Magnetoacoustic solitons in Alkali-fullerene plasmas

Abstract

Nonlinear propagation of magnetoacoustic waves in magnetized, collisionless, warm bi-ion plasmas with positive and negative ions of different masses and charge states are investigated. The two-fluid model is used here. Using reductive perturbation technique, the Korteweg-de Vries equation is derived as nonlinear dispersion relation, and its solution for the magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is obtained. Using experimental values for the plasma parameters, magnetoacoustic soliton structures for K-fullerene plasma are illustrated along with some other useful alkali-fullerene plasmas.

Appendix

To express the dependency of the soliton characteristics on the actual and experimental plasma parameters, we do the reverse coordinate conversion by changing the normalized quantities to the actual plasma parameters. This is done in the following calculation by multiplying the non-dimensional quantities by their normalization factors. Therefore,

$$\lambda ^{\prime} = \sqrt {\frac{{\delta ^{2} \frac{{B_{0}^{2} }}{{4\pi n_{ + }^{0} m_{ - } }} + \delta \mu v_{{T_{ + } }}^{2} + \sigma \mu v_{{T_{ + } }}^{2} }}{{\left( {1 + \delta ^{2} \mu } \right)}}}$$

$${\text{ }}A^{\prime} = \frac{{\left[ {\left( {\delta \mu + 1} \right)\lambda ^{\prime2} - \delta \mu - \alpha \delta \mu - \alpha \sigma \mu + 3} \right]}}{{\left[ {\left( {\delta \mu + 1} \right)\lambda ^{\prime2} + 1} \right]}},{\text{ }}B^{\prime} = \frac{{\lambda ^{\prime} }}{{\left[ {\left( {\delta \mu + 1} \right)\lambda ^{\prime2} + 1} \right]}}$$

$$\phi _{m} ^{\prime } = 3u_{0} v_{{A_{ + } }} /A^{\prime},\space \omega ^{\prime} = \sqrt {4{\text{ }}B^{\prime}/u_{0} v_{{A_{ + } }} }$$

Here $\lambda ^{\prime}$, ${\text{ }}A^{\prime}$, $B^{\prime}$, $\phi _{m} ^{\prime }$ and $\omega ^{\prime}$ are dimensional quantities.