Journal of Nuclear Energy Science & Power Generation TechnologyISSN: 2325-9809

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Research Article, J Nucl Ene Sci Power Generat Technol Vol: 6 Issue: 2

Modeling of Small Size Divertor Tokamak in Discharge withEdge Transport Barrier (ETB)

Bekheit AH*
Plasma and Nuclear Fusion Department, Atomic Energy Authority, Cairo, Egypt
Corresponding author : Amr Hasheim Bekheit
Plasma & Nuclear Fusion Department, Atomic Energy Authority, Cairo, Egypt
E-mail: [email protected] yahoo.com
Received: December 15, 2016 Accepted: January 31, 2017 Published: February 23, 2017
Citation:Bekheit AH (2017) Modeling of Small Size Divertor Tokamak in Discharge with Edge Transport Barrier (ETB). J Nucl Ene Sci Power Generat Technol 6:2. doi: 10.4172/2325-9809.1000173

Abstract

The article is the simulation of small size divertor tokamak edge transport barrier “ETB”. The modeling carries out with the multifluid transport code B2SOLPS5.0 2D with drifts and currents which was specially developed for simulation of tokamak edge transport barrier“ETB”. The emphasis is made on edge transport barrier “ETB”. The simulation demonstrated the following results: The “ETB” width has strong influence on the radial electric field. The E×B drift shear is function of “ETB” width. The ion parallel (toroidal) velocity has cocurrent direction and quite different for different “ETB” width. This difference is connected with the contribution of large E×B drift velocity in toroidal torque driven by parallel viscosity which strong influence on toroidal rotation. The plasma density, electron and ion temperatures are typical feature of small size divertor tokamakwhen the particle and heat fluxes from core plasma are low. The sizes of the barrier have ability to prevent neutral particles penetrate the barrier edge in this tokamak. The ETB width has influence on the poloidal velocity in the edge plasma of this tokamak

Keywords: ETB; ETB width; Code B2SOLPS5.0 2D

Keywords

ETB; ETB width; Code B2SOLPS5.0 2D

Introduction

The regime with an edge transport barrier is the best confinement regime for primary scenario for small size divertor tokamak operation. The edge transport barrier (ETB) is a feature of high confinement (H-mode) of tokamaks. It is a narrow region of reduced radial transport, in which steep gradients in both density and temperature are observed, forming a pedestal for core profiles [1]. Extensive studies have shown that the radial electric field profile in ‘ETB’ [2] is consistent with neoclassical radial electric field [3]. To sustain an edge transport barrier (ETB), the performance of long-pulse ELMy H-mode plasmas was improved in terms of sustained duration time for both high beta and high thermal confinement enhancement factor [4]. Simulation is one of the tools that can be used to study edge transport barrier ‘ETB’ in this tokamak. Due to the reliability and speed of today’s computer, the simulation codes can be integrated and complicated enough for results to be trustworthy [5]. However, to perform the edge simulation for this regime one has to specify the edge transport barrier width. In this article we present the preliminary results of the simulation of small size divertor tokamak. The simulation has been performed by using B2SOLPS5.0 2D multifluid transport code with full treatment of drifts and currents [3,6]. The simulation was performed for pure plasma. The results of simulation demonstrated the plasma density, electron and ion temperatures are typical feature of small size divertor tokamak when the particle and heat fluxes from the core plasma are low.
Model
There are various scalings for the edge transport barrier width ‘ ’predict a relatively wide barrier for small size divertor tokamak. According to the previous experimental experience the width of the edge transport barrier is proportional to the tokamak minor radius [7]. Following this trend we consider δ=0.0015m at the outer midplane. The core side of the barrier coincides with the inner side of the simulation domain. The following transport coefficients were chosen to simulate the barrier in this case, Figures 1 and 2 shows that, the diffusion coefficient at the core side of the barrier was reduced by a factor of ~1.4 and thermal conductivity coefficient was reduced by a factor of ~ 6.5 for wide barrier width. The narrow barrier width δ=0.000153m has also been simulated; the corresponding transport coefficients is shown in Figures 1 and 2. Also the diffusion coefficient at the core side of the barrier was reduced by factors~2.5 and thermal conductivity coefficient was reduced by a factor 6.5 for narrow barrier width. At the inner side of the simulation domain we put the density at equatorial midplane ni=ne=n= 2×1019m-3, Te=Ti=100eV which corresponds to the temperature heating Theating=0.33keV. The Simulations were performed by B2SOLPS5.02D multifluid transport code for pure plasma without impurities.
Figure 1: Distribution of diffusion coefficient at the core side for wide/narrow barrier widths. Red line is narrow width barrier and blue line is wide width barrier.
Figure 2: distribution of thermal conductivity coefficient at the core side for wide/narrow barrier widths. Red line is narrow width barrier and blue line is wide width barrier.
Simulation results
The simulation were performed for parameters of small size divertor tokamak (a=0.1m, R=0.3m, I=50kA, and BT =1.7T). The main results of simulation are: (1) the first result of simulation shows that,the obtained profile of radial electric field for the cases of wide and narrow edge transport barrier as showed in Figure 3. Indeed the radial electric field for two cases should be close to the neoclassical electric field [6,8]
Figure 3: Radial distribution of radial electric field at the wide/narrow barrier widths. Red line is narrow width barrier blue line is wide width barrier.
image
With exception of dip in separatrix vicinity. The negative part of radial electric field inside wide and narrow width ‘ETB’ domain are determined by balance between negative contribution from density and ion temperature gradient first term of equation (1) and positive contribution from co-current toroidal velocity second term of equation (1). The negative gradient contribution is comparable but bigger. Figure 3 show that, the width of ‘ETB’ has strong influence on the radial electric field. Therefore, the radial electric field is function of width ‘ETB’. The shear of the E×B drift is given by Wolf and Bekheit [9,10]
image (2)
Where image is metric coefficient? This shear is large adjacent to separatrix for wide and narrow width ‘ETB’ as showed in Figure 3. According to Rozhansky et al. [11] the critical value of E×B shear drift required for the turbulence suppression might be estimated as 3×(105- 106) s-1. The Figure 4 shows that, the calculated shear is higher than the critical value at inner part of barrier adjacent separatrix. From equations (1, 2) the width of ‘ETB’ has the form given by:
Figure 4: Radial distribution of radial electric field shears ωE×B at the wide/ narrow barrier widths. Red line is narrow width barrier blue line is wide width barrier.
image (3)
Where ‘Cs’ is sound velocity, ωci is the cyclotron frequency and Ln is the characteristic length for plasma density. For wide barrier has width is =0.001476m but for narrow barrier has width =0.000153m. Equation (3) indicates that the E×B drift shear is function of the width of ‘ETB’. (2) The second result of simulation shows that, the radial distribution of plasma density, ion and electron temperature profiles, Figures 5, 6 and 7, are rather slope inside the barrier in contrast to plasma density, ion and electron temperature for small size divertor tokamak. A noticeable plasma density, ion and electron temperatures are seen only in part of core side of barrier adjacent to separatrix. This is a typical feature of small size divertor tokamak when the particle and heat flux from the core plasma is low and corresponds to little particle and energy sources inside barrier
Figure 5: Radial distribution of plasma density in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 6: Radial distribution of ion temperature in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 7: Radial distribution of electron temperature in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
(3) The third result of simulation shows that, the distribution of parallel (toroidal) velocity at different plasma width as showed in Figure 8 shows the toroidal velocity in case of narrow ‘ETB’ width is greater than the toroidal velocity in case of wide ‘ETB’ width. In both cases, the toroidal velocities have co-current negative direction in the edge plasma of this tokamak. The reason of difference in toroidal velocity in both cases is connected with the contribution large E × B in toroidal torque driven by parallel viscosity which leads to increasing plasma toroidal rotation in the case with narrow ‘ETB’ width. (4) The fourth result of simulation shows that, the radial distribution of neutral particle density for wide/narrow ‘ETB’ width cases is showed in Figure 9 Shows the decreases of neutral particle density near separatrix, in case of narrow ‘ETB’ width are larger than the case of wide ‘ETB’ width. So the fact that the neutral density decreases near separatrix suggests that the neutral influx decreases in the case of narrow ‘ETB’ width compared to wide ‘ETB’ width. (5) The fifth result of simulation shows that, change of poloidal velocity for wide/ narrow ‘ETB’ width barrier is showed in Figure 10 shows the radial variation of poloidal velocity is the result of strong radial variation of radial electric field Er. For this, we could see the increase of poloidal velocity for inside wide/narrow ‘ETB’ width as can see from Figure 10, so it’s result increasing of negative radial electric field. (6) The sixth result of simulation shows that, the radial distribution of parallel (toroidal) current at wide/narrow ‘ETB’ width in the edge plasma of this tokamak. The parallel (toroidal) current density obtained from our simulation is showed in Figure 11. Here in the SOL the negative direction corresponds to current flowing from the inner plate. This current is the sum of the thermoelectric current flowing from outer hatter plate to the inner cooler plate and contribution from the parallel current, which closes to the radial current. In the Figure 11 the structure of parallel (toroidal) current is non-monotonic. Here at separatrix mainly the current driven by perpendicular viscosity [6] image balance the radial diamagnetic current. Figure 11 shows that, the toroidal parallel current has a spike of narrow ‘ETB’ width is greater than the toroidal current in case of wide ‘ETB’ width. The reason of this difference is connected with a large electric field in toroidal current which leads to increasing toroidal current in case of narrow ‘ETB’ width. Also Figure 11 shows ‘ETB’ lie in the region between minimum and maximum values of toroidal current. The dependence of ‘ETB’ width on plasma current density is a primary factor, which controls the energy confinement time [12].
Figure 8: Radial distribution of parallel velocity in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 9: Radial distribution of neutral particle density in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 10: Radial distribution of poloidal velocity in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 11: Radial distribution of current density in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
Figure 12: Radial distribution of stored energy in the edge plasma of this tokamak. Red line is narrow width barrier blue line is wide width barrier.
An attempt to use narrow/wide ‘ETB’ leads to systematic deviation between calculated stored energy at narrow/wide ‘ETB’ as showed in Figure 12, which decreases with increases the plasma current.

Conclusion

Modeling of small size divertor tokamak in discharge with edge transport barrier ‘ETB’ has been performed. It was demonstrated that:
The radial electric field for wide/narrow ‘ETB’ width case should be close to the neoclassical radial electric field.
The ‘ETB’ width has strong influence on the radial electric field. Therefore, the radial electric field is function in ‘ETB’ width.
The parallel velocity has co-current direction and quite different for different ‘ETB’ width. The difference between them is connected with the contribution of large E×B drift velocity in toroidal torque driven by parallel viscosity which strong influence on toroidal rotation.
The specific feature of small size divertor tokamak ‘ETB’ discharge is ion, electron temperature and plasma density in ‘ETB’ for low particle and heat flux.
The width ‘ETB’ has enough zones for turbulence suppression by the shear of poloidal E×B drift which is calculated for narrow/wide ‘ETB’ width. Also the shear of poloidal E×B drift is function of ‘ETB’ width.
The sizes of the edge transport barrier have ability to prevent neutral particles penetrate the barrier edge in this tokamak.
The ‘ETB’ width has strong influence on poloidal velocity in the edge plasma of this tokamak.
The ‘ETB’ width strong influence on the radial distribution of toroidal (parallel) current. An attempt to use narrow/wide ‘ETB’ width leads to a systematic deviation between stored energy at narrow/wide ‘ETB’ width which decreases with increases in the plasma current.

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