# Solar Wave Theory Group

## Magneto-hydrodynamic waveguides

### Magnetic slab

The 3-dimensional propagating mode solutions of the linearized MHD equations in symmetric or asymmetric slab waveguides for sausage and kink modes can be accessed in the menu on the right.

The visualizations are based on the analytical solutions of propagating waves in slab waveguides obtained by Roberts (1981) (symmetric magnetic slab) and Allcock and Erdélyi (2017) (asymmetric magnetic slab).

For the symmetric slab the following parameters are used:

$c_0 = 1, \: c_e = 1.2, \: v_A = 0.9, \: \beta_0 = 1.481 \: (v_A = 1.3, \: \beta_0 = 0.710 \text{ for fast surface modes}), \: \frac{\rho_e}{\rho_0} = 2, \: \frac{p_e}{p_0} = 2.88$.

For the asymmetric slab the following parameters are used:

$c_0 = 1, \: c_1 = 1.231, \: c_2 = 1.2, \: v_A = 0.9, \: \beta_0 = 1.481 \: (v_A = 1.3, \: \beta_0 = 0.710 \text{ for fast surface modes}), \\ \frac{\rho_1}{\rho_0} = 1.9, \: \frac{\rho_2}{\rho_0} = 2, \: \frac{p_1}{p_0} = \frac{p_2}{p_0} = 2.88.$

The parameters in this section are defined as:

 $x_0$ - Half the slab width, $v_{ph}$ - Phase speed, $c_0, c_1, c_2$ - Sound speed inside/left of/right of the slab, $v_A$ - Alfvén speed inside the slab, $c_{T}$ - Internal tube speed, $\rho_{0},\rho_{1}, \rho_{2}$ - Plasma density inside/left of/right of the slab, $p_0,p_1, p_2$ - Gas pressure inside/left of/right of the slab, $B_{0}$ - Magnetic field strength inside the slab, $\beta_{0}$ - Plasma beta inside the slab.

For a symmetric slab, the external plasmas have equal parameters, that is, $c_1 = c_2 = c_e$ and similar for $\rho$ and $p$. 