Electron cyclotron power losses in fusion reactor-grade tokamaks: Scaling laws for spatial profile and total power loss

Potential importance of electron cyclotron (EC) wave emission in the local electron power balance in the steady-state regimes of ITER operation suggested analyzing in more detail the accuracy of calculating the 1D distribution, over magnetic flux surfaces, of the net radiated power density, Pr. Recent comparison of numeric codes SNECTR, CYTRAN, CYNEQ and EXACTEC for different electron temperature profiles and average temperatures of relevance for fusion reactor-grade magnetoplasmas, has shown good agreement of results within two different tasks: (A) specular reflection in a circular cylinder (SNECTR, EXACTEC) and (B) diffuse reflection in any geometry or any type of reflection in noncircular toroids (SNECTR, CYTRAN, CYNEQ). These tasks were shown to provide, respectively, the lower and upper bounds for Pr, including that for the modulus of Pr, inverted in sign in the plasma column periphery. Here we extend the analysis to show the following approximate scaling laws on the example of calculations with CYNEQ: (i) new formula for the volume-integrated EC power loss, Ptot, which modifies the Trubnikov's formula, suggested for homogeneous electron density and temperature profiles, to the case of Ne and Te profiles typical for ITER and DEMO, and depends both on the volume-averaged values, NeAv and TeAv, and peak values; (ii) universal form of the normalized profile, Pr/Ptot, which appears to depend only on the shape of temperature and density profiles, Te(r)/TeAv and Ne(r)/NeAv ; (iii) similarity of the profile Pr as a function of an effective wall reflection coefficient, which allows for the type of reflection (diffusive or specular) and for the geometry of the vacuum chamber, and is defined to describe the degree of distributing the EC wave ray trajectories over plasma volume and to draw a quantitative parallel between the above-mentioned tasks A and B. (author)