Estimation of the Stationary Energy Confinement time in Tokamak-plasmas and Assessment of the Dynamic ITER Energy Confinement Time Scalings

The objective of this chapter is to calculate the (stationary) energy confinement time in Tokamak-plasmas with particular emphasis to the assessment of the International Thermonuclear Experimental Reactor (ITER) dynamic energy confinement time scaling. The first part of the chapter is devoted to an estimation of the energy confinement time. The nonlinear thermal balance equation for classical plasma in a toroidal geometry is analytically and numerically investigated including Ion Cyclotron Resonance Heating (ICRH) power. The determination of the equilibrium temperature and the analysis of the stability of the solution are performed by solving the energy balance equation that includes the transport relations obtained by the classical kinetic theory. In the second part of this chapter, we derive the differential equation, which is satisfied by the ITER scaling for the dynamic energy confinement time. We show that this differential equation can also be obtained from the differential equation for the energy confinement time, derived from the energy balance equation, when the plasma is near the steady state. We find that the values of the scaling parameters are linked to the second derivative of the power loss, estimated at the steady state. As an example of an application, the solution of the differential equation for the energy confinement time is compared with the profile obtained by solving numerically the balance equations (closed by a transport model) for a concrete Tokamak-plasma.