Thermal ion retarding potential analyzers (RPAs) are used to measure *in situ* auroral ionospheric plasma parameters. This article analyzes data from a low-resource RPA in order to quantify the capability of the sensor. The RPA collects a sigmoidal current–voltage (I–V) curve, which depends on a non-linear combination of Maxwellian plasma parameters, so a forward-modeling procedure is used to match the best choice plasma parameters for each I–V curve. First, the procedure is used, given constraining information about the flow moment, to find scalar plasma parameters—ion temperature, ion density, and spacecraft sheath potential—for a single I–V curve interpreted in the context of a Maxwellian plasma distribution. Second, two azimuthally separated I–V curves from a single sensor on the spinning spacecraft are matched, given constraining information on density and sheath potential, to determine the bulk plasma flow components. These flows are compared to a high-fidelity, high-resource flow diagnostic. In both cases, the procedure’s sensitivity to variations in constraining diagnostics is tested to ensure that the matching procedure is robust. Finally, a standalone analysis is shown, providing plasma scalar and flow parameters using known payload velocity and International Reference Ionosphere density as input information. The results show that the sensor can determine scalar plasma measurements as designed, as well as determine plasma DC flows to within hundreds of m/s error compared to a high-fidelity metric, thus showing their capability to replace higher-resource methods for determining DC plasma flows when coarse-resolution measurements at *in situ* spatial scales are suitable.

## I. INTRODUCTION

One instrument used to study the ionosphere is a retarding potential analyzer (RPA), which can be flown *in situ* to collect charged particles.^{1–4} The sensors vary a bias screen voltage in front of a collection surface and record the current on that surface as a function of charged particle flux that enters the sensor aperture and passes the bias screen; the current determines the number flux of the incoming particles, which can be either ions or electrons depending on the configuration. When used on satellites, as is common, the sensor moves at a supersonic velocity relative to the plasma frame and collects the full distribution of particles with relative motions that are predominantly perpendicular to the aperture. The RPAs analyzed for this project were carried onboard sounding rockets, which move at subsonic velocities (slower than or comparable to the ambient thermal ion velocity). This means that special consideration is paid to the lowest energy particles collected, whose motions may be severely distorted in the plasma sheath around the spacecraft and instrument.^{4} The particular application of interest here is multipoint observations of the auroral ionosphere; the plasma flows are large (up to several km/s) and spatially variable,^{5,6} and it is of interest to provide low-resource, coarse-resolution (hundreds of m/s), spatially distributed, localized *in situ* observations. These distributed pointwise *in situ* observations can provide a different view of the ionosphere than is allowed by remote-sensing large-scale observations such as imaging radars that average over large voxels and require long integration times.

The RPAs used in this work, known as Petite Ion Probes (PIPs), are discussed fully in Sec. II A. They collect current–voltage (I–V) curves (Fig. 1), which, for a Maxwellian plasma, can be described by the ion temperature (*T*_{i}), the ion density (*n*_{i}), the ion mass (*m*_{i}, assumed to be singly ionized oxygen^{7–10}), the sheath potential of the spacecraft (Φ_{s/c}), and the relative bulk velocity of the particles (**v**_{net}). The sensor sweeps through a voltage sequence, accepting particles with energies that can pass the screen potential and turning away particles with insufficient energy to pass the screen’s potential. This produces an I–V curve that, with complementary observations and assumptions as described in Sec. III B, can be interpreted in the context of a Maxwellian plasma distribution.^{11,12} In order to interpret the PIP data, a forward-modeling procedure is used to find the optimal plasma parameters that most closely reproduce the collected data, given constraining diagnostics. This is referred to as “parameter matching” and discussed fully in Sec. III.

This article quantifies the capability of low-resource Dartmouth PIPs to determine *in situ* plasma measurements, including both scalar plasma parameters and vector plasma flows. In order to constrain the scalar parameter matching procedure, known plasma flows from other instruments are used. Separately, these same flow observations can additionally be used as a metric to compare the plasma flow extracted from PIP observations. These flow observations are derived from measurements made by using the COrnell Wire BOom Yo–yo System (COWBOYS),^{13} a high-fidelity instrument that measures the *in situ* DC (and wave) electric field using 12 m tip-to-tip double probes. In the collisionless F-region of the ionosphere, DC and low frequency plasma flows can be found from electric field observations using force balance assumptions,^{14} typically referred to as “frozen-flux assumptions,”

such that DC flows perpendicular to the guiding dipolar magnetic field have magnitude |**E**|/|**B**| and are rotated 90° from the direction of the electric field.

The COWBOYS records **E** at a 1 kHz sampling rate. This instrument has a successful history of providing high-fidelity, high resolution electric field measurements that reveal detailed field and wave activity. However, it is not designed for low-resource use on sounding rocket missions where multipoint, distributed observations of the auroral environment are desired. COWBOYS is physically large and requires significant payload resources. After the flight, it can be a challenge to accurately determine the instrument’s attitude, because of its non-rigid wire-boom geometry.^{15} For this flight, the PIPs’ spin-phase orientation of peak thermal plasma flux was used to provide a spin-phase reference. For auroral science missions addressing DC plasma flows, and the spatial structuring thereof, we are motivated to replace the high-heritage COWBOYS instrument with arrays of low-resource PIPs, even at the cost of a significant reduction in resolution of the DC flow measurement.

The Isinglass (Ionospheric Structuring: *in situ* and Ground-based Low Altitude StudieS) rocket campaign, which launched two rockets in February–March 2017, is presented in Sec. II, along with information about the pertinent instrumentation for this work.

The general forward-modeling method for PIP data interpretation is presented in Sec. III. Scalar parameter matching results are presented in Sec. IV. These results rely on known PIP attitude, and relative and geophysical plasma flows from Global Positioning System (GPS) and COWBOYS, respectively, to match modeled I–V curves to collected data in order to extract scalar plasma parameters (*T*_{i}, *n*_{i}, and Φ_{s/c}) for ionospheric science. The scalar parameter results are compared against measurements from other instruments. *T*_{i} is compared against a temperature model driven by the plasma flow.^{16} *n*_{i} is compared against a density profile obtained from the ground-based, colocated, Poker Flat Incoherent Scatter Radar (PFISR). Φ_{s/c} is compared against a model driven by data from an electron RPA (ERPA) that flew on the payload (the ERPA, described below). New information for the mission about ion temperature and density is provided by the PIP data. The ion temperatures are shown to range between a frictional-heating expectation and an expectation from a model including wave-driven transverse heating. The density is seen to be somewhat higher than the ground-based radar observation and has localized increases near arc activity.

A comparison between the PIP-derived plasma flow and the COWBOYS flow is presented next in Sec. V. Here, the COWBOYS metric provides a trusted comparison and can be used to judge the performance of the PIPs in measuring the plasma flow. This analysis requires a pair of PIP I–V curves, PIP attitude, and estimates for density and sheath potential to extract plasma flows. The resulting plasma flows are compared against the data product from the high-resource COWBOYS instrument. These results show the fidelity of the PIP flow measurements. Finally, in Sec. VI, a “standalone” scenario is described using an iterative procedure, in which PIP data provide estimates for the flow, density, ion temperature, and payload potential, using only an International Reference Ionosphere (IRI)^{17} estimate for density and the payload’s GPS velocity as external inputs. This analysis of the PIP data, without using COWBOYS, ERPA, or PFISR data at any point, provides an assessment of standalone PIP use on future flights.

In Sec. VII, the results are used to discuss implications for the redesign of PIPs for future ionospheric sounding rocket missions. We conclude that PIPs can be useful as a low-resource alternative to high-resource DCE (DC electric field vector) instruments for certain ionospheric science questions. In particular, PIPs can be used on small suborbital spacecrafts for multipoint auroral plasma measurements, an area of interest for future ionospheric science missions.

## II. FLIGHT OVERVIEW

The Isinglass campaign launched two identical auroral sounding rockets in the winter of 2017 from Poker Flat, Alaska. The first rocket (Isinglass 303) launched on February 22nd, and the second rocket (Isinglass 304) was launched at 0750 UT on March 2nd, both into the F-region ionosphere of pre-midnight aurora. Isinglass 304 is used as the case study for this analysis, and a flight overview is presented in Fig. 2. The rockets flew north over Venetie, Alaska, where an array of ground-based cameras captured accompanying image data for the central portion of the rockets’ 365 km apogee trajectories. The flights lasted approximately 600 s, with the window of effective science flight time (exposed instrumentation and stable flight) lasting from around T+150 s to T+500 s. 304 flew through two auroral arcs that are distinguishable using camera data (Fig. 2, top and middle, before T+260 and after T+450) and which provide dynamic auroral environment data to show the flow-extracting capabilities of the PIP.^{6}

### A. Isinglass PIP design

The Dartmouth Petite Ion Probe (PIP) is a small, low-resource RPA that was designed to fly on ionospheric sounding rocket missions to measure thermal, ionospheric ions, typically dominated at these altitudes by singly ionized oxygen.^{7,12,18} The PIP contains a series of three nickel screens coated with a gold flash, followed by a spacer, and then an anode which collects the particles. The first and third screens are ground planes, and the middle screen is the bias screen, which sweeps through the voltage sequence. The bias screen sweeps 28 steps from 0 V to 5 V, at a rate of 20 sweeps/s. The anode collects a current that is converted by using a current-to-voltage preamplifier into a voltage signal; this signal is proportional to the anode current at a gain of 40 mV/nA; the measured noise level is 2 mV. The aperture for the Isinglass PIPs was a circle measuring 7 cm^{2} in area, and the PIP’s overall envelope is roughly a cube with a 3 cm side length.^{4,12} Each PIP sensor has a mass of 44 g; each pair of main payload mounted PIPs is controlled by using an electronics box (257 g, 7.6 × 10 × 4 cc). A computer rendered design showing the internal structure of the PIP appears in Fig. 3.

The PIP’s small footprint and weight make it an ideal choice for low-resource, multipoint measurements, an area of interest for ionospheric observations. It is controlled by using an Arduino microprocessor and can be manufactured in relatively large quantities;^{19} 40 copies were built for the Isinglass campaign. We reiterate here the coarse-resolution requirements (several 100 m/s resolution) for this multipoint auroral application, notable compared to high-fidelity larger-resource sensors such as those used in the Defense Meteorological Satellite Program (DMSP)^{1} with resolutions of 1 m/s–10 m/s.

The Isinglass main payloads each carried six PIPs, pointed at various elevation angles. Defining 0° as radially outward from the payload’s spin axis (roughly antiparallel to **B**), there were PIPs located at 90° (straight up), one at 45°, two located at 0° on opposing sides, one at −45°, and one at −90° (straight down). This ensures that there are PIPs looking into the ram throughout the flight as the rocket follows its trajectory. These directions, along with their associated identifications, can be seen in Fig. 4.

The spin rotation (2 s) of the main payload allows us to combine two time-delayed, spin-separated I–V curves from the same PIP to find the plasma flow (because two look directions are needed to isolate the flow vector); as the PIP rotates through the ram, measurements with a small time delay (and, therefore, angular displacement) are used to solve for the vector components of the plasma flow as described in Sec. V. This method is prone to errors when the flow changes rapidly, and future designs use paired PIPs with fixed azimuthal angle separations collecting simultaneous data.

### B. Isinglass supporting instrumentation

#### 1. ERPA

The Electron RPA (ERPA) is an RPA that collects ambient thermal electrons (below 1 eV),^{20,21} as opposed to the PIPs, which collect thermal ions. The design has a legacy of use on similar campaigns in the last decade, such as the Magnetosphere-Ionosphere Coupling in the Alfvén (MICA) Resonator campaign.^{12}

The ERPA works by collecting I–V curves, interpreted in the context of the ambient thermal electrons’ Maxwellian distribution,^{20} which can then be used to determine the electron temperature, given assumptions of isotropy and negligible drift velocities for the ambient thermal electron population. Note that in the auroral ionosphere, the electron thermal velocity is much larger than any of the other velocities of interest: the ion thermal velocity, the ion bulk flow velocity, and the payload motion (all of which are comparable to each other). Using a current balance equation, the electron temperature is used to infer the sheath potential of an idealized metal sphere in the plasma using the approximation Φ_{s/c} = −5*kT*_{e}, where *k* is the Boltzmann constant and five is a unitless constant that comes from the mass ratio between the ions and electrons of an oxygen plasma with *T*_{e} ≈ *T*_{i}.^{7,22} Because the payload is not an idealized sphere as assumed in the approximation, there is a correction factor required to account for the geometry, heterogeneous material, and imperfections in the payload. Previous studies^{11,20,22} indicate that this correction factor can be treated as an offset value related to a voltage difference, termed the *V*_{ss}, or voltage from (an idealized probe) sphere to (a non-ideal payload) skin. Adding a measured *V*_{ss}, or an approximation of it, to −5*kT*_{e} has been used in these studies as the best representation of the main payload’s sheath potential as indicated by thermal ion sensors. This expression will be referred to here as Φ_{ERPA},

#### 2. COWBOYS

The COWBOYS instrument is a high-resource double-probe DC electric field instrument^{13} that flew as a large sub-payload on the Isinglass missions. It measures the potential differences across wire booms, which measure 12 m tip-to-tip once deployed, at a 1 kHz time cadence. The COWBOYS has a considerable mass (around 30 kg) and is a heavy resource load for sounding rocket experiments.^{15}

In order to despin the COWBOYS sub-payload data and give an accurate flow direction, it is necessary to have a spin-phase reference for the data. To do this, the current recorded by the PIPs at zero bias voltage is used, which contains only information about the flux at that bias voltage at that time, rather than the shape of the I–V curve. Looking at this zero bias voltage reading as a function of time (and, thus, payload spin phase), it is easy to tell the time when the PIP’s aperture is closest to the net ram direction during a spin period. The main payload attitude solution at this time then provides the direction of the net flow (payload motion combined with the geophysical plasma flow), and the COWBOYS data provide the magnitude of the net flow. Vector removal of the GPS payload velocity, thus, provides a data product referred to as the “fused flow” vector, a measurement of the geophysical plasma flow. In this paper, the GPS velocity of the payload is denoted as **v**_{payload}, the geophysical plasma flow is denoted as **v**_{plasma}, and when they are subtracted to get relative flow to the sensor, the velocity is **v**_{net}. It is important to keep track of these velocities as both the plasma velocity and payload velocity can be on the same order of magnitude, a few km/s. The fused flow is calculated at a cadence of 0.5 Hz.

The fused flow data product uses only the measurement of the time of the peak flux from the PIPs. This information is distinct from the shape of the I–V curve that is matched in the following sections and avoids circularity in our argument when finding the flow from the PIPs and using the COWBOYS data as a metric.

#### 3. PFISR

The Poker Flat Incoherent Scatter Radar (PFISR)^{23} is an ISR that included the rocket’s trajectory in its field of view and was active before, during, and after the flight in the dedicated Isinglass 15-beam mode. Data from this mode were processed by accumulating numerous independent estimates of the radar power and autocorrelation function (ACF) over a 66 s time window (providing four or five temporal frames during the flight times of interest). The power was sampled at 3 km range resolution, and the ACFs are binned into 24 km range gates (half a pulse length) before fitting those ACFs to electron density, electron temperature, ion temperature, and line of sight ion velocity. The 24 km resolution fitted line of sight velocities from all beams are used to reconstruct vector velocities.^{23} The PFISR density data used here are computed from the radar power at 3 km resolution and are shown in the top panel of Fig. 5; the PFISR reconstructed vector velocities, and their splined profile, can be seen in the bottom panel of Fig. 2, where they are compared against a high resolution, *in situ* data product from COWBOYS.

The PFISR ion density data product used in this paper tracks the trajectory through the three-dimensional (3D) PFISR sampling space, so while the density profile may appear to have a higher cadence, this is a conflation of the spatial movement of the payload with the temporal rate of sampling. PFISR density data along the trajectory were interpolated from the density-from-power data product, with 3 km range gates along each of the 15 beams, calculated at a 66 s cadence. Note that the payload is only colocated with the PFISR field of view through the (roughly) apogee at T+314 s. The density values used here for the downleg repeat the altitude profile of the upleg data. This PFISR density data product is used as a metric for comparison with scalar parameter results and as an input parameter when solving for the flow as an output.

We use the PFISR reconstructed vector velocity data product (“VVELS”)^{23} in the sensitivity analysis presented in Sec. IV D. This flow data product is provided as a function of latitude (0.2° resolution) along the central spine of the PFISR beam fan field of view and again is calculated at a 66 s cadence.

## III. GENERAL METHOD

### A. Forward-modeling procedure

The process for forward-modeling PIP I–V curves relies on the Levenberg–Marquardt non-linear least squares minimization algorithm.^{4} LMFit is a publicly available Python package that extends the optimization procedures included in SciPy to implement the Levenberg–Marquardt algorithm.^{24} The LMFit optimization routine requires a non-linear equation, *y*, that depends on any number of variables, the set of which can be called ** γ**. The total set of variables,

**, is here further split into two sets,**

*γ***and**

*α***, which designate the role of the variable in the algorithm. For each curve,**

*β**y*(

**,**

*α***), that is, matched to a data curve at a given time step, the**

*β***variables are input as a fixed value for every iteration. The**

*α***variables are adjusted for every iteration until the algorithm settles on its set of best choice values, which is when the residual array**

*β**y*

^{measured}−

*y*

^{model}(

**,**

*α***) is minimized. For the PIP analysis described here,**

*β**y*is Eq. (2) below (normalized by the largest value of

*y*

^{measured}for that time step), which calculates an expected current,

*I*, for a given bias screen voltage,

*V*

_{screen}, subject to a number of plasma parameters,

**. The residual array is returned to the LMFit routine at each iteration, and a metric which we call the “residual,” consisting of the sum of squares of the array elements, is driven to a minimum value. This minimized metric of the residual array is stored as a metric of the goodness of the fit for the chosen**

*γ***and is referred to here as “the residual” (i.e., the bottom panel of Fig. 6).**

*γ*Each parameter within ** β** requires an initial guess and range of values within which to search, improving the efficiency of the procedure. For example, it is useful to set the lower limit of a temperature parameter at 0 K, so there are never any negative temperatures checked. A typical forward-modeled I–V curve and corresponding data appear in Fig. 1. The noise for each black data point is 0.05 nA. A useful feature of this process is the ability to choose which

**parameters are to be found through the forward-modeling process and which**

*β***parameters will be locked to constraining information from other instrumentation.**

*α*### B. PIP I–V curve parameter space

The I–V curves gathered from the PIPs (see Fig. 1) are shaped like sigmoids, which are curves containing essentially three pieces of information: an amplitude, a translation along the voltage axis, and a slope of the transition.^{12} Crudely, these three pieces of information map to the total flux of ions (current), translational acceleration or drift toward the sensor, and temperature. However, these plasma parameters are coupled in the curve parameters and underdetermined in a three-dimensional velocity space. Proper interpretation of the I–V curves requires constraining information as well as integration over the collected flux.

The PIP I–V curves rely on a large set of variables that are non-linearly related such that the LMFit procedure is required to find the parameters that produce IV curves most closely representing the measured curves. The entire equation for the subsonic RPA current collection of the PIPs appears in Eq. (2)^{4} with the instrument-frame variable definitions located in Table I. Equation (3)^{4} calculates the effective area for the sensor; the subsonic velocity of the instrument means that the effective area of the sensor depends on the choice of the particle drift velocity in every direction ({$v$_{Dx}, $v$_{Dy}, $v$_{Dz}}),

where

Variable . | Description . | IV . | V . | VI . |
---|---|---|---|---|

I | Collected current | α | α | α |

η | Combined grid transparency | |||

e | Unit charge | |||

k_{B} | Boltzmann constant | |||

m | Ion Mass | |||

n_{i} | Ion density | β | α | β |

T_{i} | Ion temperature | β | β | |

Φ_{s/c} | Sheath potential | β | α | β |

V_{screen} | Screen bias | |||

$v$_{c} | Minimum velocity of a particle | |||

That has enough energy to | ||||

Overcome Φ_{s/c} + V_{screen} | ||||

A | Velocity dependent collection area | |||

R | Radius of the aperture | |||

Velocity of particles parallel to the aperture normal | ||||

$v$_{y}, $v$_{z} | Velocities of particles in y and z directions | |||

$v$_{Dx} | Parallel drift velocity | α | β | α |

$v$_{Dy}, $v$_{Dz} | Drift velocities of particles in y and z directions | α | β | α |

Variable . | Description . | IV . | V . | VI . |
---|---|---|---|---|

I | Collected current | α | α | α |

η | Combined grid transparency | |||

e | Unit charge | |||

k_{B} | Boltzmann constant | |||

m | Ion Mass | |||

n_{i} | Ion density | β | α | β |

T_{i} | Ion temperature | β | β | |

Φ_{s/c} | Sheath potential | β | α | β |

V_{screen} | Screen bias | |||

$v$_{c} | Minimum velocity of a particle | |||

That has enough energy to | ||||

Overcome Φ_{s/c} + V_{screen} | ||||

A | Velocity dependent collection area | |||

R | Radius of the aperture | |||

Velocity of particles parallel to the aperture normal | ||||

$v$_{y}, $v$_{z} | Velocities of particles in y and z directions | |||

$v$_{Dx} | Parallel drift velocity | α | β | α |

$v$_{Dy}, $v$_{Dz} | Drift velocities of particles in y and z directions | α | β | α |

The last three columns indicate the parameter’s role in the matching procedure (** α** as input and

**as output) for the three cases presented in the following: Sec. IV: scalar parameter matching; Sec. V: flow matching; Sec. VI: standalone PIP matching (Step 3).**

*β*The forward-modeling parameter matching procedure requires assumptions about the PIP data and plasma characteristics. The first assumption is that the I–V curves used for analysis are best when the flux is highest, that is, when the PIP is most closely facing **v**_{net}. Restricting analysis to these times has the benefit of improving the parameter matching results. However, it also means that the data cadence is limited by the spin rate of the rocket, and there will only be an optimum data point once per spin.

Another assumption built into the Isinglass PIP analysis is that secondary electron suppression is not necessary. The flight occurs at night, so there is no sunlight to produce photoemission, and the spacecraft had sufficient negative charging at the flight altitude to minimize thermal electron collection.^{4} Furthermore, the thermal ions that are measured with the PIP do not have enough energy to produce secondary electron emission, even after traveling through the sheath and considering their energy gain due to the spacecraft’s motion.^{12} The original Isinglass PIP data also contain artifacts from energetic auroral electron precipitation, which are removed with a simple offset subtraction as the high energy (0.1 keV–1 keV) particles are unaffected by the screen voltages (0 V–5 V).

The next assumption is that the ion population gathered throughout the flight is singly ionized oxygen. This is a reasonable assumption at the flight altitudes of Isinglass.^{7}

Another assumption is the planar thin sheath approximation, which says that the sheath in front of the RPA accelerates the incoming particles in the direction perpendicular to the anode. This is built into the use of the current collection Eq. (2) and says that the net acceleration of particles by the sheath is the same as it would be from a sheath of zero thickness near the plane of the PIP aperture. The gold ground planes surrounding the apertures, as seen in Fig. 3, enforce this potential shape in the vicinity of the sensor apertures.

It is important to note that every time an I–V curve is created in the forward-modeling procedure, the flow vector [{$v$_{Dx}, $v$_{Dy}, $v$_{Dz}} in Eqs. (1) and (2)] is a defined quantity. Even if the output of the procedure is the flow, the procedure continuously gives the numerical integration routine [Eqs. (1) and (2)] a defined value for the flow at each attempt. The flow acts as any other variable (an ** α** or

**) in the analysis routine and is not derived directly from a feature of the I–V curve itself, such as the steepness or inflection point voltage; this is true for every variable in Table I.**

*β*The variables ** α** and

**that are inputs to Eqs. (2) and (3) are expressed in the plasma frame, but the current calculation is done in the sensor frame of the reference using the sensor-frame variables in Table I. The LMFit does this conversion within the routine by combining the PIPs’ attitude and the payload motion, both of which are known, to move from the plasma frame to the instrument frame, and then returns the**

*β***outputs back in Earth-centered Earth-fixed (ECEF) coordinates.**

*β*Ion temperature and plasma flows in the nightside F-region have been shown to be strongly linked to each other,^{16,18} so it is often appropriate to use a model that couples *T*_{i} to **v**_{plasma} by taking into account the relative velocity of the neutral gas frame. The metric used to compare *T*_{i} results is calculated using this frictional-heating model,^{8,16,25,26} which appears as follows:

For this version of the (Schunk and Sojka)^{16} relationship,^{8,25,26} the average neutral mass is taken to be atomic oxygen; the neutral wind velocity vector (31 m/s north, 81 m/s east) was taken from an averaged value over the trajectory area from the Scanning Doppler Imager (SDI) array.^{27} This neutral wind velocity seen during the Isinglass flight is generally less than a tenth of the typical km/s plasma flow magnitude. The neutral temperature is found from the NRL MSISE-00 atmosphere model provided by the Community Coordinated Modeling Center atmosphere model (https://ccmc.gsfc.nasa.gov/modelweb/models/nrlmsise00.php); at flight science altitudes, it is a relatively constant 800 K.^{30}

Using this approximation, temperature profiles can be constructed from any flow product: fused, PFISR, or flow from PIPs. It is also sometimes advantageous to link the two while parameter matching, which reduces the number of variables the algorithm must consider, a process used when finding the flow from PIPs as discussed in Sec. V.

The forward-modeling routine only returns I–V curves at screen voltages above Φ_{s/c} since $v$_{c} is limited by Φ_{s/c}; at bias screen voltages below the sheath potential, the incoming particles are poorly represented by the thin sheath potential expectations and should be excluded from the matched data.

## IV. SCALAR PLASMA PARAMETER RESULTS AND DISCUSSION

Scalar plasma parameter matching was performed first as this was the intended use of the PIP instrument for Isinglass. For this phase, ** α** includes the COWBOYS fused plasma flow vectors; the

**parameters that are the optimized output are ion density, ion temperature, and sheath potential. The results over the full flight for these three parameters are shown in Fig. 5, with different dot colors representing different PIPs and the solid line representing the metric of comparison.**

*β*### A. Density

Throughout the science portion of the flight, ion density stays relatively constant according to the PFISR density metric. The mean percent difference in density, as compared to the PFISR metric, in the middle of the flight when the 0° PIPs are best situated (250 s–400 s) is 17%. After T+400 s, the main payload moves back into a region of auroral activity (see Fig. 2), and the PFISR metric is no longer colocated with the payload. The PIPs record an increase in ionospheric density, which is not measurable by the PFISR metric. Separately, either the PIP23-0 data or the parameter matching of it has some unexplained irregularities in all three scalar outputs between T+400–450; these are interpreted as errors since the equivalent PIP24-1 does not see them. Considering that PFISR’s integration time is on the order of a minute and that the PIPs collect 20 I–V curves/s, the PIP data imply a relatively smooth density profile outside the precipitation regions; within the arcs, the PIPs respond to density on a much finer spatiotemporal scale than PFISR.

### B. Temperature

The temperature results closely follow the features of the frictional-heating temperature expectation [Eq. (4)] driven by the fused flow. In particular, there are two swells in temperature at T+325 s and T+415 s that are captured by the PIPs. The root mean square error was 199 K (19%). The primary instance of discrepancy between the frictional-heating calculation and ion temperature from PIPs can be seen near T+250 s until T+300 s, where ion temperatures from the PIPs are consistently hotter. It has been shown that in areas where ion temperature and flow are not well correlated as per Eq. (4), a significant cause of ion heating are the wave–particle interactions.^{18} Alfvénic activity associated with the auroral arc structure is observed by the electric and magnetic field instruments between T+244 s–252 s and may be contributing to these hotter ion temperatures until the payload exits the arc region near T+300 s. In addition, near T+340 s, the measured *T*_{i} again moves away from the frictional-heating model. After T+400 s, these two sensors are no longer optimally ram looking.

The additional orange curves in this panel show modeling expectations^{31} from the GEMINI-TIA model,^{28} where thermalization processes are taken into account, and the frictional perpendicular heating is partitioned into a perpendicular and a parallel spread in the bi-Maxwellian population. The model is driven by the *in situ* DCE [including a Fast Fourier Transform (FFT) of the DCE channel providing Extremely Low Frequency (ELF) wavepower at 6.5 Hz] and *in situ* precipitation data. The model run assumes a constant time history of these drivers and, thus, provides an upper bound for expected Alfvénic wave heating of the thermal ions as it assumes that the wave heating driver is long-lasting.

### C. Sheath potential

The sheath potential results agree with the estimation obtained from the Φ_{ERPA} metric [Eq. (1)] to a mean percent error of 11%, which corresponds to a root mean square error of 0.2 V. By inspecting the results visually, as seen in the bottom panel of Fig. 5, there appears to be an offset effect between the two 0° PIPs. This was traced to a preamplifier settling time issue being addressed in the circuit redesign. The V_{ss} offset portion of the Φ_{ERPA} metric was adjusted at this point to best match this fused-flow-driven scalar parameter matching, making the metric not independent of the result. We consider the sensitivity of this result, to choices of this offset, in Subsection V C below.

### D. Output response to different input flows

It is important to see the response of the matching procedure to different inputs, to check that the procedure is robust enough to handle varying levels of input constraint fidelity. In Sec. V below, on flow matching, a sensitivity study is performed by numerically varying the scalar driving input parameters and quantifying the effect on the flow output. Here, in this scalar parameter matching section and Fig. 6, we examine the dependence of the scalar parameter matching procedure to three different input datasets for the plasma flow: the fused flow as used above (blue dots), the PFISR flow data product (orange dots), and the (negative) GPS velocity alone (that is, a geophysical plasma flow of zero, green dots). The fused and PFISR flow data products provide two different standard views of the ionospheric plasma flow, from the *in situ* vs ground-based viewpoint. The zero-flow input is used in our standalone analysis below. Here, we look to see how these different driving inputs affect our interpreted scalar parameters.

The PFISR observation, shown as components in Fig. 2, and as magnitude and direction in Fig. 6, misses the localized variations recorded by the *in situ* fused flow. It is also only available until a flight time of T+400. The clearest discrepancy from the fused flow is the missed magnitude swell at T+325, which manifests in the sensitivity as an increase in the matched ion temperature output. The splined PFISR flows also miss the strong shear rotation in the fused flow just before arc entry (from T+150–175), and the matching procedure makes incorrect adjustments to temperature and density to compensate. Interestingly, the spacecraft potential estimate is relatively unaffected, showing that the potential estimate is relatively decoupled from flow, temperature, and density in the parameter matching process.

The green dots in Fig. 6 indicate the results of the scalar parameter matching when the geophysical plasma flow is taken as zero. (This is the start point for the standalone process described in Sec. VI.) Here, again the payload potential is the least affected output, though, as might be expected, it somewhat overcompensates to adjust for the smaller flow energy.

It is notable here that the matching procedure finds solutions that match the data (as shown by the low residuals in the bottom panel) but are not physically valid. This is most evident in the zero-flow case, where large excursions in density are seen when the true flow magnitude (here taken as the fused flow) is large. An iterative process could be used here bounding the allowed output values more tightly.

However, even using the low-resolution PFISR flow as an input parameter, the ion temperature output follows trends captured by the higher-fidelity-input parameter matching process, including the higher temperatures attributable to Alfvénic heating, showing that the matching procedure’s *T*_{i} output is partially decoupled from the plasma flow input. The payload potential outputs vary by roughly 0.25 V between the different inputs, but follow the trends indicated by the fused-flow-driven outputs. The PIP observations in conjunction with the ground-based radar data are able to contribute information during the scalar matching routine producing *in situ* features that are not known solely from the ground-based radar data.

## V. FLOW FROM PIPs

### A. Flow matching procedure

This flow matching section quantifies the ability of PIP data to extract plasma flows. On Isinglass, we have the possibility to use the available high-fidelity COWBOYS double-probe data for the F-region plasma flow as an independent metric to compare these PIP-derived flow results. This allows us to quantify the capability of the PIPs for measuring the flow.

In order to obtain **v**_{plasma} from PIP data, the parameter matching procedure can be configured to take input estimates for *n*_{i} and Φ_{s/c} in the ** α** parameters and return

**v**

_{net}as a

**parameter. The PFISR ion density and the ERPA-based Φ**

*β*_{s/c}information, used above as metrics, are here used as input

**parameters. The resulting output**

*α***v**

_{net}can then be separated into

**v**

_{payload}and

**v**

_{plasma}using the known GPS payload velocity. The process requires two time-delayed I–V curves because the plasma flow (perpendicular to

**B**) is a 2D vector, which requires a 2-D system of equations. The flow vector is not 3-D as the geophysical plasma flow only occurs in the

**B**

_{⊥}plane, other than small amounts of field-aligned motion, here assumed negligible when compared to

**v**

_{net}.

*T*

_{i}is also calculated during the flow matching procedure using the Schunk temperature expectation [Eq. (4)] driven by

**v**

_{plasma}. This constrains the matching routine as

*T*

_{i}is not an independent

**variable, but instead locked to another**

*β***variable.**

*β*In order to select which I–V curves were used, trials using different angular separation (time delays given the payload spin motion) and spin-phase locations were run. It was found that residuals were consistently lower when the measurements were evenly spaced away from the spin-phase angle of the maximum ram flux. It was also found that a separation of 45° led to the most accurate flows when compared to the COWBOYS flow metric. Therefore, it was decided that the first I–V curve would be measured 22.5° before the max ram and the second I–V curve would be measured 22.5° after the max ram. A 45° rotation delay corresponds to a time delay of 0.25 s according to the payload’s 0.5 Hz rotation rate.

### B. Flow matching results

While we have the opportunity here to compare these PIP flows to the COWBOYS metric, PIPs that flew on Isinglass were not particularly designed for the purpose of extracting the plasma flow; therefore, considerations must be taken into account when judging the accuracy of the flow-extracting procedure. It is useful to define the “best-scenario” cases, which adhere to the following criteria: relatively high flux, PIP field of view aligned to **v**_{net}, flows that are stable, and ion temperatures that are not too cold. There were 214 flow measurements in total (one every 2 s spin period), of which 53.3% were considered “best cases,” which we used to explore the PIP capability for measuring flows.

High flux is ensured by the fact that only two measurements, which occur near the time of the maximum ram, are matched per spin. In order to enforce aligned field of view throughout the flight, the “best scenarios” require the PIP’s aperture elevation angle to be within 20° of the ram direction, which was not met by 20.2% of measurements. A flow stability condition was enforced, meaning that the **v**_{plasma} (as seen by a relative-spin-phase, kHz sampled version of the COWBOYS data) could not change significantly in the quarter second delay between measurements. This limit was set at 100 m/s change in the flow speed in between measurements and was not met by 8.3% of measurements. Finally, a lower limit of **v**_{plasma} > 500 m/s (again, as seen by the COWBOYS data) was set to enforce a minimum ion temperature requirement through Eq. (4), which was not met by 20.5% of cases. Equation (1) algorithm has a floor temperature of 500 K (below the neutral temperature), and any flow that is locked to an ion temperature colder than that introduces error into the results.

As seen in Fig. 7, the PIPs showed the capability to measure the flow at the best scenarios to a root mean squared error of 155 m/s in magnitude and 12.5° in direction, compared to the fused flow metric. This is an exciting result which shows the capability of the low-resource PIPs to measure *in situ* DCE under certain assumptions. (We remind the reader here that the absolute spin reference used for the COWBOY fused flow data product was the spin-phase angle of the peak PIP flux; see Sec. II B 2.) It is important to say that there are some best case scenarios in which the phase angle of the flow shifts almost 180° from the expected fused flow metric. These results generally occur where the PIP-derived flow magnitude is much smaller than the fused flow metric, which may indicate that the optimization routine is finding a false minimum.

With these limitations in mind, future ionospheric missions can rely on PIPs to provide a coarse DC-**E** data product, at fundamentally finer spatial and temporal scales than an ISR, and for a lower cost than a double-probe wire-boom system (provided that high frequency wave measurements are not required). Additionally, as future flights will have higher gain, paired PIPs to collect simultaneous I–V curves, the strong and stable flow requirements enforced for Isinglass will no longer be restrictive.

### C. Flow matching sensitivity analysis

A sensitivity analysis was performed to ensure that the flow matching is not subject to an outsized influence from error in the given ** α** parameters

*n*

_{i}and Φ

_{s/c}and in the frictional-heating constraint used [Eq. (4)]. The baseline choice in Eq. (4) for effective neutral mass is simply atomic oxygen (16 amu). An MSIS prediction for the Isinglass 304 rocket event

^{29}calculates the altitude where the effective neutral mass would be 14 amu as 475 km and where it would be 18 amu as 310 km. Changing the frictional-heating constraint to use 14 (18) amu causes the matched flow magnitude to increase (decrease) less than 2% within stable regimes such as the period from T+320 s–450 s (the variations can be larger when the flow matching is variable, such as times before T+320). Thus, the flow magnitude matching process is fairly insensitive to the exact choice of effective neutral mass in the frictional-heating constraint.

Density is the least well-defined input here, as it comes not from an adjacent *in situ* instrument but from the remote-sensing ground-based PFISR instrument, which averages over large times and spatial scales and is not always colocated. Given this relatively poorly defined input, the process was run four times with the density profile scaled by 0.25, 0.5, 2, and 4, to observe the response in the found flow. As seen in Fig. 8, an inverse relationship was observed, with lower densities leading to high flow magnitudes, and vice versa. However, for the four cases, even these large input variations corresponded to errors only a few times our desired flow resolution (of several hundred m/s) compared to the original flow match. This demonstrates that the flow matching procedure is relatively robust and able to mitigate errors in ** α** parameters. For densities half the accepted amount (green curve), the returned flow had a mean percent error of 35% from the original flow (black curve), and for densities four times greater than the best model (blue curve), the average returned flow had a mean percent error of 22% from the original, as seen in Fig. 8.

Throughout the interval shown, the PIP scalar results for density can exceed the PFISR proxy by a factor of 2–4 (slightly more at the end of the interval); it is reasonable that this difference is attributed to auroral precipitation and its variations (see Fig. 2). The PFISR density proxy input likely underestimates the density in active regions (i.e., Fig. 5 near T+375 s and T+425 s), which may explain why the PIP flow magnitude overestimates the flow in those regions. In non-precipitation regions, the orange and green density-sensitivity curves conservatively bound our confidence in extracted flow magnitudes to a few hundred m/s, a desired result for science missions that use PIPs, as described in the Introduction.

The lower panel of Fig. 8 shows the sensitivity of the flow magnitude to errors in the *V*_{ss} offset component of Φ_{ERPA} [Eq. (1)]. The −0.8 V offset used in the flow matching was chosen to best match the PIP-driven flow to the fused flow data comparison. Values for this offset seen on other nightside auroral missions are typically in the −0.5 V to −1 V range,^{18,22} so a sensitivity analysis was run varying the offset accordingly. Using *V*_{ss} = −0.5 V increased the flow magnitudes by a root mean square difference of 583 m/s; a *V*_{ss} of −1 V decreased them by 400 m/s below flows. These are both within our desired flow resolution of several hundred m/s. However, note that in the Standalone analysis in Sec. VI, it is not necessary to estimate this *V*_{ss} offset, as Φ_{s/c} is found directly from the PIP analysis.

## VI. STANDALONE PIP ANALYSIS

The goal of this work is quantifying the PIP capabilities on future sounding rocket missions, so this final analysis is carried out without use of any COWBOYS, PFISR, or ERPA data except as comparison metrics. The analysis is iterative. Step 1 uses a scalar parameter matching process driven by the GPS velocity alone. Here, the resulting ** β** are the green dots in Fig. 6. Step 2 uses as input the step 1

**output for Φ**

*β*_{s/c}, together with an IRI altitude profile of density (varying from 0.29 × 10

^{11}/m

^{3}to 0.52 × 10

^{11}/m

^{3}) and a frictional-heating constraint. The step 2

**outputs are the flow matching results shown by the red dots in the top two panels of Fig. 9. Finally, step 3 uses as input the step 2 flow match result, to drive a scalar match, the**

*β***results of which are shown in the bottom three panels of Fig. 9.**

*β*Results for one PIP appear in Fig. 9 alongside the products obtained from other instruments as well as the parameter matching results from Sec. IV. This analysis (for all data, not only best-scenario cases), initiated as just described with only GPS-velocity and an IRI density profile as external inputs, provides an *in situ* density profile somewhat between the PFISR density proxy and Sec. V scalar parameter matching results. It begins to capture the increase in density seen in Sec. V in the arc after T+400. For the most part in this case, the F-region density is fairly bland, so the *in situ* estimate is well matched to the voxel-averaged PFISR proxy when it is colocated. When the PIPs were used in this same manner on a test flight from the Wallops Flight Facility in Virginia, they were shown to follow density trends consistent with the main payload altitude.^{4}

As Fig. 9 shows, the standalone PIP results follow the same trends as the data from other instruments as well as the trends of the previous results; in some cases, the standalone results improve on the assisted results of Secs. IV and V. Mean percent differences are calculated for a comparison between these standalone PIP scalar matching results and the PIP scalar matching results presented in Sec. IV, which used the fused flow data product as an input. The mean percent error was 36% for ion density, 17% for ion temperature, and 8% for sheath potential. The flow matching shown in the first two panels had a mean error, vs the fused flow data, of 422 m/s in magnitude and 35° in direction. (We remind the reader here that the absolute spin reference used for the COWBOY flow data product was the spin-phase angle of the peak PIP flux; see Sec. II B 2.) When the flow comparison is limited to the “good scenario” cases as in Sec. V, this error is 359 m/s in magnitude and 8° in direction. Thus, we demonstrate the capability of the PIPs in an ISINGLASS-like auroral environment, in conjunction with only the GPS platform velocity and an IRI density estimate, to provide plasma flows with few hundred m/s error and scalar plasma parameters to the accuracy stated above.

## VII. DISCUSSION AND CONCLUSIONS

### A. PIP redesign

The data interpretation of the Isinglass PIPs revealed that the parameter matching procedures were limited by the low gain of the sensors. Therefore, the redesigned PIP includes several features that will increase the sensor gain. The redesigned PIP will feature a square aperture which almost doubles the amount of collected particles (as well as being more analytically tractable). The gain will also be increased on the circuit itself, and the no-current output of the sensor will be dropped from 2 V to 1 V (within the 5 V digitization range) in order to allow for 4 V of range to collect I–V curves from ion fluxes. These changes increase the gain of the PIPs by either 8 or 16 times depending on the gain resistor included in the circuit.

The updated PIPs will be flown in pairs with look directions separated azimuthally by 45° so that simultaneous data points can be used to extract the flow without requiring a costly time delay between measurements. They will also be positioned in incremental elevation angles in order that a pair of PIPs is well aligned with the plasma ram throughout the prime science portion of the flight. The redesigned PIPs in their updated orientations will fly on several upcoming auroral science sounding rockets.

### B. Conclusion

The PIP sensors are low-resource RPAs designed to extract plasma measurements from auroral sounding rocket platforms. They are used in two capacities: fixed on the main payload deck as described here and placed inside small ejected sub-payloads used for multipoint measurements.^{4} This article analyzed I–V curves collected from PIPs carried on the Isinglass sounding rocket, crossing an active auroral environment over Alaska in the winter of 2017. First, the main payload PIPs were analyzed in order to extract three parameters from the plasma over the flight time: ion density, ion temperature, and sheath potential. Using a non-linear least squares minimization algorithm to forward-model I–V curves with plasma parameters matching collected PIP data, the PIPs showed the capability to determine ion temperature with a mean percent difference of 19% compared to a frictional temperature calculation driven by the flow, ion density with a mean percent difference of 17% from an ISR, and sheath potential with a mean percent error of 11% compared to an expectation based on thermal electron temperature. The analysis also revealed a time delay between the measurements of the two PIPs sharing the same Arduino shield board, which will be addressed in the future iterations of the shield design.

The PIPs were then used to calculate plasma flow vectors using two measurements from the same PIP taken in succession so that the angular displacement between the measurements was 45°. Estimates for ion density (from PFISR) and sheath potential (from ERPA) were given as alpha input parameters; beta parameter outputs were the east and north components of the plasma flow, as well as the ion temperature estimated from that flow using Eq. (4). In the scenarios where the PIPs had an ideal environment to record flows, the mean error of the flow magnitude was 155 m/s compared to the COWBOYS data product and the mean error of the phase angle of that flow was 12.5°. Sensitivity analyses were performed to ensure that the parameter matching results were not subject to an unreasonable effect from errors in input data products.

Finally, the flow calculated from the PIPs (using a calculation initiated using IRI density and GPS payload velocity information, and constrained by a frictional *T*_{i} dependence) was used as an alpha input for the scalar parameter matching procedure to illustrate that PIPs can stand alone to replace higher-resource methods of determining the DC electric field of the auroral F-region, when coarse resolutions are suitable. Overall, the PIP is shown to be an effective, low-resource sensor for auroral plasma physics research, particularly suited for multipoint observations.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## ACKNOWLEDGMENTS

ISINGLASS analysis work at Dartmouth College was funded by UNH/NASA ESPCoR grant (No. NNX15AK51A), Space grant (No. NNX15AH79H), and LCAS ISINGLASS grant (No. NNX14AH07G). The ISINGLASS team thanks the engineering groups at NSROC, NASA Wallops, and PFRR for their hard work and dedication to sounding rocket missions. The authors thank Isinglass team members M. Conde (UAF/GI) for SDI data, M. Samara and R. Michell (NASA/GSFC) for APES data, and D. Hampton (UAF/GI) for imagery data. The project was aided by SRI/PFISR and by the UAF/GI staff at the Poker Flat Research Range. PFISR operations are supported by the NSF cooperative agreement grant (No. AGS-1840962) to SRI International, and all PFISR data are available through the Madrigal database (isr.sri.com/madrigal). Modeling results from GEMINI-TIA are provided by M. Burleigh at U Michigan; the full GEMINI modeling suite is open-source software, kept and maintained in a public repository at: https://github.com/gemini3d/; Isinglass GEMINI modeling was supported by the NASA grant (No. NNX14AH07G). The authors gratefully acknowledge a significantly constructive RSI review process.

## REFERENCES

Equation (4) as written here has numerical values of 6.4145 × 10^{−04} * (velocity difference)^{2} + 800; while the numerical version used in the code to generate the plots and analysis (with the exception of the effective neutral mass sensitivity in Sec. V C) was 6.4612 × 10^{−4} * (velocity difference)^{2} + 803.