The important goal of adding to the bootstrap current a more flexible tool, capable of producing and controlling steady-state profiles with a high fraction of non-inductive plasma current, could be reached using the lower hybrid current drive (LHCD) effect. Experiments performed on FTU (Frascati Tokamak Upgrade) demonstrated that LHCD can occur at reactor-graded high plasma density, provided that the parametric instability (PI)-produced broadening of the spectrum launched by the antenna is reduced under proper operating conditions, capable of producing relatively high temperature in the outer region of plasma column. This condition was produced by operations that reduce particle recycling from the vessel walls, and enhance the gas fuelling in the core by means of fast pellet. New results of FTU experiments are presented documenting that the useful effect of temperature at the periphery, which reduces the LH spectral broadening and enhances the LH-induced hard-x ray emission level, occurs in a broader range of plasma parameters than in previous work. Modelling results show that a further tool for helping LHCD at a high density would be provided by electron cyclotron resonant heating of plasma periphery. New information is provided on the modelling, able determining frequencies, growth rates and LH spectral broadening produced by PI, which allowed assessing the new method for enabling LHCD at high densities. Further robustness is provided to theoretical and experimental fundaments of the method for LHCD at a high density.

In order to reach high luminosity, the Future Circular e + e − Collider will need very intense beams with small emittances and small beta functions in the interaction points. This is achieved with a large Piwinski angle combined with the crab waist collision scheme. Under these conditions, the luminosity and the beam-beam tune shifts are strongly influenced by the bunch length. On the other hand, in this machine, the beamstrahlung effect is dominant too, leading to an increase of bunch length and energy spread. Moreover, due to the extreme beam parameters, new important beam-beam instabilities have been found, such as the socalled coherent X-Z instability. Finally, the bunch length and energy spread are also affected by collective effects. In this paper, we study the beam-beam interaction, by focusing on the X-Z instability for FCC-ee, in the lowest energy configuration (45.6 Gev, Z-resonance), by taking into account, self-consistently, the combined effects of beamstrahlung and the machine impedance model that has been evaluated so far. Finally, we also discuss some possible mitigation methods.

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