Kinetic effects due to suprathermal ionospheric electrons: a study of auroral arc G. GARCIA, CEA; F. FORME, CESR I.Motivations : 1) Observations A fluid model developed by Noel et al (2000) shows that the increase of the electron density due to the auroral precipitation implies sharp horizontal gradients in the electron density. This leads to sharp horizontal gradients in the Pedersen conductivity. These gradients cause a horizontal current density. Because of the null divergence of the current density, very intense field-aligned current densities are created in the edges of auroral arcs. These currents are localized in space and imply the presence of a parallel electric field. In order to study the possible kinetic effects of this very intense and field-aligned electric field, we developed a kinetic model, named KIMIE (KInetic Model of Ionopheric Electrons). We consider the issue of electrons moving through an ionospheric gas of positive ions and neutrals under the influence of a dynamic electric field. The kinetic model includes electrons/electrons, electrons/ions and electrons/neutrals collisions. We solve the Langevin equation in which we find terms of friction and diffusion. We also include the interaction with the local electric field. In order to take into account the evolution of the current density, we introduce a feedback on the electric field. First of all, we observe that the electron distribution functions are non Maxwellian. We can show that suprathermal electrons are created. These electrons are the core of the issue as they carry the current. They represent around 10% of the total current density. The electrical conductivity can also be calculated. The comparison between the classical and modeled conductivity shows that the modeled one is always larger of 30%. This work applied to the study of auroral arcs could be developed to understand the energy transfers from the troposphere to the ionosphere due to relativistic electron beams coming from Terrestrial Gamma ray Flashes. ABSTRACT Spatial resolution (m) Current densities (  A.m -2 ) Current densities as a function of the spatial resolution of the instruments Magsat Dynamic Explorer Viking Freja Fast Astrid-2 Oersted Champ Two coupled models [2]: - TRANSCAR a fluid model - ELECTRO an electrodynamic model How do these characteristics affect the electron velocity distribution function (EDF)? Thermal electrons are accelerated by a parallel electric field 0.5 mV/m in the highly collisionnal E region Edge of the auroral arc auroral arc Large current densities are expected on the edges of the auroral arc -600  A/m² Fig.2 : figures are extracted from Noël et al.(2000). The top panel represents the current density as a function of altitude and horizontal position. The bottom panel represents the parallel electric field as a function of altitude and horizontal position. II. A kinetic Model (Garcia and Forme, 2006) 1)electron/electron and electron/ion collisions We use the Fokker-Planck equation which describes binary collisions between charged particles with long-range interactions: We solve the Langevin equation which is similar to the Fokker- Planck one: If a is the scattered particles and b is the scaterrers, is the friction coefficient is the angular diffusion coefficient ↔ 3) KIMIE (Kinetic Model of Ionospheric Electrons) The model is 1-D particle positions (particles move along z axe) but 3-D velocities code (vx, vy and vz are calculated). We initialize with typical ionospheric values : n e, n i, n n, T e and T i initialization parameters : density, temperature, electric field Initialization of positions, velocities V 0 z 0 t 0 Output For each particle: - F f & F diff evaluation - solve Langevin equation V n r n t n Parameters for the next time step V n+1 r n+1 t n+1 Boundary conditions Z Z // B Fig.3 : Schematic illustration of the model for a plasma in the presence of an electric field-aligned in the z-direction. The current densities increase with time. When a particle hits one of the boundaries, it is re-injected into the system according to the electron velocity distribution function f hi e. We obtain the EDF at each altitude. III. Results 1)Electron Distribution Functions (EDF) m c 2) electron/neutral collisions We include the electron/neutral collisions : elastic and inelastic collisions, thanks to the Monte-Carlo method. The electron distribution functions are non Maxwellian (difference between the solid and the dotted lines): a suprathermal tail is created and increases with time. Fig.4 : The electron distribution functions as a function of the squared velocities. The different colors correspond to different times. The solid lines show the modeled EDF whereas the dotted lines represent the Maxwellian at the corresponding temperature Fig.1 :The current densities measured as a function of spatial resolution. The different colors correspond to different satellites. The different values of the current densities come from: Olsen (1997); Christiansen et al. (2002); Stauning (2002); Weimer (2001); Ohtani et al. (1996); Ivchenko and Marklund (2002); Stasiewicz and Potemra (1998); Stasiewicz et al. (1998); Luhr et al. (1994); Amm et al. (1999); Kustov et al. (2000, 1997); Scoffield et al. (2005); Elphic et al. (1998); Carlson et al. (1998); Ritter et al. (2004); Wang et al. (2006) Fig.5 : The electric conductivity as a function of time : the pink line corresponds to the modeled conductivity and the black one to the classical conductivity 3) A detailed study of the EDF We fit the EDF by two Maxwellians in order to better understand the temporal evolution. We can show the temporal evolution of the electron density and the mean electron velocity for each Maxwellian. - The density of the core distribution decreases whereas the density of the suprathermal distribution increases. - The density of the suprathermal distribution is about 12% of the total density - The core of the distribution stays at rest whereas the suprathermal distribution drifts. - The suprathermal distribution carries the current. Conclusions : The kinetic model is useful over small spatial scales and in the presence of large current densities. The model shows that: - The electron distribution functions are non-Maxwellian - Suprathermal electrons are created - Two populations can be differentiated : a population at rest which is heated and a suprathermal population which drifts in velocities space - Suprathermal electrons (~10 % of the total electron density) carry the current - These electrons lead to the modification of the fluid values (the electrical conductivities are increased of 30 %) 2) Numerical model TGF Applications This work applied to the study of auroral arcs could be developed to understand the energy transfers from the troposphere to the ionosphere due to relativistic electron beams associated with Terrestrial Gamma ray Flashes. This issue was studied by Lehtinen et al. (1999) thanks to a Monte Carlo model. However, there are several limitations of this model : - only the high energy electrons (>2keV) are considered - the electron transport and the energy transfer are decoupled In order to study this phenomenon, we plan to couple this kinetic model KIMIE with a fluid ionospheric model named TRANSCAR. This model includes a description of precipitating electrons with a fluid description of the thermal plasma (6 ions and electrons). KIMIE will give the dynamics of electrons. We could take into account the low energy electrons and calculate the optical, gamma or radio emissions. fhnfhn f h n-1 fh2fh2 fh0fh0 f h3 f h n-2 EDF EDF obtained with the model Maxwellian named “core of the distribution” Maxwellian named “suprathermal distribution” n e,s T e,s n e,c T e,c 6.a a : the EDF as a function of the electron velocities and the fit by two Maxwellians. b : The electron density as a function of time for the core of the distribution. c : The mean electron velocity as a function of time for the core of the distribution. d : The electron density as a function of time for the suprathermal distribution. e : The mean electron velocity as a function of time for the suprathermal distribution. Bibliography : Noël, J-M, J-P St-Maurice and P-L Blelly (2000) Nonlinear model of short-scale electrodynamics in the auroral ionosphere, Ann. Geophys., 18, G. Garcia and F. Forme, A kinetic model for runaway electrons in the ionosphere, Ann. Geophys., 24, 2391–2401, 2006 Lehtinen, N. G., T. F. Bell and U. S. Inan, Monte Carlo simulation of runaway MeV electron breakdown with application to red sprites and terrestrial gamma ray flashes, J. Geophys. Res., 104, 24699, ) Conductivities We can calculate the electric conductivity from the model by the ratio of the current density by the electric field and compare to the classical conductivity 6.b Value fitted Value min Value max 6.c Value fitted Value min Value max Value fitted Value min Value max Value fitted Value min Value max 6.e 6.d