A Numerical Study of Low-frequency Waves in Hall MHD Reconnection

We make a numerical study of the Hall MHD reconnection process with various values of the plasma parameter β (the ratio of plasma pressure to magnetic pressure) ranging from 0.5 to 6.5. The reconnection rate ∂A/∂t|st in quasi-steady state is found to be in the range of 0.15 ≥ ∂A/∂t|st ≥ 0.095. The time series of the normal magnetic field By and the velocity components vx & vz at selected points are transformed into power spectra via fast Fourier transform (FFT). The results show that the frequencies of the power spectra are in the range of Ωci < ω < 8Ωci, Ωci being the proton cyclotron frequency. With the increase of β, the peak amplitude decreases and the peak frequency gets lower. Using the minimum variance analysis (MVA) the direction of propagation of the wave is determined. Th angle α between the wave vector k and the local magnetic field B increases with increasing β. The hodograph of the electric field E is plotted for selected points in the three calculated examples. The results of this work might provide a possible link between the fast reconnection rate and the whistler wave.