Magnetosonic waves in a quantum plasma with arbitrary electron degeneracy

Using a two-species quantum hydrodynamic model, we derive the quantum counterpart of magnetosonic waves, in a plasma with arbitrary degree of degeneracy and taking into account quantum diffraction effects due to the matter-wave character of the charge carriers. The weakly nonlinear aspects of the associated quantum magnetosonic wave are accessed by means of perturbation theory, with the derivation of a nonlinear evolution equation admitting solitons, namely, the Korteweg–de Vries equation. The degeneracy and quantum diffraction effects on soliton propagation are determined. A qualitative change on weakly nonlinear magnetosonic waves appears when quantum diffraction matches certain conditions, producing shock solutions instead of solitons, within the approximation level. We also include explicit numeric estimates and a discussion on the coupling (nonideality) parameter for quantum plasmas with intermediate degeneracy degree.

Figure 1

Plasma number density as a function of temperature, from Eq. (76) and a fixed fugacity $z=1$.

Figure 2

Plasma coupling parameter $g$ versus electron temperature $T$, from Eq. (77) and fugacity $z=1$.

Figure 3

Ion-acoustic speed $c_s$ as a function of temperature, from Eq. (17) and $z=1$.

Figure 4

Alfvén wave speed $v_A$ as a function of temperature, for $B_0=5$ T. (solid curve) and $B_0=10$ T (dashed curve), at $z=1$.

Figure 5

Quantum diffraction parameter $H$ as a function of temperature, from Eq. (24) and $z=1$.

Figure 6

Nonlinear dispersive coefficient $b$ as a function of temperature, from Eq. (66), for $B_0=5$ T (solid curve) and $B_0=10$ T (dashed curve), at $z=1$.

Figure 7

The ratio $\mathrm{\Omega }$ of ion-cyclotron to ion plasma frequencies as a function of temperature, for $B_0=5$ T (solid curve) and $B_0=10$ T (dashed curve), at $z=1$.