Improved calculation of synchrotron radiation losses in realistic tokamak plasmas

Abstract

Owing to the complexity of the exact calculation, synchrotron losses are usually estimated in system studies, with expressions derived from a plasma description using simplifying assumptions on the geometry, radiation absorption, and density and temperature profiles. In the present article, a complete formulation of the transport of synchrotron radiation is performed for realistic conditions of toroidal plasma geometry with elongated cross-section, using a quasi-exact method for the calculation of the absorption coefficients, and for arbitrary shapes of density and temperature profiles. The effects of toroidicity and temperature profile on synchrotron radiation losses are analysed in detail. In particular, when the electron temperature profile is almost flat in the plasma centre as, for example, in internal transport barrier confinement regimes, synchrotron losses are found to be much stronger than in the case where the profile is represented by its best generalized parabolic approximation, though both cases give approximately the same thermal energy content. Such an effect is not included in presently used approximate expressions. As an illustration, it is shown that in the case of an advanced high temperature plasma envisaged for a steady state commercial reactor, synchrotron losses represent approximately 20% of the total losses, so that this term becomes significant in the power balance of such a plasma. Finally, the authors propose a seven variable fit for the fast calculation of synchrotron radiation losses. This fit is derived from a large database which has been generated using a code implementing the complete formulation, and is optimized for massively parallel computing.1 Unless otherwise indicated, all units are SI in the present article except for the temperature, which is always expressed in keV (k 1.6022 × 10 −16 J/keV).

Simulation and Analysis of the Hybrid Operating Mode in ITER

“…The analysis used for hybrid operating point calculations incorporates the plasma power and particle balance, Bosch-Hale fusion reactivity [9], Post-Jensen coronal equilibrium radiation model [10], Albajar cyclotron radiation model [11], Hirshman and Neilson flux consumption formulation [12], in addition to several other global parameter relations. In particular, the ITER98(y,2) scaling is assumed for the global energy confinement time.…”

Fusion-Fission Research Facility (Ffrf) as a Practical Step Toward Hybrids

“…The sensitivity of LiWF regime to the synchrotron radiation can be utilized purposely in FFRF for controlling the electron temperature. (Because of importance of synchrotron radiation, more accurate simulations should be performed in future using more accurate numerical models, also available for ASTRA [16]) . As a result of synchrotron radiation and NBI fueling, in all analyzed FFRF plasma regimes, the ion temperature is higher than electron temperature.…”

RAYTEC: a new code for electron cyclotron radiative transport modelling of fusion plasmas

“…Specific issues addressed are to which extent geometry effects by themselves (i) are able to reduce the anisotropy of the emitted radiation, (ii) affect the profile of the net emitted EC wave power density dP/dV, and (iii) influence the total EC power P EC lost from the plasma. In the context of the investigations on the latter two questions, also the appropriateness of simpler models, viz., CYTRAN [4], EXACTEC [10] and a slightly modified Trubnikov formula [2,6] applied locally (to be referred to as LATF; see Appendix for details), was tested; as for the total EC power P EC , also the formula given by Albajar et al [3] and that proposed by Fidone et al [14] were considered. For these studies, ITER-like parameters have been adopted.…”

“…The estimation of the level of EC wave emission in system and 1D transport studies is usually carried out by using approximate models based on expressions for the global EC emission, see, e.g., Refs. [2,3] or routines like CYTRAN [4] and CYNEQ [5] which, to some extent, incorporate wave transport effects, but assume isotropy of the radiation field.In order to improve the modelling capability for the profile of the net EC wave power density dP/dV locally emitted (or absorbed), as a first step, recently the accuracy of the Trubnikov [6] and Robinson [7] formulae for the wave absorption coefficients was analyzed [8] and their practical suitability for calculating dP/dV was investigated [9], adopting the code EXACTEC which is based on an exact solution of wave transport for straight rays in a cylindrical plasma with circular cross section and specular wall reflection [10]. As a result, Robinson's formula was found to provide, overall, both good accuracy and numerical efficiency in modelling hot fusion plasmas.…”