The goal of this chapter is to compute the (stationary) energy confinement time in Tokamak-plasmas, with a focus on evaluating the International Thermonuclear Experimental Reactor (ITER) dynamic energy confinement time scaling. The first section of the chapter is devoted to calculating the energy confinement time. The nonlinear thermal balance equation for classical plasma in a toroidal geometry is explored analytically and numerically, taking into account the power of Ion Cyclotron Resonance Heating (ICRH). The equilibrium temperature and the stability of the solution are determined by solving the energy balance equation, which includes the transport relations obtained from classical kinetic theory. In the second section of this chapter, we develop the differential equation for the dynamic energy confinement time that is satisfied by the ITER scale. When the plasma is near the steady state, we show that this differential equation may also be obtained from the differential equation for the energy confinement time, which is derived from the energy balance equation. We discover that the scaling parameter values are related to the second derivative of the power loss, as assessed at steady state. In one application, the solution of the differential equation for the energy confinement period is compared to the profile obtained by numerically solving the balancing equations (closed by a transport model) for a specific Tokamak-plasma.
Author(S) Details
Giorgio Sonnino
Université Libre de Bruxelles (U.L.B.), Faculté de Sciences, Campus de la Plaine C.P. 231 Brussels, Belgium and Royal Military School (RMS), Av. de la Renaissance 30 1000 Brussels, Belgium.
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