Neutral beam injection (NBI) is one of the most essential ways of heating fusion plasmas in TOKAMAK and has been developed rapidly in recent years.^[1–3] In 2007, ITER selected a radio-frequency (RF)-driven ion source instead of the original filament source.^[4] The heating system requires a reliable negative ion source providing high current density (> 200 A·m with high uniformity and at low pressure < 0.3 Pa.^[5] It hence needs a high-density, large-area plasma source with good uniformity. At present, the negative RF ion source is a solenoidal coiled inductively coupled plasma (ICP) reactor developed at IPP (Max Planck Institut für Plasmaphysik), Garching.^[6,7] Compared with the former filamented arc sources, the greatest advantage of the present source is that it can endure longer operating times owing to the absence of filaments, and this has attracted increasing attention for basic physics investigation and device optimization.^[8–13]

However, some research groups indicate that there exists a major problem based on the current structure: while adding an external (horizontal) magnetic filter perpendicular to the cylindrical axis, the axial electric field and the horizontal magnetic field will lead to an E × B drift of the electrons,^[8,9] leading to a ‘Hall effect’, whereby the potential is no longer axially symmetric. The potential at one side of the chamber (towards the E × B direction) is larger than at the opposite side. Then, the radial potential drop will accordingly cause a secondary drift to extract the electrons from the confined magnetic field. As a result, this will cause radial nonuniformity of the plasma density and also strongly affect the production of H negative ions by the extracted electron flux. Detailed descriptions of the simulation and experimental work can be found in Refs. [8]–[12].

Since the main cause of this problem is the Hall effect induced by the horizontal magnetic field, we consider changing the static magnetic field configuration to avoid this Hall effect. Therefore, based on the original ICP source structure, we insert a thin tube into the chamber along the axial direction. The magnet could be placed inside the dielectric tube to generate a radial magnetic field. Thus, the E × B drift becomes a closed drift without hitting the wall. This may be one possible solution for RF source reactor optimization. For a planar coil ICP, this reactor geometry was first developed by Ventzek et al. as a step window to investigate the distributions of the plasma parameters.^[13] For a solenoidal coil ICP, Monreal et al. designed a cylindrically symmetric ICP reactor with inner antenna coils to demonstrate the control of electron temperature and electron energy distribution (EED) in low-pressure ICP.^[14] Song et al. employed a hybrid model to compare with the above experimental measurement results to investigate the static magnetic effects on the EEDs.^[15] All of the above results indicate that the shape of an ICP chamber structure will not cause a disturbance of the plasma discharge. However, it still requires a comparison, particularly under extremely high power and for a specific structure.

Except for its use as an ion source, the solenoidal coil ICP source is also widely applied in many other low-pressure plasma discharge environments, such as semiconductor fabrication facilities. A thorough investigation is necessary to understand both the properties of the plasma parameters and also the influence of the controlled parameters on the discharge status, which will provide valuable guidance for the design of the source reactor. In order to test the feasibility of the new structure, a fluid simulation is introduced based on this geometry to investigate the plasma density, potential, and electron temperature distributions, as well as the influence of the applied power and reactor geometry. A simulation based on the original regular chamber geometry under the same discharge status is also conducted for comparison. It needs to be mentioned that this paper will mainly focus on the effect of geometry on the inductive heating mechanics. The effect of the static magnetic field is not taken into consideration in the current study.

The schematic of the RF source geometry is shown in Fig. 1. Figure 1(a) shows a regular solenoidal coil ICP configuration. Figure 1(b) shows our newly retrofitted structure, in which a hollow thin tube is inserted into the RF source along the axial direction. In this way, the static magnets can be placed in the inner tube to generate a radial magnetic field. We divide each of them into two parts: the upper half is the discharge region and the lower half is the diffusion region.

Fig. 1.

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	Fig. 1. (color online) Schematic view of the reactor geometry: (a) regular solenoidal coil ion source reactor and (b) new retrofitted source reactor.

The simulation area is shown on the right-hand side of Fig. 1. The chamber reactor is set to 420 mm in height with a radius of 120 mm. The coils are located in the upper part of the chamber. Thus, the entire chamber can be divided into two parts: the discharge region (upper half) and the diffusion region (lower half). In order to limit the disturbance to the plasma discharge, we set the radius of the inner tube as 20 mm. The distance from the reactor bottom to the inner tube bottom is 60 mm. We take helium as the carrier gas and fix the gas pressure at 10 mTorr. The coil is connected to a 2 MHz RF source with available input power from 1 to 100 kW.

A fluid model is employed to simulate the discharge status in both the regular geometry and new geometry. The fluid method is widely used for the simulation of low-temperature plasma sources.^[13,15–21] Model descriptions and numerical methods can be found in our earlier work.^[16] The code we employed in this paper is a part of the MAPS (Multi-physics Analysis for Plasma Simulation) solver. MAPS is a comprehensive solver developed by Wang's group.^[22] It consists of CCP and ICP solvers. One can select a fluid model or particle-in-cell (PIC) model for simulating the CCP discharge. For ICP discharge, only the fluid model is available, temporarily. A number of experimental verifications have been conducted and the simulation results show good agreement with the corresponding experimental results, for both CCP and ICP discharges.^[23,24] This solver could effectively deal with various reactive gases, such as H, He, N, O, Ar, CF, and SiH, among others, as well as gas mixtures. In this study, we selected some of the main reactions of He plasma discharge, including ionization, excitation, de-excitation, multistep ionization, and three-body interactions, among others. The reactions and rate coefficients are listed in Table 1.

Table 1.

Table 1.

Table 1. Rate coefficients for He plasma in cms (cms for three-body collisional reaction); is the threshold energy, is the electron temperature in eV, and is the background gas temperature in eV. . No. Reaction Rate coefficient Reference 1 e + He e + He cross-sectiona [17], [18] 2 e + He e + He* 19.8 cross-sectiona [17], [18] 3 e + He e + He −19.8 cross-sectiona [17], [18] 4 e + He 2e + He 24.6 cross-sectiona [17], [18] 5 e + He 2e + He 4.8 cross-sectiona [17], [18] 6 2e + He e + He* [18] 7 e + He+ He He + He* [18] 8 He*+ He e + He + He [18] a Calculated by Boltzmann equation.

Table 1. Rate coefficients for He plasma in cms (cms for three-body collisional reaction); is the threshold energy, is the electron temperature in eV, and is the background gas temperature in eV. .

The set of fluid equations includes the continuity equation for ion/electron density

For the neutral particles, we consider only the diffusion function (Fick's law)

In this model, we approximate the temperature of the background gas as the room temperature. In fact, the background gas temperature could be heated up to more than 1000 K owing to low-pressure and high-power discharge.^[25] According to the ideal gas equation , it can be deduced that if the simulated gas temperature is lower than the real temperature, the computed neutral particle number density will be larger than the actual value. Therefore, strictly speaking, the simulated results for the plasma density are higher owing to this approximation. However, the advantage of the existing model is its computing speed: it will cost only a few hours without the neutral gas thermo-fluid module.

A new reactor geometry is proposed for the optimization of an RF ion source. The purpose of this design is to change the original transverse magnetic field to a radial magnetic field by introducing a centered dielectric tube into the RF ICP chamber. For the first step, we simulate the physical influence of the dielectric tubes without introducing the static magnetic field and negative ions. A fluid model is introduced to simulate the discharge status under this new reactor geometry. The results reveal that the inner tube causes only a minor decrease in the plasma density. The radial distribution of the plasma density in the extraction region maintains good uniformity, both with and without the inner tube. The influence of the control parameters shows that both the ion flux and the plasma density show linear behavior with respect to the applied power under high-input-power conditions (1–100 kW). In the extraction region, longer diffusion length causes less influence on the plasma density. In summary, the disturbance by the inserted dielectric tube of the plasma density and radial uniformity can be ignored. Owing to its advantage of generating the radial magnetic field, this new chamber geometry could be a practical way to optimize the current RF negative ion source structure.