HR: 1340h
AN: SM53B-0420    [Abstracts]
TI: Using Exact Particle Paths in the Calculation of Linear Ion-Electron Tearing and Dependence on the Equilibrium State Parameters
AU: * Allen, C W
EM: clintonwallen@earthlink.net
AF: N/A, 330 N. Mathilda #603, Sunnyvale, CA 94085 United States
AB: We've developed an algorithm to iteratively solve the linearized Vlasov equation for growth rates and first-order potentials of instabilities such as collisionless ion-electron tearing in a neutral sheet. It requires no assumptions about the nature of the equilibrium trajectories and can give exact (numerical) results. In this work we describe the algorithm, and its application to study the behavior of the tearing-mode starting from a Harris equilibrium over a range of the control parameters: the current sheet half-width $w$, $\frac{T_e}{T_i}$, $\frac{M_e}{M_i}$. The method starts with computing and saving several thousand equilibrium particle paths to sample the phase space for a chosen equilibrium state. Then for a given $k$, the coupled equations for $\vec{A_1}$ and $\gamma$ are solved iteratively with $\vec{J_1}$ computed from time-integrals over the saved particle paths. A new $\vec{A_1}$ is found using a Green's function to ensure the boundary- conditions are satisfied, while the correction to $\gamma$ is found from a relation involving integrals of the currents and $\vec{A_1}$. $\phi_1$ is found by assuming quasi-neutrality. The method is stable, converges for any starting values we've tried, requires less than a MB of memory, and 10MB--10GB of disk space for the paths. CPU time on a desktop PC is from $\sim 10$ minutes to an hour for each $k$. The algorithm is similar in spirit to previous work [1], but was developed independently so the implementation is different. Typical dispersion curves, plots of potentials and response functions will be shown. We've found the growth-rates can be fit quite well (correlations of 0.999) by the expression $\gamma(k)= a_x k^b(1/w-k) $ where parameters $a_x, b$ are determined from the peak growth $\gamma_x$ and wavenumber $k_x$. Preliminary results are that for parameter values $\frac{M_e}{M_i}=1$, $\frac{T_e}{T_i}=1$ the dependence of $\gamma_x$, $k_x$ on $w$, over the range $3$--$20$, is given by $k_x=0.527 w^{-1.07}$ and $\gamma_x=0.219 w^{-2.32}$ where $\gamma_x$ is scaled by $\Omega_i$, $k$ and $w$ are scaled by $\rho_i$. For $\frac{M_e}{M_i}= 1/1836$, $\frac{T_e}{T_i}=1/2$ the dependence is $k_x=0.451 w^{-1.11}$ and $\gamma_x=0.0567 w^{-2.379}$. [1] M. Brittnacher, K. B. Quest, and H. Karimabadi, J. Geophys. Res., 100, 3551, (1995); W. Daughton, J. Geophys. Res., 103, 29429, (1998).
DE: 7827 Kinetic and MHD theory
DE: 7835 Magnetic reconnection
DE: 7843 Numerical simulation studies
DE: 2753 Numerical modeling
SC: SPA-Magnetospheric Physics [SM]
MN: 2004 AGU Fall Meeting