Modeling the Plasma Flow in the Inner Heliosheath with a Spatially Varying Compression Ratio

2018

Entropy

The paper derives the polytropic indices over the last two solar cycles (years 1995–2017) for the solar wind proton plasma near Earth (~1 AU). We use ~92-s datasets of proton plasma moments (speed, density, and temperature), measured from the Solar Wind Experiment instrument onboard Wind spacecraft, to estimate the moving averages of the polytropic index, as well as their weighted means and standard errors as a function of the solar wind speed and the year of measurements. The derived long-term behavior of the polytropic index agrees with the results of other previous methods. In particular, we find that the polytropic index remains quasi-constant with respect to the plasma flow speed, in agreement with earlier analyses of solar wind plasma. It is shown that most of the fluctuations of the polytropic index appear in the fast solar wind. The polytropic index remains quasi-constant, despite the frequent entropic variations. Therefore, on an annual basis, the polytropic index of the solar wind proton plasma near ~1 AU can be considered independent of the plasma flow speed. The estimated all-year weighted mean and its standard error is γ = 1.86 ± 0.09.

the values of the polytropic index are characteristic of the thermodynamic process.…”

Section: Introductionmentioning

confidence: 99%

Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed

2018

Entropy

“…Moreover, the plasma in those subintervals may not correspond in uniform plasma with a single polytropic index. More sophisticated methods can investigate the polytropic relation in different timescales and by applying more complicated polytropic models [ 3 , 4 ].…”

Section: Discussionmentioning

confidence: 99%

“…In this consideration, the plasma may reside in a superposition of states, each described by a single polytropic index [ 3 ]. Another possibility is to have a non-homogeneous polytropic index [ 4 ].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the knowledge of the polytropic index is needed for the accurate description of the ambient solar wind expansion (e.g., [ 5 ]), the plasma dynamics within large scale structures such as magnetic clouds (e.g., [ 6 , 7 ]), planetary magnetospheres (e.g., [ 8 ]), and the inner heliosheath (e.g., [ 9 ]). Additionally, the polytropic index defines the boundary conditions across discontinuities (e.g., [ 4 , 10 , 11 ]). Plasma modeling is also essential to some recent high-profile astrophysics results, e.g., the first image of a black hole is modeled using MHD with a polytropic index [ 12 ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Calculation of the Effective Polytropic Index in Space Plasmas

Nicolaou

Wicks

2019

Entropy

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.

“…[83] An important milestone came with the connection of kappa distributions with the polytropic behaviour of plasmas, namely, the semi-empirical power-law relationship between thermal observables, i.e., the particle density, n, temperature, T, and thermal pressure, p, where the power exponent constitutes the polytropic index . The polytropic behaviour is a common characteristic of space plasmas, [14,22,56,78,[84][85][86][87][88][89][90][91][92][93][94] while the value of polytropic index is highly connected with the release and/or absorption of heat as the plasma flows and evolves. [95] The kappa distributions can lead to the polytropic relationship, and vice versa.…”

mentioning

confidence: 99%

Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling

Contributions to Plasma Physics

2020

The paper derives the complete formulations of polytropic behaviour for plasmas described by kappa distributions. This is achieved by employing both positive and negative types of phase-space kappa distributions of a Hamiltonian for a nonzero potential energy, while the cases of positive and negative potential energies are analysed separately. Then, we develop the general polytropic-barometric formula that describes the profiles of density, temperature, and thermal pressure. Furthermore, it is shown how the kappa and polytropic indices can be derived from observational measurements of the temperature altitude gradient. As an example, we calculated the kappa ≈ 3.35 and polytropic ≈ 0.74 indices of the terrestrial atmosphere at ∼100 km, revealing the existence of heating processes that add thermal energy to atmospheric particles. K E Y W O R D S kappa distributions, polytropic index, space plasmas 1 INTRODUCTION Gases and other classical particle systems are characterized by (a) weakly interacting particles, (b) short-range interactions-restricted to particles' first neighbours, (c) absence of any collective-behaviour among particles, and, most important, (d) absence of any local correlations among particles. This last property is certainly related to the former ones, but it is the cornerstone of the basic consideration of the classical Boltzmann-Gibbs statistical mechanics. [1] As a result, when these particle systems reside at thermal equilibrium, they have their phase-space described by the celebrated Maxwell-Boltzmann distribution. On the other hand, the kappa distributions were found to describe particle systems characterized by (a) weakly and/or strongly-interacting particles, (b) short-and/or long-range interactions, (c) collective-behaviour among particles, and again, most important, (d) existence of local correlations among particles. In fact, the kappa index that governs and parameterizes these distributions is inversely related to the correlation coefficient; thus, the higher the value of kappa, the closer we reach the classical limit of Maxwell-Boltzmann distributions, and the smaller the correlation coefficient is among particles. [2,3] Ideal particle systems with all the above properties are the collisionless and weakly coupled plasmas, where the Debye shielding induces local correlations among particles (Figure 1). [4-7] Especially, the space and astrophysical plasmas are such examples of particle systems with correlations described by kappa distributions [8,9] (also, see the book of kappa distributions: [10]). The equation-of-state and the velocity distribution function are two different topics and should not be confused. For instance, in the case of classical plasmas, both the equation-of-state and the velocity distribution function are