Experimental evaluation of the Lundquist number for the Earth's magnetopause and magnetotail

A realistic appraisal of the Lundquist number based on experimental determination of both the resistivity and the scale sizes is necessary for determining the validity of MHD theories and numerical Simulations of important dynamical processes, such as reconnection, within the Earth's magnetosphere. On the basis of previously published ISEE I and GeotaiI observations of low-frequency waves, identified as lower hybrid drift waves, and various experimental estimates of scale sizes, the Lundquist number is calculated for the magnetotail plasma sheet and the magnetopause of the Earth. This calculation is made using the quasi-linear expression for the anomalous resistivity. If nonlinear effects and/or additional wave modes are important, the Lundquist number would be reduced. For typical values of the magnetic field, density, temperature, wave electric-field amplitude, and scale size, it is shown that the Lundquist number ranges from the order of tenths to tens for the active, thinned near-Earth plasma sheet and for the deep tail and ranges from the order of tenths to one hundred for the magnetopause.