# Solar Wave Theory Group (SWAT)

## 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 were 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 symbols in the dispersion diagrams and in general in this site are:

$r_a$ The flux tube radius.

$v_{ph}$ Phase speed.

$c_0$ Sound speed inside the flux tube, i.e. $r < r_a$.

$c_e$ Sound speed outside the flux tube, $r > r_a$.

$v_A$ Alfvén speed inside the flux tube.

$v_{Ae}$ External Alfvén speed.

$c_k$ Kink speed.

$c_{T}$ Internal tube speed.

$c_{Te}$ External tube speed.

$\rho_{0}$ Plasma density inside the flux tube.

$\rho_{e}$ Plasma density outside the flux tube.

$p_0$ Gas pressure inside the flux tube.

$p_e$ Gas pressure outside the flux tube.

$B_{0}$ Magnetic field strength inside the tube.

$B_{e}$ Magnetic field strength outside the tube.

$\beta_{0}$ Plasma beta inside the tube.

$\beta_{e}$ Plasma beta outside the tube.