Validity of the fluid description of critical β and Alfven time scale of ballooning instability onset in the near-Earth collisionless high-β plasma -: art. no. A02211

[1] For a realistic, highly stretched, two-dimensional tail configuration, in which the pressure gradient force is balanced with the curved field line tension force at the equator, the growth rates and the real frequencies of the ideal magnetohydrodynamic (MHD) and two component fluid (nonideal MHD) ballooning modes, in which the phrase two component fluid'' means that the Hall and the electron pressure gradient terms are included in the generalized Ohm's law, the ion bounce frequency omega(bi), the ion magnetic drift frequency omega(di), the ion diamagnetic drift frequency omega(*i), and the ion cyclotron frequency omega(ci) are calculated numerically at the equator as a function of X from the near-Earth tail (X = - 15 R-E) to the midtail (X = - 30 R-E). Contrary to the well-known dipole field case, in which the bounce frequency decreases with increasing \X\, the ion bounce frequency increases with \X\ for the tail configuration. The ion magnetic drift frequency dominated by the curvature drift frequency also increases with increasing \X\. The exact growth rates of the ideal and nonideal ballooning modes, gamma(e) and gamma(ne), which are nearly equal, are given by 1.22 V-A/R-c, where V-A is the Alfven velocity and R-c is the field line curvature radius at the equator, and satisfy omega(bi), omega(di), omega(*i) < gamma(e) < omega(ci) on average in the near-Earth tail at X similar to - 15 R-E. Also, the ion motion remains adiabatic in the near-Earth tail at X similar to - 15 R-E. Therefore it is a posteriori verified that the fluid or MHD description of the linear stability of the ballooning instability is valid, and the critical beta and the Alfven time scale tau(A) similar to R-c/V-A of the ballooning instability onset obtained by the fluid theory are validated in the near-Earth tail as close as 15 R-E from the Earth. Despite the plasma being collisionless and high-beta in the near-Earth tail, the subtle collisionless kinetic effects due to the field line curvature in high-beta collisionless plasma are not significant enough to invalidate the fluid description in the near-Earth tail. The Alfven time scale of an e-folding growth of the Alfven wave trapped within R-c in the equatorial region is of the order of a few tens of seconds or less in the near-Earth tail. It is faster than the bounce time of the bulk of ions and can explain the observed rapid time scale of a substorm onset. There is excellent agreement between the critical beta and the Alfven time scale obtained analytically for the two component fluid plasma and those obtained by a three-dimensional particle simulation.