# Solar Wave Theory Group

## Magneto-hydrodynamic waveguides

### Magnetic Flux Tube

The 3-dimensional standing mode solutions of the linearized MHD equations in a cylindrical geometry for sausage, kink and fluting modes for upto $n=6$, can be seen to the right. The visualizations are based on the solutions obtained by Edwin and Roberts (1983).

Here, $n$ is the azimuthal wave number. For all cases the following parameters are used:

$c_0 = 1, \: v_A = 2, \: v_{Ae} = 5, \: \frac{\rho_e}{\rho_0} = 0.21, \: \frac{p_e}{p_0} = 0.05$ $, \: \frac{B_e}{B_0} = 1.1456, \: \beta_0 = 0.3, \: \beta_e = 0.0114$.

The parameters in a magnetic flux tube waveguide are defined as:

 $r_a$ - Flux tube radius. $v_{ph}$ - Phase speed, $c_0, c_e$ - Sound speed inside/outside the flux tube, $v_A,v_{Ae}$ - Alfvén speed inside/outside the flux tube, $c_k$ - Kink speed, $c_{T},c_{Te}$ - Internal/external tube speed, $\rho_{0},\rho_{e}$ - Plasma density inside/outside the flux tube, $p_0,p_e$ - Gas pressure inside/outside the flux tube, $B_{0},B_{e}$ - Magnetic field strength inside/outside the tube, $\beta_{0},\beta_{e}$ - Plasma beta inside/outside the tube. 