on the nature of kink mhd waves, vorticity and compressibility versus restoring forces

In order to study the nature of kink mhd waves, zero beta plasma in a thintwisted magnetic-flux tube is considered. we use two parameters, the ratio of restoringforces and the ratio of the parallel vorticity to the compressibility to study the effect ofmagnetic twist on the nature of kink waves. our aim is to invstigate whether the natureof the wave obtained from studying these two parameters are the same or not. thetwo parameters give two different twist parameters in which the wave becomes purelyalfvénic. the first parameter indicates that both in the internal and external regionsof the tube, the wave can become purely magnetoacostic but the second parameterindicates that the wave can become magnetoacostic only in the external region of thetube. our conclusion is that the two parameters are not equivalent for determining thenature of the wave.