Effects of background noise on fit parameters of plasma scattering angle distributions

The presence of noise in plasma particle measurements by scientific instruments causes inaccuracies in the determined plasma bulk parameters. This study demonstrates and evaluates the effects of noise in the determination of typical distribution functions describing the scattering angles of plasma particles passing through thin foils. First, we simulate measurements of plasma particles passing through a thin carbon foil, considering that their scattering angles follow kappa-like distribution functions, as being addressed in previous studies. We work with these specific distributions because we can produce them in the laboratory. We add Poisson-distributed background noise to the simulated data. We fit the simulated measurements and compare the fit parameters with the input parameters. As expected, we find that the discrepancy between the initial parameters and those derived from the fits increases with the relative increase of the noise. The misestimations exhibit characteristic trends as functions of the signal-to-noise ratio and the input parameters. Second, we examine the scattering angle distributions measured with a laboratory experiment of protons passing through a thin carbon foil for different signal-to-noise ratios. These measurements support the simulation results, although they exhibit a larger discrepancy than found in the simulations. Finally, we discuss how we can improve the accuracy of estimated distribution parameters in space and ground-based applications by excluding data-points from the tails of the distribution functions. Although our results exhibit the effects of noise in a specific type of distribution functions, we explain that this technique can be applied to and optimized for other specific data-sets.

Electrostatic Dust-Acoustic Rogue Waves in an Electron Depleted Dusty Plasma

The formation of gigantic dust-acoustic (DA) rouge waves (DARWs) in an electron depleted unmagnetized opposite polarity dusty plasma system is theoretically predicted. The nonlinear Schrödinger equation (NLSE) is derived by employing the reductive perturbation method. It is found that the NLSE leads to the modulational instability (MI) of DA waves (DAWs), and to the formation of DARWs, which are caused by to the effects of nonlinearity and dispersion in the propagation of DAWs. The conditions for the MI of DAWs and the basic properties of the generated DARWs are numerically identified. It is also seen that the striking features (viz., instability criteria, amplitude and width of DARWs, etc.) of the DAWs are significantly modified by the effects of super-thermality of ions, number density, mass and charge state of the plasma species, etc. The results obtained from the present investigation will be useful in understanding the MI criteria of DAWs and associated DARWs in electron depleted unmagnetized opposite polarity dusty plasma systems like Earth’s mesosphere (where the D-region plasma could suffer from electron density depletion), cometary tails, Jupiter’s magnetosphere, and F-ring of Saturn, etc.

Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities

The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb’s path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q- and 1/q- entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications.

Statistical Uncertainties of Space Plasma Properties Described by Kappa Distributions

The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.

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.

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.

Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas

Kappa distributions received impetus as they provide efficient modelling of the observed particle distributions in space and astrophysical plasmas throughout the heliosphere. This paper presents (i) the connection of kappa distributions with statistical mechanics, by maximizing the associated q-entropy under the constraints of the canonical ensemble within the framework of continuous description; (ii) the derivation of q-entropy from first principles that characterize space plasmas, the additivity of energy, and entropy; and (iii) the derivation of the characteristic first order differential equation, whose solution is the kappa distribution function.

Electron Acceleration to MeV Energies at Jupiter and Saturn

The radiation belts and magnetospheres of Jupiter and Saturn show significant intensities of relativistic electrons with energies up to tens of megaelectronvolts (MeV). To date, the question on how the electrons reach such high energies is not fully answered. This is largely due to the lack of high-quality electron spectra in the MeV energy range that models could be fit to. We reprocess data throughout the Galileo orbiter mission in order to derive Jupiter's electron spectra up to tens of MeV. In the case of Saturn, the spectra from the Cassini orbiter are readily available and we provide a systematic analysis aiming to study their acceleration mechanisms. Our analysis focuses on the magnetospheres of these planets, at distances of L > 20 and L > 4 for Jupiter and Saturn, respectively, where electron intensities are not yet at radiation belt levels. We find no support that MeV electrons are dominantly accelerated by wave-particle interactions in the magnetospheres of both planets at these distances. Instead, electron acceleration is consistent with adiabatic transport. While this is a common assumption, confirmation of this fact is important since many studies on sources, losses, and transport of energetic particles rely on it. Adiabatic heating can be driven through various radial transport mechanisms, for example, injections driven by the interchange instability or radial diffusion. We cannot distinguish these processes at Saturn with our technique. For Jupiter, we suggest that the dominating acceleration process is radial diffusion because injections are never observed at MeV energies.

MeV proton flux predictions near Saturn's D ring

Radiation belts of MeV protons have been observed just outward of Saturn's main rings. During the final stages of the mission, the Cassini spacecraft will pass through the gap between the main rings and the planet. Based on how the known radiation belts of Saturn are formed, it is expected that MeV protons will be present in this gap and also bounce through the tenuous D ring right outside the gap. At least one model has suggested that the intensity of MeV protons near the planet could be much larger than in the known belts. We model this inner radiation belt using a technique developed earlier to understand Saturn's known radiation belts. We find that the inner belt is very different from the outer belts in the sense that its intensity is limited by the densities of the D ring and Saturn's upper atmosphere, not by radial diffusion and satellite absorption. The atmospheric density is relatively well constrained by EUV occultations. Based on that we predict an intensity in the gap region that is well below that of the known belts. It is more difficult to do the same for the region magnetically connected to the D ring since its density is poorly constrained. We find that the intensity in this region can be comparable to the known belts. Such intensities pose no hazard to the mission since Cassini would only experience these fluxes on timescales of minutes but might affect scientific measurements by decreasing the signal-to-contamination ratio of instruments.