Landau quantization effects on hybrid waves in semiconductor plasmas

The impact of Landau quantization on the lower hybrid waves (LHWs) exciting in the semiconductor plasmas, due to classical electron beam, is studied. The quantum hydrodynamic model is employed to derive the dispersion relation of low-frequency electrostatic waves for instability analysis of the LHWs. The quantum effects include Fermi degenerate pressure, Bohm potential, Landau quantization, and exchange-correlation potential for semiconductor plasma species. The dispersion relation is elaborated both quantitatively and qualitatively for the special case of GaAs in the presence of external magnetic field $$\mathbf{B}_0$$. The impact of different plasma parameters such as density ratios of electrons and holes $$\alpha $$, beam temperature $$T_{\mathrm{b}}$$, speed of beam electrons $$v_0$$, propagation angle $$\theta $$, cyclotron frequency $$\omega _{\mathrm{ce}}$$, temperature of electrons and holes $$T_{\mathrm{e}}$$, $$T_{\mathrm{h}}$$ and Landau quantization $$\eta $$, on the dispersion relation of LHWs, is studied. The instability of the LHWs remarkably increases by increasing the concentration of the semiconductor electrons, propagation angle of the wave vector and the beam speed, for the magnetic quantization parameter. However, the instability decreases by increasing the temperature of beam. It is noticed that at $$(T_{\mathrm{b}}>v_0)$$, the $$\eta $$ has no effect on the instability.