Neutral beam injection (NBI) systems based on negative hydrogen ion sources—rather than the positive ion sources that have typically been used to date—will be used in the future magnetically confined nuclear fusion experiments to heat the plasma. The collisions between the fast negative ions and neutral background gas result in a significant number of high-energy positive ions being produced in the acceleration area, and for the high-power long-pulse operation of NBI systems, this acceleration of positive ions back to the ion source creates heat load and material sputtering on the source backplate. This difficulty cannot be ignored, with the neutral gas density in the acceleration region having a significant impact on the flux density of the backstreaming positive ions. In the work reported here, the pressure gradient in the acceleration region was estimated using an ionization gauge and a straightforward 1D computation, and it was found that once gas traveled through the acceleration region, the pressure dropped by nearly one order of magnitude, with the largest pressure drop occurring at the plasma grid. The computation also revealed that the pressure drop in the grid gaps was substantially smaller than that in the grid apertures.

Topics
Electrostatics, Underwater instruments, Vacuum apparatus, Monte Carlo methods, Plasma confinement, Fusion experiments, Tokamaks, Ion source, Laser physics, Viscosity

  • A simple 1D calculation is used to predict the pressure gradient in a high-power negative ion source accelerator.

  • The calculation has the primary pressure drop occurring in the aperture, whereas experiments show that it occurs mainly in the grid gaps.

  • The pressure decreases linearly when the pumping speed is neglected, whereas experiments indicate that it actually decreases exponentially.

Topics
Electrostatics, Underwater instruments, Vacuum apparatus, Monte Carlo methods, Plasma confinement, Fusion experiments, Tokamaks, Ion source, Laser physics, Viscosity

Auxiliary heating systems are needed to deliver more energy for lengthy pulses in large tokamak devices such as EAST (Experimental and Advanced Superconducting Tokamak) and ITER (International Thermonuclear Experimental Reactor).1,2 For plasma heating and current driving, EAST has been equipped with neutral beam injection (NBI) systems based on positive ion sources. However, future massive fusion reactors such as ITER,3,4 DEMO,5 and CFETR6 require high beam energy, and negative ions have a substantially better neutralization efficiency than do positive ions.

As higher-energy and longer-pulse neutral beams are generated by ion sources, the backplate of the arc chamber and acceleration grids will collect more backstreaming particles, and the production processes and behavior of the backstreaming electrons and positive ions have already been well studied.7–9 According to the estimation by Hu et al., the particle flux of the first category accounts for 13.88% of the total beam current and the power flux of the first category accounts for ∼6.5% of the total beam power at EAST-NBI.10 Those studies were all based on estimating the pressure gradient in the acceleration region of an RF negative ion source, and herein we describe an ionization-gauge experiment and a specific computation for estimating the acceleration pressure.

As shown in Fig. 1, HUNTER (Hefei Utility Negative ions Test Equipment with RF source) has been designed and developed at the Institute of Plasma Physics, Chinese Academy of Sciences (known as ASIPP, from Anhui Institute of Plasma Physics) to explore RF negative ion sources for NBI applications.11,12 The negative ion accelerator is a single-stage acceleration system comprising three grids, i.e., a plasma grid (PG), an extraction grid (EG), and a ground grid (GG), each made of copper and divided into four identical segments. In the first research phase, only the middle two groups of segments were used for extraction to match the single RF driver. Each segment consisted of 6 × 5 apertures, the aperture spacing was 22 × 20 mm2, and the aperture geometry of each grid is shown in Fig. 2.13,14 The first gap (PG-EG) and the second gap (EG-GG) were used for beam extraction and acceleration, respectively, and to suppress the leakage of secondary electrons and steer the negative ion beam, a molybdenum grid [electron suppression grid (ESG)] was attached to the EG at the same electric potential.

FIG. 1.
Image of HUNTER with an RF source.
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Image of HUNTER with an RF source.

FIG. 1.
Image of HUNTER with an RF source.
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Image of HUNTER with an RF source.

Close modal
FIG. 2.
Left: 3D diagram of negative ion source. Right: detailed geometries of grid apertures (units: mm).
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Left: 3D diagram of negative ion source. Right: detailed geometries of grid apertures (units: mm).

FIG. 2.
Left: 3D diagram of negative ion source. Right: detailed geometries of grid apertures (units: mm).
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Left: 3D diagram of negative ion source. Right: detailed geometries of grid apertures (units: mm).

Close modal

A straightforward 1D calculation was used to estimate the pressure gradient in the RF negative ion source accelerator. During the test, only ten channels on the PG participated in the extraction and the rest were closed, and the ESG was not installed in the negative ion source. Considering the symmetry, one of the beam extraction channels was selected to calculate the channel diameter.

Figure 3 shows a simplified structural model of the negative ion source accelerator. The surface of the PG facing the arc chamber is taken as the x-axis zero point, and the beam extraction direction is the positive direction of the x-axis. This allows the diameter function of a single beam channel to be described as
d(x)=0.02,x∈0,0.0028,RegionI−209x−0.0028+0.022,x∈0.0028,0.0064,RegionII,54x+0.006,x∈0.0064,0.008,RegionIII0.02,x∈0.008,0.014,RegionIV,0.012,x∈0.014,0.019,RegionV,47x−0.019+0.012,x∈0.019,0.026,RegionVI,0.02,x∈0.026,0.044,RegionVII,0.16,x∈0.044,0.054,RegionVIII.(m)
FIG. 3.
Simplified structure of negative ion source accelerator.
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Simplified structure of negative ion source accelerator.

FIG. 3.
Simplified structure of negative ion source accelerator.
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Simplified structure of negative ion source accelerator.

Close modal
However, region I is no longer an independent channel because of the overlapping holes, and the 30 holes are merged into a channel that for calculation convenience is reduced to a cuboid channel with a cross-section of 0.11 × 0.12 m2 and a length of 0.0028 m. The electrode plates are integrated, so regions IV and VII are cuboid channels with a cross-section of 0.253 × 0.266 m2 and lengths of 0.006 and 0.018 m, respectively. Therefore, the modified function can be described as
d(x)=[0.11×0.12],x∈[0.0028],RegionI,cuboid−209(x−0.0028)+0.002,x∈[0.0028,0.0064],RegionII,conical54x+0.006,x∈[0.0064,0.008],RegionIII,conical[0.253×0.266],x∈(0.0008,0.014),RegionIV,cuboid0.012,x∈[0.014,0.019],RegionV,circular47(x−0.019)+0.012,x∈[0.019,0.026],RegionVI,conical[0.253×0.266],x∈(0.026,0.044),RegionVII,cuboid0.16,x∈[0.044,0.054],RegionVIII,circular(m).
Generally, the nature of the fluid flow in the channel is assessed using the product of p̄ (the average pressure of the gas in the channel) and d (the diameter of the channel):15 it is viscous flow for p̄d>0.67Pa⋅m⁠, molecular flow for p̄d<0.02Pa⋅m⁠, and transition flow for 0.02Pa⋅m<p̄d<0.67Pa⋅m⁠. According to the current operating parameters of HUNTER, the operating gas is hydrogen, the arc chamber pressure is 0.5 Pa, the gas flow rate is 0.2 Pa·m3/s, and the vacuum pumping rate is 2 m3/s. Considering that there is no discharge plasma in the chamber and the temperature is room temperature, for convenience we assume a constant temperature of 300 K for the gas and the components. Because the gas pressure does not change much in region Ⅰ, we assume an average gas pressure of 0.5 Pa. Therefore, the product of p̄ and d can be expressed as
p̄d≈pmd=0.5×0.11=0.55Pa⋅m∈0.02,0.67Pa⋅m,
and so the flow in region Ⅰ is transition flow.
The molecular mean free path is
λ̄=3.107×10−24Tpσ2,
where T (K) is the temperature, p (Pa) is the gas pressure, and σ (m) is the molecular diameter. Taking T = 300 K, p ≈ pm = 0.5 Pa, and σ = 2.75 × 10−10 m, we obtain λ̄ ≈ 0.024 650 6 m.
The transition flow conductance of the cuboid channel can be expressed as
(1)
where Un (m3/s) is the viscous flow conductivity of the cuboid channel, Kj is the shape coefficient of the cuboid channel for transition flow (see Fig. 4),15  Uf (m3/s) is the molecular flow conductance of the cuboid channel, and a (m) is the length of the short side of the cross section. Taking Kj ≈ 1.04 and a = 0.11 m, the conductance of region Ⅰ can be simplified as
(2)
FIG. 4.
Shape coefficient Kj of cuboid channel for transition flow.
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Shape coefficient Kj of cuboid channel for transition flow.

FIG. 4.
Shape coefficient Kj of cuboid channel for transition flow.
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Shape coefficient Kj of cuboid channel for transition flow.

Close modal
The viscous flow conductance of the cuboid channel can be expressed as
(3)
where a and b (m) are the side lengths of the cross section, η (Pa·s) is the viscosity coefficient, L (m) is the channel length, p̄ (Pa) is the average gas pressure in the channel, and ψ is the shape coefficient of the cuboid channel for viscous flow, which is related to the side lengths of the cross section as shown in Fig. 5;15 here, we take ψ = 0.38.
FIG. 5.
Shape coefficient ψ of cuboid channel for viscous flow.
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Shape coefficient ψ of cuboid channel for viscous flow.

FIG. 5.
Shape coefficient ψ of cuboid channel for viscous flow.
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Shape coefficient ψ of cuboid channel for viscous flow.

Close modal
Considering the influence of temperature on the viscosity coefficient, the latter can be expressed as
(4)
where M (kg/mol) is the gas molar mass and C (K) is the Sutherland constant, which for hydrogen is C = 76 K. Therefore, the viscosity coefficient is η ≈ 7.031 61 × 10−6 Pa s at 300 K.
Substituting the various parameters into Eq. (3), we obtain
(5)
and the molecular flow conductance of the cuboid channel can be expressed as
(6)
where Kj is the shape coefficient of the cuboid channel for molecular flow (see Table I);15 here, we take Kj = 1.11. Substituting the various parameters into Eq. (6), we obtain
(7)
TABLE I.

Shape coefficient Kj of cuboid channel for molecular flow.

b/a12/31/21/31/51/81/10
Kj 1.108 1.126 1.151 1.198 1.297 1.400 1.444 
b/a12/31/21/31/51/81/10
Kj 1.108 1.126 1.151 1.198 1.297 1.400 1.444 
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Substituting Eqs. (5) and (7) into Eq. (2), we obtain
(8)
and from the definition of conductance, we have
(9)
where Q (Pa·m3/s) is the intake air volume. Considering that each grid is composed of two segments, there are two beam extraction channels in region I. Using Q = 0.2 Pa·m3/s and P0 = p(x)∣x=0 = 0.5 Pa and substituting Eq. (8) into Eq. (9), we obtain
(10)
(11)
(12)
By applying the same method, the gas pressure in the acceleration region can be expressed as
(13)
and substituting the various parameters into Eq. (13), we obtain the pressure at special positions as follows:
(14)
(15)
(16)
(17)
(18)
(19)
(20)
With a vacuum pumping rate of 2 m3/s and a gas flow rate of 0.2 Pa·m3/s, the ultimate gas pressure is 0.1 Pa, and the calculation shows that P8 is larger than 0.1 Pa, which meets the actual operating conditions. From the above calculation, the gas pressure profile in the accelerator is obtained as shown in Fig. 6, and we find that the main pressure-decreasing trend is in the aperture rather than the gird gaps, with the largest pressure drop occurring at the extraction grid.
FIG. 6.
Gas pressure profile in negative ion source accelerator.
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Gas pressure profile in negative ion source accelerator.

FIG. 6.
Gas pressure profile in negative ion source accelerator.
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Gas pressure profile in negative ion source accelerator.

Close modal

As shown in Fig. 7, Schiesko et al. calculated the pressure profile in a negative ion source accelerator to estimate the flux density of the backstreaming positive ions.9 The difference was that their calculation was for a source pressure of 0.4 Pa, which is close to that required in ITER; their profile for MANITU (Multi Ampere Negative Ion Test Unit) and our profile for HUNTER were both calculated from the source pressure and the conductance of the grid apertures. Schiesko et al. also tested using their computation for the ITER NBI extraction system, and the pressure profile that was produced agreed to within 20% with a thorough Monte Carlo model.9 Krylov and Hemsworth used simple models that could be verified by comparison with “classical” cases in which the Knudsen formula for gas conductance is applicable, and then they used a Monte Carlo model for the complex geometry of the beam source, demonstrating agreement to within 5%.16 Straightforward 1D computation is used frequently in the industry, and the acceptable difference between the calculated results and the real values offers help in designing ion source accelerators.

FIG. 7.
Pressure and electrostatic potential in accelerator of NBI testbed MANITU.
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Pressure and electrostatic potential in accelerator of NBI testbed MANITU.

FIG. 7.
Pressure and electrostatic potential in accelerator of NBI testbed MANITU.
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Pressure and electrostatic potential in accelerator of NBI testbed MANITU.

Close modal

The experiments were performed at HUNTER, and with no plasma present, they were operated solely with gas input. A slim pipe containing a vacuum gauge was extended to the accelerator’s assigned location through the reserved flange on the back plate of the arc chamber; this pipe had a length and inner diameter of ∼1 and 0.01 m, respectively, and because it had very low gas flow conductance, a sufficiently long gas ingress time was required to ensure that the pressure recorded by the vacuum gauge accurately reflected the local environment. Two campaigns were conducted, one with single turbopump operation and the other with double turbopump operation, and for each campaign the air intake was set at 50–130 Pa·L/s for different source pressures.

The pressure profile with single turbopump operation is shown in Fig. 8. In this case, the pressure decreased exponentially at each gas flow rate; it decreased rapidly in the first grid aperture, and the largest pressure drop occurred at the plasma grid, which differs from the computational prediction. On the whole in the experiment, the gas pressure decreased by an order of magnitude after passing through the accelerator and did not decrease after the GG. By contrast, the calculation predicts significantly lower pressure drops in the grid gaps than those in the grid apertures.

FIG. 8.
Pressure profile with single turbopump operation.
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Pressure profile with single turbopump operation.

FIG. 8.
Pressure profile with single turbopump operation.
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Pressure profile with single turbopump operation.

Close modal

The pressure profile with double turbopump operation is shown in Fig. 9, and these pressure characteristics are similar to those with single turbopump operation. Increasing the pumping speed led to less-accurate results, and the pressure after the second gap differed less with variation in the gas flow rate. Under each gas flow rate, the pressure at the arc chamber was less than that at the beginning of the PG, and the cause of this phenomenon is still being analyzed.

FIG. 9.
Pressure profile with double turbopump operation.
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Pressure profile with double turbopump operation.

FIG. 9.
Pressure profile with double turbopump operation.
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Pressure profile with double turbopump operation.

Close modal

In Fig. 10, comparing the pressures at the same gas flow rate and different pumping speeds shows that the pressure difference in the first gap was less than that in the second gap. At every position in the accelerator, the pressure was twice as high under double turbopump operation as it was under single turbopump operation.

FIG. 10.
Pressure profiles with gas flow rate of 90 Pa·L/s.
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Pressure profiles with gas flow rate of 90 Pa·L/s.

FIG. 10.
Pressure profiles with gas flow rate of 90 Pa·L/s.
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Pressure profiles with gas flow rate of 90 Pa·L/s.

Close modal

In this study, a straightforward 1D calculation was used to predict the pressure gradient in a high-power negative ion source accelerator, and after two gaps, it was found that the pressure was reduced by almost half. However, in experiments, the pressure was observed to decrease more rapidly with near-exponential decrease, and it was logical for the pressure gradient to be influenced significantly by the pumping speed. In the calculation, the main pressure decreases were in the apertures rather than in the gird gaps as observed experimentally; the pressure decreased linearly because the pumping speed was neglected, whereas the experimental results indicated that it decreased exponentially. Future work will include simulations involving the gas flow status.

This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFC2202700).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Wu Mingshan was born in July 1991 and graduated from the University of Science and Technology of China in 2020 with a doctorate in science. Currently, he is a postdoctoral researcher at Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences. His research mainly focuses on applying the theory of low-temperature plasma physics in the field of electric thrusters, which entails conducting simulation analysis and experimental research on the Hall Micro Thruster and performing thrust performance calibration of sub-micro Newton thrusters.

© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).