Parallel Electric Field in Nonlinear Magnetosonic Waves in Tow- and Three-Component Plasmas

With theory and electromagnetic particle simulations, we have studied the electric field parallel to the magnetic field, $E_ {\parallel}$, in nonlinear magnetosonic waves in an electron-ion (e-i) plasma and in an electron-positron-ion (e-p-i) plasma. Our theory for the e-i plasma shows that the integral of $E_{||}$ along the magnetic field, $F=-\int E_{\parallel}ds$, is given as $ eF \sim \epsilon \Gamma_e T_e$ in small-amplitude ($\epsilon \ll 1$) pulses in a warm plasma with electron temperature $T_e$, where $\Gamma_e$ is the specific heat ratio. In a cold plasma, it is given as $eF \sim \epsilon^2 m_i v_A^2$, where $v_A$ is the Alfven speed. For the e-p-i plasma, $F$ is large if the positron-to-ion density ratio $n_{p0}/n_{i0}$ is small. These theoretical predictions were verified with simulations. Furthermore, the relation $n_{e0} eF \sim \epsilon(\rho v_A^2+\Gamma_e p_{e0})(n_{i0}/n_{e0})$ is found to fit fairly well to the simulation results for shock waves with $\epsilon \sim O(1)$ in e-i and e-p-i plasmas, where $\rho$ is the mass density and $p_{e0}$ is the electron pressure. These results indicate that $E_{\parallel}$ can be strong in nonlinear magnetosonic waves.