Ion-wake-induced anomaly of dust lattice mode in the presence of an external magnetic field

We report a theoretical investigation of the dust lattice (DL) mode in two-dimensional Yukawa crystals in the presence of asymmetric ion flow and an external magnetic field perpendicular to the crystal plane. Two mutually perpendicular modes are found to be coupled due to Lorentz force. Interaction among the dust grains along the vertical direction of ion flow is strongly affected due to the formation of an ion wake. This causes anisotropy in interaction strength along two mutually perpendicular directions. Both hybrid modes are studied as characteristics of different ion flow speeds and magnetic field strengths. The study shows a fluctuation in DL mode frequency driven by the strength of the particle-wake interaction. The effect of ion flow on polarization of the hybrid wave amplitudes is discussed in detail. Results show a possible mechanism of anomalous phase transition in dusty plasma.

Figure 1

(a) Normalized wake potential for Mach number $M=0.5$ [solid (blue) line], $M=0.3$ [dashed (red) line], and $M=0.15$ [dotted (green line]), having magnetic field $B=0.04$ T. (b) Vertical confinement mechanism of particle-wake interaction with an increase in strength of the wake potential, from left to right. (c) Effective spring constant $K_z$ vs $M$ (Mach number) for the given set of plasma parameters.

Figure 2

Dispersion relation profiles with different Mach numbers $M$ and magnetic field strengths $B$ for a Coulomb coupling parameter $\Gamma =824$ and screening strength $\kappa =2.9$. (a) Normalized frequency dependence of both the upper hybrid (UH; solid line) and the lower hybrid (dotted line) waves at $M=0.3$ [(green) squares), $M=0.18$ [(blue) crosses], and $M=0.11$ [(red) circles], for a given magnetic field $B=0.08$ T and upper hybrid cutoff ${\omega }_c=4.27$. (b) $M=0.6$ [(green) squares], $M=0.4$ [(blue) crosses], and $M=0.25$ [(red) circles] with $B=0.06$ T and cutoff ${\omega }_c=3.21$.

Figure 3

(a) Normalized frequency dependence of both the upper hybrid (UH; solid line) and the lower hybrid (LH; dotted line) waves at $M=0.4$ [(green) squares], $M=0.23$ [((blue) crosses], and $M=0.17$ [(red) circles], for a given magnetic field $B=0.08$ T. (b) Polarization $P$ vs Mach number $M$, for both the UH [solid (green) line] and lower hybrid (LH) (green dotted) waves for a given wave number $ka/\pi =0.6$ and magnetic field strength $B=0.08$ T. (c) Strength of the spring constant $k_z$ vs $f\left(B\right)={{\omega }_{\mathrm{pi}}}^2/{{\omega }_{\mathrm{ci}}}^2$ for the given set of plasma parameters. (d) $P$ vs $M$ for a given wave number $ka/\pi =0.6$ and different magnetic fields: $B=0.08$ T [UH, (green) crosses with solid line; LH, (green) crosses with dotted line] and $B=0.06$ T [UH, (blue) circles with solid line; LH, (blue) circles with dotted line].