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The influence of the intrinsic spin of electrons on the excitation of transverse electromagnetic surface waves in magnetized plasma is considered. We use a fluid formalism to include quantum corrections due to the Bohm potential and magnetization energy of electrons due to its spin. The effects of both quantum corrections are shown in the dispersion relation for the propagation of surface waves. Also, it is found that the phase and group velocities are increased due to the quantum effects. In the nonrelativistic motion of electrons, the spin effects become noticeable even when the external magnetic field is relatively low.

Already in the 1960’s, the excitation spectrum of quantum plasmas was studied by Pines. Since Pines’s pioneering paper, a number of researchers studied the theoretical quantum statistical properties of plasmas [

Several authors incorporated the effect of the dispersion caused by the quantum Bohm potential and/or the spin effect in the study of plasma waves [

In the present work, we study the quantum effects introduced by both the Bohm potential and the spin of electrons in propagation of surface waves in electron magnetoplasma. We will derive and analyze the dispersion relation of the excitation of transverse electromagnetic (TM) surface waves by using fluid (QHD) model.

We consider a homogeneous quantum plasma half-space under an external strong magnetic field

By employing the QHD model, we can write the dynamic equations of an electron as follows:

where,

Here

We now study the response of the system to any small perturbations and assume that every physical quantity

The electromagnetic fields of TM surface waves

The Equation (1) can be linearized, by assuming that the equilibrium quantities

The Equations (8)-(10) display that Bohm potential and the spin quantum effects enhance the perturbation velocity of the electrons. The continuity Equation (3) yields the following wave equation for the perturbed electron density:

where,

To obtain the above Equations (7)-(11), the very slow nonlocal variation are neglected, (i.e.,

where,

By substituting the values of

where,

It is worth to notice that the parameters

The inhomogeneous differential Equations (13) and (14) are dependent relations. We have solved them together (as in Ref. [

where,

Here,

The general dispersion relation for the electromagnetic surface waves in quantum magnetized plasma has also been obtained as follows:

where,

The quantum corrections appear due to the spin effects, which are proportional to

The classical and the quantum corrected modes in magnetized or unmagnetized plasma are studied numerically through the dispersion relation (21) in this section. By taking the same procedure in Ref. [

In the first, we plot the dispersion relation (21) of the surface modes in

The most remarkable effects of quantum contribution is the increase in the effective group velocity (

But in the case of quantum magnetized plasma, there are more different surface modes can be excited. So, we have numerically solved the dispersion relation (21) and some of these solutions are investigated in Figures 2(a)-(d). In the case of unmagnetized, the surface modes are initially excited with high frequency

Besides, the effect of external magnetic field on the excitation of TM surface waves is investigated in the

A comparison between the dispersion of the modes in quantum magnetized plasma with and without spin effects is investigated in

To summarize, we have solved the full set of equations of quantum hydrodynamic model which describes the spin dynamics of electrons. The quantum corrections to the excitation and propagation of surface waves in quantum plasma under an external magnetic field have been investigated. These corrections are due to Bohm potential and to spin of electrons. It showed how contribution of both quantum effects modifies the plasma current density and thereby introduces a correction term in the dispersion relation, which, in turn gives rise to new modes. The dispersion relation for these waves is solved numerically for normal variables of frequency and wave number. This dispersion equation is studied for different cases and investigated graphically (classical or

quantum, magnetized or unmagnetized and with or without spin effect). It is found that the phase and group velocities are increased due to the quantum effects. It is also noted that increase of magnetic field tends to increase the frequency of the excited modes. Besides, when the spin effect is taken into account, it is similar to the effect of increasing magnetic field.

Bahaa F.Mohamed,Salah Y.Elbakry,Abrar A.Salah, (2016) Surface Waves Excitation in Magnetized Spin Quantum Plasmas. Journal of Modern Physics,07,335-343. doi: 10.4236/jmp.2016.73034