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Numerical simulation of beam current control mechanism in the thermionic electron gun
Vacuum 164 (2019) 278–285
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Numerical simulation of beam current control mechanism in the thermionic electron gun
T
Jikang Fana,b,∗, Yong Penga,b, Junqiang Xua,b, Haiying Xua,c, Dongqing Yanga,b, Xiaopeng Lia,b,d, Qi Zhoua,b a
School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China Key Laboratory of Controlled Arc Intelligent Additive Manufacturing Technology, Nanjing University of Science and Technology, Nanjing, 210094, China c Beijing Aeronautical Manufacturing Technology Research Institute, Beijing, 100024, China d State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, 150001, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electron beam welding Thermionic electron gun Numerical simulation Beam current control CST software
The thermionic electron gun is one of essential parts of electron accelerators and vacuum tubes. For electron beam generation it is basically configured by cathode, anode and it can have control electrode. In common electron guns, beam current is typically controlled by the bias voltage on the Wehnelt electrode. To deeply study the control mechanism of electron beam current, a three-dimensional model of a 60 kV/6 kW thermionic electron gun is established and the simulation of electric field distribution with CST software is shown in this paper. The particle tracking model is used to track the movement of emitted electrons and the quantitative relationship between beam current and bias voltage is established. Results show that electron beam current is inversely proportional to the bias voltage within a certain range. As the bias voltage increases, the electric field distribution in electron gun changes and the equipotential line of accelerating voltage moves towards the emitting surface of cathode, therefore the Effective Emitting Area (EEA) of cathode decreases and, accordingly, the beam current also decreases. Besides, when the bias voltage is fixed, fluctuations of the accelerating voltage cause fluctuations of the beam current, which is especially severe when the beam current is small.
1. Introduction Electron guns can provide electron beams with required parameters and are used in a variety of applications, including metallurgical applications such as melting, welding, coating, annealing, heat treatment and surface hardening [1–5]. Although the electron gun is usually only a small fraction of the entire machining system, its characteristics are crucial for the quality of the emitted electron beams [6]. Today, a wide variety of electron guns are in use with different accelerating voltages, power, beam configurations and transmitter types, but these are usually axisymmetric thermionic electron guns [7,8]. The structure of a thermionic electron gun is shown in Fig. 1. It consists of a cathode, a Wehnelt electrode (also known as control electrode) and an anode. The cathode is fixed by a special clamping tool and heated directly by the passing current. When the cathode is heated to a certain temperature, the energy of the electrons is greater than the vacuum potential and work function, so the electrons can be emitted towards the anode under the action of the accelerating voltage [9]. In state of the art electron guns, the primary means of beam current
∗
adjustment is to change the voltage on the Wehnelt electrode [10], which is at a negative bias voltage with respect to the cathode. In accordance with the physical law that like charges repel, when considerable negative bias voltage is applied to the Wehnelt electrode, the electric field is capable of repelling the escaped electrons back towards the cathode despite the potential difference between the cathode and the anode, thereby shutting off the beam current. If reducing the bias voltage, the electric field below the cathode surface will turn into accelerating electric field and the electrons begin to move towards the anode. Therefore the beam current can be adjusted by changing the bias voltage on the Wehnelt electrode [11]. The thermionic electron gun usually works under vacuum condition of tens or even hundreds of thousands of volts, so the emitted electrons move at a normalized speed of light ranging from 0.3 to 0.7. It is quite difficult to study the beam current control process by using the experimental method, which is expensive, laborious and time-consuming. Numerical simulation plays an increasingly important role in the analysis and optimization of such electron guns. It allows to study various electron-optical problems which are analytically intractable and
Corresponding author. School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China. E-mail address: [email protected] (J. Fan).
https://doi.org/10.1016/j.vacuum.2019.03.040 Received 8 January 2019; Received in revised form 19 March 2019; Accepted 21 March 2019 Available online 23 March 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 2. Models of the cathode, Wehnelt electrode and anode.
Fig. 1. The structure of a thermionic electron gun.
difficult to perform by direct experiments. The numerical simulation of electron guns provides both detailed insight into physics essence of electrons motion and basic method for improving quality of electron beam [12]. Ghalib-ul-Islam et al. [13] simulated a hairpin source electron beam gun for maximum emission density and low emissivity of the beam through optimizing electromagnetic focusing process using EGUN program. Reinard Becker and William B. Herrmannsfeldt [14] discussed the application of computer simulation in the design and optimization of the essential components of electron guns. Pavel Jánský et al. [15] proposed a numerical simulation method of the hairpin thermionic electron gun. A new algorithm for simulating space charge limited emission was developed and implemented in the EOD program, which enables to simulate the electric optical system. Hoseinzade et al. [16] studied the influence of the voltage applied to the focusing electrode, inclination angle of emission electrode and the diameter of focusing electrode on the beam emittance and beam diameter of the electron gun, and simulated the electron beam trajectories of different parameters by using CST. Alberto Leggieri et al. [17] simulated the electric field distributions and beam dynamics by Finite Element Method to evaluate the thermal mechanical effects induced by the cathode heating on the whole device. Studying the beam current control mechanism in thermionic electron guns is the prerequisite for the optimization of control scheme and mechanical design. In this paper, a three-dimensional model of thermionic electron gun for electron beam welding is established. The electric field distribution, relationship between bias voltage and beam current, beam current control principle and the influence of accelerating voltage fluctuations are simulated through the CST software, which gives us a further understanding of the beam current control mechanism of thermionic electron guns.
Fig. 3. Relative positional relationship of cathode, Wehnelt electrode and anode.
their relative positional relationship is shown in Fig. 3. The explanation of dimension and position parameters in Figs. 2 and 3 are as follows. D1: side width of the cathode emitting surface; D2: side length of the cathode emitting surface; Ra: radius of the Wehnelt electrode emitting aperture; Rb: spherical radius of the Wehnelt electrode; Rc: radius of anode emission aperture; H1: distance between cathode emitting surface and anode; H2: distance between the cathode emitting surface and the bottom of the Wehnelt electrode emitting aperture. The values of these parameters (D1, D2, Ra, Rb, Rc, H1, H2) are shown in Table 1 and remain unchanged during the numerical simulation in order to ensure the consistency of the simulation results.
2. Simulation models 2.1. Electron gun model The electron gun simulated is a direct-heating Q60-A thermionic electron gun independently developed by China Aviation Manufacturing Technology Research Institute [18]. The established 3D models of cathode, Wehnelt electrode and anode are shown in Fig. 2 [19]. The models are imported into the CST software based on the actual size. The cathode, Wehnelt electrode and anode are placed sequentially from top to bottom along the axis of the electron gun and
Table 1 The values of dimensions and position parameters.
279
Parameter
D1
D2
Ra
Rb
Rc
H1
H2
Value (mm)
2
2
2
20
2.5
20
0.5
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space charge limited emission current and this emission mode is called the space charge limited emission mode. At this time, the maximum current emission density JeR is a function of the acceleration voltage (seen as Curve 2 in Fig. 4) and can be obtained by the Child-Langmuir formula, as Eq. (2)[24].
2.2. Cathode emission model The cathode used herein is a direct-heating ribbon cathode which has been widely used in electron beam welding machines and can be considered as a small resistance in the circuit. The electrons escaping from the cathode have two emission modes in the thermionic electron gun, namely temperature-limited emission and space charge-limited emission [11]. The electrons emitted from a thermionic cathode belong to the Maxwellian tail of the Fermi-Dirac distribution, and the thermionic saturation current density is given by the Richardson-Dushman equation [20]. When an accelerating electric field is applied to the cathode, the potential barrier decreases and the emission increases following the Schottky's law, so that the thermionic current density JeT can be approximated by the Schottky modified Richardson-Dushman thermal electron emission formula, as Eq. (1)[21].
JeT =
AT 2exp(
−(Eφ − e3/2ε1/2 KT
)
JeR = C
U 3/2 d2
(2)
Where C is constant related to the characteristics of the particle and gun geometry, U is the voltage difference between the cathode and the anode, and d is the distance between the cathode and the anode. According to Eq. (2), we can get the saturation current of the electron gun as shown in Eq. (3).
Ia = JeR ·S = C
U 3/2 ·S = G·U 3/2 d2
(3)
Where S is the area of the cathode emitting surface, G is called perveance. In the space charge limited emission mode, high temperature of cathode must be set by adjusting the heating current so that even at the maximum accelerating voltage sufficient electrons are still available. Under these conditions, the cathode will be surrounded by a cloud of “superfluous” electrons which have an inherent charge and limit any further emission of electrons. When the accelerating voltage is Uc, the relationship between electron emission current density and the temperature is shown in Fig. 4(Curve 2). When the temperature is lower than T1, the cathode works in temperature limited emission mode. When the cathode temperature is higher than T2, it works in space charge limited emission mode and the current emission density reaches the maximum value Jc. At this moment, the beam current almost remains unaffected by variations of the cathode temperature. In practical use, the cathode works in the space charge limited emission mode in order to keep the electrons beam current constant. During the simulation, we define the emission type of the particle source as space charge limited emission mode. The cathode heating temperature is set to 2700 K and the work function is 4.54 eV.
(1)
Where A is the theoretical value of the Richardson emission constant, T is cathode temperature, Eφ is the cathode work function, e is the electron charge, ɛ is the electric field strength, and K is the Boltzmann constant. According to Eq. (1), when the acceleration voltage is fixed, the emitted beam current density is a function of the cathode temperature, seen as Curve 1 in Fig. 4. In this case, the emission current density JeT strongly depends upon the temperature of the cathode so that a low variation in temperature (ΔT in Fig. 4) has a considerable influence on the beam current (ΔJeT in Fig. 4). This emission mode is called temperature-limited emission mode [22,23]. For electron beam welding with stringent requirements in terms of weld seam reproducibility, this type of dependency is extremely detrimental. Actually, under the action of an accelerating electric field, space charge occurs between the cathode and the anode. At this time, the lowest potential point is between the two poles, which is called virtual cathode. As a consequence, the electrons leaving the cathode form a stationary cloud, which repels the incoming electrons from cathode by the coulombian force impressed by the space charge. Hence, the beam current saturates to a fixed value and limits the electric field becoming no linear no more. This phenomenon is regulated by the Child and Langmuir law. Based on Child and Langmuir's space charge theory, when given a fixed accelerating voltage, the accelerating electric field is only able to extract a given maximum electron current from the cathode due to geometric parameters such as the distance between the cathode and the anode, etc. The maximum electron current is referred to as
2.3. Simulation environment model CST is a simulation software for analyzing the relativistic and nonrelativistic motions of freely charged particles and electromagnetic fields. It is especially suitable for quickly and effectively analyzing the motion of electrons in electromagnetic fields and the optimization of electron guns structure [25,26]. In the simulation environment, the materials of cathode, anode, and Wehnelt electrode are set to ideally conductive materials, and the background is set to vacuum. Since the final drop position of the electron beam is far from the anode, the axial minimum of the background space is set to 300 mm. The rated power and operating voltage of Q60-A thermionic electron gun are 6 kW and 60 kV respectively. In the simulation model, the anode potential is set to 0 V, the cathode potential is set to −60 kV, and the maximum beam current is set to 100 mA. The bias voltage between cathode and Wehnelt electrode potential ranges from 0 V to 1000 V, namely the potential of Wehnelt electrode ranges from −60 kV to −61 kV. Since no other factors are shielded when the electron gun model is established, the boundary conditions are all set to open state and the magnetic field component is set to zero. Before simulating, it is necessary to mesh the electron gun. The electron gun model is meshed by automatic meshing method and local encrypted meshing method. The whole electron gun model is automatically meshed first, then the areas near the cathode, Wehnelt electrode and anode are locally encrypted. 2.4. Theoretical emission model According to the cathode emission model, if no space charge effects are considered, the value of electric field strength (ε ) could be estimated
Fig. 4. Cathode emission model. 280
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by Eq. (4).
ε=
Ua d
(4)
In order to include the effect of space charge, the value ε of can be found by the space charge limited distribution of the field as Eq. (5) [27].
ε=
4 Ua 3 d
(5)
For this electron gun, a directly heated tungsten cathode has been and work function employed with A = 15 × 103 A m2 K2 Eφ = 4.54 eV at the temperature of T = 2700 K. Based on Eq. (1) and Eq. (4), the cathode can emit a current density of JeT = 2.52 A/cm2. JeT can be seen as the saturation current density (JeR) in the space-charge emission mode. According to Child-Langmuir Eq. (3), the perveance G can be given by Eq. (6).
G=
JeR⋅S U 3/2
Fig. 6. Trajectory of electron beam when the bias voltage is 0 V.
along the central axis. The electrons escaping from the cathode are completely in the accelerating electric field, and can move towards the workpiece through the emission aperture of anode. At this time, the electron beam current depends only on the cathode heating temperature and the space charge limiting current. The motion process of the electrons is tracked by CST software when the bias voltage is 0 V, and the trajectory of electrons is shown in Fig. 6. Under the action of the electric field, electrons move from the cathode to the workpiece through the small emission aperture of the anode, and react with the workpiece. During the movement of the electron beam, due to the electric focusing action of the Wehnelt electrode, the electron beam forms a crossover at a certain position on the central axis called the ‘beam waist’. ‘Beam waist’ is known as the position of real crossover, of which the shape and position results both from the geometry and the voltage applied to the control electrode [28]. Once the electron beam passes through the anode and into a region free of electrical field, its geometric shape will not change until it reaches the focusing lens.
(6)
Considering the desired accelerating voltage (60 kV) and saturation current density (2.52 A/cm2), the perveance for this electron gun is 6.86 × 10−3 μperv. If all the cathode surface was the emitter, the desired current (100 mA) could be obtained with a cathode surface of 3.97 mm2, so the model of cathode surface area in this paper is set to 4 mm2. Note that, under the control voltage on the Wehnelt electrode, not all the cathode surface can emit electrons to the anode. According to the above analysis, the beam current should be related to the emission state of electrons in front of the cathode surface. 3. Simulation results and discussions 3.1. Electric field distribution The motion state of the electrons is determined by the internal electric field of the electron gun. Studying the distribution of the electric field inside the electron gun is the premise for realizing the electron beam current control mechanism. When the bias voltage between the cathode and the Wehnelt electrode is 0 V, the simulation results of the electric field distribution inside the electron gun are shown in Fig. 5. We can see in Fig. 5(a), the potential gradually increases from −60000 V to 0 V along the central axis from the cathode to the anode, reaching 0 V on the anode surface. We can see in Fig. 5(b), the potential gradually increases and reaches 0 V on the anode surface from the Wehnelt electrode to the central axis, which causes the electrons to move towards the central axis, generating a focus position
3.2. Beam current control principle The change in bias voltage causes a change of the electric field inside the electron gun and thus the movement behavior of the electrons changes. To study the influence of different bias values on the internal electric field of the electron gun, we maintain the accelerating voltage at −60 kV and select different bias voltages (250 V, 500 V, 750 V, 1000 V) to simulate the electric field. In order to observe the details of the electric field change, only the local electric field around the cathode is analyzed, and the processing result only shows the equipotential lines higher than −60 kV. At different bias voltages, the distribution of the
Fig. 5. Electric field distribution. 281
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Fig. 7. Electric field distribution at different bias voltages. 282
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equipotential lines around the cathode is shown in Fig. 7. As shown in Fig. 7(a), when the bias voltage is 250 V, the potential at both the upper and the periphery of the cathode is lower than −60 kV, but the potential below the lower surface of the cathode is higher than −60 kV. At this point, the electrons escaping from the cathode are completely in the accelerating electric field, and all electrons can be emitted to the anode. When the bias voltage increases to 500 V, as shown in Fig. 7(b), the −60 kV equipotential line below the cathode moves from the periphery to the middle, so the electrons escaping from the edge of the cathode are in the decelerating electric field and the electrons escaping from the center position of the cathode are in the accelerating electric field. Only the electrons in the accelerating electric field can move towards the anode, while the electrons in the decelerating electric field remain around the cathode, which is equivalent to that only a part of the cathode surface is capable of emitting electrons to the anode [29]. When the bias voltage continues increasing to 750 V, as shown in Fig. 7(c), the −60 kV equipotential line continues to move towards the middle. Only a small part of the escaped electrons in the center of the cathode are in the emission state and other parts of the electrons are in the emission suppression state. When the bias voltage increases to 1000 V, as shown in Fig. 7(d), the −60 kV equipotential lines below the cathode coincide at a certain position, causing the potential under the cathode is less than −60 kV, at which time all the electrons escaping from the cathode are in the emission suppression state and the beam current is 0 mA. According to the above simulation results, the bias voltage is to adjust the beam current by adjusting the emission state of the electrons escaping from the cathode. During the bias voltage adjustment process, only the electrons escaping from part of cathode surface can be accelerated towards the anode due to the control of the electric field. This part of the cathode surface is referred to as the Effective Emitting Area (EEA) in this paper. As shown in Fig. 7, the reason why bias voltage can adjust the beam current is that the bias voltage can change the EEA of the cathode. To observe the change state of the EEA when the bias voltage changes, the emission states of the electrons on the cathode surface are captured when the bias voltages are 500 V and 750 V and the results are shown in Fig. 8. When the bias voltage is 500 V, the EEA is larger than that when the bias voltage is 750 V, so that more electrons can be emitted, which proves the role and function of EEA of the cathode.
Table 2 Simulated and theoretically calculated beam current under different bias voltages. Bias Voltage (V)
Simulated Beam Current (mA)
Effective Emitting Area (mm2)
Theoretical Beam Current (mA)
Error (mA)
0 250 350 400 450 500 550 600 650 700 750 800 850 1000
100.00 100.00 100.00 97.47 86.23 70.84 57.16 41.94 28.47 17.84 8.32 1.80 0.00 0.00
4.00 4.00 4.00 3.90 3.45 2.83 2.30 1.68 1.14 0.71 0.33 0.08 0.00 0.00
100.80 100.80 100.80 98.28 86.94 71.32 57.96 42.34 28.73 17.89 8.32 2.01 0.00 0.00
0.80 0.80 0.80 1.01 0.71 0.48 0.80 0.40 0.26 0.05 0.00 0.21 0.00 0.00
current density is only related to the acceleration voltage, but beam current can be adjusted by adjusting the EEA of the cathode according to the electric field simulation results. Although it is known that the bias voltage and the beam current are approximately inversely proportional within a certain range [30], the quantitative relationship among the bias voltage, EEA and beam current is rarely studied. Here, the CST software is used to track the motion of electrons in the electron gun, and the beam current and EEA corresponding to different bias voltage conditions are obtained. When the acceleration voltage is set to 60 kV and the maximum beam current is set to 100 mA, the simulation results are shown in Table 2. It is assumed that the change in bias voltage only changes the EEA without changing the emission mode of the electron. According to Eq. (3) and the ratio of the EEA to the total emitting surface of the cathode, we can get Eq. (7) to calculate the theoretical beam current value.
I = Ia⋅
3 s se = G·U 2 · e s s
(7)
Where Se is the area of EEA. The theoretical beam currents under different bias voltages are shown in Table 2. We can see that the simulation results are very close to the calculated results. The maximum error is only 1.01 mA. In order to visually observe the trend of beam current with bias voltage, the relationship between bias voltage and beam current is drawn as in Fig. 9 based on the results of the simulation. We can see that the beam current varies with the bias voltage. When
3.3. Relationship between bias voltage and beam current It can be seen from Child-Langmuir formula that when the electron gun works in the space charge emission mode, the saturation beam
Fig. 8. EEA at different bias voltages. 283
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influence of the acceleration voltage fluctuation on the beam current value also increases. When the bias voltage is 450 V, the beam current fluctuates from −0.94 mA to 0.95 mA and the change rate ranges from −1.09% to 1.10%. When the bias voltage increases to 600 V, the beam current fluctuates from −1.13 mA to 1.19 mA and the change rate ranges from −2.69% to 2.91%. As the bias voltage increases to 750 V, although the beam current value is small, the acceleration voltage fluctuation has a greater influence on the beam current. At this time, the beam current fluctuates from −1.53 mA to 1.55 mA, and the change rate ranges from −19.59% to 18.03%. In summary, when the bias voltage and the cathode temperature are fixed, the fluctuations of the accelerating voltage cause the fluctuations of beam current, which is particularly severe when the beam current value is small. Therefore, in order to make the beam current highly repeatable and reliable, the accelerating voltage should have less ripple and higher stability. 4. Conclusions
Fig. 9. The relationship between bias voltage and beam current.
(1) The relationship between bias voltage and beam current is quantitatively analyzed with CST software. Over a range of bias voltage, the electron beam current is inversely proportional to the bias voltage. (2) The concept of Effective Emitting Area (EEA) has been introduced as a cathode figure of merit. The ability of the bias voltage to modify the beam current can be identified in the capability of bias voltage to regulate the excitation states of surface electrons in different positions of the cathode. Hence, EEA can be identified as the area of the cathode where the emission takes place. The saturation effect can be also seen as the reduction of that area. The reason why the beam current can be adjusted by adjusting the bias voltage is that the bias voltage regulates the EEA. (3) When the bias voltage and the cathode temperature are fixed, the fluctuations of the accelerating voltage will cause the fluctuations of beam current, which is particularly severe when the beam current is small.
Table 3 Effect of voltage fluctuation on beam current. Bias voltage (V)
Accelerating voltage (kV)
Beam current (mA)
Change value (mA)
Change rate (%)
450
59.4 60 60.6 59.4 60 60.6 59.4 60 60.6
85.29 86.23 87.18 40.81 41.94 43.16 6.79 8.32 9.87
−0.94 0 0.95 −1.13 0.00 1.19 −1.53 0.00 1.55
−1.09 0 1.10 −2.69 0.00 2.91 −19.59 0.00 18.03
600
750
the bias voltage is lower than 350 V, all the electrons escaping from the cathode are completely emitted. When the bias voltage is between 350 V and 850 V, the beam current decreases as the bias voltage increases, and they are approximately linear. When the bias value reaches 850 V or higher, the electrons escaping from the cathode are suppressed. No electrons are emitted and the beam current is 0 mA. Assuming that the bias voltage is X and the emitted electron beam current is Y, the linear relationship between the beam current and the bias voltage is obtained according to the least squares method when the bias voltage is between 350 V and 850 V, as shown in Eq. (8).
Y = −0.25X + 195.8
Acknowledgment The research is financially supported by National Nature Science Foundation of China (No. 51805265, 51805266), Natural Science Foundation of Jiangsu Province (No. BK20180472), and the State Key Lab of Advanced Welding and Joining of Harbin Institute of Technology.
(8)
In this formula, the linear correlation coefficient R2 is 0.99. We conclude that the electron beam current is linearly proportional to the bias voltage within a certain range and the linearity is very high.
Appendix A. Supplementary data
3.4. Influence of accelerating voltage fluctuations
References
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.vacuum.2019.03.040.
In the electron beam welding process, the welding power is determined by the accelerating voltage and beam current. When the welding beam current is constant, the higher the acceleration voltage, the greater the welding power. However, when the accelerating voltage changes, the electric field inside the electron gun changes accordingly, which has an influence on the emission of electrons and beam current. When the high voltage fluctuates at 1% below and above 60 kV (59.4 kV and 60.6 kV respectively), the influence of accelerating voltage fluctuations on the beam current is simulated at different bias voltages (450 V, 600 V, 750 V) and the results are shown in Table 3. As can be seen from Table 3, when the accelerating voltage fluctuates downward, the beam current value will decrease accordingly. When the accelerating voltage fluctuates upward, the beam current value will increase accordingly. As the bias value increases, the
[1] M. Iqbal, I. Shaukat, A. Mahmood, K. Abbas, M.A. Haq, Surface modification of mild steel with Boron Carbide reinforcement by electron beam melting, Vacuum 85 (2010) 45–47, https://doi.org/10.1016/j.vacuum.2010.03.009. [2] J. Karlsson, A. Snis, H. Engqvist, J. Lausmaa, Characterization and comparison of materials produced by Electron Beam Melting (EBM) of two different Ti-6Al-4V powder fractions, J. Mater. Process. Technol. 213 (2013) 2109–2118, https://doi. org/10.1016/j.jmatprotec.2013.06.010. [3] W. Zhang, H. Fu, J. Fan, R. Li, H. Xu, F. Liu, B. Qi, Influence of multi-beam preheating temperature and stress on the buckling distortion in electron beam welding, Mater. Des. 139 (2018) 439–446, https://doi.org/10.1016/j.matdes.2017.11.016. [4] Y. Sun, X. Lin, X. He, J. Zhang, M. Li, G. Song, X. Li, Y. Zhao, Effects of substrate rotation on the microstructure of metal sheet fabricated by electron beam physical vapor deposition, Appl. Surf. Sci. 255 (2009) 5831–5836, https://doi.org/10.1016/ j.apsusc.2009.01.013. [5] M. Ormanova, P. Petrov, D. Kovacheva, Electron beam surface treatment of tool steels, Vacuum 135 (2017) 7–12, https://doi.org/10.1016/j.vacuum.2016.10.022. [6] A.V. Shcherbakov, M.V. Ivashchenko, A.S. Kozhechenko, M.S. Gribkov, Parametric analysis in the design of technological electron beam guns, Russ. Electr. Eng. 87
284
Vacuum 164 (2019) 278–285
J. Fan, et al.
[18] Y. Ye, C. Zuo, H. Xu, X. Sang, Application of CST simulation Technology in focusing parts of electron beam guns, Aeronaut. Manuf. Technol. 60 (2017) 78–82, https:// doi.org/10.16080/j.issn1671-833x.2018.09.078. [19] X. Sang, H. Xu, C. Zuo, K. Fan, CST simulation on effect of beam source component struture size on beam quality in electron guns, Aeronaut. Manuf. Technol. 9 (2017) 60–64, https://doi.org/10.16080/j.issn1671-833x.2017.09.060. [20] R. Martin, Theory and Design of Charged Particle Beams, Second, WILEY-VEH Verlag Gmbh & Co.KGaA, Weinheim, 2008. [21] J.D. Kowalczyk, M. Hadmack, J. Madey, Laser cooling to counteract back-bombardment heating in microwave thermionic electron guns, FEL 2013 Proc. 35th Int. Free. Laser Conf, 2013, pp. 79–81. [22] Y.S. Yeh, M.H. Tsao, H.Y. Chen, T.-H. Chang, Improved computer program for magnetron injection gun design, Int. J. Infrared Millim. Waves 21 (2000) 1397–1415, https://doi.org/10.1023/a:1026400906433. [23] S. Coulombe, J. Meunier, Thermo-field emission : a comparative study, J. Phys. D Appl. Phys. 30 (1997) 776–780. [24] V.V. Altsybeyev, V.A. Ponomarev, Application of Gauss's law space-charge limited emission model in iterative particle tracking method, J. Comput. Phys. 324 (2016) 62–72, https://doi.org/10.1016/j.jcp.2016.08.007. [25] H. Spachmann, U. Becker, Electron gun simulation with CST PARTICLE STUDIO, Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip. 558 (2006) 50–53, https://doi.org/10.1016/j.nima.2005.11.075. [26] Y.X. Wei, M.G. Huang, S.Q. Liu, B.L. Hao, P.K. Liu, Numerical simulation of TWT electron gun, Vacuum 92 (2013) 90–94, https://doi.org/10.1016/j.vacuum.2012. 12.003. [27] V.A. Syrovoi, A theory of narrow relativistic electron beams, J. Commun. Technol. Electron. 52 (2007) 910–931, https://doi.org/10.1134/S106422690708013X. [28] C. Shen, Y. Peng, K. Wang, Q. Zhou, Measurement of power density distribution and beam waist simulation for electron beam, Radiat. Phys. Chem. 83 (2013) 8–14, https://doi.org/10.1016/j.radphyschem.2012.09.016. [29] B. Qi, J. Fan, W. Zhang, F. Liu, H. Wang, A novel control grid bias power supply for high-frequency pulsed electron beam welding, Vacuum 133 (2016) 46–53, https:// doi.org/10.1016/j.vacuum.2016.08.015. [30] O.K. Nazarenko, Circuitry of Electron Beam Welding Current Control, first ed, E.O.Paton Electric Welding Institute of the NAS of Ukraine, Kiev, 2013.
(2016) 41–45, https://doi.org/10.3103/S1068371216010089. [7] A. Nehra, L.M. Joshi, R.K. Gupta, S. Sharma, Y. Choyal, R.K. Sharma, Design and simulation of pole piece for focusing of multi-beam electron gun, J. Infrared, Millim. Terahertz Waves 32 (2011) 793–800, https://doi.org/10.1007/s10762011-9783-8. [8] S.P. Sabchevski, G.M. Mladenov, S. Wojcicki, J. Dabek, An analysis of electron guns for welding, J. Phys. D Appl. Phys. 29 (1996) 1446–1453, https://doi.org/10.1088/ 0022-3727/29/6/006. [9] D.M. Goebel, R.M. Watkins, Compact lanthanum hexaboride hollow cathode, Rev. Sci. Instrum. 81 (2010) 1–6, https://doi.org/10.1063/1.3474921. [10] K. Bücker, M. Picher, O. Crégut, T. LaGrange, B.W. Reed, S.T. Park, D.J. Masiel, F. Banhart, Electron beam dynamics in an ultrafast transmission electron microscope with Wehnelt electrode, Ultramicroscopy 171 (2016) 8–18, https://doi.org/ 10.1016/j.ultramic.2016.08.014. [11] lng H. Schultz, Electron Beam Welding, (1993), https://doi.org/10.3131/jvsj.3. 206. [12] S. Sabchevski, G. Mladenov, A. Titov, I. Barbarich, Modelling and simulation of beam formation in electron guns, Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrom., Detect. Assoc. Equip. 381 (1996) 185–193, https://doi.org/10. 1016/S0168-9002(96)00830-3. [13] G.U. Islam, A. Rehman, M. Iqbal, Z. Zhou, Simulation and test of a thermioic hairpin source DC electron beam gun, Optik 127 (2016) 1905–1908, https://doi.org/10. 1016/j.ijleo.2015.11.132. [14] R. Becker, W.B. Herrmannsfeldt, The design of electron and ion guns, beams, and collectors, J. Phys. Conf. Ser. 2 (2004) 152–163, https://doi.org/10.1088/17426596/2/1/019. [15] P. Jánský, J. Zlámal, B. Lencová, M. Zobač, I. Vlček, T. Radlička, Numerical simulations of the thermionic electron gun for electron-beam welding and micromachining, Vacuum 84 (2009) 357–362, https://doi.org/10.1016/j.vacuum.2009. 07.007. [16] M. Hoseinzade, M. Nijatie, A. Sadighzadeh, Numerical simulation and design of a thermionic electron gun, Chin. Phys. C 40 (2016) 1–7, https://doi.org/10.1088/ 1674-1137/40/5/057003. [17] A. Leggieri, D. Passi, F. Di Paolo, B. Spataro, E. Dyunin, Design of a sub-millimetric electron gun with analysis of thermomechanical effects on beam dynamics, Vacuum 122 (2015) 103–116, https://doi.org/10.1016/j.vacuum.2015.09.013.
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Numerical simulation of beam current control mechanism in the thermionic electron gun
T
Jikang Fana,b,∗, Yong Penga,b, Junqiang Xua,b, Haiying Xua,c, Dongqing Yanga,b, Xiaopeng Lia,b,d, Qi Zhoua,b a
School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China Key Laboratory of Controlled Arc Intelligent Additive Manufacturing Technology, Nanjing University of Science and Technology, Nanjing, 210094, China c Beijing Aeronautical Manufacturing Technology Research Institute, Beijing, 100024, China d State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, 150001, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electron beam welding Thermionic electron gun Numerical simulation Beam current control CST software
The thermionic electron gun is one of essential parts of electron accelerators and vacuum tubes. For electron beam generation it is basically configured by cathode, anode and it can have control electrode. In common electron guns, beam current is typically controlled by the bias voltage on the Wehnelt electrode. To deeply study the control mechanism of electron beam current, a three-dimensional model of a 60 kV/6 kW thermionic electron gun is established and the simulation of electric field distribution with CST software is shown in this paper. The particle tracking model is used to track the movement of emitted electrons and the quantitative relationship between beam current and bias voltage is established. Results show that electron beam current is inversely proportional to the bias voltage within a certain range. As the bias voltage increases, the electric field distribution in electron gun changes and the equipotential line of accelerating voltage moves towards the emitting surface of cathode, therefore the Effective Emitting Area (EEA) of cathode decreases and, accordingly, the beam current also decreases. Besides, when the bias voltage is fixed, fluctuations of the accelerating voltage cause fluctuations of the beam current, which is especially severe when the beam current is small.
1. Introduction Electron guns can provide electron beams with required parameters and are used in a variety of applications, including metallurgical applications such as melting, welding, coating, annealing, heat treatment and surface hardening [1–5]. Although the electron gun is usually only a small fraction of the entire machining system, its characteristics are crucial for the quality of the emitted electron beams [6]. Today, a wide variety of electron guns are in use with different accelerating voltages, power, beam configurations and transmitter types, but these are usually axisymmetric thermionic electron guns [7,8]. The structure of a thermionic electron gun is shown in Fig. 1. It consists of a cathode, a Wehnelt electrode (also known as control electrode) and an anode. The cathode is fixed by a special clamping tool and heated directly by the passing current. When the cathode is heated to a certain temperature, the energy of the electrons is greater than the vacuum potential and work function, so the electrons can be emitted towards the anode under the action of the accelerating voltage [9]. In state of the art electron guns, the primary means of beam current
∗
adjustment is to change the voltage on the Wehnelt electrode [10], which is at a negative bias voltage with respect to the cathode. In accordance with the physical law that like charges repel, when considerable negative bias voltage is applied to the Wehnelt electrode, the electric field is capable of repelling the escaped electrons back towards the cathode despite the potential difference between the cathode and the anode, thereby shutting off the beam current. If reducing the bias voltage, the electric field below the cathode surface will turn into accelerating electric field and the electrons begin to move towards the anode. Therefore the beam current can be adjusted by changing the bias voltage on the Wehnelt electrode [11]. The thermionic electron gun usually works under vacuum condition of tens or even hundreds of thousands of volts, so the emitted electrons move at a normalized speed of light ranging from 0.3 to 0.7. It is quite difficult to study the beam current control process by using the experimental method, which is expensive, laborious and time-consuming. Numerical simulation plays an increasingly important role in the analysis and optimization of such electron guns. It allows to study various electron-optical problems which are analytically intractable and
Corresponding author. School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China. E-mail address: [email protected] (J. Fan).
https://doi.org/10.1016/j.vacuum.2019.03.040 Received 8 January 2019; Received in revised form 19 March 2019; Accepted 21 March 2019 Available online 23 March 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 2. Models of the cathode, Wehnelt electrode and anode.
Fig. 1. The structure of a thermionic electron gun.
difficult to perform by direct experiments. The numerical simulation of electron guns provides both detailed insight into physics essence of electrons motion and basic method for improving quality of electron beam [12]. Ghalib-ul-Islam et al. [13] simulated a hairpin source electron beam gun for maximum emission density and low emissivity of the beam through optimizing electromagnetic focusing process using EGUN program. Reinard Becker and William B. Herrmannsfeldt [14] discussed the application of computer simulation in the design and optimization of the essential components of electron guns. Pavel Jánský et al. [15] proposed a numerical simulation method of the hairpin thermionic electron gun. A new algorithm for simulating space charge limited emission was developed and implemented in the EOD program, which enables to simulate the electric optical system. Hoseinzade et al. [16] studied the influence of the voltage applied to the focusing electrode, inclination angle of emission electrode and the diameter of focusing electrode on the beam emittance and beam diameter of the electron gun, and simulated the electron beam trajectories of different parameters by using CST. Alberto Leggieri et al. [17] simulated the electric field distributions and beam dynamics by Finite Element Method to evaluate the thermal mechanical effects induced by the cathode heating on the whole device. Studying the beam current control mechanism in thermionic electron guns is the prerequisite for the optimization of control scheme and mechanical design. In this paper, a three-dimensional model of thermionic electron gun for electron beam welding is established. The electric field distribution, relationship between bias voltage and beam current, beam current control principle and the influence of accelerating voltage fluctuations are simulated through the CST software, which gives us a further understanding of the beam current control mechanism of thermionic electron guns.
Fig. 3. Relative positional relationship of cathode, Wehnelt electrode and anode.
their relative positional relationship is shown in Fig. 3. The explanation of dimension and position parameters in Figs. 2 and 3 are as follows. D1: side width of the cathode emitting surface; D2: side length of the cathode emitting surface; Ra: radius of the Wehnelt electrode emitting aperture; Rb: spherical radius of the Wehnelt electrode; Rc: radius of anode emission aperture; H1: distance between cathode emitting surface and anode; H2: distance between the cathode emitting surface and the bottom of the Wehnelt electrode emitting aperture. The values of these parameters (D1, D2, Ra, Rb, Rc, H1, H2) are shown in Table 1 and remain unchanged during the numerical simulation in order to ensure the consistency of the simulation results.
2. Simulation models 2.1. Electron gun model The electron gun simulated is a direct-heating Q60-A thermionic electron gun independently developed by China Aviation Manufacturing Technology Research Institute [18]. The established 3D models of cathode, Wehnelt electrode and anode are shown in Fig. 2 [19]. The models are imported into the CST software based on the actual size. The cathode, Wehnelt electrode and anode are placed sequentially from top to bottom along the axis of the electron gun and
Table 1 The values of dimensions and position parameters.
279
Parameter
D1
D2
Ra
Rb
Rc
H1
H2
Value (mm)
2
2
2
20
2.5
20
0.5
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space charge limited emission current and this emission mode is called the space charge limited emission mode. At this time, the maximum current emission density JeR is a function of the acceleration voltage (seen as Curve 2 in Fig. 4) and can be obtained by the Child-Langmuir formula, as Eq. (2)[24].
2.2. Cathode emission model The cathode used herein is a direct-heating ribbon cathode which has been widely used in electron beam welding machines and can be considered as a small resistance in the circuit. The electrons escaping from the cathode have two emission modes in the thermionic electron gun, namely temperature-limited emission and space charge-limited emission [11]. The electrons emitted from a thermionic cathode belong to the Maxwellian tail of the Fermi-Dirac distribution, and the thermionic saturation current density is given by the Richardson-Dushman equation [20]. When an accelerating electric field is applied to the cathode, the potential barrier decreases and the emission increases following the Schottky's law, so that the thermionic current density JeT can be approximated by the Schottky modified Richardson-Dushman thermal electron emission formula, as Eq. (1)[21].
JeT =
AT 2exp(
−(Eφ − e3/2ε1/2 KT
)
JeR = C
U 3/2 d2
(2)
Where C is constant related to the characteristics of the particle and gun geometry, U is the voltage difference between the cathode and the anode, and d is the distance between the cathode and the anode. According to Eq. (2), we can get the saturation current of the electron gun as shown in Eq. (3).
Ia = JeR ·S = C
U 3/2 ·S = G·U 3/2 d2
(3)
Where S is the area of the cathode emitting surface, G is called perveance. In the space charge limited emission mode, high temperature of cathode must be set by adjusting the heating current so that even at the maximum accelerating voltage sufficient electrons are still available. Under these conditions, the cathode will be surrounded by a cloud of “superfluous” electrons which have an inherent charge and limit any further emission of electrons. When the accelerating voltage is Uc, the relationship between electron emission current density and the temperature is shown in Fig. 4(Curve 2). When the temperature is lower than T1, the cathode works in temperature limited emission mode. When the cathode temperature is higher than T2, it works in space charge limited emission mode and the current emission density reaches the maximum value Jc. At this moment, the beam current almost remains unaffected by variations of the cathode temperature. In practical use, the cathode works in the space charge limited emission mode in order to keep the electrons beam current constant. During the simulation, we define the emission type of the particle source as space charge limited emission mode. The cathode heating temperature is set to 2700 K and the work function is 4.54 eV.
(1)
Where A is the theoretical value of the Richardson emission constant, T is cathode temperature, Eφ is the cathode work function, e is the electron charge, ɛ is the electric field strength, and K is the Boltzmann constant. According to Eq. (1), when the acceleration voltage is fixed, the emitted beam current density is a function of the cathode temperature, seen as Curve 1 in Fig. 4. In this case, the emission current density JeT strongly depends upon the temperature of the cathode so that a low variation in temperature (ΔT in Fig. 4) has a considerable influence on the beam current (ΔJeT in Fig. 4). This emission mode is called temperature-limited emission mode [22,23]. For electron beam welding with stringent requirements in terms of weld seam reproducibility, this type of dependency is extremely detrimental. Actually, under the action of an accelerating electric field, space charge occurs between the cathode and the anode. At this time, the lowest potential point is between the two poles, which is called virtual cathode. As a consequence, the electrons leaving the cathode form a stationary cloud, which repels the incoming electrons from cathode by the coulombian force impressed by the space charge. Hence, the beam current saturates to a fixed value and limits the electric field becoming no linear no more. This phenomenon is regulated by the Child and Langmuir law. Based on Child and Langmuir's space charge theory, when given a fixed accelerating voltage, the accelerating electric field is only able to extract a given maximum electron current from the cathode due to geometric parameters such as the distance between the cathode and the anode, etc. The maximum electron current is referred to as
2.3. Simulation environment model CST is a simulation software for analyzing the relativistic and nonrelativistic motions of freely charged particles and electromagnetic fields. It is especially suitable for quickly and effectively analyzing the motion of electrons in electromagnetic fields and the optimization of electron guns structure [25,26]. In the simulation environment, the materials of cathode, anode, and Wehnelt electrode are set to ideally conductive materials, and the background is set to vacuum. Since the final drop position of the electron beam is far from the anode, the axial minimum of the background space is set to 300 mm. The rated power and operating voltage of Q60-A thermionic electron gun are 6 kW and 60 kV respectively. In the simulation model, the anode potential is set to 0 V, the cathode potential is set to −60 kV, and the maximum beam current is set to 100 mA. The bias voltage between cathode and Wehnelt electrode potential ranges from 0 V to 1000 V, namely the potential of Wehnelt electrode ranges from −60 kV to −61 kV. Since no other factors are shielded when the electron gun model is established, the boundary conditions are all set to open state and the magnetic field component is set to zero. Before simulating, it is necessary to mesh the electron gun. The electron gun model is meshed by automatic meshing method and local encrypted meshing method. The whole electron gun model is automatically meshed first, then the areas near the cathode, Wehnelt electrode and anode are locally encrypted. 2.4. Theoretical emission model According to the cathode emission model, if no space charge effects are considered, the value of electric field strength (ε ) could be estimated
Fig. 4. Cathode emission model. 280
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by Eq. (4).
ε=
Ua d
(4)
In order to include the effect of space charge, the value ε of can be found by the space charge limited distribution of the field as Eq. (5) [27].
ε=
4 Ua 3 d
(5)
For this electron gun, a directly heated tungsten cathode has been and work function employed with A = 15 × 103 A m2 K2 Eφ = 4.54 eV at the temperature of T = 2700 K. Based on Eq. (1) and Eq. (4), the cathode can emit a current density of JeT = 2.52 A/cm2. JeT can be seen as the saturation current density (JeR) in the space-charge emission mode. According to Child-Langmuir Eq. (3), the perveance G can be given by Eq. (6).
G=
JeR⋅S U 3/2
Fig. 6. Trajectory of electron beam when the bias voltage is 0 V.
along the central axis. The electrons escaping from the cathode are completely in the accelerating electric field, and can move towards the workpiece through the emission aperture of anode. At this time, the electron beam current depends only on the cathode heating temperature and the space charge limiting current. The motion process of the electrons is tracked by CST software when the bias voltage is 0 V, and the trajectory of electrons is shown in Fig. 6. Under the action of the electric field, electrons move from the cathode to the workpiece through the small emission aperture of the anode, and react with the workpiece. During the movement of the electron beam, due to the electric focusing action of the Wehnelt electrode, the electron beam forms a crossover at a certain position on the central axis called the ‘beam waist’. ‘Beam waist’ is known as the position of real crossover, of which the shape and position results both from the geometry and the voltage applied to the control electrode [28]. Once the electron beam passes through the anode and into a region free of electrical field, its geometric shape will not change until it reaches the focusing lens.
(6)
Considering the desired accelerating voltage (60 kV) and saturation current density (2.52 A/cm2), the perveance for this electron gun is 6.86 × 10−3 μperv. If all the cathode surface was the emitter, the desired current (100 mA) could be obtained with a cathode surface of 3.97 mm2, so the model of cathode surface area in this paper is set to 4 mm2. Note that, under the control voltage on the Wehnelt electrode, not all the cathode surface can emit electrons to the anode. According to the above analysis, the beam current should be related to the emission state of electrons in front of the cathode surface. 3. Simulation results and discussions 3.1. Electric field distribution The motion state of the electrons is determined by the internal electric field of the electron gun. Studying the distribution of the electric field inside the electron gun is the premise for realizing the electron beam current control mechanism. When the bias voltage between the cathode and the Wehnelt electrode is 0 V, the simulation results of the electric field distribution inside the electron gun are shown in Fig. 5. We can see in Fig. 5(a), the potential gradually increases from −60000 V to 0 V along the central axis from the cathode to the anode, reaching 0 V on the anode surface. We can see in Fig. 5(b), the potential gradually increases and reaches 0 V on the anode surface from the Wehnelt electrode to the central axis, which causes the electrons to move towards the central axis, generating a focus position
3.2. Beam current control principle The change in bias voltage causes a change of the electric field inside the electron gun and thus the movement behavior of the electrons changes. To study the influence of different bias values on the internal electric field of the electron gun, we maintain the accelerating voltage at −60 kV and select different bias voltages (250 V, 500 V, 750 V, 1000 V) to simulate the electric field. In order to observe the details of the electric field change, only the local electric field around the cathode is analyzed, and the processing result only shows the equipotential lines higher than −60 kV. At different bias voltages, the distribution of the
Fig. 5. Electric field distribution. 281
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Fig. 7. Electric field distribution at different bias voltages. 282
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equipotential lines around the cathode is shown in Fig. 7. As shown in Fig. 7(a), when the bias voltage is 250 V, the potential at both the upper and the periphery of the cathode is lower than −60 kV, but the potential below the lower surface of the cathode is higher than −60 kV. At this point, the electrons escaping from the cathode are completely in the accelerating electric field, and all electrons can be emitted to the anode. When the bias voltage increases to 500 V, as shown in Fig. 7(b), the −60 kV equipotential line below the cathode moves from the periphery to the middle, so the electrons escaping from the edge of the cathode are in the decelerating electric field and the electrons escaping from the center position of the cathode are in the accelerating electric field. Only the electrons in the accelerating electric field can move towards the anode, while the electrons in the decelerating electric field remain around the cathode, which is equivalent to that only a part of the cathode surface is capable of emitting electrons to the anode [29]. When the bias voltage continues increasing to 750 V, as shown in Fig. 7(c), the −60 kV equipotential line continues to move towards the middle. Only a small part of the escaped electrons in the center of the cathode are in the emission state and other parts of the electrons are in the emission suppression state. When the bias voltage increases to 1000 V, as shown in Fig. 7(d), the −60 kV equipotential lines below the cathode coincide at a certain position, causing the potential under the cathode is less than −60 kV, at which time all the electrons escaping from the cathode are in the emission suppression state and the beam current is 0 mA. According to the above simulation results, the bias voltage is to adjust the beam current by adjusting the emission state of the electrons escaping from the cathode. During the bias voltage adjustment process, only the electrons escaping from part of cathode surface can be accelerated towards the anode due to the control of the electric field. This part of the cathode surface is referred to as the Effective Emitting Area (EEA) in this paper. As shown in Fig. 7, the reason why bias voltage can adjust the beam current is that the bias voltage can change the EEA of the cathode. To observe the change state of the EEA when the bias voltage changes, the emission states of the electrons on the cathode surface are captured when the bias voltages are 500 V and 750 V and the results are shown in Fig. 8. When the bias voltage is 500 V, the EEA is larger than that when the bias voltage is 750 V, so that more electrons can be emitted, which proves the role and function of EEA of the cathode.
Table 2 Simulated and theoretically calculated beam current under different bias voltages. Bias Voltage (V)
Simulated Beam Current (mA)
Effective Emitting Area (mm2)
Theoretical Beam Current (mA)
Error (mA)
0 250 350 400 450 500 550 600 650 700 750 800 850 1000
100.00 100.00 100.00 97.47 86.23 70.84 57.16 41.94 28.47 17.84 8.32 1.80 0.00 0.00
4.00 4.00 4.00 3.90 3.45 2.83 2.30 1.68 1.14 0.71 0.33 0.08 0.00 0.00
100.80 100.80 100.80 98.28 86.94 71.32 57.96 42.34 28.73 17.89 8.32 2.01 0.00 0.00
0.80 0.80 0.80 1.01 0.71 0.48 0.80 0.40 0.26 0.05 0.00 0.21 0.00 0.00
current density is only related to the acceleration voltage, but beam current can be adjusted by adjusting the EEA of the cathode according to the electric field simulation results. Although it is known that the bias voltage and the beam current are approximately inversely proportional within a certain range [30], the quantitative relationship among the bias voltage, EEA and beam current is rarely studied. Here, the CST software is used to track the motion of electrons in the electron gun, and the beam current and EEA corresponding to different bias voltage conditions are obtained. When the acceleration voltage is set to 60 kV and the maximum beam current is set to 100 mA, the simulation results are shown in Table 2. It is assumed that the change in bias voltage only changes the EEA without changing the emission mode of the electron. According to Eq. (3) and the ratio of the EEA to the total emitting surface of the cathode, we can get Eq. (7) to calculate the theoretical beam current value.
I = Ia⋅
3 s se = G·U 2 · e s s
(7)
Where Se is the area of EEA. The theoretical beam currents under different bias voltages are shown in Table 2. We can see that the simulation results are very close to the calculated results. The maximum error is only 1.01 mA. In order to visually observe the trend of beam current with bias voltage, the relationship between bias voltage and beam current is drawn as in Fig. 9 based on the results of the simulation. We can see that the beam current varies with the bias voltage. When
3.3. Relationship between bias voltage and beam current It can be seen from Child-Langmuir formula that when the electron gun works in the space charge emission mode, the saturation beam
Fig. 8. EEA at different bias voltages. 283
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influence of the acceleration voltage fluctuation on the beam current value also increases. When the bias voltage is 450 V, the beam current fluctuates from −0.94 mA to 0.95 mA and the change rate ranges from −1.09% to 1.10%. When the bias voltage increases to 600 V, the beam current fluctuates from −1.13 mA to 1.19 mA and the change rate ranges from −2.69% to 2.91%. As the bias voltage increases to 750 V, although the beam current value is small, the acceleration voltage fluctuation has a greater influence on the beam current. At this time, the beam current fluctuates from −1.53 mA to 1.55 mA, and the change rate ranges from −19.59% to 18.03%. In summary, when the bias voltage and the cathode temperature are fixed, the fluctuations of the accelerating voltage cause the fluctuations of beam current, which is particularly severe when the beam current value is small. Therefore, in order to make the beam current highly repeatable and reliable, the accelerating voltage should have less ripple and higher stability. 4. Conclusions
Fig. 9. The relationship between bias voltage and beam current.
(1) The relationship between bias voltage and beam current is quantitatively analyzed with CST software. Over a range of bias voltage, the electron beam current is inversely proportional to the bias voltage. (2) The concept of Effective Emitting Area (EEA) has been introduced as a cathode figure of merit. The ability of the bias voltage to modify the beam current can be identified in the capability of bias voltage to regulate the excitation states of surface electrons in different positions of the cathode. Hence, EEA can be identified as the area of the cathode where the emission takes place. The saturation effect can be also seen as the reduction of that area. The reason why the beam current can be adjusted by adjusting the bias voltage is that the bias voltage regulates the EEA. (3) When the bias voltage and the cathode temperature are fixed, the fluctuations of the accelerating voltage will cause the fluctuations of beam current, which is particularly severe when the beam current is small.
Table 3 Effect of voltage fluctuation on beam current. Bias voltage (V)
Accelerating voltage (kV)
Beam current (mA)
Change value (mA)
Change rate (%)
450
59.4 60 60.6 59.4 60 60.6 59.4 60 60.6
85.29 86.23 87.18 40.81 41.94 43.16 6.79 8.32 9.87
−0.94 0 0.95 −1.13 0.00 1.19 −1.53 0.00 1.55
−1.09 0 1.10 −2.69 0.00 2.91 −19.59 0.00 18.03
600
750
the bias voltage is lower than 350 V, all the electrons escaping from the cathode are completely emitted. When the bias voltage is between 350 V and 850 V, the beam current decreases as the bias voltage increases, and they are approximately linear. When the bias value reaches 850 V or higher, the electrons escaping from the cathode are suppressed. No electrons are emitted and the beam current is 0 mA. Assuming that the bias voltage is X and the emitted electron beam current is Y, the linear relationship between the beam current and the bias voltage is obtained according to the least squares method when the bias voltage is between 350 V and 850 V, as shown in Eq. (8).
Y = −0.25X + 195.8
Acknowledgment The research is financially supported by National Nature Science Foundation of China (No. 51805265, 51805266), Natural Science Foundation of Jiangsu Province (No. BK20180472), and the State Key Lab of Advanced Welding and Joining of Harbin Institute of Technology.
(8)
In this formula, the linear correlation coefficient R2 is 0.99. We conclude that the electron beam current is linearly proportional to the bias voltage within a certain range and the linearity is very high.
Appendix A. Supplementary data
3.4. Influence of accelerating voltage fluctuations
References
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.vacuum.2019.03.040.
In the electron beam welding process, the welding power is determined by the accelerating voltage and beam current. When the welding beam current is constant, the higher the acceleration voltage, the greater the welding power. However, when the accelerating voltage changes, the electric field inside the electron gun changes accordingly, which has an influence on the emission of electrons and beam current. When the high voltage fluctuates at 1% below and above 60 kV (59.4 kV and 60.6 kV respectively), the influence of accelerating voltage fluctuations on the beam current is simulated at different bias voltages (450 V, 600 V, 750 V) and the results are shown in Table 3. As can be seen from Table 3, when the accelerating voltage fluctuates downward, the beam current value will decrease accordingly. When the accelerating voltage fluctuates upward, the beam current value will increase accordingly. As the bias value increases, the
[1] M. Iqbal, I. Shaukat, A. Mahmood, K. Abbas, M.A. Haq, Surface modification of mild steel with Boron Carbide reinforcement by electron beam melting, Vacuum 85 (2010) 45–47, https://doi.org/10.1016/j.vacuum.2010.03.009. [2] J. Karlsson, A. Snis, H. Engqvist, J. Lausmaa, Characterization and comparison of materials produced by Electron Beam Melting (EBM) of two different Ti-6Al-4V powder fractions, J. Mater. Process. Technol. 213 (2013) 2109–2118, https://doi. org/10.1016/j.jmatprotec.2013.06.010. [3] W. Zhang, H. Fu, J. Fan, R. Li, H. Xu, F. Liu, B. Qi, Influence of multi-beam preheating temperature and stress on the buckling distortion in electron beam welding, Mater. Des. 139 (2018) 439–446, https://doi.org/10.1016/j.matdes.2017.11.016. [4] Y. Sun, X. Lin, X. He, J. Zhang, M. Li, G. Song, X. Li, Y. Zhao, Effects of substrate rotation on the microstructure of metal sheet fabricated by electron beam physical vapor deposition, Appl. Surf. Sci. 255 (2009) 5831–5836, https://doi.org/10.1016/ j.apsusc.2009.01.013. [5] M. Ormanova, P. Petrov, D. Kovacheva, Electron beam surface treatment of tool steels, Vacuum 135 (2017) 7–12, https://doi.org/10.1016/j.vacuum.2016.10.022. [6] A.V. Shcherbakov, M.V. Ivashchenko, A.S. Kozhechenko, M.S. Gribkov, Parametric analysis in the design of technological electron beam guns, Russ. Electr. Eng. 87
284
Vacuum 164 (2019) 278–285
J. Fan, et al.
[18] Y. Ye, C. Zuo, H. Xu, X. Sang, Application of CST simulation Technology in focusing parts of electron beam guns, Aeronaut. Manuf. Technol. 60 (2017) 78–82, https:// doi.org/10.16080/j.issn1671-833x.2018.09.078. [19] X. Sang, H. Xu, C. Zuo, K. Fan, CST simulation on effect of beam source component struture size on beam quality in electron guns, Aeronaut. Manuf. Technol. 9 (2017) 60–64, https://doi.org/10.16080/j.issn1671-833x.2017.09.060. [20] R. Martin, Theory and Design of Charged Particle Beams, Second, WILEY-VEH Verlag Gmbh & Co.KGaA, Weinheim, 2008. [21] J.D. Kowalczyk, M. Hadmack, J. Madey, Laser cooling to counteract back-bombardment heating in microwave thermionic electron guns, FEL 2013 Proc. 35th Int. Free. Laser Conf, 2013, pp. 79–81. [22] Y.S. Yeh, M.H. Tsao, H.Y. Chen, T.-H. Chang, Improved computer program for magnetron injection gun design, Int. J. Infrared Millim. Waves 21 (2000) 1397–1415, https://doi.org/10.1023/a:1026400906433. [23] S. Coulombe, J. Meunier, Thermo-field emission : a comparative study, J. Phys. D Appl. Phys. 30 (1997) 776–780. [24] V.V. Altsybeyev, V.A. Ponomarev, Application of Gauss's law space-charge limited emission model in iterative particle tracking method, J. Comput. Phys. 324 (2016) 62–72, https://doi.org/10.1016/j.jcp.2016.08.007. [25] H. Spachmann, U. Becker, Electron gun simulation with CST PARTICLE STUDIO, Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip. 558 (2006) 50–53, https://doi.org/10.1016/j.nima.2005.11.075. [26] Y.X. Wei, M.G. Huang, S.Q. Liu, B.L. Hao, P.K. Liu, Numerical simulation of TWT electron gun, Vacuum 92 (2013) 90–94, https://doi.org/10.1016/j.vacuum.2012. 12.003. [27] V.A. Syrovoi, A theory of narrow relativistic electron beams, J. Commun. Technol. Electron. 52 (2007) 910–931, https://doi.org/10.1134/S106422690708013X. [28] C. Shen, Y. Peng, K. Wang, Q. Zhou, Measurement of power density distribution and beam waist simulation for electron beam, Radiat. Phys. Chem. 83 (2013) 8–14, https://doi.org/10.1016/j.radphyschem.2012.09.016. [29] B. Qi, J. Fan, W. Zhang, F. Liu, H. Wang, A novel control grid bias power supply for high-frequency pulsed electron beam welding, Vacuum 133 (2016) 46–53, https:// doi.org/10.1016/j.vacuum.2016.08.015. [30] O.K. Nazarenko, Circuitry of Electron Beam Welding Current Control, first ed, E.O.Paton Electric Welding Institute of the NAS of Ukraine, Kiev, 2013.
(2016) 41–45, https://doi.org/10.3103/S1068371216010089. [7] A. Nehra, L.M. Joshi, R.K. Gupta, S. Sharma, Y. Choyal, R.K. Sharma, Design and simulation of pole piece for focusing of multi-beam electron gun, J. Infrared, Millim. Terahertz Waves 32 (2011) 793–800, https://doi.org/10.1007/s10762011-9783-8. [8] S.P. Sabchevski, G.M. Mladenov, S. Wojcicki, J. Dabek, An analysis of electron guns for welding, J. Phys. D Appl. Phys. 29 (1996) 1446–1453, https://doi.org/10.1088/ 0022-3727/29/6/006. [9] D.M. Goebel, R.M. Watkins, Compact lanthanum hexaboride hollow cathode, Rev. Sci. Instrum. 81 (2010) 1–6, https://doi.org/10.1063/1.3474921. [10] K. Bücker, M. Picher, O. Crégut, T. LaGrange, B.W. Reed, S.T. Park, D.J. Masiel, F. Banhart, Electron beam dynamics in an ultrafast transmission electron microscope with Wehnelt electrode, Ultramicroscopy 171 (2016) 8–18, https://doi.org/ 10.1016/j.ultramic.2016.08.014. [11] lng H. Schultz, Electron Beam Welding, (1993), https://doi.org/10.3131/jvsj.3. 206. [12] S. Sabchevski, G. Mladenov, A. Titov, I. Barbarich, Modelling and simulation of beam formation in electron guns, Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrom., Detect. Assoc. Equip. 381 (1996) 185–193, https://doi.org/10. 1016/S0168-9002(96)00830-3. [13] G.U. Islam, A. Rehman, M. Iqbal, Z. Zhou, Simulation and test of a thermioic hairpin source DC electron beam gun, Optik 127 (2016) 1905–1908, https://doi.org/10. 1016/j.ijleo.2015.11.132. [14] R. Becker, W.B. Herrmannsfeldt, The design of electron and ion guns, beams, and collectors, J. Phys. Conf. Ser. 2 (2004) 152–163, https://doi.org/10.1088/17426596/2/1/019. [15] P. Jánský, J. Zlámal, B. Lencová, M. Zobač, I. Vlček, T. Radlička, Numerical simulations of the thermionic electron gun for electron-beam welding and micromachining, Vacuum 84 (2009) 357–362, https://doi.org/10.1016/j.vacuum.2009. 07.007. [16] M. Hoseinzade, M. Nijatie, A. Sadighzadeh, Numerical simulation and design of a thermionic electron gun, Chin. Phys. C 40 (2016) 1–7, https://doi.org/10.1088/ 1674-1137/40/5/057003. [17] A. Leggieri, D. Passi, F. Di Paolo, B. Spataro, E. Dyunin, Design of a sub-millimetric electron gun with analysis of thermomechanical effects on beam dynamics, Vacuum 122 (2015) 103–116, https://doi.org/10.1016/j.vacuum.2015.09.013.
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