ФИЗИКА ПЛАЗМЫ, 2011, том 37, № 4, с. 350-366
= ТОКАМАКИ
УДК 533.9
PELLET INJECTION IN H-MODE ITER PLASMA WITH PRESENCE OF INTERNAL TRANSPORT BARRIERS © 2011 г. P. Leekhaphan and T. Onjun*
School of Bio-Chemical Engineering and Technology, Sirindhorn International Institute of Technology, Thammasat University, Klongluang, Pathumthani, Thailand * School of Manufacturing Systems and Mechanical Engineering, Sirindhorn International Institute of Technology, Thammasat University, Klongluang, Pathumthani, Thailand Поступила в редакцию 19.01.2010 г.
The impacts of pellet injection in ITER type-I ELMy H-mode plasma with the presence of ITB are investigated using self-consistent core-edge simulations of 1.5D BALDUR integrated predictive modelling code. In these simulations, the plasma core transport is predicted using a combination of a semi-empirical Mixed B/gB anomalous transport model, which can self-consistently predict the formation of ITBs, and the NCLASS neoclassical model. For simplicity, it is assumed that toroidal velocity for roExB calculation is proportional to local ion temperature. In addition, the boundary conditions are predicted using the pedestal temperature model based on magnetic and flow shear stabilization width scaling; while the density of each plasma species, including both hydrogenic and impurity species, at the boundary are assumed to be a large fraction of its line averaged density. For the pellet's behaviors in the hot plasma, the Neutral Gas Shielding (NGS) model by Milora-Foster is used. It was found that the injection of pellet could result in further improvement of fusion performance from that of the formation of ITB. However, the impact of pellet injection is quite complicated. It is also found that the pellets cannot penetrate into a deep core of the plasma. The injection of the pellet results in a formation of density peak in the region close to the plasma edge. The injection of pellet can result in an improved nuclear fusion performance depending on the properties of pellet (i.e., increase up to 5% with a speed of 1 km/s and radius of 2 mm). A sensitivity analysis is carried out to determine the impact of pellet parameters, which are: the pellet radius, the pellet velocity, and the frequency of injection. The increase in the pellet radius and frequency were found to greatly improve the performance and effectiveness of fuelling. However, changing the velocity is observed to exert small impact.
1. INTRODUCTION
Magnetically confined thermonuclear fusion concept, such as tokamak, has long been explored as an environmentally-friendly and cheap source of energy. However, its scientific and technological feasibility has not been demonstrated. Therefore, an international project called 'the International Thermonuclear Experimental Reactor (ITER)' has been initiated [1]. Of its particular interest is the high-confinement mode (H-mode) operation due to its great enhancement of plasma performance. The plasma performance in H-mode plasma can be further improved by a formation of internal transport barriers (ITBs) [2] due to a steepening of the temperature gradient in the plasma core profiles. In addition, an effective reactant fuelling method must be developed for ITER since ITER is expected to be the first tokamak able to confine fusion pulse for approximately 1 h. In general, the plasma fuelling can be achieved either by conventional gas puffing or by pellet injections [3]. Although the conventional gas puffing is a simple and somewhat effective method for plasma fuelling, it relies solely on the thermal and particle transports, which are often hindered in the plasma core. On the other hand, the pellet injection relies on the high momentum of frozen hydrogen-
ic pellets to penetrate into the hot plasma. Therefore, pellet injection is considered a more efficient and effective fuelling scheme [4, 5]. Besides, the fuelling aspect, pellet injection can also be used to increase the peaking of the density profile to increase the nuclear fusion reaction rate [5]. As a result, it is crucial to investigate the interactions of pellet and ITB in H-mode plasma, especially impacts on fuelling and fusion performance.
Extensive theoretical and experimental investigation of pellet injection in high-temperature plasma has been carried out in recent years [6—13]. Once a pellet is injected into the hot plasma, it is exposed to the energy fluxes from the energetic particles, resulting in the ablation of the pellet. The rate is determined by the energy flux available and the flux required to remove the particles from the pellet surface, dissociate, ionize and accelerate them [12]. The review of the study of pellet injection can be found in [6]. Although pellet injection in ITB plasma offers the potential for improved performance, it was unclear whether the ITB would survive the injection of frozen pellets [14]. Therefore, several experiments were designed to study pellet injection in ITB plasma. The experimental investigation of pellet injection in JET plasma with ITB are described
Table 1. Notations used in this paper
Symbol Units Description Symbol Units Description
Pellet surface erosion rate q Safety factor
rP mm Effective initial pellet radius s Magnetic shear
ap Ablatant atomic number ®E x B Shearing rate
nm m-3 Molecular density of solid hydrogen Yitg W rr tot,avg MJ Linear growth rate Averaged stored plasma energy
R m Major radius Er Radial electric field
r m Minor radius V Poloidal flux
P Normalized minor radius vth m/s Electron thermal velocity
Pi Ion gyro-radius ve m/s Poloidal velocity
xb m2/s Thermal transport coefficient with Bohm scaling Z e Ion charge number Elementary charge
xgB m2/s Thermal transport coefficient with gyro-Bohm scaling Pi P Pa Pa Ion pressure Plasma pressure
xi m2/s Ion thermal transport coefficient Jp MA Plasma current
Xe m2/s Electron thermal transport coefficient ac Normalized critical pressure gradient of ballooning mode
Dh m2/s Hydrogenic particle transport coefficient Z ^eff,edge P a,avg MW Edge effective charge Averaged a-heating power
Dz m2/s Impurity particle transport coefficient P 1 a,total P * aux MW MW Total a-heating power Auxiliary heating power
BT Tesla Vacuum toroidal magnetic field at R n l nped 1020 m-3 1020 m-3 Line-averaged density Pedestal density
Be Tesla Poloidal magnetic field ni 1019 m-3 Ion density
Tesla Toroidal magnetic field ne 1019 m-3 Electron density
S95 Plasma triangularity at 95% flux surface nD nT 1019 m-3 1019 m-3 Deuterium density Tritium density
K95 Plasma elongation at 95% flux surface nHe nBe 1018 m-3 1018 m-3 Helium density Beryllium density
T keV Ion temperature Subscript
T e keV Electron temperature 0 Centre
a m Plasma minor radius ped Pedestal
in [15, 16]. It was found that pellet injection from the low-field neither penetrates deeply into the plasma nor alters the ITB. On the other hand, pellet injection from the high-field side could fuel the core plasma, but the ITB is destroyed in the process. Garzotti et al. [14] attempted to simulate the same event using JETTO, TRB, and CUTIE codes, each yielding different results. As plasma parameters of JET and ITER are fundamentally different, the interaction between pellet injection and ITB in JET may not necessarily translate to ITER. A preliminary simulation result of pellet injection in ITER-like cases with ITB may be found in [17], where it was found that ITB formation depends strongly on pellet penetration depth, but the ITB itself is not destroyed as is the case for JET plasmas.
The present study aims to study the impacts of pellet injection in type-I ELMy H-mode ITER plasma with ITB via self-consistent simulations using BAL-DUR integrated predictive modelling code. Note that a similar study of pellet injection in non-ITB ITER plasma using BALDUR code was described by Wisit-sorasak and Onjun in [13]. In this work, the Neutral Gas Shielding (NGS) model by Milora-Foster [18] is incorporated to describe the dynamics of pellet injection. It is worth mentioning that the NGS model is not a complete pellet model since several effects, such as VB drift effects, are not included. However, it is believe that the combination of core transport and pellet model is sufficient to provide an inside understanding of impacts of the pellet on plasma with the presence of ITB. A series of deuterium pellets with the radius and velocity of 2.0 mm and 1 km/s are injected into the tokamak with the frequency of 0.5 Hz during the time from 1200 to 1220 s. The plasma core transport is described by a combination of the NCLASS neoclassical transport model [19] and the modified Mixed Bohm/gyro-Bohm (Mixed B/gB) anomalous core transport model with ITB effects included [20]. It is assumed in these simulations that the toroidal velocity for the electric field (as well as ®E x B) calculation is proportional to the local ion temperature. This toroidal velocity assumption was validated against 10 optimized shear discharges from JET and the predictions yield reasonable agreement [21]. Note that the notations used in this paper can be found in Table 1. The pedestal temperature is given by one of the best pedestal temperature model in [22], where the pedestal width based on the flow shear and magnetic shear width scaling [23] and the infinite-n ballooning mode limit pressure gradient model are used together. The density of each hydrogenic and impurity species at the top of the pedestal is described by a simple model, called a dynamic boundary density model that assumes the proportionality between the pedestal density of each specie and its line averaged density. Using the conditions above, the temperature and density profiles are obtained from the simulations. It should be
noted that the impurity species considered in this work are helium and beryllium. A parametric sensitivity analysis is also carried out to determine the impact of altering fundamental pellet parameters
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.