Empirically derived kappa distributions are becoming increasingly widespread in space physics as the power law nature of various suprathermal tails is melded with more classical quasi‐Maxwellian ...cores. Two different mathematical definitions of kappa distributions are commonly used and various authors characterize the power law nature of suprathermal tails in different ways. In this study we examine how kappa distributions arise naturally from Tsallis statistical mechanics, which provides a solid theoretical basis for describing and analyzing complex systems out of equilibrium. This analysis exposes the possible values of kappa, which are strictly limited to certain ranges. We also develop the concept of temperature out of equilibrium, which differs significantly from the classical equilibrium temperature. This analysis clarifies which of the kappa distributions has primacy and, using this distribution, the kinetic and physical temperatures become one, both in and out of equilibrium. Finally, we extract the general relation between both types of kappa distributions and the spectral indices commonly used to parameterize space plasmas. With this relation, it is straightforward to compare both spectral indices from various space physics observations, models, and theoretical studies that use kappa distributions on a consistent footing that minimizes the chances for misinterpretation and error. Now that the connection is complete between empirically derived kappa distributions and Tsallis statistical mechanics, the full strength and capability of Tsallis statistical tools are available to the space physics community for analyzing and understanding the kappa‐like properties of the various particle and energy distributions observed in space.
In this paper we examine the physical foundations and theoretical development of the kappa distribution, which arises naturally from non-extensive Statistical Mechanics. The kappa distribution ...provides a straightforward replacement for the Maxwell distribution when dealing with systems in stationary states out of thermal equilibrium, commonly found in space and astrophysical plasmas. Prior studies have used a variety of inconsistent, and sometimes incorrect, formulations, which have led to significant confusion about these distributions. Therefore, in this study, we start from the
N
-particle phase space distribution and develop seven formulations for kappa distributions that range from the most general to several specialized versions that can be directly used with common types of space data. Collectively, these formulations and their guidelines provide a “toolbox” of useful and statistically well-grounded equations for future space physics analyses that seek to apply kappa distributions in data analysis, simulations, modeling, theory, and other work.
Abstract
We provide a simple geometric explanation for the source of switchbacks and associated large and one-sided transverse flows in the solar wind observed by the Parker Solar Probe (PSP). The ...more radial, sub-Parker spiral structure of the heliospheric magnetic field observed previously by Ulysses, ACE, and STEREO is created within rarefaction regions where footpoint motion from the source of fast into slow wind at the Sun creates a magnetic fieldline connection across solar wind speed shear. Conversely, when footpoints move from the source of slow wind into faster wind, a super-Parker spiral field structure is formed: below the Alfvén critical point, one-sided transverse field-aligned flows develop; above the Alfvén critical point, the field structure contracts between adjacent solar wind flows, and the radial field component decreases in magnitude with distance from the Sun, eventually reversing into a switchback. The sub-Parker and super-Parker spirals behave functionally as opposites. Observations from PSP confirm the paucity of switchbacks within rarefaction regions and immediately outside these rarefaction regions, we observe numerous switchbacks in the magnetic field that are directly associated with abrupt transients in solar wind speed. The magnetic field strength, the radial component of the magnetic field, the speed gradients, radial Alfvén speed, and the ratio of the sound speed to the radial Alfvén speed all conform to predictions based on the sub-Parker and super-Parker spirals within rarefaction regions and solar wind speed enhancements (spikes or jets), respectively. Critically, the predictions associated with the super-Parker spiral naturally explain the observations of switchbacks being associated with unexpectedly large and one-sided tangential flows.
Solar Probe Plus (SPP) will be the first spacecraft to fly into the low solar corona. SPP’s main science goal is to determine the structure and dynamics of the Sun’s coronal magnetic field, ...understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Understanding these fundamental phenomena has been a top-priority science goal for over five decades, dating back to the 1958 Simpson Committee Report. The scale and concept of such a mission has been revised at intervals since that time, yet the core has always been a close encounter with the Sun. The mission design and the technology and engineering developments enable SPP to meet its science objectives to: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles. The SPP mission was confirmed in March 2014 and is under development as a part of NASA’s Living with a Star (LWS) Program. SPP is scheduled for launch in mid-2018, and will perform 24 orbits over a 7-year nominal mission duration. Seven Venus gravity assists gradually reduce SPP’s perihelion from 35 solar radii (
R
S
) for the first orbit to
<
10
R
S
for the final three orbits. In this paper we present the science, mission concept and the baseline vehicle for SPP, and examine how the mission will address the key science questions
Abstract
In this paper, we develop the transport equation of kappa, the fundamental thermodynamic parameter that labels kappa distributions of particle velocities. Using the recently developed ...concept of entropy defect, we are able to formulate the transport equation of kappa as a function of a general, positive or negative, rate of entropy change. Then, we derive the particular case of exchanging plasma ions with low-dimensionality, newly born pickup protons, which interact and decrease the entropy of the flow of otherwise kappa-distributed plasma protons. Finally, we apply the transport equation of kappa to the solar wind plasma protons, which leads to the radial profile of kappa values, as well as the evolution of the kappa distributions through the heliosphere. The results show that the solar wind kappa decreases with increasing heliocentric distance, corresponding to plasmas residing in stationary states far from classical thermal equilibrium. Moreover, in the outer heliosphere and the heliosheath, kappa reaches its lowest values and is spread across the far-equilibrium region of 1.5 <
κ
< 2.5, which coincides with independent observations provided by NASA’s Interstellar Boundary Explorer mission.
Abstract
Solar wind magnetic fluctuations exhibit anisotropy due to the presence of a mean magnetic field in the form of the Parker spiral. Close to the Sun, direct measurements were not available ...until the recently launched Parker Solar Probe (PSP) mission. The nature of the anisotropy and geometry of the magnetic fluctuations play a fundamental role in dissipation processes and in the transport of energetic particles in space. Using PSP data, we present measurements of the geometry and anisotropy of the inner heliosphere magnetic fluctuations, from fluid to kinetic scales. The results are surprising and different from 1 au observations. We find that fluctuations evolve characteristically with size scale. However, unlike 1 au solar wind, at the outer scale, the fluctuations are dominated by wavevectors quasi-parallel to the local magnetic field. In the inertial range, average wavevectors become less field aligned, but still remain more field aligned than near-Earth solar wind. In the dissipation range, the wavevectors become almost perpendicular to the local magnetic field in the dissipation range, to a much higher degree than those indicated by 1 au observations. We propose that this reduced degree of anisotropy in the outer scale and inertial range is due to the nature of large-scale forcing outside the solar corona.
Abstract
The paper derives the one-to-one connecting relationships between plasma heating and its polytropic index, and addresses the consequences through the transport equation of temperature. ...Thermodynamic polytropic processes are classified in accordance to their polytropic index, the exponent of the power-law relationship of thermal pressure expressed with respect to density. These processes generalize the adiabatic one, where no heating is exchanged between the system and its environment. We show that, in addition to heating terms, the transport equation of temperature depends on the adiabatic index, instead of a general, nonadiabatic polytropic index, even when the plasma follows nonadiabatic processes. This is because all the information regarding the system's polytropic index is contained in the heating term, even for a nonconstant polytropic index. Moreover, the paper (i) defines the role of the polytropic index in the context of heating; (ii) clarifies the role of the nonadiabatic polytropic index in the transport equation of temperature; (iii) provides an alternative method for deriving the turbulent heating through the comparably simpler polytropic index path; and, finally, (iv) shows a one-component plasma proof-of-concept of this method and discusses the implications of such derived connecting relationships in the solar wind plasma in the heliosphere.
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
/Δ
m
∼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.
Recent advances in Space Physics theory have shown the connection between non-extensive Statistical Mechanics and space plasmas by providing a theoretical basis for the empirically derived kappa ...distributions commonly used to describe the phase-space distribution functions of these systems. The non-equilibrium temperature and the kappa index that govern these distributions are the two independent controlling parameters of non-equilibrium systems. The significance of the kappa index is primarily given by its role in identifying the non-equilibrium stationary states and measuring their 'thermodynamic distance' from thermal equilibrium, while its physical meaning is connected to the correlation between the system's particles. The classical, single stationary state at equilibrium is generalized into a whole set of different non-equilibrium stationary states labeled by the kappa index. This paper addresses certain crucial issues about the physical meaning and role of the kappa index in identifying stationary states. The origin of the emerged inconsistencies is that the kappa index is not an invariant physical quantity, but instead depends on the degrees of freedom of the system's particles. This leads in several misleading conclusions, such as (1) only large kappa index, practically infinite, can characterize the many-particle kappa distribution, and (2) the correlation between particles depends on the total number of the system's particles. Here we show that a modified kappa index, invariant for any number of degrees of freedom, can be naturally defined. Then, we develop and examine the relevant corrected formulation of many-particle multidimensional kappa distribution, and discuss the physical meaning of the invariant kappa index.
Abstract
The recently developed concept of “entropic defect” is important for understanding the foundations of thermodynamics in space plasma physics, and more generally for systems with physical ...correlations among their particles. Using this concept, this paper derives the basic formulation of the distribution function of velocities (or kinetic energies) in space plasma particle populations. Earlier analyses have shown how the formulation of kappa distributions is interwoven with the presence of correlations among the particles’ velocities. This paper shows, for the first time, that the reverse is true: the thermodynamics of particles’ physical correlations are consistent only with the existence of kappa distributions.
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