This by increasing radiation power loss and consequently decreases

This paper describes the behavior
of plasma parameters in the E-divertor region of GAMMA 10/PDX numerically by
using the multi-fluid code (LINDA) code during injection of hydrogen (H) and
Argon (Ar). A remarkable reduction in the electron temperature is observed for
Ar injection. For only Ar 6.0 ×1017 m-3 injection, Te on the target plate
reduces to about 10 eV. Te also reduces according to the increment of H
injection. The ion temperature Ti on the target plated reduces according to the
increment of injected H neutral density. A tendency of saturation in the
particle flux and the electron density is observed at the higher H injection in
case of simultaneous injection of H and Ar. Initially the heat flux slightly
increases due to neutral injection, however the heat flux reduces at the higher
neutral injection. The charge exchange loss enhances significantly during H
seeding. The radiation power loss also enhances for Ar injection.

 

Keywords: GAMMA 10/PDX, E-Divertor,
LINDA code, Ar injection, hydrogen injection, plasma detachment.

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1. Introduction

In the future plasma fusion devices
such as ITER and DEMO, control of the high heat and particle fluxes on to the
target plates of the divertor is one of the critical issues. The divertor is
expected to be exposed to high heat load. Chemical and physical sputtering are
produced on the divertor plates due to high upstream heat and particle fluxes
strike on the target plates 1. Therefore, it is necessary to protect the
plasma facing components (PFCs) from high upstream heat load. The detached
plasma regime has been considered as one of the solution for the power handing
problem of the future fusion devices such as ITER and DEMO 2-6. Radiator gas
injection into the plasma edge region is one of the possible ideas to minimize
the heat load on the divertor plates, because radiator gas strongly enhances
the electron power loss channels by increasing radiation power loss and
consequently decreases the electron temperature 1-3. On the other hand,
hydrogen atomic and molecular processes play a key role to reduce the ion
temperature by enhancing the charge-exchange loss. In addition to these above
physical processes, the volume recombination processes such as Molecular
Activated Recombination (MAR) 4-5,19 and Electron Ion Recombination (EIR)
20) are also very much important atomic and molecular processes at the low
temperature plasma (< 5 eV) to generate detached plasma. GAMMA 10/PDX is a linear plasma confinement device 7. In GAMMA 10/PDX, divertor simulation research (E-Divertor) has been progressed to clarify the effect of radiator gases on the plasma detachment 8-10. The E-divertor project has been aimed to investigate the physical mechanism of plasma detachment, radiation cooling, impurity transport, etc. The generation of a detached plasma by radiator gas seeding has been observed in the D-module of GAMMA 10/PDX 8-10. Simultaneous injection of H and Ar has shown a promising effect on the reduction of ion flux 8. Numerical simulation studies have been effectively progressed to reveal physical mechanism of divertor plasma physics 6, 11-17. A numerical simulation study is a power tools to explain the detailed physical mechanism related to the plasma detachment. The divertor simulation studies have been effectively performed by developing the multi-fluid code and the Monte-Carlo code. The plasmas transport in the divertor region are described by a fluid code while the neutral model can be defined by either a fluid model or a Monte-Carlo model. A numerical simulation study by using the LINDA (Linear Divertor Analysis with fluid model) code has been performed in the end-cell of GAMMA 10/PDX with a view to explaining the physical mechanism of plasma detachment during gas injection in the E-divertor region of GAMMA 10/PDX 15-17. In the LINDA code, the plasmas transport have been modeled by solving the fluid equations while the neutrals profile have been modeled by the 1D fluid equations, we are planning to improve the neutral model in the future. The aim of the study is to investigate the effects of H and Ar injection on the E-divertor region of GAMMA 10/PDX.   2. Simulation model The 27 m long GAMMA 10/PDX is the world largest tandem mirror device which consists of multiple-cell 7. The mesh structure of the simulation area is designed according to the magnetic field configuration of the GAMMA 10/PDX. Figure 1 shows the mesh structure of the simulation region. A tungsten target plate is designed at the end of the mesh structure. The number of mesh in the z and r direction are 321 and 50, respectively. Hydrogen plasma flows out from upstream to downstream region. On the other hand, neutral particles (H, Ar) are transported from downstream to upstream region. The LINDA code consists of four fluid equations: continuity equation, diffusion equation for the perpendicular direction, momentum balance equation, ion and electron energy balance equations 16. The upstream boundary conditions are defined as fixed boundary (on the z-axis ni = 5× 1018 m-3, Te =30 eV and Ti = 100 eV, while the Neumann boundary conditions are applied on the periphery region. The divertor boundary conditions are applied on the target plate. The flux limits concept 11,12 for the parallel viscosity and electron thermal conductivity is also used in this modeling. The hydrogen atomic processes and radiation cooling, ionization, radiative recombination of Ar are considered in the LINDA code 18. Since GAMMA 10/PDX is a linear plasma confinement device, the fluid neutral model works well for the GAMMA 10/PDX geometry. In this study, the neutral models for both the impurity Ar and H are given by fluid equations which are solved iteratively together with the fluid equations in the self-consistence manner. As for the hydrogen neutral model, neutral density assumed to be uniform in the mirror throat region (z~10.3 m) and reduces exponentially in the plug/barrier-cell. The recycling hydrogen neutrals are also considered in the LINDA code. The hydrogen neutral model is written as follows Equation (1) describes hydrogen neutral density in the plug/barrier region (7.5 m ? z ? 10.045 m) while equation (2) describes hydrogen neutral density in the end cell (10.055 m ? z ? 10.705 m). The distribution of hydrogen neutral particles on the z-axis is shown in Fig. 2(a). The increase in the H neutral density near the target plate is observed. The increasing part in the H density profile near the target plate comes from the recycling H neutral. The distribution of Ar neutral density is assumed to be uniform in the end-cell (10.055 m ? z ? 10.705 m) and reduces exponentially in the plug/barrier-cell (7.50 m ? z ? 10.45 m). The 2D profile of Ar neutral density is shown in Fig. 2(b). The distribution of Ar neutral particles along the perpendicular direction to the magnetic field line is uniform. The Ar neutral model in the plug/barrier region is given by the following formula,   3. Simulation results and discussion The injected Ar density has been fixed at 6 × 1017m-3, while the injected hydrogen neutral atom density has been varied from 0.0 to 2.8 × 1018 m-3. The neutral models for the simulation condition are shown in Fig. 2. The simulation results are summarized in Figs. 3 to 5. The 2-dimensional profiles of the electron temperature are shown in Fig. 3. Reduction in the electron temperature is shown for without any gas injection. The recycling hydrogen neutrals are included in the present study. Due to the above, reduction in the electron temperature is observed near the target for without any gas injection condition. Furthermore, the reduction rate has been enhanced when hydrogen gas is artificially injected. For only H 4× 1017 m-3, injection, the electron temperature near the target plate reduces to about 14 eV. Moreover, a remarkable reduction in the electron temperature is shown for the Ar seeding. For only Ar 6× 1017 m-3, injection, the electron temperature on the target plate reduces to about 10 eV, which indicates the radiation cooling effects of Ar neutral particles.   The dependence of the electron temperature (Te) on the target plate (at r=0 cm) as a function of the injected hydrogen neutral density is plotted in Fig. 4 (a). The electron temperature on the target plate reduces with the increasing H injection. For the strongest H injection, the electron temperature on the target plate reduces to about 5 eV. It is shown that the reduction in the electron temperature for simultaneous seeding of H and Ar is higher than that of only H injection. The dependence of ion temperature (Ti) on the target plate as a function of injected Ar neutral density is shown in Fig. 4 (b). The reduction rate of ion temperature is almost similar for only H injection and simultaneous injection of Ar and H. However, a slight influence of Ar seeding on the ion temperature has been observed in the range of low hydrogen density. The dependence of electron density (ne) on the target plate on the injected H neutral density is shown in Fig. 4 (c). The electron density increases with the increasing H injection. It is recognized that the electron density is higher for the simultaneous seeding of Ar and H than that of only H seeding, which indicates ionization effects of Ar neutral particles. During the simultaneous seeding of Ar and H, the electron density becomes saturate at the higher H injection. On the other hand, for only H injection, the electron density continue to increase with the increasing H injection.     Figure 4(d) shows the dependence of particle flux ((?_i) on the target plate as a function of the injected H neutral density. At the lower H gas injection region, the particle flux is almost similar for simultaneous injection of Ar and H compared with the only H seeding. However, the tendency has been changed according to increasing H neutral density. During the simultaneous seeding of Ar and H, the particle flux becomes saturate at the higher H injection. On the other hand, for only H injection, the particle flux continue to increase with increasing H injection. In Fig. 4(d) the variation of heat flux is also plotted as a function of the H neutral density. A slight increase in the heat flux is shown at the lower neutral injection. However, at the higher H injection, the heat flux starts to reduce. The energy loss processes have also been investigated to explore the physical mechanism of energy loss processes during neutral seeding. The dependence of the CX (charge-exchange) loss (H^++H^0?H^0+H^+) and recombination loss (H^++e?H) as a function of the injected hydrogen neutral density is shown in Fig. 5 (a). The CX loss increases significantly during H injection. As a result, the ion temperature significantly reduces via the CX loss as shown in Fig. 4(b). Furthermore, the CX loss increases with the increasing hydrogen injection. The CX reaction rate coefficient () is almost nearly flat profile in the temperature range
from10 eV to 100 eV 18. Therefore, the CX loss strongly depends on the ion
temperature, proton, and hydrogen neutral density. Because of this, CX loss
increases with the increasing neutral density, although the ion temperature is
reduced with the increasing hydrogen neutral density. On the other hand, the
recombination loss is very small. However, the recombination loss increases as
the electron density is reduced. The recombination processes play a driving
role at the low temperature region (Te < 1 eV). In this study, Te reduces to about 3 eV. At such the temperature range ionization reaction rate coefficient is much higher than that of the recombination rate 18. As shown in Fig 5(b), the power loss due to the ionization of hydrogen neutral particles increases with the increasing H neutral density. This power loss is slightly high for only H injection comparing to the simultaneous injection of Ar and H. The radiative power loss of Ar increases significantly during Ar injection. The Ar radiation power loss slightly increases with increasing H injection.