ФИЗИКА ПЛАЗМЫ, 2010, том 36, № 10, с. 883-896
= ТОКАМАКИ =
УДК 533.9
BEHAVIORS OF IMPURITY IN ITER PLASMA WITH STANDARD TYPE I ELMY H-MODE AND STEADY-STATE SCENARIOS
© 2010 Y. Pianroj, C. Chuchinda, P. Leekhaphan, and T. Onjun
Sirindhorn International Institute of Technology, Thammasat University, Klongluang, Pathumthani, Thailand Received November 16, 2009; in final form, February 08, 2010
Self-consistent simulations of impurity behaviors in ITER plasmas in standard Type I ELMy H-mode and steady-state scenarios are investigated using 1.5D BALDUR integrated predictive modeling code. In these simulations, the plasma core transports, including electron and ion thermal, hydrogenic and impurity transports are predicted using a linear combination of anomalous and neoclassical transports. An anomalous transport is calculated using a theory-based Multimode (MMM95) model; while the neoclassical transport is calculated using NCLASS model. The temperature and density boundary conditions are described at the top of the pedestal. Two different models for hydrogenic and impurity boundary density conditions are considered. The first model is called a "static boundary density model," in which the hydrogenic and impurity densities at the boundary are fixed. For the second model, called a "dynamic boundary density model," the hydrogenic and impurity densities at the boundary are assumed to be a large fraction of its line-averaged density. For simplicity, the pedestal temperature is assumed to be a constant in all simulations. The combination of a core transport model together with the boundary density models is used to simulate the time evolution of plasma current, temperature, and density profiles for ITER plasmas in standard type I ELMy H-mode and steady-state scenarios. As a result, the behaviors of impurity in ITER plasmas can be investigated. It is found in both ITER scenarios that the total amount of impurity, including beryllium and helium, in plasma core increases rapidly in early state and reaches a steady-state value. The level of impurity content in the steady state depends sensitively on the impurity boundary conditions. The effective charge at the edge is found to be about 1.4 and 1.1 using a static boundary density model and a dynamic boundary density model, respectively. It is also found that the hydrogenic and impurity transports in ITER plasmas for both scenarios is dominated by the kinetic ballooning modes, while the ITG and TEM modes provide the largest contributions for both thermal transports in most of region. In addition, a sensitivity study is carried out to investigate the impacts of pedestal temperature, pedestal density and line-averaged density on the impurity behaviors. It is found that increasing the pedestal temperature results in a reduction of the impurity content. On the other hand, increasing the pedestal density, line-averaged density or impurity influx result in an increase of the impurity content.
1. INTRODUCTION
The concept of magnetically confined thermonuclear fusion using tokamaks has been an interest in scientists and engineers' community for a long period of time because of its potential to provide an environmentally-friendly and cheap energy source. However, scientific and technological feasibility of fusion energy has not yet been demonstrated. Therefore, an international project called the International Thermonuclear Experimental Reactor (ITER) [1] has been initiated. One of the most important concerns in ITER experiments is the behaviors of impurity, in particular the question of an impurity accumulation. It is known that the retention of the helium ash or alpha particles generated from D—T nuclear fusion reaction is inevitable. The accumulation of impurity can result in severe problems, such as fuel dilution, enhancement of core radiation, and degradation of fusion performance [2]. As a result, it is crucial to investigate the impurity behaviors in the ITER plasmas, in particular the issue of impurity accumulation, to increase a possibility to use thermonuclear fusion for energy source of the future.
Impurity accumulation in the confinement-enhanced H-mode plasma, as would be expected in ITER, has been anticipated. In fact, one of primary goals for ITER is to improve the understanding of helium accumulation and to develop a method for enhancement of helium exhaust [3]. Yamada et al. [4] studied the radial distribution of impurity in tokamak and helical system by using 1.5D transport code toroidal transport analysis linkage (TOTAL) to simulate the high-Z impurity from the plasma facing component materials. It was found the critical level of impurity concentration in ITER equals to 4.0% for carbon, 0.1% for iron and 0.008% for tungsten with respect to electron density. Moreover impurity from low-Z materials, such as beryllium and carbon, under bombardment conditions characteristic of magnetic fusion experiment is reviewed in [5]. Several experiments were designed to investigate on this issue and have confirmed an affirmative observation [6]. A comprehensive review of experiments on helium accumulation and exhaust can be found in [6]. Various simulations of ITER cases have also been conducted to study an im-
purity accumulation in ITER, especially that of the helium ash. Burbaumer et al. [7] carried out simulations on ITER-like cases using 1.5D transport code and found that temperature and helium density reach steady-state values under an appropriate burn control system. Recent work by Onjun and Pianroj [8] also indicates quasi-steady-state density of helium, as well as that of carbon. A simple modeling of ITER impurity is also carried out by Leekhaphan and Onjun [9], which reports that the level of steady-state impurity content in ITER with type I ELMy H-mode scenario depends sensitively on the boundary conditions and transport. A more comprehensive integrated modeling of ITER reference scenarios can be found in [10], where various issues concerning ITER operations are addressed. However, impurity behavior studied in the paper focused on the accumulation of helium and beryllium in standard H-mode and steady-state scenario of ITER plasma.
The present study aims to predict, via self-consistent simulations, the plasma profiles, including current, temperature, and density for type I ELMy H-mode and steady-state ITER discharges. In these simulations, the plasma core transport is described using a combination of an anomalous and neoclassical transport. An anomalous transport is calculated using the theory-based multimode (MMM95) model; while the neoclassical transport is calculated using NCLASS model. In addition, the boundary conditions for temperature and density are described at the top of the pedestal. Two different models for hydrogenic and impurity boundary conditions are considered. The first model is called a static boundary model, in which the hydrogenic and impurity densities at the edge are fixed. Consequently, the edge effective charge is constant. In the second model, hydrogenic and impurity densities are assumed to be a large fraction of its line-averaged density. As a result, the hydrogenic and impurity densities (as well as edge effective charge) are varied. For the pedestal temperature, it is assumed to be a constant. With these simulations, the behaviors of impurity in ITER plasmas can be studies. In addition, a parametric sensitivity study is carried out to determine the impacts of pedestal temperature, pedestal density, line-averaged density and impurity influx on the impurity behaviors, mainly on the impurity transport and accumulation.
This paper is organized as follows: brief descriptions of relevant components of the BALDUR code, including the anomalous transport are given in Section 2; the prediction of ITER plasma profiles for standard type I ELMy H-mode and steady-state scenarios are presented and discussed in Section 3; sensitivity analysis is found in Section 4; and a summary is given in Section 5.
2. BALDUR INTEGRATED PREDICTIVE MODELING CODE
The BALDUR integrated predictive modeling code [11] is a 1.5-dimensional transport code designed to simulate a wide variety of plasma conditions in tokamaks. The BALDUR code follows the time evolution of electron and ion temperatures, charged particle densities, and the poloidal magnetic flux density as a function of magnetic flux surface. The shapes of the flux surfaces are determined by solving axisym-metric equilibrium force balance equations, given boundary conditions that may be changing with time. BALDUR provides a detailed and self-consistent treatment of neutral hydrogen and impurity transport, multi-species effects, several forms of auxiliary heating, fast alpha particles and fusion heating, plasma compression effects, ripple losses, and scrape-off layer. In addition, there are various options available to treat the axisymmetric effects of large scale instabilities such as sawtooth oscillations, saturated tearing modes, and high-n ballooning modes. Various physical processes incorporated in the code are: transport, plasma heating, helium influx, boundary conditions, plasma equilibrium shape and sawtooth oscillations. The models for each process are combined to self-consis-tently solve for plasma properties. BALDUR code predicts fusion heating and helium ash accumulation via the nuclear fusion rate, coupled with Fokker— Planck package used to calculate the slowing down of the spectrum of fast alpha particles on each flux surface. Also the fusion heating component of the BAL-DUR code calculates the production rate of thermal helium ions and the rate of the depletion of deuterium and tritium ions within the plasma core. The basic diffusion equations solved in BALDUR in Gaussian units are:
djn = dd (rF«) + S» a = 1'2'/' h>
dt r dr
si=id j Q j='• «•
SB, = £ araCA(„/
dt 4ndr \_r dr J dr where na is the number density of species a, Ej is the energy density of thermal ions or of electrons, and Be
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