Gerard Belmont

Polytropic indices in collisionless plasmas: Theory and measurements

All theories and models based upon fluid methods are dependent upon p pairs of parameters (p=1 for MHD) which are the polytropic indices γ⫽ and γ⊥ of each of the p fluid populations, and their results can sometimes be greatly affected by changes in these indices. For these fluid descriptions of collisionless plasmas, there was no general method up to now for determining the right values γ⫽ and γ⊥ to be injected, depending on the local physical situation. Are the different populations isothermal (γ⫽ = γ⊥ = 1), isobaric (γ⫽ = γ⊥ = 0), adiabatic (γ⫽ = γ⊥ = 5/3 if the variations are isotropic, but this hypothesis of isotropy is generally not verified in a magnetoplasma) or anything else? These choices may be made by going back to complete kinetic calculations in each specific situation, thereby losing the ease of the fluid methods. This paper shows that the use of polytropic laws is justified for plasma variations belonging to any linear low-frequency wave, and it provides the correct values to be used for the polytropic indices in these cases, thanks to a general kinetic calculation. In these terms, the polytropic indices γ⫽ and γ⊥ must be considered as the interface between kinetic and fluid sides of the physics. The dependence of the indices upon the mode and upon the particle population considered is emphasized. An experimental case concerning a fast magnetosonic mode observed on board the Giotto spacecraft close to comet Halley is completely analyzed from this point of view. Electron measurements are used, simultaneously with magnetic field ones, and all the correlations between the four parameters p⫽, p⊥, n, and Bz are explained; for doing so, the theory is made more sophisticated to account for the fact that the coldest and densest part of the electron distribution function is not, in this case, accessible to the detector.

Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 ...

Landau and non-Landau linear damping: Physics of the dissipation

For linear Langmuir waves, it is well known that the energy exchanges generally lead to a continuous dissipation, on average, from the electric form to the kinetic one. Many papers have estimated these exchanges and indeed shown that the classical Landau value γL, characterizing the electric field damping, can be derived from this estimation. The paper comes back to this demonstration and its implicit assumption of “forgetting the initial conditions.” The limits of the usual energy calculations have become much apparent recently when non-Landau solutions, decreasing with damping rates smaller than γL, have been evidenced [Belmont et al., Phys. Plasmas 15, 052310 (2008)]. Taking advantage of the explicit form provided in this paper for the perturbed distribution function, the dissipation process is revisited here in a more general way. It is shown that the energy calculations, when complete (i.e., when the role of the initial conditions is not excluded by the very hypotheses of the calculations), are indee...

BV technique for investigating 1‐D interfaces

To investigate the internal structure of the magnetopause with spacecraft data, it is crucial to be able to determine its normal direction and to convert the measured time series into spatial profiles. We propose here a new single-spacecraft method, called the BV method, to reach these two objectives. Its name indicates that the method uses a combination of the magnetic field (B) and velocity (V) data. The method is tested on simulation and on Cluster data, and a short overview of the possible products is given. We discuss its assumptions and show that it can bring a valuable improvement with respect to previous methods.

Rotational/ Compressional nature of the Magnetopause: application of the BV technique on a magnetopause case study

The magnetopause boundary implies two kinds of variations: a density/ temperature gradient and a magnetic field rotation. These two kinds are always observed in a close vicinity of each other, if not inseparably mixed. We present a case study from the Cluster data where the two are clearly separated and investigate the natures of both layers. We evidence that the first one is a slow shock while the second is a rotational discontinuity. The interaction between these two kinds of discontinuities is then studied with the help of 1,5-D magnetohydrodynamics simulations. The comparison with the data is quite positive and leads to think that most of the generic properties of the magnetopause may be interpreted in this sense.

First demonstration of an asymmetric kinetic equilibrium for a thin current sheet

The modeling of steady state collisionless asymmetric tangential current layers is a challenging and poorly understood problem. For decades now, this difficulty has been limiting numerical models to approximate equilibria built with locally Maxwellian current layers and theoretical analyses to the very restricted Harris equilibrium. We show how the use of any distribution functions depending only on local macroscopic quantities results in a strong alteration of the current layer internal structure, which converges toward an unpredictable quasi-steady state with emission of ion scale perturbations. This transient can be explained in terms of ion kinetic and electron fluid physics. We demonstrate, for the first time, the validity of an asymmetric kinetic equilibrium model as well as its usability as an initial condition of hybrid kinetic simulations. This offers broad perspectives for the current sheet modeling, for which the early phase of instabilities can be studied within the kinetic formalism.

Magnetopause orientation: Comparison between generic residue analysis and BV method

Determining the direction normal to the magnetopause layer is a key step for any study of this boundary. Various techniques have been developed for this purpose. We focus here on generic residue analysis (GRA) methods, which are based on conservation laws, and the new iterative BV method, where B represents the magnetic field and V refers to the ion velocity. This method relies on a fit of the magnetic field hodogram against a modeled geometrical shape and on the way this hodogram is described in time. These two methods have different underlying model assumptions and validity ranges. We compare here magnetopause normals predicted by BV and GRA methods to better understand the sensitivity of each method on small departures from its own physical hypotheses. This comparison is carried out first on artificial data with magnetopause-like noise. Then a statistical study is carried out using a list of 149 flank and dayside magnetopause crossings from Cluster data where the BV method is applicable, i.e., where the magnetopause involves a single-layer current sheet, with a crudely C-shaped magnetic hodogram. These two comparisons validate the quality of the BV method for all these cases where it is applicable. The method provides quite reliable normal directions in all these cases, even when the boundary is moving with a varying velocity, which distorts noticeably the results of most of the other methods.

Electric and magnetic contributions to spatial diffusion in collisionless plasmas

We investigate the role played by the different self-consistent fluctuations for particle diffusion in a magnetized plasma. We focus especially on the contribution of the electric fluctuations and how it combines with the (already investigated) magnetic fluctuations and with the velocity fluctuations. For that issue, we compute with a hybrid code the value of the diffusion coefficient perpendicular to the mean magnetic field and its dependence on the particle velocity. This study is restricted to small to intermediate level of electromagnetic fluctuations and focuses on particle velocities on the order of few times the Alfven speed. We briefly discuss the consequences for cosmic ray modulation and for the penetration of thermal solar wind particles in the Earth magnetosphere.