3D modeling of a double-driver ion source considering ion magnetization: an investigation of plasma symmetry modulation methods

A three-dimensional fluid model of a double-driver negative hydrogen ion source for China Fusion Engineering Test Reactor (CFETR) neutral beam injection is developed. In this model, the magnetic filter field is generated by 16 permanent magnets, which are surrounded by a soft iron. In order to accurately describe the transportation of charged species in the presence of strong magnetic field, both the electron magnetization and ion magnetization are taken into account, and the accuracy of the model has been proved by comparison with experimental data. By employing this model, the spatial distributions of the plasma parameters have been investigated, and three methods are proposed to optimize the symmetry at the bottom of the expansion region of a double-driver source. The results indicate that by adjusting the power of Driver I while keeping the power of Driver II constant, the symmetry of the electron density and negative hydrogen ion density could be improved. Furthermore, the inclusion of partition improves the symmetry of the electron temperature and density but has no impact on the regulation of the negative hydrogen ion density distribution. Finally, the application of magnetic shield can not only improve the symmetry of the electron density and negative hydrogen ion density, but also increase their densities at the bottom of the expansion region.

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Introduction
China Fusion Engineering Test Reactor (CFETR) is the forthcoming tokamak fusion facility planned in China's magnetic confinement fusion development roadmap, with the goal of overcoming the physical and engineering technical challenges that exist between International Thermonuclear Experimental Reactor (ITER) and Demonstration Fusion Reactor (DEMO) [1][2][3].Considering the neutralization efficiency, heat load control, and long-term operational reliability, the negative ionbased neutral beam injection (N-NBI) system is the optimal choice for CFETR [4][5][6][7].In the N-NBI system, energetic hydrogen or deuterium ions produced by negative hydrogen ion source (NHIS) are neutralized and then injected into the fusion device, to transfer energy to plasmas through coulomb collisions with charged particles [8].In the investigation of NHIS, research usually starts from a single-driver source, which is designed to tackle the physical issues related to the plasma generation and transport, especially in the presence of a magnetic filter [9][10][11][12].Then, the research is expanded to a multi-driver source, such as half-size and full-size ion sources, with the aim of addressing the operational challenges encountered in multi-driver ion sources, such as coupling between multiple drivers, plasma uniformity control and design of the large-size magnetic filter.
Since 1996, the reliability of RF-driven NHIS for ITER NBI has been investigated at Max-Planck-Institut für Plasmaphysik (IPP), Germany [13].Initially, a smallscale prototype source with 1/8 domain was experimentally designed, including the short-pulse source BATMAN (Bavarian Test Machine for Negative Ions) [14] and the longpulse source MANITU (Multi Ampere Negative Ion Test Unit) [15].Subsequently, the half-size sources RADI (former radial injector of W7-AS) and ELISE (Extraction from a large ion source experiment), which were half the height but had the same width as the full-size ITER source, were established [16], and many experimental investigations have been performed on them.For instance, Fantz et al measured the plasma uniformity in RADI by optical emission spectroscopy, and the results revealed that plasma depletion occurred in the central channel at the bottom of the expansion region due to the magnetic filter field, and the loss could be mitigated by increasing the power [17].Subsequently, they demonstrated for the first time that the asymmetry of co-extracted electrons in ELISE depended on the combination of magnetic filter and bias potential [18].Schiesko et al focused on the spatial distribution of plasma parameters near the grid of RADI, and they found that the plasma was homogeneous in the direction perpendicular to the magnetic field lines when the field strength was below 0.6 mT [19].Wünderlich et al tested the plasma parameters under three conditions: without magnet, with magnets to strengthen the plasma grid (PG) filter field and with magnets to weaken the PG filter field.The experimental results indicated that external magnets could substantially reduce the number of co-extracted electrons when the PG current field was strengthened, while no impact on the number of ions was observed [20].
In terms of simulation, Zielke et al developed a 2D cylindrically symmetric fluid model to explore the effects of the RF Lorentz force and neutral depletion on the power coupling efficiency in the case without external magnetic field [21].Nocentini et al utilized the finite element method to design the PG and magnetic configuration, aiming to achieve a more uniform magnetic filter field distribution and thus a homogeneous plasma beam [22].Yang et al developed a 1D particlein-cell/Monte Carlo collision (PIC/MCC) model, in which the plasma loss at the sidewall was estimated by a loss estimation model to reduce the computational cost, to study the plasma transport through a Gaussian profile magnetic field [23,24].By using a 2D PIC model, Hatayama et al investigated the impact of magnetic field strength, and they revealed the optimal value for H − extraction [25].Fubiani and Boeuf employed a 2.5D PIC/MCC model to compare the electron current distribution at the top and bottom of the PG in ELISE under different bias voltages, and they presented that the difference diminished at higher bias voltages [26].
Although the above experimental and numerical investigations provide valuable insights for the design of multi-driver ion source, there still exist some problems.For instance, most of the simulations are performed by a 1D/2D/2.5Dmodel, and the self-consistent three-dimensional (3D) modelling of multidriver ion source is very limited.In a low-dimensional model, the complex magnetic field configuration generated by permanent magnets cannot been considered properly, so the magnetic field distribution is usually assumed to have a Gaussian profile [26][27][28].This assumption is inappropriate for models with relatively large magnetic field gradients [26].Moreover, the plasma homogeneity along the direction of magnetic field cannot be evaluated by a low dimensional model.Therefore, a 3D self-consistent model with real magnetic field configuration is necessary, for a deep insight into the NHIS properties.Besides, the plasma uniformity, which depends on the transport of charged particles under the electromagnetic force, is an essential issue in NHIS.Therefore, ion magnetization, which has a non-negligible effect on the plasma homogeneity especially in the region with strong magnetic field, should be taken into account.However, in most of the models mentioned above, the ion magnetization has been neglected.Therefore, a 3D fluid model including ion magnetization is developed for a double-driver ion source in this work, and three methods are proposed to optimize the plasma spatial symmetry.

Model description
The structure of NHIS with double drivers is illustrated in figure 1.The dimension of each driver is 14 cm both in radius and length.The coil has a radius of 15 cm, and the wire has a radius of 0.5 cm.The two drivers are referred to as Driver I (centered at x = 28 cm) and Driver II (centered at x = 72 cm), and the corresponding coil powers are P absI and P absII , respectively.The expansion region is 100 cm in length, 50 cm in width and 25 cm in height.The magnetic filter consists of 16 permanent magnets, which are arranged symmetrically on both side walls along the x-direction, at 5 cm intervals, to generate a magnetic field in the negative y-direction.Each magnet has dimensions of 9 cm in length, 5 cm in width, 2 cm in height, and a remanent magnetization of 1.03 T. A soft iron is employed to modify the direction of magnetic field lines and amplify the magnetic field in the expansion region [29].In addition, a metal partition with a height of h p is placed on the top of the expansion region to hinder the drift induced by the magnetic field.
A 3D fluid model is implemented in COMSOL Multiphysics to investigate the plasma properties in the double-driver ion source.The fluid model consists of a plasma module, an electromagnetic module, and a magnetostatics module, which has been described in detail in our previous work [9], so only a brief description is given here.In the plasma module, the electron behavior is governed by the continuity, momentum balance, and energy conservation equations.For ions and neutral particles, only the continuity and momentum balance equations are needed, and their temperature is assumed to be 600 K. Due to the presence of magnetic filter field, the mobility, diffusion coefficient and conductivity of electrons and ions (including H + , H 2 + , H 3 + and H − ) are expressed as tensors.In the electromagnetic module, the electromagnetic field is calculated by introducing the magnetic vector potential.Besides, the magnetostatics module is adopted to get the magnetic filter field distribution generated by permanent magnets based on the conservation of magnetic flux.

Results and discussion
In this work, magnetization of ions has been taken into account, and its influence on the plasma properties has been demonstrated by comparing with the results obtained in the case without magnetization of ions at gas pressure of 0.6 Pa and frequency of 2 MHz.Besides, the simulation results in a single-driver NHIS have also been validated by the experimental measurement to illustrate the accuracy of the model.Subsequently, three methods are proposed to regulate the spatial distribution of various plasma parameters, including varying the coil power, adding a partition, and adding a magnetic shield.

Effect of ion magnetization
The distribution of the magnetic field in the xz-plane (y = 25 cm) of the double-driver source is illustrated in figure 2  The directions of magnetic field and electric field are presented in figures 2(c) and (f ).It is clear that the magnetic field is mainly along the negative y-axis, while the electric field is oriented from the center of the chamber to the wall.The driver and expansion regions have opposite electric field directions along the z-axis.Therefore, electrons may transport along the negative x-axis in the driver region due to the E × Bdrift, while they drift along the positive x-axis at the bottom of the expansion region.Under the electric field force, positive ions transport towards the walls, and negative ions drift in the opposite direction.Considering the ion magnetization, the transport of ions perpendicular to the direction of the magnetic field is impeded, and the motion along the magnetic field is enhanced.
In the presence of magnetic filter field, electrons are considered to be strongly magnetized, because their cyclotron frequency is greatly larger than the elastic collision frequency.The cyclotron frequency for ions is much lower than the elastic collision frequency, they are usually assumed to be unmagnetized in previous works [26,28].However, ions might be magnetized in NHIS due to the existence of strong magnetic field in the vicinity of the magnet block, so ion magnetization should be considered as this impacts the plasma transportation to some extent.In order to illustrate the necessity of the consideration of ion magnetization, the ratios between the cyclotron frequency (defined as where e, B, m H + (H − ) is elementary charge, magnetic field, ion mass, respectively) and the ion collision frequency (defined as ν H + (H − ) = σ el N n υ H + (H − ) , where σ el , N n , υ H + (H − ) is the elastic collision cross section between ions and neutrals, neutral number density, ion drift velocity, respectively) in the xzplane (y = 25 cm) of double-driver source are presented in figure 3. Results illustrate that the frequency ratio is larger  than 1 in most region for H + and H − ions due to the strong B and the light m H + (H − ) , indicating that it is essential to consider ion magnetization in NHIS.In particular, the maxima of the frequency ratio appear near the center of both driver regions as well as in the middle of the expansion region due to the weak electric field there (see figure 2(d)), which results in the lower ion drift velocity and thus the lower collision frequency.
The comparison of plasma parameters in the xz-plane (y = 25 cm), calculated without and with ion magnetization, is illustrated in figure 4. When ion magnetization is not considered, both the maxima of the electron density and H + ion density appear in the driver region, and the density in Driver II is higher than that in Driver I.When ion magnetization is considered, the H + ion density rises from 3.15 × 10 18 m −3 to 3.22 × 10 18 m −3 .This is because the transport of ions to the vessel wall is hindered by the magnetic field, and thus the loss of ions is reduced when ion magnetization is taken into account.Besides, the maximum electron density increases from 3.35 × 10 18 m −3 to 3.41 × 10 18 m −3 due to the ambipolar diffusion effect.Note that the H − density increases obviously and exhibits a more pronounced off-axis (x = 28 cm for Driver I and x = 72 cm for Driver II) distribution in the case with ion magnetization, which is attributed to the E × B-drift.The two orders of magnitude difference between the electron density and the H − density explains why a slight change in the electron density distribution leads to a significant change in the H − density distribution.
Figure 5 presents the influence of ion magnetization on the spatial distributions of plasma parameters in the xy-plane (z = 22 cm).Figure 5(e) indicates that the H + density exhibits two maxima, located at the positions corresponding to Driver I and II, respectively.When ion magnetization is considered, H + ions more easily transport along the magnetic field line (y-direction), resulting in a more uniform distribution along the y-axis (figure 5(f )).The electron density distribution exhibits similar variation (figure 5(b)), which is caused by the reduced potential drop along the y-direction due to the decline of the ion density gradient.It is worth noting that although the maximum value of the electron density decreases in the case with ion magnetization, the averaged density in the xyplane becomes higher, which promotes the generation of H − ions, as shown in figure 5(h).Indeed, the H − density in the case with ion magnetization is three times higher than that without consideration of ion magnetization.Besides, the electron temperature is higher at the vessel walls near the magnetic block and the value at the center of the chamber is much lower, both in the cases without and with ion magnetization (see figures 5(c) and (d)), due to the constraint of energetic electrons in the region with strong magnetic field.By introducing the ion magnetization, the electron temperature throughout the chamber drops, because electrons loss more energy due to the enhanced ionization.
In order to detect the influence of ion magnetization on the plasma uniformity more clearly, figure 6 presents the distributions of the electron density and H − density along four  intercept lines (x = 30, 50, 70 cm and y = 25 cm) as depicted in figure 5(a).Triangular and circular symbols represent the results in the cases without and with ion magnetization, respectively.Figures 6(a) and (c) present the results along intercept lines in the y-direction, and the inhomogeneity degree α is defined as α = (n max − n min )/2n ave [30], where n max , n min , and n ave refer to the maximum, minimum, and average density along the intercept line.Figures 6(b) and (d) show the results along the intercept line in the x-direction, and the asymmetry degree β is defined as β = (n I − n II )/(n I + n II ) [26],  where n I and n II represent the density at x = 28 cm (n I ) and 72 cm (n II ).It is clear that when ion magnetization is taken into account, α decreases significantly by approximately 0.3 for both the electron density and H − density.The change in β for the electron density is less obvious, whereas the uniformity of the H − density becomes worse, i.e. an increase of approximately 0.13 is observed in β.
To validate the model developed in this work, the simulation results have been compared with experimental measurements in a single-driver source of a test-bed in Southwestern Institute of Physics (SWIP), and the reactor geometry has been introduced in detail in [9].In the experiment, a surface wave probe is used to measure the electron density along y-direction at x = 16.5 cm and z = 23 cm, under different pressures at 5 kW.It can be seen from figure 7 that the electron density distribution obtained in the absence of ion magnetization is less uniform than the experimental results.While, when ion magnetization is taken into account, the calculated plasma profile agrees quite well with experimental data.Therefore, the ion magnetization is included in the subsections, for more consistent simulation of the actual physical process.

Effect of coil power
In this subsection, the influence of the power of Driver I on the plasma parameters is discussed, and the power of Driver II is fixed at 40 kW.The pressure is fixed at 0.6 Pa.When an input power of 40 kW is applied for both drivers, the electron  density maximum occurs at the off-center position of each driver (figure 8(a)).This is because electrons transport along the negative x-direction due to the E × B-drift, which enhances the loss on the left wall and reduces the loss on the right wall of each driver region.Besides, the maximum electron density in Driver II is higher than that in Driver I, and this can be explained by the discrepancy in the magnetic field distribution, as shown in figure 2(a) above.Indeed, the magnetic field on the left wall of driver II (at x = 58 cm) is stronger than that on the left wall of Driver I (at x = 14 cm), which reduces wall loss in Driver II and consequently leads to the higher electron density there.
In order to optimize the plasma symmetry in the doubledriver source, the power of Driver I has been adjusted, as shown in figure 8.When P absI is 42 kW, the maximum electron density in Driver I increases from 3.23 × 10 18 m −3 to 3.39 × 10 18 m −3 , while the electron density in Driver II remains almost unchanged, giving rise to the better symmetry.As P absI rises further, the electron density in Driver I gradually becomes comparable and even exceeds that in Driver II, and the symmetry becomes worse again when P absI is above 48 kW.In contrast to the electron density, the influence of P absI on the electron temperature and H − density is less obvious, which is therefore not shown here.
Figure 9 shows the variation of the electron density (first row), electron temperature (second row), H − density (third row) and plasma potential (fourth row) in the xy-plane (z = 22 cm) with P absI .It is clear from figures 9(a), (e) and (i) that the asymmetry in the electron density, electron temperature and H − density at the lower portion of the expansion region is also pronounced at P absI of 40 kW.For instance, the electron density and H − density in Expansion region I is lower than in Expansion region II, which is again due to the E × B-drift along the positive x-direction.Whereas, the electron temperature in Expansion region I is slightly higher than in Expansion region II.
With the increase of P absI , a greater number of electrons are transported from Driver I to Expansion region I, resulting in a significant rise in the electron density and H − density there.For instance, the maximum electron density in Expansion region I increases from 11.6 × 10 16 m −3 to 15.5 × 10 16 m −3 , and the maximum H − density rises from 2.0 × 10 15 m −3 to 2.6 × 10 15 m −3 as P absI changes from 40 kW to 52 kW.Although P absII is fixed at 40 kW, the electron density in Expansion region II also exhibits a slight increase.This is due to the transport of electrons along the positive xdirection in the expansion region.However, the H − density in Expansion region II decreases slightly, which is related to the change in the potential at the bottom of the expansion region.Indeed, as P absI increases, the potential in Expansion region II declines faster, giving rise to the symmetric potential distribution in the expansion region (see figures 9(m)-(p)).Note that although the H − density in Expansion region II exhibits a slight decline, the total H − generation in the whole expansion chamber is enhanced, i.e. the volume-averaged H − density increases from 3.34 × 10 15 m -3 at P absI = 40 kW to 3.63 × 10 15 m -3 at P absI = 52 kW.Besides, the electron temperature in the Expansion region I and II decreases with P absI , which can be attributed to the enhanced collisional energy loss caused by the higher electron density.Comparing the results obtained at various powers, it is concluded that the asymmetry of the electron density between Expansion regions I and II is minimized at 48 kW, and the optimal parameter for H − density is 52 kW.

Effect of partition height
In this subsection, a metal partition is applied in the middle of the expansion region to limit the drift of electrons in the x-direction, and thereby improve the spatial symmetry of the plasma parameters.As shown in figure 1, the partition is located at x = 50 cm, with height (h p ) of 4 cm, 8 cm, 12 cm, and 16 cm.The pressure is 0.6 Pa, and the power for both drivers is fixed at 40 kW.
Figure 10 presents the spatial distributions of the electron temperature (first row) and H − density (second row) in the xz-plane (y = 25 cm) at various partition heights.The electron density in this plane is almost unchanged with increasing h p and is therefore not shown here.The electron temperature in the driver region remains unchanged as partition height rises, whereas an increase is observed on the right side of the partition.This is because electrons drift along the negative xdirection in the upper part of the expansion region, and only energetic electrons can reach the surface of the partition which has a higher potential gradient there.Besides, partition height has an influence on the H − density distribution in Expansion region I, due to the fact that low energy H − ions can hardly reach the vicinity of the partition.
The spatial distributions of the plasma parameters in the xy-plane (z = 22 cm) at the bottom of the expansion region for various partition heights are given in figure 11.It is clear that as partition height increases, the deflection of electrons from Expansion region I to Expansion region II is prevented, giving rise to more electron loss on the left side of the partition, and thus both the electron density in Expansion region I and II becomes lower.Since the decrease of the electron density in Expansion region II with partition height is more pronounced, the maximum electron density in Expansion region I becomes comparable to that in region II at h p = 16 cm, indicating the better symmetry is achieved.However, the continuity of the electron density in the whole expansion region becomes worse.
Besides, as partition becomes higher, the electron temperature in Expansion region I decreases slightly, while the value in region II rises significantly.This is due to the fact that the higher partition prevents electrons drift along the negative x-direction in the upper part of the expansion region, so more energetic electrons are accumulated on the right side of the partition (see figures 10(a)-(d)).Since the electron temperature at the bottom of the expansion region is mainly determined by the downward energy transportation, the electron temperature at the bottom of Expansion region II rises with partition height, and a reverse trend is observed in region I.It is concluded that the electron temperature in region II gradually exceeds that in region I as partition height rises, indicating that the symmetry of the electron temperature can be adjusted by changing h p .
The H − density in Expansion region I decreases monotonically with increasing h p , whereas the value in Expansion region II first increases and then decreases.This is because when h p is less than 8 cm, the transport of H − ions along the positive x-direction at the bottom of the expansion region is not affected, while the transport of H − ions in the negative x-direction at the top of the expansion region is hindered (see figures 10(e) and (f )).As a result, the H − density in Expansion region I declines and the density in Expansion region II becomes higher.However, when h p is greater than 8 cm, the partition is high enough to hinder the transport of H − ions along the positive x-direction (see figures 10(g) and (h)), and meanwhile H − ions in the whole expansion region slightly move upwards because of the stronger electric field in the z-direction caused by the partition (see figures 11(m)-(p)).As a result, both the H − density in Expansion region I and II decreases when partition is higher than 8 cm.Consequently, it is concluded that the addition of partition has no effect on improving the H − density symmetry.

Effect of magnetic shield
Finally, the influence of magnetic shield on the plasma parameters are discussed.The pressure is 0.6 Pa, and the power for both drivers is fixed at 40 kW.To minimize the penetration of the magnetic field into the driver region, high-permeability iron (4 × 10 3 relative permeability) is applied on the back plate located at the intersection of the driver region and expansion region, as shown in figure 1. Figure 12(a) illustrates the magnetic filter field distribution in the xz-plane with the implementation of magnetic shield, and a comparison between the magnetic induction intensity in the cases with and without magnetic shield along x = 28 cm is depicted in figure 12(b).It is clear that the application of magnetic shield effectively reduces the magnetic induction intensity throughout the whole chamber, especially in the driver region.However, the ratio of ion cyclotron frequency to collision frequency is still larger than 1 in most regions throughout the chamber (not shown here), indicating that the ions are still magnetized.
Figure 13 illustrates the distributions of the plasma parameters in the xz-plane (y = 25 cm) with and without magnetic shield.It can be found that the inclusion of magnetic shield leads to a significant decrease in both the electron density and electron temperature in the driver region, because the weaker magnetic field in the driver region reduces the localization.As a result, more electrons could transport to the bottom of the expansion region, and this enhances the production of negative hydrogen ions there.Consequently, the maximum of H − density moves downwards with a much higher value.
Figure 14 illustrates the distributions of the plasma parameters in the xy-plane (z = 22 cm) with and without magnetic shield, and the results indicate that when magnetic shield is applied, the maximum electron density at the bottom of the expansion region increases by approximately three times, and the maximum negative hydrogen ion density increases by approximately twice.This is again due to the enhanced downward transportation of electrons, which promotes the production of H − ions.Meanwhile, the electron temperature decreases significantly, due to the increased collision frequency caused by the higher electron density.Besides, the symmetry of the electron density and H − density has also been improved by the reduction of the magnetic field near the driver region.

Conclusion
A 3D fluid model is developed in this work for investigation of the double-driver ion source, which is designed by SWIP for the NBI system in CFETR.The magnetic filter field is induced by 16 permanent magnets, and the magnetic induction intensity is about 70 Gs at the center of the bottom of the expansion region, and it is about 1.56 × 10 3 Gs at the wall near the magnet.In this work, the magnetization of both electrons and ions is taken into account to make the model more accurate and reliable.Indeed, magnetization of ions has an important influence on the plasma properties.For instance, the inhomogeneity of the electron density and negative hydrogen ion density at the bottom of the expansion region in the y-direction is significantly reduced.However, there is a more pronounced off-axis displacement of the negative hydrogen ions in the xz-plane, and the symmetry of the negative hydrogen ion density in the x-direction becomes worse.A comparison between experiments and simulations in a single-driver source indicates that with ion magnetization taken into account in the model, the numerical results agree much better with experimental data.
In order to suppress the asymmetry of the plasma parameters due to horizontal drift caused by the magnetic filter field, three methods have been proposed, i.e. varying the power of Driver region I, changing the height of partition and adding a magnetic shield.When P absII is fixed at 40 kW, the electron density in Driver I increases strikingly with P absI , while the value in Driver II is almost unchanged, resulting in the best symmetry at P absI of 42 kW.At the bottom of the expansion region, both the electron density in region I and II increases with P absI , while the H − density in Expansion region I increases with P absI but the value in Expansion region II declines, with the best symmetry appearing at 48 kW.Besides, the symmetry of the electron density and temperature at the bottom of the expansion region could also be improved by increasing the partition height, but the influence on the symmetry of the H − density is less obvious.Note that the addition of a partition may reduce the efficiency of NHIS, so its application is limited.Finally, a magnetic shield is introduced, which could reduce the magnetic field throughout the driver region.Therefore, the locality of the electron density is weakened, which gives rise to the higher electron density at the bottom of the expansion region and thus enhances the production of negative hydrogen ions there.Besides, the symmetry of the electron density and H − density becomes better when magnetic shield is applied.Therefore, it is concluded that application of magnetic shield is the most effective method in enhancing both the symmetry of the plasma parameters and the density of negative hydrogen ions.In the future work, the model will be extended to the ion sources with 4 drivers or 8 drivers, with surface production of negative hydrogen ions taken into account, to make the model more helpful for the development of the full-scale NHIS.

Figure 1 .
Figure 1.Schematic diagram of the double-driver NHIS.
(a).Note that the xz-planes below are all taken at y = 25 cm by default.It is clear that the magnetic field strength is approximately 70 Gs at the bottom center of the expansion region, and it reduces to 10-30 Gs in the driver region.The magnetic field strength in the whole xy-plane (z = 22 cm) ranges from 31 to 1.56 × 10 3 Gs, and figure 2(b) shows only the magnetic field distribution in the vital extracted region (i.e. 10 cm < x < 90 cm and 9 cm < y < 41 cm) of this plane.Note that if not specified, the xy-planes below are all plotted at x = 22 cm by default.It is observed that the magnetic field is strong near the magnet block and weak in the center of the chamber.The electric field distribution in the xzplane (y = 25 cm) of the double-driver source is illustrated in figure2(d).There is a stronger electric field near the vessel walls and a weaker electric field near the center of both driver regions and expansion region.
Figure 2(e) shows the electric field distribution in the vital extracted region of xyplane (z = 22 cm).It can be found that the left side at the bottom of the expansion region has higher values compared to the right side.

Figure 2 .
Figure 2. Magnetic filter field configuration generated by the permanent magnet in the (a) xz-plane (y = 25 cm) and (b) xy-plane (z = 22 cm).The direction of magnetic fields in the yz-plane (x = 50 cm) and xy-plane (z = 22 cm) is given as normalized arrows (c).Electric field in the (d) xz-plane (y = 25 cm) and (e) xy-plane (z = 22 cm).The direction of electric field in the xz-plane (y = 25 cm) is given as normalized arrows (f).

Figure 3 .
Figure 3. Distributions of the ratio of cyclotron frequency to collision frequency for (a) H + and (b) H − .The power is 40 kW, and the pressure is 0.6 Pa.

Figure 4 .
Figure 4. Spatial distributions of the electron density, H + density and H − density in the xz-plane (y = 25 cm) in the cases without and with ion magnetization.The power is 40 kW, and the pressure is 0.6 Pa.

Figure 5 .
Figure 5. Spatial distributions of the electron density, electron temperature, H + density and H − density in the xy-plane (z = 22 cm) in the cases without and with ion magnetization.The power is 40 kW, and the pressure is 0.6 Pa.

Figure 6 .
Figure 6.Distributions of the electron density and H − density along four intercept lines indicated in figure 5(a).The power is 40 kW, and the pressure is 0.6 Pa.

Figure 7 .
Figure 7. Normalized electron density obtained from the simulation (red curve with square symbol for the case without ion magnetization and blue curve with triangular symbol for the case with ion magnetization) and experimental measurement (pink curve with circular symbol) at (a) 0.3 Pa and (b) 0.5 Pa.The power is fixed at 5 kW.

Figure 8 .
Figure 8. Distributions of the electron density in the xz-plane (y = 25 cm) for various P absI , and P absII is fixed at 40 kW.

Figure 9 .
Figure 9. Distributions of the electron density (first row), electron temperature (second row), H − density (third row) and plasma potential (fourth row) in the xy-plane (z = 22 cm) for various P absI , and P absII is fixed at 40 kW.

Figure 10 .
Figure 10.Distributions of the electron temperature (first row) and H − density (second row) in the xz-plane (y = 25 cm) for various partition heights.

Figure 11 .
Figure 11.Distributions of the electron density (first row), electron temperature (second row), H − density (third row) and electric field in the z-direction (fourth row) in the xy-plane (z = 22 cm) for various partition heights.

Figure 12 .
Figure 12.(a) Magnetic filter field configuration in the case with magnetic shield.(b) Comparison of magnetic filter field configuration at the intercept line x = 28 cm in the cases with and without magnetic shield.

Figure 13 .
Figure 13.Distributions of the electron density (first row), electron temperature (second row) and H − density (third row) in the xz-plane (y = 25 cm) in the cases with and without magnetic shield.

Figure 14 .
Figure 14.Distributions of the electron density (first row), electron temperature (second row) and H − density (third row) in the xy-plane (z = 22 cm) in the cases with and without magnetic shield.