Search

The famous Hill’s solution describing a spherical vortex with nested toroidal pressure surfaces, bounded by a sphere, propelling itself in an ideal Eulerian fluid, is re-derived using Galilei symmetry and the Bragg–Hawthorne equations in spherical coordinates. The correspondence between equilibrium Euler equations of fluid dynamics and static magnetohydrodynamic equations is used to derive a generalized vortex type solution that corresponds to dynamic fluid equilibria and static plasma equilibria with a nonzero azimuthal vector field component, satisfying physical boundary conditions. Separation of variables in Bragg–Hawthorne equation in spherical coordinates is used to construct further new fluid and plasma equilibria with nested toroidal flux surfaces, featuring respectively boundary vorticity sheets and current sheets. Finally, the instability of the original Hill’s vortex with respect to certain radial perturbations of the spherical flux surface is proven analytically and illustrated numerically.

Abstract: We hereby present results on ion acceleration mechanisms in non equilibrium plasmas generated by microwaves or high intensity laser pulses. Experiments point out that in magnetized plasmas X–B conversion takes place for under resonance values of the magnetic field, i.e. an electromagnetic mode is converted into an electrostatic wave. The strong self-generated electric field, of the order of 107 V/m, causes a E × B drift which accelerates both ions and electrons, as it is evident by localized sputtering in the plasma chamber. These fields are similar (in magnitude) to the ones obtainable in laser generated plasmas at intensity of 1012 W/cm2. In this latter case, we observe that the acceleration mechanism is driven by electrons drifting much faster than plasma bulk, thus generating an extremely strong electric field ∼107 V/m. The two experiments confirm that ions acceleration at low energy is possible with table-top devices and following complementary techniques: i.e. by using microwave-driven (producing CW beams) plasmas, or non-equilibrium laser-driven plasmas (producing pulsed beams). Possible applications involve ion implantation, materials surface modifications, ion beam assisted lithography, etc. [Copyright &y& Elsevier]