International Journal of Modern Physics B, Feb 10, 2007
We solve analytically the out-of-equilibrium initial stage that follows the injection of a radial... more We solve analytically the out-of-equilibrium initial stage that follows the injection of a radially finite electron beam into a plasma at rest and test it against particle-in-cell simulations. For initial large beam edge gradients and not too large beam radius, compared to the electron skin depth, the electron beam is shown to evolve into a ring structure. For low enough transverse temperatures, filamentation instability eventually proceeds and saturates when transverse isotropy is reached. The analysis accounts for the variety of very recent experimental beam transverse observations.
The development of the resistive kink instability into the nonlinear regime is analyzed dynamical... more The development of the resistive kink instability into the nonlinear regime is analyzed dynamically. Two small parameters are involved: the fixed dimensionless resistivity η and the time-dependent amplitude A of the m=1 mode, that measures the amount of nonlinearities in the system. While, for A small, the outer domain is predicted to be ruled by linear ideal magnetohydrodynamic equations, one tracks self-consistently the location of the critical layer and derives the dominant dynamical equations inside it. As A becomes of order η1/2, a nonlinear exponential growth due to a balance between convective and mode coupling terms is predicted for moderately low values of η and the early nonlinear regime below this threshold is quantitatively computed. The nonlinear saturation of the instability should take place for A at most of the order η1/3. This analysis provides a general pattern to model the onset of the nonlinear regime of internal modes.
Transport Theory and Statistical Physics, Jan 10, 2003
... b * & Yves Elskens a pages 399-411. ... The ultimate evolution is intrinsically nonli... more ... b * & Yves Elskens a pages 399-411. ... The ultimate evolution is intrinsically nonlinear, not only if the initial field amplitude is large, as in O'Neil's seminal trapping picture for one wave (O'Neil, [1965]19. O'Neil, TM 1965. Collisionless damping of nonlinear plasma oscillations. Phys. ...
The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanis... more The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.
International Journal of Modern Physics B, Feb 10, 2007
We solve analytically the out-of-equilibrium initial stage that follows the injection of a radial... more We solve analytically the out-of-equilibrium initial stage that follows the injection of a radially finite electron beam into a plasma at rest and test it against particle-in-cell simulations. For initial large beam edge gradients and not too large beam radius, compared to the electron skin depth, the electron beam is shown to evolve into a ring structure. For low enough transverse temperatures, filamentation instability eventually proceeds and saturates when transverse isotropy is reached. The analysis accounts for the variety of very recent experimental beam transverse observations.
The development of the resistive kink instability into the nonlinear regime is analyzed dynamical... more The development of the resistive kink instability into the nonlinear regime is analyzed dynamically. Two small parameters are involved: the fixed dimensionless resistivity η and the time-dependent amplitude A of the m=1 mode, that measures the amount of nonlinearities in the system. While, for A small, the outer domain is predicted to be ruled by linear ideal magnetohydrodynamic equations, one tracks self-consistently the location of the critical layer and derives the dominant dynamical equations inside it. As A becomes of order η1/2, a nonlinear exponential growth due to a balance between convective and mode coupling terms is predicted for moderately low values of η and the early nonlinear regime below this threshold is quantitatively computed. The nonlinear saturation of the instability should take place for A at most of the order η1/3. This analysis provides a general pattern to model the onset of the nonlinear regime of internal modes.
Transport Theory and Statistical Physics, Jan 10, 2003
... b * & Yves Elskens a pages 399-411. ... The ultimate evolution is intrinsically nonli... more ... b * & Yves Elskens a pages 399-411. ... The ultimate evolution is intrinsically nonlinear, not only if the initial field amplitude is large, as in O'Neil's seminal trapping picture for one wave (O'Neil, [1965]19. O'Neil, TM 1965. Collisionless damping of nonlinear plasma oscillations. Phys. ...
The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanis... more The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.
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