ions exit the ESA, are post-accelerated to 16 kV, and then are analyzed in a time-of-flight (TOF) mass spectrometer. This triple-coincidence, TOF subsystem effectively rejects random background while maintaining high detection efficiency for negative ions. Mass analysis distinguishes heliospheric hydrogen from interstellar helium and oxygen. In normal sensor operations, eight energy steps are sampled on a 2-spin per energy step cadence so that the full energy range is covered in 16 spacecraft spins. Each year in the spring and fall, the sensor is operated in a special interstellar oxygen and helium mode during part of the spacecraft spin. In the spring, this mode includes electrostatic shutoff of the low resolution (7°×7°) quadrants of the collimator so that the interstellar neutrals are detected with 3.5°×3.5° angular resolution. These high angular resolution data are combined with star positions determined from a dedicated star sensor to measure the relative flow difference between filtered and unfiltered interstellar oxygen. At the end of 6 months of operation, full sky maps of heliospheric neutral hydrogen from 0.01 to 2 keV in 8 energy steps are accumulated. These data, similar sky maps from IBEX-Hi, and the first observations of interstellar neutral oxygen will answer the four key science questions of the IBEX mission.     

The Plasma Ion and Electron Instruments for the Genesis Mission

The Genesis Ion Monitor (GIM) and the Genesis Electron Monitor (GEM) provide 3-dimensional plasma measurements of the solar wind for the Genesis mission. These measurements are used onboard to determine the type of plasma that is flowing past the spacecraft and to configure the solar wind sample collection subsystems in real-time. Both GIM and GEM employ spherical-section electrostatic analyzers followed by channel electron multiplier (CEM) arrays for detection and angle and energy/charge analysis of incident ions and electrons. GIM is of a new design specific to Genesis mission requirements whereas the GEM sensor is an almost exact copy of the plasma electron sensors currently flying on the ACE and Ulysses spacecraft, albeit with new electronics and programming. Ions are detected at forty log-spaced energy levels between ∼ 1 eV and 14 keV by eight CEM detectors, while electrons with energies between ∼ 1 eV and 1.4 keV are measured at twenty log-spaced energy levels using seven CEMs. The spin of the spacecraft is used to sweep the fan-shaped fields-of-view of both instruments across all areas of the sky of interest, with ion measurements being taken forty times per spin and samples of the electron population being taken twenty four times per spin. Complete ion and electron energy spectra are measured every ∼ 2.5 min (four spins of the spacecraft) with adequate energy and angular resolution to determine fully 3-dimensional ion and electron distribution functions. The GIM and GEM plasma measurements are principally used to enable the operational solar wind sample collection goals of the Genesis mission but they also provide a potentially very useful data set for studies of solar wind phenomena, especially if combined with other solar wind data sets from ACE, WIND, SOHO and Ulysses for multi-spacecraft investigations. This revised version was published online in August 2006 with corrections to the Cover Date.     

PEACE: A PLASMA ELECTRON AND CURRENT EXPERIMENT

An electron analyser to measure the three-dimensional velocity distribution of electrons in the energy range from 0.59 eV to 26.4 keV on the four spacecraft of the Cluster mission is described. The instrument consists of two sensors with hemispherical electrostatic energy analysers with a position-sensitive microchannel plate detectors placed to view radially on opposite sides of the spacecraft. The intrinsic energy resolutions of the two sensors are 12.7% and 16.5% full width at half maximum. Their angular resolutions are 2.8° and 5.3° respectively in an azimuthal direction and 15° in a polar direction. The two sensors will normally measure in different overlapping energy ranges and will scan the distribution in half a spacecraft rotation or 2 s in the overlapped range. While this is the fastest time resolution for complete distributions, partial distributions can be recorded in as little as 62.5 ms and angular distributions at a fixed energy in 7.8 ms. The dynamic range of the instrument is sufficient to provide accurate measurements of the main known populations from the tail lobe to the plasmasheet and the solar wind. While the basic structure of the instrument is conventional, special attention has been paid in the design to improving the precision of the instrument so that a relative accuracy of the order of 1% could be attained in flight in order to measure the gradients between the four spacecraft accurately; to decreasing the minimum energy covered by this technique from 10 eV down to 1 eV; and to providing good three dimensional distributions.     

Finite-Difference Modeling of Acoustic and Gravity Wave Propagation in Mars Atmosphere: Application to Infrasounds Emitted by Meteor Impacts

The Jovian Auroral Distributions Experiment (JADE) on Juno provides the critical in situ measurements of electrons and ions needed to understand the plasma energy particles and processes that fill the Jovian magnetosphere and ultimately produce its strong aurora. JADE is an instrument suite that includes three essentially identical electron sensors (JADE-Es), a single ion sensor (JADE-I), and a highly capable Electronics Box (EBox) that resides in the Juno Radiation Vault and provides all necessary control, low and high voltages, and computing support for the four sensors. The three JADE-Es are arrayed 120^° apart around the Juno spacecraft to measure complete electron distributions from ～0.1 to 100 keV and provide detailed electron pitch-angle distributions at a 1 s cadence, independent of spacecraft spin phase. JADE-I measures ions from ～5 eV to ～50 keV over an instantaneous field of view of 270^°×90^° in 4 s and makes observations over all directions in space each 30 s rotation of the Juno spacecraft. JADE-I also provides ion composition measurements from 1 to 50 amu with m/Δm～2.5, which is sufficient to separate the heavy and light ions, as well as O+ vs S+, in the Jovian magnetosphere. All four sensors were extensively tested and calibrated in specialized facilities, ensuring excellent on-orbit observations at Jupiter. This paper documents the JADE design, construction, calibration, and planned science operations, data processing, and data products. Finally, the Appendix describes the Southwest Research Institute [SwRI] electron calibration facility, which was developed and used for all JADE-E calibrations. Collectively, JADE provides remarkably broad and detailed measurements of the Jovian auroral region and magnetospheric plasmas, which will surely revolutionize our understanding of these important and complex regions.     

The Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) for the Mars Express Mission

The general scientific objective of the ASPERA-3 experiment is to study the solar wind – atmosphere interaction and to characterize the plasma and neutral gas environment with within the space near Mars through the use of energetic neutral atom (ENA) imaging and measuring local ion and electron plasma. The ASPERA-3 instrument comprises four sensors: two ENA sensors, one electron spectrometer, and one ion spectrometer. The Neutral Particle Imager (NPI) provides measurements of the integral ENA flux (0.1–60 keV) with no mass and energy resolution, but high angular resolution. The measurement principle is based on registering products (secondary ions, sputtered neutrals, reflected neutrals) of the ENA interaction with a graphite-coated surface. The Neutral Particle Detector (NPD) provides measurements of the ENA flux, resolving velocity (the hydrogen energy range is 0.1–10 keV) and mass (H and O) with a coarse angular resolution. The measurement principle is based on the surface reflection technique. The Electron Spectrometer (ELS) is a standard top-hat electrostatic analyzer in a very compact design which covers the energy range 0.01–20 keV. These three sensors are located on a scanning platform which provides scanning through 180^∘ of rotation. The instrument also contains an ion mass analyzer (IMA). Mechanically IMA is a separate unit connected by a cable to the ASPERA-3 main unit. IMA provides ion measurements in the energy range 0.01–36 keV/charge for the main ion components H⁺, He⁺⁺, He⁺, O⁺, and the group of molecular ions 20–80 amu/q. ASPERA-3 also includes its own DC/DC converters and digital processing unit (DPU).     

RPC-ICA: The Ion Composition Analyzer of the Rosetta Plasma Consortium

The Ion Composition Analyzer (ICA) is part of the Rosetta Plasma Consortium (RPC). ICA is designed to measure the three-dimensional distribution function of positive ions in order to study the interaction between the solar wind and cometary particles. The instrument has a mass resolution high enough to resolve the major species such as protons, helium, oxygen, molecular ions, and heavy ions characteristic of dusty plasma regions. ICA consists of an electrostatic acceptance angle filter, an electrostatic energy filter, and a magnetic momentum filter. Particles are detected using large diameter (100 mm) microchannel plates and a two-dimensional anode system. ICA has its own processor for data reduction/compression and formatting. The energy range of the instrument is from 25 eV to 40 keV and an angular field-of-view of 360° × 90° is achieved through electrostatic deflection of incoming particles.     

ACTIVE SPACECRAFT POTENTIAL CONTROL

Charging of the outer surface or of the entire structure of a spacecraft in orbit can have a severe impact on the scientific output of the instruments. Typical floating potentials for magnetospheric satellites (from +1 to several tens of volts in sunlight) make it practically impossible to measure the cold (several eV) component of the ambient plasma. Effects of spacecraft charging are reduced by an entirely conductive surface of the spacecraft and by active charge neutralisation, which in the case of Cluster only deals with a positive potential. The Cluster spacecraft are instrumented with ion emitters of the liquid-metal ion-source type, which will produce indium ions at 5 to 8 keV energy. The operating principle is field evaporation of indium in the apex field of a needle. The advantages are low power consumption, compactness and high mass efficiency. The ion current will be adjusted in a feedback loop with instruments measuring the spacecraft potential (EFW and PEACE). A stand-alone mode is also foreseen as a back-up. The design and principles of the operation of the active spacecraft potential control instrument (ASPOC) are presented in detail. Flight experience with a similar instrument on the Geotail spacecraft is outlined.     

Electron,Proton, and Alpha Monitor on the Advanced Composition Explorer spacecraft

The Electron, Proton, and Alpha Monitor (EPAM) is designed to make measurements of ions and electrons over a broad range of energy and intensity. Through five separate solid-state detector telescopes oriented so as to provide nearly full coverage of the unit-sphere, EPAM can uniquely distinguish ions (Ei≳50 keV) and electrons (Ee≳40 keV) providing the context for the measurements of the high sensitivity instruments on ACE. Using a ΔE×E telescope, the instrument can determine ion elemental abundances (E≳0.5 MeV nucl−1). The large angular coverage and high time resolution will serve to alert the other instruments on ACE of interesting anisotropic events. The experiment is controlled by a microprocessor-based data system, and the entire instrument has been reconfigured from the HI-SCALE instrument on the Ulysses spacecraft. Inflight calibration is achieved using a variety of radioactive sources mounted on the reclosable telescope covers. Besides the coarse (8 channel) ion and (4 channel) electron energy spectra, the instrument is also capable of providing energy spectra with 32 logarithmically spaced channels using a pulse-height-analyzer. The instrument, along with its mounting bracket and radiators weighs 11.8 kg and uses about 4.0 W of power. To demonstrate some of the capabilities of the instrument, some initial performance data are included from a solar energetic particle event in November 1997. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modelling Electrostatic Sheath Effects on Swarm Electric Field Instrument Measurements

The Electric Field Instrument (EFI) was designed to measure ionospheric ion flow velocities, temperatures and distribution functions at the ram face of the European Space Agency’s Swarm spacecraft. These flow velocities, combined with the known orbital velocity of the satellite and local magnetic field, will be used to infer local electric fields from the relation E=?v×B. EFI is among a class of many particle sensors and flow meters mounted on satellites to monitor in situ plasma conditions. The interpretation of the measurements made with EFI and similar sensors relies on a spacecraft sheath model. A common approach, valid in the relatively cold and dense ionospheric plasma, is to assume a potential drop in a thin sheath through which particle deflection and energisation can be calculated analytically. In such models, sheath effects only depend on the spacecraft floating potential, and on the angle of incidence of particles with respect to the normal to the surface. Corrections to measurements are therefore local as they do not depend on the geometry of nearby objects. In an actual plasma, satellites are surrounded by electrostatic sheaths with a finite thickness. As a result, local corrections to particle distribution functions can only be seen as an approximation. A correct interpretation of measured particle fluxes or particle distribution functions must, at least in principle, account for the extent and shape of the sheath in the vicinity of the measuring instrument. This in turn requires a careful analysis of the interaction of the satellite with the surrounding plasma, while accounting for detailed aspects of the geometry, as well as for several physical effects. In this paper, the validity of the thin sheath model is tested by comparing its predictions with detailed PIC (Particle In Cell) calculations of satellite-plasma interaction. Deviations attributed to sheath finite thickness effects are calculated for EFI measurements, with representative plasma parameters encountered along the planned Swarm orbit. Finite thickness effects of the plasma sheaths are found to induce EFI velocity measurement errors not exceeding 37 m/s, with larger errors occurring in plasmas that are simultaneously tenuous (10⁹ m^?3 or lower) and warm (0.5 eV or higher).