Calculations of energy losses due to atomic processes in tokamaks with applications to the International Thermonuclear Experimental Reactor divertor

Abstract

Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many processes. In order to identify the key features of these experiments and calculations and the relative role of the primary atomic processes, simple quasianalytic models and the latest atomic physics rate coefficients and cross sections have been used to assess the relative roles of central radiation losses through bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange and hydrogen radiation losses from the scrape-off layer and divertor plasma and impurity radiation losses from the divertor plasma. This anaysis indicates that bremsstrahlung from the plasma center and impurity radiation from the plasma edge and divertor plasma can each play a significant role in reducing the power to the divertor plates, and identifies many of the factors which determine the relative role of each process. For instance, for radiation losses in the divertor to be large enough to radiate the power in the divertor for high power experiments, a neutral fraction of 10 -3 to 10 -2 and an impurity recycling rate of n e τ recycle of 10 16 s m -3 will be required in the divertor.

Calculation and experimental test of the cooling factor of tungsten

“…Anyhow, the cooling factor for the case of negligible transport as presented in figure 3 is not valid at the edge of a fusion plasma (approximately below a few hundred eV, depending on the device). It may be noted that the occurence of such effects and their implications on the cooling factor have been investigated in [10]. In , which denotes the cooling factor only for radiation due to recombination including Bremsstrahlung and the mean charge of the ionization equilibrium for different electron temperatures.…”

“…Still, the radiative cooling by W is a concern and the maximum tolerable W concentration is an important value for ITER and a future fusion reactor. This value, however, is based on calculations of the cooling factor [9,10] using the average ion model, a model which does not calculate quantummechanical wave functions of the levels in each ion, but uses scale formulas based on a hydrogenic orbital model. In this work, the Cowan code [11] is used for level resolved calculations in order to calculate a cooling factor based on more detailed atomic physics.…”

Transport analysis of high radiation and high density plasmas in the ASDEX Upgrade tokamak

“…This model solves the time-dependent ionization equations as the sum of bremsstrahlung, line radiation, recombination and ionization contributions [10]. Hereby the so-called cooling factors L z (T e ) [11], yielded by the Atomic Data and Structure Analysis (ADAS) database [12] are used. As illustrated in Fig.…”

High-Z plasma facing components in fusion devices: boundary conditions and operational experiences

“…The maximum tolerable values are 3¡ 0 10 [49,50]. using the radiation loss parameters of [49,50]. The fitted exponent should only serve as a guideline for the overall trend of the limit, since for high-Z elements, which are not fully ionised around the working point of the fusion reactor, the ionisation equilibria and the radiation will depend on the detailed structure of the ion.…”

“…Increasing their fraction, the operational window narrows quickly until there is finally no steady state solution at all. The maximum tolerable values are 3¡ 0 10 [49,50]. using the radiation loss parameters of [49,50].…”