Control of chaotic magnetic fields in tokamaks

Symplectic Maps for Diverted Plasmas

“…A special set of coils, known as the ergodic limiter, have been proposed to create a chaotic layer at the tokamak plasma edge in order to separate the plasma from the wall [4]. Since then different kinds of limiters were installed in tokamaks to control the plasma confinement [12,13,31].…”

Interference of robust tori on the resonance overlap

“…These resonances are called isochronous resonances because all of them have the same order s : r. This is a very important point because we can theoretically introduces as much as resonance chains that we desire to develop the study. Since the distances among these resonances are controlled by the resonance condition, equation (17), and the widths of the separatrices are controlled by the perturbation parameter, α in equation (15) On the other hand if we introduce other terms in the perturbation of equation (15), all only θ 1 -dependent, they can be grouped in such way that a common pre-factor can be put in evidence playing a very interesting role in the dynamics. For instance, if this pre-factor is a polynomial with real roots, it means that the perturbation will be algebraically zero in these roots even when it is turned on.…”

“…The relevance of this study for the field of non-linear dynamics comes from the richness of the dynamics of this toy model and certainly from the results obtained with the Hamiltonian developed above. But our interest is also to give a contribution to the field of plasma physics because this concept of robust tori can be adapted in the Hamiltonian approaches used to confine plasma in Tokamaks since the control of chaotic magnetic fields in Tokamaks is a very important question [17]. It is also well known that there is much instability inside the plasma chamber and many efforts are carried to prolong the time of plasma confinement.…”

Non-twist field line mappings for tokamaks with reversed magnetic shear

“…Since the equilibrium field is axisymmetric, we may set the azimuthal angle, ϕ t = t, as a time-like variable, and put the magnetic field line equations in a Hamiltonian form [19] …”