[1] Collisionless magnetic reconnection requires the violation of ideal MHD by various kinetic-scale effects whose relative importance is uncertain. Recent research has highlighted the potential importance of wave-particle interactions by showing that Vlasov simulations of unstable ion-acoustic waves predict an anomalous resistivity that can be at least an order of magnitude higher than a popular analytical quasi-linear estimate. Here, we investigate the nonlinear evolution of the ion-acoustic instability and its resulting anomalous resistivity by examining the properties of a statistical ensemble of Vlasov simulations. The simulations differ in their initial electric noise field but are otherwise identical with a Maxwellian electron-ion plasma of low number density and low electron to ion temperature ratio, appropriate to collisionless space plasmas. By studying the evolution of an ensemble of 104 Vlasov simulations with reduced mass ratio m i /m e = 25, we show that (1) the probability distribution of anomalous resistivity values produced during the linear, quasi-linear, and nonlinear evolution of the ion-acoustic instability is approximately Gaussian, (2) the ensemble mean of the ion-acoustic resistivity during the nonlinear regime is higher than estimates at quasi-linear saturation, and (3) the ensemble standard deviation is comparable to the ensemble mean. We argue that the large variability during the nonlinear phase is due to electron and ion bounce motion which is sensitive to the initial conditions. We demonstrate that the results are essentially similar for a real mass ratio simulation.Citation: Petkaki, P., M. P. Freeman, T. Kirk, C. E. J. Watt, and R. B. Horne (2006), Anomalous resistivity and the nonlinear evolution of the ion-acoustic instability,

We present imaging and spectroscopic observations of an isolated C1-class solar flare, obtained with the Atmospheric Imaging Assembly (AIA) and Extreme ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO). We obtain excellent agreement between the peak flare temperatures estimated using the EVE spectra with those obtained from GOES and, most importantly, from the ratio of the 94 Å and 131 Å AIA channels, which are found to be dominated by Fe xviii and Fe xxi. These results confirm that these two AIA bands can be reliably used to provide temperature diagnostics for the peak and gradual phases of solar flares. The flare kernels, probable sources of chromospheric evaporation, are seen as strong localised emission in the AIA bands at the footpoints of flare loops. The flare loops are close to isothermal during the gradual phase. We have run several hydrodynamic simulations (using the HYDRAD code) to study the cooling of the flare loops. We find good overall agreement between observed and predicted electron temperatures and densities when a gradual increase and decrease of the heating is assumed.

No abstract

The dissipation of Alfve n wave packets propagating in an inhomogeneous three-dimensional magnetic Ðeld is numerically studied in the Wentzel-Kramers-Brillouin (WKB) approximation. The dissipation rate is found to scale proportionally to the logarithm of viscosity and/or resistivity, i.e., much faster than the scaling found for two-dimensional conÐgurations (phase mixing, resonance absorption). This phenomenon is related to the exponential separation of neighboring rays ; estimations of the corresponding rate are consistent with the behavior of the Kolmogorov entropy in this kind of structure. The scaling law is the e-folding dissipation time and S is the Reynolds number) holds not only in an irregular t d P ln S (t d magnetic Ðeld (which was studied by Similon & Sudan), but is also veriÐed in quasi-uniform magnetic structures, which contain very small chaotic regions. This study can apply to the heating of low-collision plasmas, e.g., in astrophysical contexts such as the solar corona.

[1] Vlasov simulations of the current-driven ion-acoustic instability produced in Maxwellian and non-Maxwellian (Lorentzian, k = 2) electron-ion plasma with number density 7 Â 10 6 cm À3 , reduced mass ratio m i /m e = 25, and electron to ion temperature ratio T e /T i = 1 are presented and compared. A concise stability analysis of current-driven ionacoustic waves in Maxwellian and non-Maxwellian plasmas modeled by generalized Lorentzian distribution function with index 2 k 7 and electron to ion temperature ratio 1 T e /T i 100 is also presented. The ion-acoustic instability is excited in low temperature ratio Lorentzian (k = 2) plasma for lower absolute electron drift velocity (up to half the critical electron drift velocity of a Maxwellian). The anomalous resistivity resulting from ion acoustic waves in a Lorentzian plasma is a strong function of the electron drift velocity and in the work presented here varies by a factor of $100 for a 1.5 increase in the electron drift velocity. Furthermore, ion-acoustic anomalous resistivity is excited for electron drift velocities that would be stable for Maxwellian plasmas. The magnitude of resistivity which can be generated by unstable ion-acoustic waves may be important for magnetic reconnection at the magnetopause.