The influence of the magnetic topology on transport and stability has been investigated in four stellarators: an almost shearless medium size flexible heliac (TJ-II), a medium size and a large heliotron (CHS and LHD) with shear, and a quasihelically symmetric device (HSX) with moderate shear. All of these have variable rotational transform profiles and magnetic ripples. Using these capabilities, bifurcated states can appear and plasma can jump from one to another with subsequent changes in the transport properties. Low rational values of ι/2π can create transport barriers in LHD and TJ-II when they are located close to the plasma core or at the edge. The key ingredient for transport barriers is a positive and sheared electric field. Internal transport barriers also appear in CHS, but the role of rationals is not clear yet in this device. The time evolution of the electric field shows the onset of a bifurcation triggered either by the rational or by the presence of the ion and electron roots. The electric potential inside ITBs follows the ECE-temperature profile in a fast time scale. The plasma stability properties and its effect on the viscosity are also studied in the HSX, and the influence of the dynamics of rational surface is studied in the LHD and TJ-II stellarators.
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