In the presence of an external gravitational potential, stability conditions for local helical instabilities and quasi-helical instabilities, which occur in a cylindrical plasma with a constant pitch of the magnetic field, are derived by using the energy integral. A dispersion relation and growth rates of quasi-helical modes are obtained analytically from the equation of motion with a method
Even if Suydam's condition is satisfied, quasi-helical instabilities occur and have the maximum growth rate only for κ·B>O, where κ and B are the wavevector of the perturbation and the magnetic field, respectively.
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