Sumários

Transport theory 3

17 dezembro 2020, 16:00 Paulo Rodrigues

Simple applications of transport theory: Temperature profile relaxation for uniform and localised heat sources and discussion of the results. Brief and qualitative introduction to the turbulent transport in tokamaks: The physical mechanism of the Ion-Temperature Gradient (ITG) instability; The energy cascade from large (machine-size) to small (Larmor radius) scales; The suppressing role of sheared flows; The multiscale nature of the problem and the need for a more detailed description (gyrokinetic) of transport in fusion plasmas.


Transport theory 2

15 dezembro 2020, 17:00 Paulo Rodrigues

Estimation of diffusion coefficients and transport timescales: Random-walking processes and their associated diffusivity; Collisions between particles in gyromotion and the different scalings of particle and thermal transport; Comparison of estimated diffusivities and their experimental values. Neoclassical effects on transport: Collisions between particles in guiding-centre orbits and their consequences; Toroidal canonical momentum, estimation of the diffusion coefficient, and the differences caused by different orbit topologies (passing or trapped); Calculation of the trapped-particle fraction in a tokamak; Comparison of estimated neoclassical diffusion coefficients with experimental values. 


Transport theory 1

10 dezembro 2020, 16:00 Paulo Rodrigues

Transport in a 1D cylindrical plasma: assumptions and orderings. Derivation of a coupled set of three diffusion equations for the particle-number density, temperature, and magnetic field. Discussion of the different diffusion coefficients, their relation with the resistivity, and physical implications.


Tokamak 4 (online class)

3 dezembro 2020, 16:00 Paulo Rodrigues

Assessing the operational space for tokamaks: which is the highest beta stably attainable for a given plasma current? The interplay of the equilibrium beta limit and the Kruskal-Shafranov limit; The empirical Troyon beta limit, its dependences on plasma geometry and profile shape, and the optimised elongated plasma cross section; Qualitative discussion of the vertical-displacement instability in elongated plasmas and its mitigation.


Tokamak 3

26 novembro 2020, 16:00 Paulo Rodrigues

Stability assessment using the simplified surface-current model: Harmonic-type solution for the perturbations, poloidal and toroidal mode numbers; Matching at the plasma-vacuum interface; The eigenvalue problem written in terms of the safety factor q, poloidal and toroidal mode numbers; The stability condition q>1 and  Kruskal-Shafranov stability limit for the plasma current.