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.