Effects of magnetic field strength in the discharge channel on the performance of a multi cusped field thruster Effects of magnetic field strength in the discharge channel on the performance of a mult[.]
Effects of magnetic field strength in the discharge channel on the performance of a multi-cusped field thruster Peng Hu, Hui Liu, Yuanyuan Gao, and Daren Yu Citation: AIP Advances 6, 095003 (2016); doi: 10.1063/1.4962548 View online: http://dx.doi.org/10.1063/1.4962548 View Table of Contents: http://aip.scitation.org/toc/adv/6/9 Published by the American Institute of Physics AIP ADVANCES 6, 095003 (2016) Effects of magnetic field strength in the discharge channel on the performance of a multi-cusped field thruster Peng Hu, Hui Liu, Yuanyuan Gao, and Daren Yua Lab of Plasma Propulsion, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China (Received June 2016; accepted 30 August 2016; published online September 2016) The performance characteristics of a Multi-cusped Field Thruster depending on the magnetic field strength in the discharge channel were investigated Four thrusters with different outer diameters of the magnet rings were designed to change the magnetic field strength in the discharge channel It is found that increasing the magnetic field strength could restrain the radial cross-field electron current and decrease the radial width of main ionization region, which gives rise to the reduction of propellant utilization and thruster performance The test results in different anode voltage conditions indicate that both the thrust and anode efficiency are higher for the weaker magnetic field in the discharge channel C 2016 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/) [http://dx.doi.org/10.1063/1.4962548] I INTRODUCTION The Multi-cusped Field Thruster is a novel concept in electric propulsion, and it was investigated as early as 1962 by Janes et al.1 The physical process of a Multi-cusped Field Thruster can be described as follows As shown in figure 1, the thruster employs several alternating polarity permanent magnets to create periodic magnetic field The electrons emitted from the cathode can reach the discharge channel along the magnetic field lines in the plume region, and then some electrons are trapped by the multi-cusped magnetic field in the discharge channel These electrons move back and forth with the competition between the mirror force and the electric field force in the cusped field Meanwhile, the xenon atoms supplied by the upstream gas distributor can be ionized during the electron-atom collision process The generated ions are accelerated by the mainly axial electric field near the exit and spurted out of the thruster, thus forming the thrust.2 The laser-induced fluorescence (LIF) experiments3–5 and Particle-in-Cell (PIC) simulations6,7 have validated that the main acceleration region locates near the downstream of the thruster exit Meanwhile, as the electrons are strongly confined by the mainly axial magnetic field in the discharge channel, the main ionization region can be established near the axis of the ultimate stage, as shown in figure Recent studies on the Multi-cusped Field Thrusters show that improving the ionization rate in the discharge channel is the key aspect for the performance optimization.8–12 Many thrusters with different configurations are designed in many institutions In HEMP-T 3050, the increased cusp-mirror ratio in each stage is helpful to increase the electron confinement and enhance the ionization.8 In MIT’s Diverging Cusped Filed Thruster (DCFT), a strong magnetic mirror near the axis is employed to improve the ionization rate.9–11 In HIT’s low power Cusped Field Thruster, the discharge channel with spacer can also promote the ionization process.13 In the down-scaled HEMP-Thruster, changing the size of permanent magnets can affect the ionization process and the performance shows a significant difference.14 All the results demonstrated that the ionization process in the discharge channel is closely related with the cusped field there, and this naturally raises the question of how the strength of magnetic field in the discharge channel affect the ionization a Electronic mail: yudaren@hit.edu.cn 2158-3226/2016/6(9)/095003/8 6, 095003-1 © Author(s) 2016 095003-2 Hu et al AIP Advances 6, 095003 (2016) FIG Schematic of the Multi-cusped Field Thruster with two stages and the performance of thruster In this paper, by changing the outer diameter of the magnets, four thrusters with different magnetic field strength in the discharge channel are investigated It is organized as follows: In the second part, the relevant design of the thrusters and the comparative experiments are induced along with the experimental conditions and diagnostic devices The experimental results on the discharge characteristics and performance are presented and discussed in the third part Finally, the conclusions are made in the last part II EXPERIMENTAL SETUP The thruster used in our experiment is shown in Figure The length and inner diameter of boron nitride channel are 56 mm and 22 mm, respectively A stainless steel anode is mounted at the upstream of the BN discharge chamber, and it also serves as a propellant gas distributor The thruster employs two stages of permanent magnetic rings, the length of each stage is 16 mm and 40 mm, respectively, and the gap between these two magnet rings is mm The thruster contains two cusped configurations, the first cusp locates in the discharge channel, and the second cusp locates near the exit [in Figure 2(a)] Besides, the cathode used for our experiments is a LaB6 hollow cathode developed at Plasma Propulsion Laboratory of Harbin Institute of Technology The diameter of the cathode orifice is 0.5 mm A tungsten heater coil is used to heat the emitter to its operating temperature The keeper is used to ignite the cathode discharge The cathode is mounted in the plume region with a fixed flow rate of sccm Xenon throughout the experiments Four thrusters are tested in our experiments, the magnet rings have the same inner diameter of 26 mm, the outer diameter (Do) changes from 54 mm to 66 mm and the corresponding magnetic FIG (a) A 3D view of the cusped field thruster in our experiment The magnetic lines are simulated by the FEMM software and two cusped fields can be formed in this thruster (b) The cross sectional view of the thruster 095003-3 Hu et al AIP Advances 6, 095003 (2016) FIG The Magnetic fields of Multi-cusped Field Thrusters with different outer diameters are simulated by the FEMM software fields are simulated by the FEMM software As shown in figure 3, with the increase of Do, the magnetic field strength in the discharge channel can be increased significantly, especially for the middle plane (Z = −24 mm) of ultimate stage, in which the magnetic field strength increases near linearly with Do [figure 4(a)] Besides, as shown in figure 4(b), the positions of zero magnetic points can be well maintained, and this implies that the magnetic field geometry in the discharge channel changes little It should be noted that the magnetic field in the exit plane changes little, as shown in figure 4(c) The typical mirror ratio, which can be defined by the formula of Rm = B p /Br , in which B p represents the magnetic field strength of the point cusp at Z = −24 mm, and Br represents the magnetic field strength of the ring cusp at Z = −40 mm As we can see in figure 4(d), the mirror ratio decreases significantly with the increase of Do To be convenient for explanation, the outer diameter of magnet ring is used to name these magnetic fields, namely, F54, F58, F62, and F66 FIG The magnetic field strength in the thrusters with different outer diameters (a) Radial magnetic field distribution in the middle plane (Z = -24) of ultimate stage (b) Magnetic field distribution along the central axis (c) Radial magnetic field distribution in the exit plane (d) The typical mirror ratio in different magnetic field cases 095003-4 Hu et al AIP Advances 6, 095003 (2016) The experiments were conducted in the Plasma Propulsion Laboratory of Harbin Institute of Technology (HPPL) The stainless-steel vacuum chamber has a length of m and an inner diameter of 1.2 m It is equipped with two diffusion pumps, one rotary pump, and three mechanical booster pumps The baseline pressure of the vacuum chamber is 1.0 × 10−3 Pa The back ground chamber pressure for this facility is 2.40 × 10−3 Pa when operating the thruster at 5sccm anode flow and 3sccm cathode flow of xenon A three-thread torsion balance was used for thrust measurement, which can transform the thruster force to an equivalent rotation angle The equivalent rotation angle could be recorded by the displacement of a laser spot on a steel ruler, which is reflected by a mirror fixed on the balance.15 In the small-angle approximation (the typical rotation angle can be estimated to be 5.5 × 10−3 rads), the thruster force can be calculated by its linearity relationship with the displacement of laser spot During the calibration, the discharge is off and the gas is still flowing from the thruster and the cathode The thrust stand calibration is performed using weights (each weight is 0.4g) attached to the middle part of a thin nylon fiber, one end of which is attached to the central axis of thruster via a pulley, the other end of nylon fiber is wound around a spool and can be released remotely using a stepper motor The motor raises and lowers the masses to adjust the equivalent force, which could lead to an equal proportion of laser spot displacements on the steel ruler The thrust is calculated by the mean value of 10 repeated measurements In typical, the standard deviation of the repeated measurements is 0.49 mN, and the thrust uncertainty is about 3.5% of the overall thrust.16 The plasma plume diagnostics used in our experiments include a Faraday probe and a Retarding Potential Analyzer (RPA).17,18 The Faraday probe was mounted on a rotational stage with the distance of 32 cm from the pivot at angles of up to 80◦ from the thruster axis The ion collecting area of Faraday probe was 0.75 cm2, both the probe collector and guard ring were biased to -30 V, and the collected current was recorded by measuring the voltage across a 200.3 Ω shunt resistor The position of RPA was about 35 cm from the exit and a fixed angle of 30◦ from the axis was selected This position was close to the current density peak of the plume III EXPERIMENTAL RESULTS AND DISCUSSIONS Figure shows the experimental results in 400V anode voltage for different magnetic field cases, and the anode flow rate is fixed at 10 sccm The estimation methods of ion current Ii , electron current Ie in figure 5(a) can be described as follows The ion current density is calculated by the formula of j(θ) = I p (θ)/A p , in which θ is the azimuthal angle, I p (θ) is the collected ion current of Faraday probe, A p is the probe collector area If the ion current density is symmetric, the ion π/2 current Ii can be calculated by the integration formula of Ii = 2πR2 j(θ) sin(θ) dθ, where R is the distance from the thruster exit plane to the Faraday probe.19 However, the test results in FIG The test results on the fixed operation condition with 10 sccm anode flow rate and 400 V anode voltage (a) Components of the discharge current (b) Current utilization η c , propellant utilization η p and beam divergence efficiency ηu 095003-5 Hu et al AIP Advances 6, 095003 (2016) figure 7(a) indicate that the ion current density distributions are not asymmetric In order to better approximate the true value, the average of the integrated ion current density in both sides (from to 80 degrees and to -80 degrees) is used for the estimation of ion current For example, in the F54 case, the average ion current is 0.565A, and its uncertainty caused by the asymmetric plume is 0.045A Besides, considering the ion current uncertainty caused by the charge exchange ions,20 the combined uncertainty of the measured ion current is about 0.056A As shown in figure 5(a), when Do is increased from 54 mm to 66 mm, the discharge current decreases significantly from 0.67A to 0.51 A The ion current Ii also shows a clear decrease from 0.565A to 0.418A, while the electron current Ie changes little from 0.101A to 0.092A Meanwhile, as shown in figure 5(b), the current utilization η c [= Ii /(Ii + Ie )] shows an insignificant difference According to former researches on the cusped field thrusters, the electron confinement in the magnetic field is expected to be significant near the ultimate separatrix region (shown in figure 1), the electrons are strongly hindered and the main acceleration region is formed near the exit.4,6 Therefore, it can be speculated that the small change of electron current Ie and current utilization η c in different magnetic fields should be attributed to the well maintained magnetic field near the exit [in figure 4(c)] Besides, as shown in figure 5(b), when Do is increased from 54 mm to 66 mm, the propellant ˙ (where M, e, m ˙ are the mass of a Xe atom, electron charge, and Xe utilization η p [= Ii M/em] mass flow rate, respectively) exhibits a clear decrease from 0.50 to 0.37 The decrease of propellant utilization η p shows the significant change of ionization process In the discharge channel, as the confined electrons in the cusped field are concentrated near the axis,2,6,21 the main ionization region is formed near the axis region, which is visually characterized by the emergence of a bright cylindrical light, as shown in figure 6(a) When Do is increased from 54 mm to 66 mm, the magnetic field strength along the radial direction in the discharge channel can be enhanced accordingly [in figure 4(a)] It is reasonable that the radial cross-field electron current in the main ionization region is restrained with the enhancement of magnetic field strength, and the ionization region in the discharge channel becomes narrower.22 The intensity images are extracted from the photographs in figure 6(a) Then their contours of the constant image intensity are obtained, as shown in figure 6(b) It is clear that the constant image intensity contours shrinks radially with the increase of Do, which is consistent with the narrowing ionization region in the discharge channel The similar results in a ring-cusp ion engine discharge chamber also indicates that the discharge is less efficient for the decrease of ionization volume in a stronger magnetic field case.23 As the electrons are confined near the axis region, the neutral gas near the wall cannot be well ionized,24 which is the key factor for the low propellant utilization in figure 5(b) Besides, as shown in figure 4(d), the mirror ratio for the upstream cusp decreases clearly with the increase of Do Therefore, it is speculated that more FIG (a) Photographs of plasma discharge in the channel for the thrusters with different magnetic fields during 400 V and 10 sccm operation These photographs were taken with identical settings on a commercial digital single-lens reflex (DSLR) camera installed in a side window of the vacuum chamber (b) The contours of the constant image intensity 095003-6 Hu et al AIP Advances 6, 095003 (2016) FIG Plasma plume diagnostic tests on the fixed operation condition with 10 sccm anode flow rate and 500 V anode voltage (a) The ion energy distribution functions in different magnetic field cases are calculated by the test results of RPA, which was fixed in the plume region Its positions was about 35 cm from the exit with a fixed angle of 30◦ from the axis (b) The ion current density distributions in different magnetic fields electrons could escape from the upstream cusp and reach the anode, this factor may also lead to a smaller ionization ratio in the upstream cusp The narrowing ionization region in the discharge channel could also lead to the change of ion energy and ion current density distribution in the plume region In the stronger magnetic field case, the ions generated in the narrower ionization region could have smaller initial potential differences As a result, the ion energy becomes more uniform, which can be validated by the test results of RPA probe [in figure 7(a)] that the ion energy distribution function (IEDF) shows a remarkable decrease in the FWHM (full width at half maximum) from 65 eV to 47 eV Meanwhile, as shown in figure 7(b), the collimated hollow plume is formed and the ion current density in large angles is decreased significantly And as a result, the beam divergence efficiency η θ , which can be calculated π by the formula of η θ =< cosθ >2 = [ 2πIRi j(θ) sin(θ) cos(θ) dθ]2, shows a clear increase from 0.67 to 0.71 in figure 5(b) Besides, the insignificant variation of peak energy shown in figure 7(a) indicates that the ion speed νi changes little Therefore, it is speculated that the change of ion current density ji (∝ ni νi , where ni is the density of ions) in figure 7(b) should be attributed to the change of ni , which is relevant with the radial variation of ionization region in the discharge channel Besides, it is particularly worth mentioning that some similar test results were also presented in T Matlock’s work An external electromagnet (EM) was mounted on the DCFT thruster, which could alter the strength of the magnetic field in the main acceleration region formed near the ultimate separatrix region.20,25 The results show that when the magnetic field near the ultimate separatrix is increased, the propellant utilization decreases monotonically, meanwhile, the plume divergence efficiency increases But influence mechanisms caused by the magnetic field near the ultimate separatrix are very different T Matlock noted that the electron current is closely related to the magnetic field near ultimate separatrix region When the magnetic field strength in this region is increased, the electron current is restrained and less electrons could reach the main ionization region in the discharge channel As a result, the ionization process is restrained and the propellant utilization is decreased accordingly While in our work, the ionization region in the discharge channel is more directly affected by the change of magnetic field in the discharge channel Besides, in T Matlock’s work, when the magnetic field strength near the exit is increased, the field lines near the ultimate separatrix are bended back towards the anode, the acceleration electric field tend to be focused and the divergence efficiency is increased accordingly The increase of magnetic field in the discharge channel could also lead to the increasing divergence efficiency, which is relevant with the radial variation of ionization region in the discharge channel Figure shows the measured performance results of thrust T, anode efficiency η a and specific impulse Isp in four magnetic field cases with the same anode flow rate of 10 sccm The anode efficiency is calculated by the formula of η a = T 2/2mI ˙ dU (U is the anode voltage, Id is the discharge current, and m˙ is the anode mass flow rate) The specific impulse is calculated by the formula of 095003-7 Hu et al AIP Advances 6, 095003 (2016) FIG The tests results of (a) thrust, (b) anode efficiency and (c) specific impulse versus anode voltage in different magnetic field cases The anode flow rate of is fixed at 10 sccm Isp = T/mg ˙ (g is the acceleration of gravity) It is clear that both the higher anode voltage and weaker magnetic field in the discharge channel could lead to the improvement of performance The similar effects between discharge voltage and magnetic field strength should be interpreted in terms of radial expansion of ionization region In the high-voltage case, it is speculated that the high electron temperature could promote the ionization process in the discharge channel Besides, according to the former analyses, the increased radial cross-field electron current in the weaker magnetic field case could give rise to the radial expansion of ionization region So the ionization process is promoted in the discharge channel, and the thrust and anode efficiency are improved accordingly As we can see in figure 8(a), when anode voltage increases from 300V to 500V, the thrust is increased by 51.6 % (from 9.1 mN to 13.8 mN) in the weaker magnetic field case of F54, which is higher than the increase of 34.6 % (from 7.8 mN to 10.5 mN) in the stronger magnetic field case of F66 The smaller thrust increase rate in the stronger magnetic field should be attributed to the stronger restrain effects on the radial expansion of ionization region in the discharge channel IV CONCLUSIONS In summary, the magnetic field in the discharge channel plays a very important role in the performance of the Multi-cusped Field thruster It is found that increasing the magnetic field strength in the discharge channel could lead to the decrease of radial cross-field electron current, and a narrower ionization region can be formed, as a result, the atoms near the wall cannot be well ionized, which is a key factor for the low propellant utilization Besides, the decreasing mirror ratio with the increase of magnetic field could also lead to a smaller ionization ratio and the propellant utilization is decreased accordingly The effect of magnetic field strength on the ionization is consistent with the performance results in different anode voltage conditions Both the thrust and anode efficiency are higher in the weaker magnetic field strength case in the discharge channel Furthermore, the effects of magnetic field strength in the discharge channel on the ion acceleration and the forming of the hollow plume should be studied in further research 095003-8 Hu et al AIP Advances 6, 095003 (2016) ACKNOWLEDGMENTS The authors would like to acknowledge the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No 51421063) and National Natural Science Foundation of China (Grant Nos.11505041, 51277036 and 11275055) G S Janes, J 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Physics D: Applied Physics 47(4), 045201 (2014) 23 Hann-Shin Mao, Doctor’s Thesis, University of California, 2013 24 Daniel G Courtney, Paulo Lozano, and Manuel Martìnez-Sànchez, in presented at the 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Hartford, USA, 21 - 23 July, 2008, Paper No AIAA 2008-4631 25 Taylor S Matlock, Fuzhou Hu, and Manuel Martìnez-Sànchez, in presented at the 32nd International Electric Propulsion Conference, Wiesbaden, Germany, 11-15 September, 2011, Paper No IEPC-2011-178 ... higher in the weaker magnetic field strength case in the discharge channel Furthermore, the effects of magnetic field strength in the discharge channel on the ion acceleration and the forming of the. .. simulations6,7 have validated that the main acceleration region locates near the downstream of the thruster exit Meanwhile, as the electrons are strongly confined by the mainly axial magnetic field in. .. stronger magnetic field should be attributed to the stronger restrain effects on the radial expansion of ionization region in the discharge channel IV CONCLUSIONS In summary, the magnetic field