Polytropic Behavior of Solar Wind Protons Observed by Parker Solar Probe

A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during the process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on-board Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We also address a polytropic behavior in the density and temperature fluctuations in short-time intervals, which we analyze in order to derive the effective polytropic index of small time-scale processes. The large-scale variations of the solar wind proton density and temperature which are associated with the plasma expansion through the heliosphere, follow a polytropic model with a polytropic index ~5/3. On the other hand, the short time-scale fluctuations which may be associated with turbulence, follow a model with a larger polytropic index. We investigate possible correlations between the polytropic index of short time-scale fluctuations and the plasma speed, plasma beta, and the magnetic field direction. We discuss the scenario of mechanisms including energy transfer or mechanisms that restrict the particle effective degrees of freedom.Comment: 20 pages, 9 figure

Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA)

In-situ measurements of space plasma throughout the solar system require high time resolution to understand the plasma's kinetic fine structure and evolution. In this context, research~is conducted to design instruments with the capability to acquire the plasma velocity distribution and its moments with high cadence. We study a new instrument design, using a constant magnetic field generated by two permanent magnets, to analyze solar wind protons and $\alpha$-particles with high time resolution. We determine the optimal configuration of the instrument in terms of aperture size, sensor position, pixel size and magnetic field strength. We conduct this analysis based on analytical calculations and SIMION simulations of the particle trajectories in our instrument. We evaluate the velocity resolution of the instrument as well as Poisson errors associated with finite counting statistics. Our instrument is able to resolve Maxwellian and $\kappa$-distributions for both protons and $\alpha$-particles. This method retrieves measurements of the moments (density, bulk speed and temperature) with a relative error below 1%. Our instrument design achieves these results with an acquisition time of only 5 ms, significantly faster than state-of-the-art electrostatic analyzers. Although the instrument only acquires one-dimensional cuts of the distribution function in velocity space, the simplicity and reliability of the presented instrument concept are two key advantages of our new design

On the Determination of Kappa Distribution Functions from Space Plasma Observations

The velocities of space plasma particles, often follow kappa distribution functions. The kappa index, which labels and governs these distributions, is an important parameter in understanding the plasma dynamics. Space science missions often carry plasma instruments on board which observe the plasma particles and construct their velocity distribution functions. A proper analysis of the velocity distribution functions derives the plasma bulk parameters, such as the plasma density, speed, temperature, and kappa index. Commonly, the plasma bulk density, velocity, and temperature are determined from the velocity moments of the observed distribution function. Interestingly, recent studies demonstrated the calculation of the kappa index from the speed (kinetic energy) moments of the distribution function. Such a novel calculation could be very useful in future analyses and applications. This study examines the accuracy of the specific method using synthetic plasma proton observations by a typical electrostatic analyzer. We analyze the modeled observations in order to derive the plasma bulk parameters, which we compare with the parameters we used to model the observations in the first place. Through this comparison, we quantify the systematic and statistical errors in the derived moments, and we discuss their possible sources

The impact of non-equilibrium plasma distributions on solar wind measurements by Vigil's Plasma Analyser

In order to protect society from space weather impacts, we must monitor space weather and obtain early warnings for extreme events if possible. For this purpose, the European Space Agency is currently preparing to launch the Vigil mission towards the end of this decade as a space-weather monitor at the fifth Lagrange point of the Sun--Earth system. Vigil will carry, amongst other instruments, the Plasma Analyzer (PLA) to provide quasi-continuous measurements of solar wind ions. We model the performance of the PLA instrument, considering typical solar wind plasma conditions, to compare the expected observations of PLA with the assumed input conditions of the solar wind. We evaluate the instrument performance under realistic, non-equilibrium plasma conditions, accounting for temperature anisotropies, proton beams, and the contributions from drifting $\alpha$-particles. We examine the accuracy of the instrument's performance over a range of input solar wind moments. We identify sources of potential errors due to non-equilibrium plasma conditions and link these to instrument characteristics such as its angular and energy resolution and its field of view. We demonstrate the limitations of the instrument and potential improvements such as applying ground-based fitting techniques to obtain more accurate measurements of the solar wind even under non-equilibrium plasma conditions. The use of ground processing of plasma moments instead of on-board processing is crucial for the extraction of reliable measurements.Comment: 26 pages, 11 figures; accepted for publication in Space Weathe

On the Calculation of the Effective Polytropic Index in Space Plasmas

The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the plasma density and temperature measurements for a certain polytropic index, and then, we apply the standard analysis to derive the polytropic index. We explore the accuracy of the derived polytropic index for a range of uncertainties in the modeled density and temperature and repeat for various polytropic indices. Our analysis shows that the uncertainties in the plasma density introduce a systematic error in the determination of the polytropic index which can lead to artificial isothermal relations, while the uncertainties in the plasma temperature increase the statistical error of the calculated polytropic index value. We analyze Wind spacecraft observations of the solar wind protons and we derive the polytropic index in selected intervals over 2002. The derived polytropic index is affected by the plasma measurement uncertainties, in a similar way as predicted by our model. Finally, we suggest a new data-analysis approach, based on a physical constraint, that reduces the amount of erroneous derivations

The Polytropic Behavior of Solar Wind Protons as Observed by the Ulysses Spacecraft during Solar Minimum

We analyze proton bulk parameters derived from Ulysses observations and investigate the polytropic behavior of solar wind protons over a wide range of heliocentric distances and latitudes. The large-scale variations of the proton density and temperature over heliocentric distance indicate that plasma protons are governed by subadiabatic processes (polytropic index γ < 5/3), if we assume protons with three effective kinetic degrees of freedom. From the correlation between the small-scale variations of the plasma density and temperature in selected subintervals, we derive a polytropic index γ ∼ 1.4 on average. Further examination shows that the polytropic index does not have an apparent dependence on the solar wind speed. This agrees with the results of previous analyses of solar wind protons at ∼1 au. We find that the polytropic index varies slightly over the range of the heliocentric distances and heliographic latitudes explored by Ulysses. We also show that the homogeneity of the plasma and the accuracy of the polytropic model applied to the data points vary over Ulysses' orbit. We compare our results with the results of previous studies that derive the polytropic index of solar wind ions within the heliosphere using observations from various spacecraft. We finally discuss the implications of our findings in terms of heating mechanisms and the effective degrees of freedom of the plasma protons

Resolving Space Plasma Species With Electrostatic Analyzers

Electrostatic analyzers resolve the energy-per-charge distributions of charged plasma particles. Some space plasma instruments use electrostatic analyzers among other units, such as aperture deflectors and position sensitive detectors, in order to resolve the three-dimensional energy (velocity) distribution functions of plasma particles. When these instruments do not comprise a mass analyzer unit, different species can be resolved only if there are measurable differences in their energy-per-charge distributions. This study examines the ability of single electrostatic analyzer systems in resolving co-moving plasma species with different mass-per-charge ratios. We consider examples of static plasma consisting of two species of heavy negative ions measured by a typical electrostatic analyzer design, similar to the electron spectrometer on board Cassini spacecraft. We demonstrate an appropriate modeling technique to simulate the basic features of the instrument response in the specific plasma conditions and we quantify its ability to resolve the key species as a function of the spacecraft speed and the plasma temperature. We show that for the parameter range we examine, the mass resolution increases with increasing spacecraft speed and decreasing plasma temperature. We also demonstrate how our model can analyze real measurements and drive future instrument designs

The Impact of Turbulent Solar Wind Fluctuations on Solar Orbiter Plasma Proton Measurements

Solar Orbiter will observe the Sun and the inner heliosphere to study the connections between solar activity, coronal structure, and the origin of the solar wind. The plasma instruments on board Solar Orbiter will determine the three-dimensional velocity distribution functions of the plasma ions and electrons with high time resolution. The analysis of these distributions will determine the plasma bulk parameters, such as density, velocity, and temperature. This paper examines the effects of short-time-scale plasma variations on particle measurements and the estimated bulk parameters of the plasma. For the purpose of this study, we simulate the expected observations of solar wind protons, taking into account the performance of the Proton-Alpha Sensor (PAS) on board Solar Orbiter. We particularly examine the effects of Alfv\'enic and slow-mode-like fluctuations, commonly observed in the solar wind on timescales of milliseconds to hours, on the observations. We do this by constructing distribution functions from modeled observations and calculate their statistical moments in order to derive plasma bulk parameters. The comparison between the derived parameters with the known input allows us to estimate the expected accuracy of Solar Orbiter proton measurements in the solar wind under typical conditions. We find that the plasma fluctuations due to these turbulence effects have only minor effects on future SWA-PAS observation

Distinct polytropic behavior of plasma during ICME-HSS Interaction

Interplanetary Coronal Mass Ejections (ICMEs) and High Speed Streams (HSSs) are noteworthy drivers of disturbance of interplanetary space. Interaction between them can cause several phenomena, such as; generation of waves, enhanced geo-effectiveness, particle acceleration, etc. However, how does thermodynamic properties vary during the ICME-HSS interaction remain an open problem. In this study, we investigated the polytropic behavior of plasma during an ICME-HSS interaction observed by STEREO and Wind spacecraft. We find that the ICME observed by the STEREO-A has polytropic index $\alpha = 1.0$, i.e., exhibiting isothermal process. Moreover, Wind spacecraft observed the HSS region, non-interacting ICME, and ICME-HSS interaction region. During each regions we found $\alpha$=1.8, $\alpha$=0.7, and $\alpha$=2.5, respectively. It implies that the HSS region exhibits a nearly adiabatic behaviour, ICME region is closely isothermal, and the ICME-HSS interaction region exhibits super-adiabatic behaviour. The insufficient expansion of the ICME due to the interaction with HSS triggers the system for heating and cooling mechanisms which dependent on the degrees of freedom of plasma components

Determining the Bulk Parameters of Plasma Electrons from Pitch-Angle Distribution Measurements

Electrostatic analysers measure the flux of plasma particles in velocity space and determine their velocity distribution function. There are occasions when science objectives require high time-resolution measurements, and the instrument operates in short measurement cycles, sampling only a portion of the velocity distribution function. One such high-resolution measurement strategy consists of sampling the two-dimensional pitch-angle distributions of the plasma particles, which describes the velocities of the particles with respect to the local magnetic field direction. Here, we investigate the accuracy of plasma bulk parameters from such high-resolution measurements. We simulate electron observations from the Solar Wind Analyser’s (SWA) Electron Analyser System (EAS) on board Solar Orbiter. We show that fitting analysis of the synthetic datasets determines the plasma temperature and kappa index of the distribution within 10% of their actual values, even at large heliocentric distances where the expected solar wind flux is very low. Interestingly, we show that although measurement points with zero counts are not statistically significant, they provide information about the particle distribution function which becomes important when the particle flux is low. We also examine the convergence of the fitting algorithm for expected plasma conditions and discuss the sources of statistical and systematic uncertainties