Magnetosonic solitons in a fermionic quantum plasma

Starting from the governing equations for a quantum magnetoplasma including the quantum Bohm potential and electron spin-$1∕2$ effects, we show that the system of quantum magnetohydrodynamic (QMHD) equations admits rarefactive solitons due to the balance between nonlinearities and quantum diffraction and tunneling effects. It is found that the electron spin-$1∕2$ effect introduces a pressurelike term with negative sign in the QMHD equations, which modifies the shape of the solitary magnetosonic waves and makes them wider and shallower. Numerical simulations of the time-dependent system shows the development of rarefactive QMHD solitary waves that are modified by the spin effects.

Figure 1

Sagdeev potential $\Psi \left(Z\right)$ (upper panel) and the profile of the solitary wave $Z\left(\xi \right)$ (lower panel), for $v_0=0.01$ (dashed lines), 0.5 (solid lines), and 0.7 (dotted lines). The other parameters are $\epsilon =5$, $c_s=0.1$, $v_B=0.2$, and $\mid {\omega }_{ce}\mid {\omega }_C∕{\omega }_{pe}^2=1$.

Figure 2

Sagdeev potential $\Psi \left(Z\right)$ (upper panel) and the profile of the solitary wave $Z\left(\xi \right)$ (lower panel), for $\epsilon =1$ (dashed lines), 5 (solid lines), and 10 (dotted lines). The other parameters are $v_0=0.5$, $c_s=0.1$, $v_B=0.2$, and $\mid {\omega }_{ce}\mid {\omega }_C∕{\omega }_{pe}^2=1$.

Figure 3

Time-dependent dynamics of the normalized magnetic field $b$, for $\epsilon =5$ (left column) and 10 (right column). The other parameters are $c_s=0.1$, $v_B=0.2$, and $\mid {\omega }_{ce}\mid {\omega }_C∕{\omega }_{pe}^2=1$.