The potential importance of electron cyclotron (EC) emission in the local electron power balance in the steady state regimes of ITER operation with high temperatures, as well as in the DEMO reactor, requires accurate calculation of the one dimensional (over magnetic surfaces) distribution of the net radiated power density, P EC (ρ). When the central electron temperature increases to ~30 keV, the local EC radiative loss comprises a substantial fraction of the heating power from fusion alphas and is close to the total auxiliary NBI heating power, P EC (0) Ӎ 0.3P α (0) Ӎ P aux (0). In the present paper, the model of EC radiative transport in an axisymmetric toroidal plasma is extended to the case of an inhomogeneous magnetic field B(R, Z). The impact of such inhomogeneity on local and total power losses is analyzed in the framework of this model by using the CYNEQ code. It is shown that, for the magnetic field B, temperature T e , density n e , and wall reflec tion coefficient R w expected in ITER and DEMO, accurate simulations of the EC radiative loss require self consistent 1.5D transport analysis (i.e., one dimensional simulations of plasma transport and two dimen sional simulations of plasma equilibrium). It is shown that EC radiative transport can be described with good accuracy in the 1D approximation with the surface averaged magnetic field, B(ρ) = 〈B(R, Z)〉 ms . This makes it possible to substantially reduce the computational time required for time dependent self consistent 1.5D transport analysis. Benchmarking of the CYNEQ results with available results of the RAYTEC, EXACTEC, and CYTRAN codes is performed for various approximations of the magnetic field.

Abstract.A model is developed to quantitatively interpret the electron cyclotron (EC) spectra in tokamak T-10 at frequencies lower than the first EC harmonic at the plasma edge. The model is based on the almost free propagation and isotropy of EC radiation in between the vacuum chamber wall and the cut-off zone in plasma. The inverse problem for the reconstruction of the velocity distribution function of superthermal electrons (in parallel and perpendicular momenta, and magnetiс flux surfaces at the plasma edge) is formulated and solved. It is shown that in the Ohmic discharges in the tokamak T-10 the superthermal electrons are the trapped particles at the low magnetic field side of toroid. Their mean kinetic energy lies in the range ~ 150-200 keV, and the density fraction is about ~ 10 -4 relative to the main plasma.

Институт физики токамаков НИЦ «Курчатовский институт», Москва, Россия 2 Троицкий институт инновационных и термоядерных исследований, Троицк, РоссияРазработана модель многопроходного поглощения внешнего электронного циклотронного излучения (ЭЦИ) в токамаках, ис-пользуемого для преодоления радиационного барьера (burn-through) на начальной стадии разряда. Модель основана на полу-аналитическом решении задачи переноса ЭЦИ в случае многократного отражения излучения от стенок вакуумной камеры. Проведены оценки эффективности поглощения инжектируемого излучения для характерных значений электронной температу-ры и плотности на начальной стадии разряда в ИТЭР. A model is developed for multi-pass absorption of external electron cyclotron radiation (ECR) in tokamaks, which is used at initial stage of discharge to support the impurity radiation barrier (burn-through). Model is based on a semi-analytical solution of the ECR transport problem in the case of multiple reflection of radiation from the wall of the vacuum chamber. We estimate the efficiency of absorption of injected radiation for typical values of the electron temperature and density at the initial stage of discharge in ITER.Key words: electron cyclotron radiation, tokamak, ITER, multi-pass absorption, initial stage of discharge, ECH-assisted startup of discharge. ВВЕДЕНИЕИз-за технологических особенностей токамака-реактора ИТЭР омический пробой рабочего газа в нём возможен только в узком диапазоне значений давления плазмы и дефектов полоидального магнит-ного поля. В связи с этим для надёжного создания плазмы -преодоления радиационного барьера (burnthrough) -на начальной стадии в ИТЭР планируется использовать уже доказавший свою эффектив-ность электронно-циклотронный (ЭЦ) резонансный нагрев [1][2][3].Особенностью задачи моделирования начальной стадии разряда является, во-первых, то, что пара-метры плазмы на начальной стадии трудно предсказуемы, а для практических расчётов используют эм-пирические базы данных для параметров плазмы сразу после электрического пробоя. Поэтому для прак-тических оценок требуется проведение расчётов в довольно широком диапазоне значений температуры и плотности электронов. Во-вторых, методы расчёта ЭЦ-нагрева холодной разреженной плазмы недос-таточно развиты. Существует область параметров (наиболее холодная и разреженная плазма из числа возможных после пробоя), где ЭЦ-излучение заведомо не поглощается за один проход, а после первого отражения не преобразуется в волну другого типа, поглощаемую целиком на втором проходе.Моделирование начальной стадии разряда в ИТЭР с помощью нульмерного (0D) кода в [4] показа-ло, что в широком диапазоне начальных условий при учёте примесей бериллия для преодоления радиа-ционного барьера необходимо поглощение внешнего ЭЦ-излучения мощностью 3 МВт, для углеродных примесей даже 5 МВт поглощённой мощности ЭЦ-нагрева может оказаться недостаточно для достиже-ния пробоя. Однако в [4] не проводились расчёты эффективности поглощения внешнего ЭЦ-нагрева.Моделирование ЭЦ-нагрева проводилось с помощью кинетических кодов, ...

Radiative Transfer (RT) in a continuous spectrum in plasmas is caused by the emission and absorption of electromagnetic waves (EM) by free electrons. For a wide class of problems, the deviation of the velocity distribution function (VDF) of free electrons from the thermodynamic equilibrium, the Maxwellian VDF, can be neglected. In this case, RT in the geometric optics approximation is reduced to a single transport equation for the intensity of EM waves with source and sink functions dependent on the macroscopic parameters of the plasma (temperature and density of electrons). Integration of this equation for RT of radio-frequency EM waves in laboratory plasmas with highly reflecting metallic walls is substantially complicated by the multiple reflections which make the waves with the long free path the dominant contributors to the power balance profile. This in turn makes the RT substantially nonlocal with the spatial–spectral profile of the power balance determined by the spatial integrals of the plasma parameters. The geometric symmetry of the bounding walls, especially when enhanced by the diffuse reflectivity, provides a semi-analytic description of the RT problem. Analysis of the accuracy of such an approach reveals an approximate self-similarity of the power balance profile and the radiation intensity spectrum in both approximate and ab initio modeling. This phenomenon is shown here for a wide range of plasma parameters and wall reflectivity, including data from various numeric codes. The relationship between the revealed self-similarity and the accuracy of numeric codes is discussed.

It is predicted that in ITER, due to high values of electron temperature and magnetic field strength, electron cyclotron (EC) radiation emitted by plasma will be a significant source (together with external EC radiation injected for auxiliary plasma heating and non-inductive current drive) of additional thermal and electromagnetic loads for microwave and optical diagnostics. The spectral distribution of plasma EC radiation is particularly important to consider in millimeter-wave diagnostics, namely for high- and low-magnetic-field side reflectometry, plasma position reflectometry, and collective Thomson scattering diagnostic, because the transmission lines of these diagnostics yield the transport of EC waves emitted by the plasma. The development of semi-analytical methods used to describe the spectral distribution of plasma-generated EC radiation in tokamaks, starting from the work of S. Tamor, is based on the dominance of multiple reflections of this radiation from the first wall in a toroidal axially symmetric vacuum chamber. Here, we present calculations using the CYNEQ code of the spectral intensity of the EC radiation emerging from the plasma to the first wall and port plugs for five scenarios of ITER operation. This code uses the symmetry-based effect of approximate isotropy and homogeneity of radiation intensity in a substantial part of the phase space and has been successfully tested by comparison with first-principles codes. The energy flux density in the range of 30–200 kW/m2 is predicted for wall reflectance in the range of 0.6–0.95. The possible effect of this radiation on in-vessel components and diagnostics is assessed by calculating the surface density of the energy absorbed by various materials of the ITER first wall.