Abstract
Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can ensure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integrable Hamiltonian of the individual particles, hinting at some stability of the confinement when considering a toroidal geometry in the large aspect ratio limit.
Highlights
Insuring confinement of a hot plasma using a magnetic field, is one of the key issues to sustain in order to achieve magnetically confined fusion reactors
We find out that in this setting no hyperbolic point emerges when looking at the effective potential driving the motion, meaning that in these type of cylindrical configurations, we do not expect a breaking of the magnetic moment when going back to a toroidal geometry due to separatrix crossings such as the one displayed in [7] or the presence of Hamiltonian chaos due to this mechanism [7,8,9,10,11]
We built self-consistent solutions of the Vlasov equation in a cylindrical magnetized plasma, these solutions correspond to a thermodynamic equilibrium of a non self-consistent “passive”
Summary
Insuring confinement of a hot plasma using a magnetic field, is one of the key issues to sustain in order to achieve magnetically confined fusion reactors. In these regards the emergence of a transport barrier that gives rise to the so-called H-mode has been a key ingredient in the design of most recent machines [1,2]. This paper is organized as follows: in the first part we present the idealized configuration and the passive particle thermal equilibrium from [6], building from this we discuss the self-consistent approach with one species, and move on to a real full self-consistent solution with two species
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