normally in fluid ( water) with cylindrical symmetry, can produce transverse modes by using a oscillatory object at given local region. as i understand that in these system , particles move in z- direction having the velocity shear in the radial direction that resulted the transverse mode. it may be true or false. similar to this,
in d.c. discharge plasma, ions are streaming toward the cathode sheath edge. if there is no perturbation then at given height or location in the sheath edge, ions have same velocity. therefore, no shear or force in radial direction. but in the case when we perturbed the local sheath edge by a cylindrical symmetric object then the situation is more complex. since, object radii (r) is greater then the debye length of electron and ions, so that the screening region radius is in mm. this object having its own sheath around it. ( ions with radial and -z direction velocity). now, my question is that is it possible that ions outside the screening region and inside the screening region having diff. velocity component( z - component).? at the cathode sheath edge, ions are streaming and ions which are not affected by object ( outside the screening length) have same velocity but ions which affected by the object ( inside the screening region of object) streaming with less velocity.is there a possibility for velocity shear starts from sheath edge of object to object ( shear length is screening length)? . if shear is produced then is it excite the modes? please give your comments on the given query.
Dear Mangilal,
I guess the answer is No.
Generally speaking, in fact, the existence of shear forces depends on the structure of the stress tensor. Now, as far as I understand no magnetic field occurs in your problem, so all stresses in your system are of purely mechanical origin. Moreover, the set-up of your experiment includes no source of angular momentum. Accordingly, I am allowed to suppose the initial value of the total angular momentum is exactly zero at all times. It follows that the stress tensor is symmetrical, hence angular momentum is conserved and no shear force may conceivably arise.
To put it in other words, should any shear force arise your d.c. discharge plasma could be the source of angular momentum ex nihilo, i.e. a perpetuum mobile: you should be able to measure a net torque on the wall of your discharge chamber as soon as you switch on the power. But this would violate the symmetry properties of the Poisson's equation of electrostatics, as the direction of the torque would depend on the relative position of the electrodes.
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