Localized whistlers in magnetized spin quantum plasmas

The nonlinear propagation of electromagnetic (EM) electron-cyclotron waves (whistlers) along an external magnetic field, and their modulation by electrostatic small but finite amplitude ion-acoustic density perturbations are investigated in a uniform quantum plasma with intrinsic spin of electrons. The effects of the quantum force associated with the Bohm potential and the combined effects of the classical as well as the spin-induced ponderomotive forces (CPF and SPF, respectively) are taken into consideration. The latter modify the local plasma density in a self-consistent manner. The coupled modes of wave propagation is shown to be governed by a modified set of nonlinear Schrödinger-Boussinesq-like equations which admit exact solutions in form of stationary localized envelopes. Numerical simulation reveals the existence of large-scale density fluctuations that are self-consistently created by the localized whistlers in a strongly magnetized high density plasma. The conditions for the modulational instability (MI) and the value of its growth rate are obtained. Possible applications of our results, e.g., in strongly magnetized dense plasmas and in the next generation laser-solid density plasma interaction experiments are discussed.

Figure 1

(Color online) Whistler solitary solution of Eqs. (28, 29) with associated electric field $W$ (upper panel) and density perturbation $N$ (lower panel) for $\Theta =0.8$ (solid line) and 0.82 (dashed line). The other parameter values are $n_0={10}^{34}{\text{m}}^{-3}$, $B_0=5\times {10}^8\text{T}$, ${\omega }_c/{\omega }_{pe}=15.6$, $\omega =0.4$, $M\left(\equiv v_g/c_s\right)=234.54,V_g^{\prime }=-1.81,v_g=2.98\times {10}^8\text{m}/\text{s}$.

Figure 2

(Color online) Whistler solitary solution of Eqs. (28, 29) with associated electric field $W$ (upper panel) and density perturbation $N$ (lower panel) for $B_0=5.8\times {10}^8\text{T}$ (solid line) and $5.9\times {10}^8\text{T}$ (dashed line). The other parameter values are $n_0={10}^{34}{\text{m}}^{-3}$, $\Theta =0.8$, $\omega =\mathrm{0.4.}$ The corresponding $M$ values are $M=234.88$ (solid line) and 234.91 (dashed line).

Figure 3

(Color online) Whistler solitary solution of Eqs. (28, 29) with associated electric field $W$ (upper panel) and density perturbation $N$ (lower panel) for $\omega =0.4$ (solid line) and 0.38 (dashed and dotted line). The other parameter values are $B_0=5\times {10}^8\text{T}$, $n_0={10}^{36}{\text{m}}^{-3}$ (for solid and dashed line) and $2.1\times {10}^{36}{\text{m}}^{-3}$ (for dotted line), $\Theta =0.2$. The values of $M$ are $M=35.38$ (for solid and dashed line) and 22.23 (for dotted line).

Figure 4

(Color online) Ducted whistler obtained as solution of Eqs. (28, 29) with associated electric field $W$ (upper panel) and density perturbation $N$ (lower panel) for $\omega =0.189$, $B_0=5\times {10}^8\text{T}$, $n_0=7\times {10}^{35}{\text{m}}^{-3}$, $\Theta =0.7$. The other parameters are $M=45.24$, $V_g^{\prime }=0.262,H=0.11,v_g=2.37\times {10}^8\text{m}/\text{s}$.