Dust-acoustic shocks in strongly coupled dusty plasmas

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.

Figure 1

Real (positive, upper curves) and imaginary (negative, lower curves) parts of the linear dispersion relation for dust-acoustic waves in both (a) weakly and (b) strongly coupled dusty plasmas. Here we have $n_{i0}=5\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{e0}=3.3\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{d0}=1\times {10}^{11}{\mathrm{m}}^{-3}$, $Z_d=1700$, $k_B{T}_i=0.05\mathrm{eV}$, and $k_B{T}_e=2.5\mathrm{eV}$.

Figure 2

Shock solution to Burgers's equation for the three different models. Here we have $n_{i0}=5\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{e0}=3.3\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{d0}=1\times {10}^{11}{\mathrm{m}}^{-3}$, $Z_d=1700$, $k_B{T}_i=0.05\mathrm{eV}$, $k_B{T}_e=2.5\mathrm{eV}$, $\eta \approx 0.23$, and $\tilde{U}=0.1$.

Figure 3

Shock solution to Burgers's equation for different dissipation coefficients. Here we have $n_{i0}=5\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{e0}=3.3\times {10}^{14}{\mathrm{m}}^{-3}$, $n_{d0}=1\times {10}^{11}{\mathrm{m}}^{-3}$, $Z_d=1700$, $k_B{T}_i=0.05\mathrm{eV}$, $k_B{T}_e=2.5\mathrm{eV}$, and $\tilde{U}=0.1$.

Figure 4

Shock originating in Region A, propagating in Region B.

Figure 5

Contour plots of a shock which is a solution to Burgers's equation for Region A. Plot (a) shows that the shock is stable in Region A, whereas plot (b) shows that if this shock is propagating in Region B its width increases with time.

Figure 6

Shock originating in Region B, propagating in Region A.

Figure 7

Contour plots of a shock which is a solution to Burgers's equation for Region B. Plot (a) shows that the shock is stable in Region B, whereas plot (b) shows that if this shock is propagating in Region A its width decreases with time.