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Plasma diagnostic with inductive probes in the discharge channel of a pulsed plasma thruster
Vacuum xxx (2014) 1e7
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Plasma diagnostic with inductive probes in the discharge channel of a pulsed plasma thruster Matthias Lau*, Georg Herdrich Institute of Space Systems, University of Stuttgart, Pfaffenwaldring 29, 70569 Stuttgart, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2013 Received in revised form 11 July 2014 Accepted 16 July 2014 Available online xxx
Research of magnetoplasmadynamic Pulsed Plasma Thrusters (PPTs), or iMPDs, at the Stuttgart Institute of Space Systems (IRS), led to the thruster design ADD SIMP-LEX. For optimization of the thruster's discharge behavior and of the plasma acceleration, the magnetic self-field is measured. Inductive miniaturized probes are introduced and used to acquire data at points of the volume inside of the thruster's discharge channel. The results are used for analysis to identify the extend of the discharge zone along the discharge channel of the PPT. Measured magnetic field signals along the centerline of the discharge channel are presented. The underlying distribution of the dynamic discharge current is deduced from Amperes circuital law and interpreted in a two-dimensional plot against camera images for the current-plasma-interaction, current motion and validity of today's discharge models. The evaluation of the calculated integral discharge current in a plane of the discharge channel against the recorded thruster discharge current is presented and discussed. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Inductive probes Magnetic field measurement Current density distribution iMPD Pulsed plasma thruster
1. Introduction The pulsed magnetoplasmadynamic thruster (iMPD), represents a robust and simple design for secondary propulsion needs of satellites, for example target pointing, attitude control, formation flight, and drag compensation. Relatively high mean exhaust velocities ce and efficient propellant utilization are achieved through the pulsed operation mode. This beneficially limits power consumption and allows for thrust adjustment without losses in Dv. The common choice of propellant is solid Polytetrafluoroethylene (PTFE), or Teflon™. Without the need for injection, feed lines, valves and tanks, the weight and system complexity are exceptionally low. The overall low complexity is main criteria for minimum operational risk and high affordability, with cost savings of one to two orders of magnitude in comparison. The easy handling and long flight heritage also justify primary propulsion tasks for iMPDs, under the condition of increase of the generally low thrust efficiency of this type of electric thruster. The development of ADD SIMP-LEX (Advanced Stuttgart Impulsing MagnetoPlasmadynamic thruster for Lunar EXploration) tackled this problem, by achieving world leading thrust efficiencies around 30%, together with the APPT thrusters developed at the RIAME and Kurchatov Institutes in Moscow, Russia [1e4]. This was * Corresponding author. E-mail address: [email protected] (M. Lau).
made possible through a close technology exchange as part of a cooperation contract. Beyond the demonstrated performance, the ADD SIMP-LEX also invites continued efforts, to even further increase the thrust efficiency. For this, the common approach of electrical and geometric parameter variation was found to require extension to the level of discharge formation and energy transfer mechanisms. The relatively poor universal validity and qualitative character of discharge models also suggest the rethinking of the thruster's working principle and idealized model of a moving current sheet [5]. This model has been extended and refined by the work of many researchers, yet never led to a universally satisfying and applicable solution. The goal is to utilize the observed trends derived from data of experimental parametric studies at IRS, to focus the experimental efforts on observations, which are not mirrored by current models. At first, this leads towards the extraction of possible explanations, deeper insight into the physical mechanisms and possibly, even towards a new and more unified theory. The second output is the development of new and more effective optimization methods, i.e. the shaping and design of the electric and magnetic self-fields. With more data on the formation, progression and interaction of the fields, new ways to optimize the energy transfer to the propellant and to balance the ratio of ablation energy and kinetic energy of the plasma can be identified. This is also important to identify and to introduce better technologies to the thrusters and for thruster scaling.
http://dx.doi.org/10.1016/j.vacuum.2014.07.023 0042-207X/© 2014 Elsevier Ltd. All rights reserved.
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This process requires the united efforts of researchers and data in the field from around the world, to generate the output in the near term and to ensure universal validity and applicability of the results. For this reason, the members of the International PPT-andiMPD-Working Group, founded at the IRS in Stuttgart, are concentrating their expertise on the matter and consolidate in this point to continue in refining the thrusters towards space application. 2. Theory The discharge model usually employed for treatment of the working principle of an iMPD is the slug model introduced by Jahn [5]. The model itself will only briefly be described herein, as far as necessary for the analysis and presentation of the experimental data and the resulting implications with respect to the discharge current density distribution. A thorough discussion of the model would go beyond the scope of this paper. The reader is therefore referred to literature for a more in-depth description. 2.1. Discharge model A pulsed magnetoplasmadynamic thruster uses energy stored in a capacitor bank to create and to ionize plasma from a block of solid propellant in a very high current discharge pulse. After charging the capacitors, controlled thruster ignition is realized using a spark plug. Upon initiation, a breakdown occurs across the face of the propellant. The resulting high pulse current transfers energy to create and sustain the plasma. The ionized particles are accelerated by means of the electromagnetic Lorentz force, thus creating a small thrust force. The magnetic field is the self-field of the current. The schematic overview in Fig. 1, shows the current I in the form of an intermittent region of changing volume. The slug model however, assumes a current sheet of fixed geometry and mass. Sheet canting is neglected and the electrodes are considered to be of infinite width. This assumption is problematic, as it neglects edge effects and deformations of the electric field that are common in miniaturized or high efficiency thruster electrode designs. The current density is assumed to be homogeneously distributed over the current sheet and therefore only depends on the integral current I from the capacitors varying over time. The magnetic self-field strength remains constant behind the current sheet and can be calculated through amperes law, neglecting the displacement current term:
B¼
m0 I : d
ahead of the plasma is set to zero, assuming a linear drop over the sheet thickness. Considering Eq. (1) shows, that fields and the current are only treated on an integral level. The highly dynamic field configurations, interactions between fields and particles as well as the distributed current density remain unaccounted for. It becomes obvious, that computed results from such a model can be qualitative at best. Major model refining attempts were directed at modifications to introduce more complex field distributions, sophisticated electrode geometries and ablation models for estimation of the mass bit per pulse [6e11]. The additional data altered the obtained simulation results, but remained behind expectations and specific to the respective thruster development. This limits the model's applications towards the extraction of parameter trends and complicates the development and evaluation of engineering tools for preliminary thruster design. A stifling issue is the understanding of the current as a progressing sheet. The concept of a sheet running along the electrodes of the thruster, like on rails, can hardly be observed in experimental thruster studies. This observation becomes all the more apparent, with increasing deviation of the electrode shape from the parallel plate configuration. It is also not suited to explain effects like latetime-ablation, uneven propellant mass ejection and thrust vector misalignment. A camera shot of the discharge channel of the thruster ADD SIMP-LEX, as shown in Fig. 2, does show little resemblance to the moving sheet theory. The shot was taken with a DICAM-2 micro channel plate camera, with an exposure time of 50 ns and a spectral range between 380 and 900 nm. The area between the electrodes in Fig. 2 can be divided into three zones of distinct brightness. The brightest zone (1) appears near the cathode, a darker zone (2) with a roughly triangular shape beneath it, and finally an almost completely dark zone (3) near the anode. It should be noted here, that this sectioning can only be of qualitative nature and does not represent a clear indicator of the current flow in the thruster. It does however demonstrate the lack of reason to assume a moving current sheet to explain this data. Only little is known about the complex fields and plasma distributions and interactions inside of the thruster during operation. Preliminary work with inductive magnetic field probes had shown very promising results in acquiring spatial and time resolved information of the magnetic field distribution between the thruster electrodes [6]. It was concluded, to use this approach to investigate the theory of a moving current sheet inside of ADD SIMP-LEX, by
(1)
here, B is the magnetic flux density, m0 is the magnetic permeability in vacuum and d is the width of the electrodes. The magnetic field
Fig. 1. Schematic overview of an iMPD-thruster.
Fig. 2. Side view of ADD SIMP-LEX discharge channel at 2.7 ms after thruster ignition.
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means of measuring the magnetic vector field and deriving the respective current density vector field. Early attempts for a procedure involving a small Rogowski-coil can be found from Palumbo and Begun [12]. 2.2. The inductive magnetic field probe An inductive magnetic field probe utilizes a small coil to measure the field with high spatial and temporal resolution. The underlying physics is based on the faraday law:
rot E ¼
vB : vt
(2)
here, E and B are the electric and magnetic field vectors in the coil and in the thruster respectively. Transforming Eq. (2) into the integral form and using Stokes' theorem leads to:
I vA
Eds ¼ Uind ¼
d dt
Z BdA:
(3)
A
(4)
herein, u is the angular frequency, n is the number of coil windings and B0 is the amplitude of the applied magnetic field. The calculated sensitivity factor ε reflects the aberration of the theoretically induced voltage ui and the measured induced voltage uexp:
εexp ¼
uexp : ui =nA
three orders of magnitude higher. To perform a probe calibration, experimental data is generated for varying sinusoidal field frequencies at constant field magnitude and vice versa. The resulting sensitivity factors are then averaged, to obtain the valid calibration factor c for all measurements within the probe range. The factor c is the inverse of the sensitivity factor, but has been chosen for convenience. A single induction coil only senses the magnetic field normal to and inside of its coil winding area. The calculation of a field vector therefore requires three measurements at any given point, to cover all three dimensional field components. If the vector information of the magnetic flux density is known, the respective current density can then be found by means of a MatLab™-based threedimensional curl calculation, according to Ampere's circuital law:
j¼
1 ðV BÞ; m0
(6)
with j representing the current density vector. 3. Experimental procedure
In Eq. (3), Uind is the measured voltage output response of the inductive probe and A is the area of a single coil winding. This shows that the probe design is a compromise between high spatial resolution and desired sensitivity to the change in magnetic field density. The induced voltage also depends on the frequency of the change in the magnetic field. This is important, because the eigenfrequency of any coil used must be high enough, to not run into sampling limits. This is usually given, for small coil dimensions as used in this study. For ADD SIMP-LEX, the difference between the thruster discharge frequency around 100 kHz and the first eigenfrequency is in the order of at least one magnitude. Magnetic fields of very low frequency or of direct nature cannot be detected, as too little or no voltage will be induced. For the reasons given above, any probe must be carefully calibrated, to comply with the frequency and amplitude range of the measurement environment. For this, the probes output signal is compared to the theoretical voltage output uexp induced in the center of a pair of Helmholtz coils. Assuming an alternating magnetic field of arbitrary frequency and applying it to Eq. (3), allows for calculation of the theoretical probe response:
ui ¼ nAjuB0 ejut :
3
For experimental investigation of the magnetic field, the field vectors were mapped at discrete points of three horizontal planes within the thruster discharge channel. The planes were chosen to include points of interest near the cathode (z ¼ 10 mm), centered between the electrodes (z ¼ 0 mm) and near the anode (z ¼ 10 mm). An overview of the standard measurement grid in each plain can be taken from Fig. 3. Since the space inside the thruster is limited, the utilization of an array was not practical and single probes were used. The vacuum test facility 17 at IRS has been used for all tests. It has been described in other publications [6] which the reader is kindly referred to. To speed up the measurement process and to reduce the number of vacuum tests, the axis table at IRS was upgraded with a remote controlled z-axis for full 3D-motion capability. In addition, PEEK was used for the probe holder instead of aluminum and a redesigned simplified the probe fixation (Fig. 4). The plastic material reduced coupling issues and signal noise experienced during earlier measurements. The ambient pressure during measurements inside the vacuum chamber was kept below 104 mbar via a rotary vane and turbo-molecular pumping system. The test cylindrical test chamber has a diameter of 0.3 m and a length of 1 m and is made of stainless steel. 3.1. Thruster setup The ADD SIMP-LEX thruster utilized in the experiments features four capacitors with a total capacitance of 80 mF (Fig. 5). The
(5)
In case of an ideal probe response to the magnetic field of the Helmholtz coils, the voltage magnitudes will be equal and ε equals nA. For a more detailed description of the standard setup for calibration of an inductive probe, including the Helmholtz coils, the reader is referred to literature [13]. A pair of Helmholtz coils normally doesn't generate a magnetic field of the same magnitude like the field of the pulsed thruster. The experimental apparatus to provide an equally strong alternating magnetic field in the Helmholtz coils was not available. The reason can be found in the strong required currents necessary to drive the field. Hence, the measurement range of the inductive probe was calibrated up to a maximum magnetic flux density of 0.71 mT. For comparison, the expected flux density amplitude during thruster operation is up to
Fig. 3. Topdown view of thruster anode with measurement point grid of each x-yplane, z-axis positive direction out of the picture, all dimensions in mm.
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Fig. 6. Inductive probe designs.
Fig. 4. Improved 3D axis table.
capacitor voltage was set to 1300 V through a DC-power supply for all tests. The electrodes of the discharge channel have an initial width of 20 mm at the PTFE and an initial electrode gap of 20 mm. Both of the electrodes, the anode and cathode, are flared and diverge at an overall angle of 20 degree. In addition, the electrodes are tongue shaped, linearly reducing their width from the PTFE to the tip region (see Fig. 3). The solid PTFE-propellant was placed as two blocks between the electrodes, forming a V-shape to simulate side feeding (see Fig. 3). A semiconductor ignition plug driven by a self-made ignition module triggered the thruster operation. The igniter voltage was set to 1000 V, to deliver 10 mJ. The electrodes were cleaned before each test, to ensure comparability of the measurement data. 3.2. Inductive probes Inductive probes are designed at IRS to measure the magnetic field [14]. A probe is supported by a long thin rod to keep the mounting interface away from the thruster discharge. The sensor coil is located at the far end of the rod. The coil is specially wound to create no parasitic induction area between its output leads, to avoid unwanted induction coupling. Attention was given to calibration, to check for parasitic areas, by exposing the probe to a magnetic field normal to the sensor coil axis. The signal path away from the coil is carefully shielded to prevent any capacitive or inductive coupling. This includes the probe connection interface for installation of the probe on the axis table. For protection from the plasma, the rod is embedded in an insulating shell.
Fig. 5. The iMPD-thruster ADD SIMP-LEX.
In Fig. 6 the probe design employs a two-layer coil with a PVCcore diameter of 1 mm. Each layer is fixed with epoxy resin. The coil is crimped to a 2 mm copper tube with a length of 30 cm for shielding. The twisted coil wires are connected to small BNC wires, leading out of the test chamber. The probe is embedded in epoxy resin for protection and coated with a liquid glass treatment. Two epoxy-probes were chosen for the measurements. Both of them are part of an ongoing miniaturization and material testing effort at IRS. Increasing the number of coil windings is also intended. The probe shown in Fig. 6 above is not fully tested yet and embeds the sensor tip in glass instead of epoxy to reduce the size. It was thus only used complementary. The small 0.5 mm inner diameter of the glass required coating of a silver shield layer to the inner tube wall and reduction of the coils size. Application of the silver was performed with the coil inside, to prevent damages from pushing the coil into the glass tube. A sectional drawing in Fig. 7 illustrates this tip assembly. The coil is made of 0.1 mm copper wire with 5e10 turns. 4. Results Camera shots taken with a common Olympus E-1 DSLR camera as well as the DICAM-2 MCP camera were compared prior to the test, to verify that the inductive probe has no effect on the observed pulse brightness distribution over time. It is assumed that this can be an indicator for the energy and momentum transfer during a pulse. To support this conclusion, current signals were compared and no influence beyond typical repeatability of the intrusive probe was found. In Fig. 8 a small bow shock is observed, originating at the probe tip. Its presence suggests testing the applicability of conical-probes for further investigation. Note, that the exposure time of the image in Fig. 8 is 0.125 s compared to the 105 s of the discharge. The inductive probes performed very well with the improved shielding techniques. Signal noise could almost fully be eliminated (see Fig. 9). The signals show the magnetic field development over time for positions along the centerline of the thruster (y ¼ z ¼ 0). As the probe is moved downstream, the magnetic field strength decreases. This indicates the main current to run near the PTFE, rather than passing by the probe. At around 7 ms, the magnetic field is almost homogenous for all centerline positions. Measurements show, that this is the point of thruster current reversal (see also Fig. 12). The reason for this intersection not crossing the centerline
Fig. 7. Sectional drawing of inductive probe tip with glass tube.
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Fig. 8. DSLR image of the electrodes with bow shock (magnified and highlighted by a white line) ahead of the inductive probe.
could hint to further need for improving of the inductive probe setup. Exemplary results for the calculated current density vector field are presented for an x-z-plane through the thrusters centerline (y ¼ 0) in Fig. 10. Presentation of all results obtained would be outside of the scope of this paper. Plots show the current density distribution between 1 and 6 ms, i.e. for the first half cycle of the discharge. Arrows indicate the 2D-vector direction. The magnitude of the current density is illustrated by a color map. As predicted from the magnetic field, the data clearly indicates the breakdown and subsequent begin of the discharge pulse near the PTFE surface. The current carrying hot zone then advances into the interelectrode gap without losing cohesion and stays within 40 mm of the propellant at all times. It is interesting to note, that no separation of the current carrying zone is visible [15]. Instead, the current zone recedes towards the propellant surface as the pulse progresses. It is therefore concluded from the data, that the presence of a moving current sheet is highly unlikely and not supported by the data. It is noted here, that the streamline patterns between the measurement points are purely qualitative in nature and do not represent actual experimental data. To compare the visual plasma phenomena to the calculated current density, time correlated shots of the discharge channel were taken with the DICAM-2. The shots are presented in Fig. 11 and show little congruence with the current density plots. The plasma formation and subsequent light emission does not appear to be linked to the path of the discharge current. Any attempt to deepen the understanding must therefore first deal with the origins
Fig. 10. Current density plots at y ¼ 0 for the first half cycle of the discharge.
Fig. 9. Magnetic field for 7 positions along the thruster discharge channel centerline, distance from PTFE in mm.
of light emission and the underlying physical implications to explain the observations from an empirical point of view. To support the absence of a link, the location and presence of excited carbon C2 and carbon ions Cþ near the cathode during the € nherr using first 12 ms of the discharge has been confirmed by Scho wavelength filtered high-speed-camera imaging [16]. Both species were detected concentrated mainly in the region 1 in Fig. 2. They
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Fig. 11. Side view shots of the discharge channel for the first half cycle of the discharge, plasma flowing from left to right.
were not detected in the discharge path found by the inductive €nherr, it probes. While no distinct current sheet was found by Scho is suggested that the plasma is created in the current, not downstream of it. This supports the idea of an intermittent region as the plasma origin, indicated in Figs. 1 and 11 with lower light emission as the plasma is only created there. The lack of ability of the current to create carbon ions after 5 ms, and a mere thermal acceleration of neutrals is also mentioned. This is supported by the fading current at 6 ms in Fig. 10 and absence of light emission visible in Fig. 11. While these results provide spatial information, particle densities are also investigated for ADD SIMP-LEX by emission spectroscopy and MacheZehnder interferometry in literature [17]. Both diagnostic approaches yield matching results. The electron density is found to be about 1017 cm3 at 1300 V discharge voltage, which allows for classification of the plasma as a thermal lowtemperature plasma. Maximum ionization levels found are carbon ions Cþþ and fluorine ions Fþ. The idea that the current zone only expands to a fraction of the electrode length would leave the rest of the electrodes to charring and sputtering depending on the form of the electric and magnetic field. This can be observed on the electrode tips of ADD SIMP-LEX, which show respective patterns. It also points toward better understanding the possible impact of field-shaping, to optimize the electrode shape and to minimize its length. The path and interactions of particles must hence be clear first, to then link it to the formation and shape of the electric and magnetic fields. Depending on acceleration in the electric field and deviation in the magnetic field, a particle will leave or will not leave the discharge chamber. Examination of Fig. 11 suggests that the light emission is the result of accelerated heavy particle interactions, most likely with neutrals. Ions emitted from the anode either exit the thruster or collide with the cathode. The dark area near the anode (see also Fig. 2) supports this idea, since no ions return to the anode [16] and therefore no interactions occur and no emission is detected. The bright area near the cathode is assumed to be created due to particle impacts, which cause electrode material to be ejected. When the ejected particles collide with incoming ions, more emission could be detected. In this case, the moving of the high emission zone near the cathode can be caused by the increasingly bent paths of the ions between anode and cathode. Instead of a moving sheet, data hints towards an outburst of a plasma, conceivable as a pulsed sweep of plasma wind. It should be noted, that the thrust vector would vary over time under such conditions. In turn, better coordination of early strong acceleration by the electric field and matching deviation of the plasma during a pulse promises gains in thrust efficiency and evaluation of the level of optimization of a thruster. To investigate the reliability of the data, the computed current density was integrated over the z ¼ 0 mm x-y-plane grid area between the electrodes. In theory, the resulting current integral signal should show the same qualitative behavior in time as the current measurement signal from a HoKa current sensor of one of the thruster's capacitors. The magnitudes of the current signals' amplitudes cannot be compared, as the few measurement points in the time frame of this work offer insufficient grid resolution. The diagram in Fig. 12 shows two graphs for comparison of the measured and grid-integrated current signals of the ADD SIMP-LEX thruster. The experimental data, acquired by a custom made HoKacurrent monitor [18] on the terminal of a capacitor, is indicated by the fine line. Signals show remarkably good agreement in time for the first peak. A discrepancy between the two signals occurs after 8 ms leading to mismatch of the second peaks. This can partly be explained by an unwanted energy exchange between the thruster's
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found to match in time for the first discharge peak only. The second peak shows a delay. Although absolute values for the current cannot be compared, the ratios of the first to second current peaks also match, indicating feasibility of the presented analysis and diagnostics. Although the maturity of the inductive probes at IRS is high, future efforts have to include an increase in the resolution of available empirical data of ADD SIMP-LEX. Further, introduction of a calibration of the inductive probes with sinusoidal signals of magnitudes comparable to the PPT is required to increase the MatLab™ calculation accuracy. The presented analysis can be considered a first step and needs confirmation from other sources of information. To further clarify the impact of the intrusive probe on the thruster discharge behavior, thrust measurements with the probe have to be compared to nominal thruster operation. Further experimental investigations should focus on higher spatial grid fidelity of the particle densities and magnetic field measurements inside of the discharge channel of ADD SIMP-LEX to complement and confirm the theories of this work. This is challenging due to the need to better resolve the discharge with the spectrometer. Fig. 12. Comparison of current signals from a single capacitor current measurement and MatLab™-integration of the current density.
Acknowledgments
front and back capacitors, causing an internal current flow. This energy exchange would not be present in the field between the electrodes and consequently only be detected by the current sensor, not the inductive probe. The ratios of 1st to 2nd peak amplitude match very well, even for a low measurement point grid resolution. This supports feasibility of the comparison analysis approach in Fig. 12.
The authors gratefully acknowledge funding by the German Aerospace Center and German Federal Ministry of Economics and Technology under contract number 50-RS-1002.
5. Conclusion The presented data was used to analyze the dynamic discharge current and its self-induced magnetic field in an iMPD Pulsed Plasma Thruster. (1) It is found that the concept of a detached current sheet that accelerates down the electrodes (slug-model) as a modeling approach is not supported. Hence, the current is unlikely to act like a magnetic pressure plasma ejector piston, pushing the plasma with its sheet surface. A suggestion for an appropriate treatment is the emanation of the pulsed plasma from an intermittent region expanding and contracting within range of the PTFE-surface. (2) High-Speed-Camera shots revealed three recurring zones between the electrodes. Light emission is found unlikely to be linked to the discharge current distribution. Any attempt to explain the observations must include ion particle energy, momentum exchange and movement trajectory, as well as the distribution of the inherent electric and magnetic vector fields to investigate ion bombardment of the cathode. (3) A three dimensional curl calculation of magnetic field measurements revealed the current density vector field. The 2D-current density plots are derived using a MatLab™-program. The plots show a strong concentration of the main current within 4 cm of the PTFE-surface. The magnitude of the derived current density of 104 A/m2 is lower than expected. (4) The inductive probes and measurement apparatus performed well, but indicate potential for further improvement. The miniaturization must be enforced to mitigate the probe impact, increase spatial resolution and foster the setup of probe arrays for faster data acquisition. The grounding of the probe must be improved to prevent noise from the discharge to be reflected on the probe and cause signal distortion. This can be implemented together with an optical data transfer interface, which is already successfully employed for current sensors. (5) Comparison of the empirically and semi-empirically determined discharge current is
References [1] Popov GA, Antropov NN. Ablative PPT. New quality, new perspectives. Acta Astronaut 2006;59:175e80. [2] Nawaz A, Albertoni R, Herdrich G, Auweter-Kurtz M. Thrust efficiency optimization of SIMP-LEX. In: 26th international symposium on space technology and science (ISTS), Hamamatsu, Japan; 2008. [3] Ziemer JK, Choueiri EY, Jahn RG. Scaling laws for pulsed electric propulsion with application to the pluto express mission. In: 24th international electric propulsion conference, Moscow,Russia; 1995. [4] Arrington LA, Haag TW. Multi-axis thrust measurement of the EO-1 pulsed plasma thrusters. AIAA-99e2290, Tech Report. NASA; September 1999 [NASA/ TM-1999-2-9396]. [5] Jahn RG. Physics of electric propulsion. New York: McGraw-Hill Series in Missile And Space Technology; 1968. [6] Nawaz A, Lau M, Herdrich G, Auweter-Kurtz M. Investigation of the magnetic field in a pulsed plasma thruster, AIAA-37161e865. AIAA J November, 2008;46(11). [7] Shaw P, Lappas VJ. Modeling of a pulsed plasma thruster; simple design, complex matter. In: Space propulsion conference, San Sebastian, Spain; 2010. €nherr T, Komurasaki K, Herdrich G. Study on plasma creation and prop[8] Scho agation in a pulsed magnetoplasmadynamic thruster, vol. 50. World Academy of Science, Engineering and Technology; February 2011. p. 557e63. [9] Keidar M, Boyd ID, Beilis II. Ionisation and ablation phenomena in an ablative plasma accelerator. J Appl Phys 2004;96(10):5420e8. [10] Rooney D, Moeller T, Keefer D, Rhodes R, Merkle C. Experimental and computer studies of a pulsed plasma accelerator. In: 43rd joint propulsion conference, AIAA 2007-5225, Cincinnati, Ohio; 2007. [11] Turchi P, Mikellides P. Modeling of ablation-fed pulsed plasma thrusters. In: 31st joint propulsion conference, AIAA-95-2915, San Diego, CA; 1995. [12] D.J. Palumbo, M. Begun, Plasma acceleration in pulsed ablative arc discharges, Fairchild Industries, AFOSR-TR-0623. €nherr T, Komurasaki K. Experimental [13] Lau M, Manna S, Herdrich G, Scho investigation of the current density in the discharge plasma of ADD SIMP-LEX. In: 48th joint propulsion conference, Atlanta, GA; 2012. [14] Decker G, Honea DL. Magnetic probes with nanosecond response time for plasma experiments. J Phys Sci Instruments January 1972;5:481e4. [15] Koizumi H, Noji R, Komurasaki K. Plasma acceleration processes in a pulsed plasma thruster. Phys Plasmas March 2007;14:033506. €nherr T, Komurasaki K, Kawashima R, Arakawa Y, Herdrich G. Evaluation [16] Scho of discharge behavior of the pulsed plasma thruster SIMP-LEX, AIAA 20106530. In: 46th joint propulsion conference, Nashville, TN; 2010. €nherr T, Nees F, Arakawa Y, Komurasaki K, Herdrich G. Characteristics of [17] Scho plasma properties in an ablative pulsed plasma thruster. Phys Plasmas March 2013;20:033503. [18] Lau M, Herdrich G, Karrer N. Power train configuration study on a pulsed plasma thruster with state-of-the-art high current monitors, AIAA-20134122. In: 49th joint propulsion conference, San Jose, CA, USA; 2013.
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Vacuum journal homepage: www.elsevier.com/locate/vacuum
Plasma diagnostic with inductive probes in the discharge channel of a pulsed plasma thruster Matthias Lau*, Georg Herdrich Institute of Space Systems, University of Stuttgart, Pfaffenwaldring 29, 70569 Stuttgart, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2013 Received in revised form 11 July 2014 Accepted 16 July 2014 Available online xxx
Research of magnetoplasmadynamic Pulsed Plasma Thrusters (PPTs), or iMPDs, at the Stuttgart Institute of Space Systems (IRS), led to the thruster design ADD SIMP-LEX. For optimization of the thruster's discharge behavior and of the plasma acceleration, the magnetic self-field is measured. Inductive miniaturized probes are introduced and used to acquire data at points of the volume inside of the thruster's discharge channel. The results are used for analysis to identify the extend of the discharge zone along the discharge channel of the PPT. Measured magnetic field signals along the centerline of the discharge channel are presented. The underlying distribution of the dynamic discharge current is deduced from Amperes circuital law and interpreted in a two-dimensional plot against camera images for the current-plasma-interaction, current motion and validity of today's discharge models. The evaluation of the calculated integral discharge current in a plane of the discharge channel against the recorded thruster discharge current is presented and discussed. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Inductive probes Magnetic field measurement Current density distribution iMPD Pulsed plasma thruster
1. Introduction The pulsed magnetoplasmadynamic thruster (iMPD), represents a robust and simple design for secondary propulsion needs of satellites, for example target pointing, attitude control, formation flight, and drag compensation. Relatively high mean exhaust velocities ce and efficient propellant utilization are achieved through the pulsed operation mode. This beneficially limits power consumption and allows for thrust adjustment without losses in Dv. The common choice of propellant is solid Polytetrafluoroethylene (PTFE), or Teflon™. Without the need for injection, feed lines, valves and tanks, the weight and system complexity are exceptionally low. The overall low complexity is main criteria for minimum operational risk and high affordability, with cost savings of one to two orders of magnitude in comparison. The easy handling and long flight heritage also justify primary propulsion tasks for iMPDs, under the condition of increase of the generally low thrust efficiency of this type of electric thruster. The development of ADD SIMP-LEX (Advanced Stuttgart Impulsing MagnetoPlasmadynamic thruster for Lunar EXploration) tackled this problem, by achieving world leading thrust efficiencies around 30%, together with the APPT thrusters developed at the RIAME and Kurchatov Institutes in Moscow, Russia [1e4]. This was * Corresponding author. E-mail address: [email protected] (M. Lau).
made possible through a close technology exchange as part of a cooperation contract. Beyond the demonstrated performance, the ADD SIMP-LEX also invites continued efforts, to even further increase the thrust efficiency. For this, the common approach of electrical and geometric parameter variation was found to require extension to the level of discharge formation and energy transfer mechanisms. The relatively poor universal validity and qualitative character of discharge models also suggest the rethinking of the thruster's working principle and idealized model of a moving current sheet [5]. This model has been extended and refined by the work of many researchers, yet never led to a universally satisfying and applicable solution. The goal is to utilize the observed trends derived from data of experimental parametric studies at IRS, to focus the experimental efforts on observations, which are not mirrored by current models. At first, this leads towards the extraction of possible explanations, deeper insight into the physical mechanisms and possibly, even towards a new and more unified theory. The second output is the development of new and more effective optimization methods, i.e. the shaping and design of the electric and magnetic self-fields. With more data on the formation, progression and interaction of the fields, new ways to optimize the energy transfer to the propellant and to balance the ratio of ablation energy and kinetic energy of the plasma can be identified. This is also important to identify and to introduce better technologies to the thrusters and for thruster scaling.
http://dx.doi.org/10.1016/j.vacuum.2014.07.023 0042-207X/© 2014 Elsevier Ltd. All rights reserved.
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This process requires the united efforts of researchers and data in the field from around the world, to generate the output in the near term and to ensure universal validity and applicability of the results. For this reason, the members of the International PPT-andiMPD-Working Group, founded at the IRS in Stuttgart, are concentrating their expertise on the matter and consolidate in this point to continue in refining the thrusters towards space application. 2. Theory The discharge model usually employed for treatment of the working principle of an iMPD is the slug model introduced by Jahn [5]. The model itself will only briefly be described herein, as far as necessary for the analysis and presentation of the experimental data and the resulting implications with respect to the discharge current density distribution. A thorough discussion of the model would go beyond the scope of this paper. The reader is therefore referred to literature for a more in-depth description. 2.1. Discharge model A pulsed magnetoplasmadynamic thruster uses energy stored in a capacitor bank to create and to ionize plasma from a block of solid propellant in a very high current discharge pulse. After charging the capacitors, controlled thruster ignition is realized using a spark plug. Upon initiation, a breakdown occurs across the face of the propellant. The resulting high pulse current transfers energy to create and sustain the plasma. The ionized particles are accelerated by means of the electromagnetic Lorentz force, thus creating a small thrust force. The magnetic field is the self-field of the current. The schematic overview in Fig. 1, shows the current I in the form of an intermittent region of changing volume. The slug model however, assumes a current sheet of fixed geometry and mass. Sheet canting is neglected and the electrodes are considered to be of infinite width. This assumption is problematic, as it neglects edge effects and deformations of the electric field that are common in miniaturized or high efficiency thruster electrode designs. The current density is assumed to be homogeneously distributed over the current sheet and therefore only depends on the integral current I from the capacitors varying over time. The magnetic self-field strength remains constant behind the current sheet and can be calculated through amperes law, neglecting the displacement current term:
B¼
m0 I : d
ahead of the plasma is set to zero, assuming a linear drop over the sheet thickness. Considering Eq. (1) shows, that fields and the current are only treated on an integral level. The highly dynamic field configurations, interactions between fields and particles as well as the distributed current density remain unaccounted for. It becomes obvious, that computed results from such a model can be qualitative at best. Major model refining attempts were directed at modifications to introduce more complex field distributions, sophisticated electrode geometries and ablation models for estimation of the mass bit per pulse [6e11]. The additional data altered the obtained simulation results, but remained behind expectations and specific to the respective thruster development. This limits the model's applications towards the extraction of parameter trends and complicates the development and evaluation of engineering tools for preliminary thruster design. A stifling issue is the understanding of the current as a progressing sheet. The concept of a sheet running along the electrodes of the thruster, like on rails, can hardly be observed in experimental thruster studies. This observation becomes all the more apparent, with increasing deviation of the electrode shape from the parallel plate configuration. It is also not suited to explain effects like latetime-ablation, uneven propellant mass ejection and thrust vector misalignment. A camera shot of the discharge channel of the thruster ADD SIMP-LEX, as shown in Fig. 2, does show little resemblance to the moving sheet theory. The shot was taken with a DICAM-2 micro channel plate camera, with an exposure time of 50 ns and a spectral range between 380 and 900 nm. The area between the electrodes in Fig. 2 can be divided into three zones of distinct brightness. The brightest zone (1) appears near the cathode, a darker zone (2) with a roughly triangular shape beneath it, and finally an almost completely dark zone (3) near the anode. It should be noted here, that this sectioning can only be of qualitative nature and does not represent a clear indicator of the current flow in the thruster. It does however demonstrate the lack of reason to assume a moving current sheet to explain this data. Only little is known about the complex fields and plasma distributions and interactions inside of the thruster during operation. Preliminary work with inductive magnetic field probes had shown very promising results in acquiring spatial and time resolved information of the magnetic field distribution between the thruster electrodes [6]. It was concluded, to use this approach to investigate the theory of a moving current sheet inside of ADD SIMP-LEX, by
(1)
here, B is the magnetic flux density, m0 is the magnetic permeability in vacuum and d is the width of the electrodes. The magnetic field
Fig. 1. Schematic overview of an iMPD-thruster.
Fig. 2. Side view of ADD SIMP-LEX discharge channel at 2.7 ms after thruster ignition.
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means of measuring the magnetic vector field and deriving the respective current density vector field. Early attempts for a procedure involving a small Rogowski-coil can be found from Palumbo and Begun [12]. 2.2. The inductive magnetic field probe An inductive magnetic field probe utilizes a small coil to measure the field with high spatial and temporal resolution. The underlying physics is based on the faraday law:
rot E ¼
vB : vt
(2)
here, E and B are the electric and magnetic field vectors in the coil and in the thruster respectively. Transforming Eq. (2) into the integral form and using Stokes' theorem leads to:
I vA
Eds ¼ Uind ¼
d dt
Z BdA:
(3)
A
(4)
herein, u is the angular frequency, n is the number of coil windings and B0 is the amplitude of the applied magnetic field. The calculated sensitivity factor ε reflects the aberration of the theoretically induced voltage ui and the measured induced voltage uexp:
εexp ¼
uexp : ui =nA
three orders of magnitude higher. To perform a probe calibration, experimental data is generated for varying sinusoidal field frequencies at constant field magnitude and vice versa. The resulting sensitivity factors are then averaged, to obtain the valid calibration factor c for all measurements within the probe range. The factor c is the inverse of the sensitivity factor, but has been chosen for convenience. A single induction coil only senses the magnetic field normal to and inside of its coil winding area. The calculation of a field vector therefore requires three measurements at any given point, to cover all three dimensional field components. If the vector information of the magnetic flux density is known, the respective current density can then be found by means of a MatLab™-based threedimensional curl calculation, according to Ampere's circuital law:
j¼
1 ðV BÞ; m0
(6)
with j representing the current density vector. 3. Experimental procedure
In Eq. (3), Uind is the measured voltage output response of the inductive probe and A is the area of a single coil winding. This shows that the probe design is a compromise between high spatial resolution and desired sensitivity to the change in magnetic field density. The induced voltage also depends on the frequency of the change in the magnetic field. This is important, because the eigenfrequency of any coil used must be high enough, to not run into sampling limits. This is usually given, for small coil dimensions as used in this study. For ADD SIMP-LEX, the difference between the thruster discharge frequency around 100 kHz and the first eigenfrequency is in the order of at least one magnitude. Magnetic fields of very low frequency or of direct nature cannot be detected, as too little or no voltage will be induced. For the reasons given above, any probe must be carefully calibrated, to comply with the frequency and amplitude range of the measurement environment. For this, the probes output signal is compared to the theoretical voltage output uexp induced in the center of a pair of Helmholtz coils. Assuming an alternating magnetic field of arbitrary frequency and applying it to Eq. (3), allows for calculation of the theoretical probe response:
ui ¼ nAjuB0 ejut :
3
For experimental investigation of the magnetic field, the field vectors were mapped at discrete points of three horizontal planes within the thruster discharge channel. The planes were chosen to include points of interest near the cathode (z ¼ 10 mm), centered between the electrodes (z ¼ 0 mm) and near the anode (z ¼ 10 mm). An overview of the standard measurement grid in each plain can be taken from Fig. 3. Since the space inside the thruster is limited, the utilization of an array was not practical and single probes were used. The vacuum test facility 17 at IRS has been used for all tests. It has been described in other publications [6] which the reader is kindly referred to. To speed up the measurement process and to reduce the number of vacuum tests, the axis table at IRS was upgraded with a remote controlled z-axis for full 3D-motion capability. In addition, PEEK was used for the probe holder instead of aluminum and a redesigned simplified the probe fixation (Fig. 4). The plastic material reduced coupling issues and signal noise experienced during earlier measurements. The ambient pressure during measurements inside the vacuum chamber was kept below 104 mbar via a rotary vane and turbo-molecular pumping system. The test cylindrical test chamber has a diameter of 0.3 m and a length of 1 m and is made of stainless steel. 3.1. Thruster setup The ADD SIMP-LEX thruster utilized in the experiments features four capacitors with a total capacitance of 80 mF (Fig. 5). The
(5)
In case of an ideal probe response to the magnetic field of the Helmholtz coils, the voltage magnitudes will be equal and ε equals nA. For a more detailed description of the standard setup for calibration of an inductive probe, including the Helmholtz coils, the reader is referred to literature [13]. A pair of Helmholtz coils normally doesn't generate a magnetic field of the same magnitude like the field of the pulsed thruster. The experimental apparatus to provide an equally strong alternating magnetic field in the Helmholtz coils was not available. The reason can be found in the strong required currents necessary to drive the field. Hence, the measurement range of the inductive probe was calibrated up to a maximum magnetic flux density of 0.71 mT. For comparison, the expected flux density amplitude during thruster operation is up to
Fig. 3. Topdown view of thruster anode with measurement point grid of each x-yplane, z-axis positive direction out of the picture, all dimensions in mm.
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Fig. 6. Inductive probe designs.
Fig. 4. Improved 3D axis table.
capacitor voltage was set to 1300 V through a DC-power supply for all tests. The electrodes of the discharge channel have an initial width of 20 mm at the PTFE and an initial electrode gap of 20 mm. Both of the electrodes, the anode and cathode, are flared and diverge at an overall angle of 20 degree. In addition, the electrodes are tongue shaped, linearly reducing their width from the PTFE to the tip region (see Fig. 3). The solid PTFE-propellant was placed as two blocks between the electrodes, forming a V-shape to simulate side feeding (see Fig. 3). A semiconductor ignition plug driven by a self-made ignition module triggered the thruster operation. The igniter voltage was set to 1000 V, to deliver 10 mJ. The electrodes were cleaned before each test, to ensure comparability of the measurement data. 3.2. Inductive probes Inductive probes are designed at IRS to measure the magnetic field [14]. A probe is supported by a long thin rod to keep the mounting interface away from the thruster discharge. The sensor coil is located at the far end of the rod. The coil is specially wound to create no parasitic induction area between its output leads, to avoid unwanted induction coupling. Attention was given to calibration, to check for parasitic areas, by exposing the probe to a magnetic field normal to the sensor coil axis. The signal path away from the coil is carefully shielded to prevent any capacitive or inductive coupling. This includes the probe connection interface for installation of the probe on the axis table. For protection from the plasma, the rod is embedded in an insulating shell.
Fig. 5. The iMPD-thruster ADD SIMP-LEX.
In Fig. 6 the probe design employs a two-layer coil with a PVCcore diameter of 1 mm. Each layer is fixed with epoxy resin. The coil is crimped to a 2 mm copper tube with a length of 30 cm for shielding. The twisted coil wires are connected to small BNC wires, leading out of the test chamber. The probe is embedded in epoxy resin for protection and coated with a liquid glass treatment. Two epoxy-probes were chosen for the measurements. Both of them are part of an ongoing miniaturization and material testing effort at IRS. Increasing the number of coil windings is also intended. The probe shown in Fig. 6 above is not fully tested yet and embeds the sensor tip in glass instead of epoxy to reduce the size. It was thus only used complementary. The small 0.5 mm inner diameter of the glass required coating of a silver shield layer to the inner tube wall and reduction of the coils size. Application of the silver was performed with the coil inside, to prevent damages from pushing the coil into the glass tube. A sectional drawing in Fig. 7 illustrates this tip assembly. The coil is made of 0.1 mm copper wire with 5e10 turns. 4. Results Camera shots taken with a common Olympus E-1 DSLR camera as well as the DICAM-2 MCP camera were compared prior to the test, to verify that the inductive probe has no effect on the observed pulse brightness distribution over time. It is assumed that this can be an indicator for the energy and momentum transfer during a pulse. To support this conclusion, current signals were compared and no influence beyond typical repeatability of the intrusive probe was found. In Fig. 8 a small bow shock is observed, originating at the probe tip. Its presence suggests testing the applicability of conical-probes for further investigation. Note, that the exposure time of the image in Fig. 8 is 0.125 s compared to the 105 s of the discharge. The inductive probes performed very well with the improved shielding techniques. Signal noise could almost fully be eliminated (see Fig. 9). The signals show the magnetic field development over time for positions along the centerline of the thruster (y ¼ z ¼ 0). As the probe is moved downstream, the magnetic field strength decreases. This indicates the main current to run near the PTFE, rather than passing by the probe. At around 7 ms, the magnetic field is almost homogenous for all centerline positions. Measurements show, that this is the point of thruster current reversal (see also Fig. 12). The reason for this intersection not crossing the centerline
Fig. 7. Sectional drawing of inductive probe tip with glass tube.
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Fig. 8. DSLR image of the electrodes with bow shock (magnified and highlighted by a white line) ahead of the inductive probe.
could hint to further need for improving of the inductive probe setup. Exemplary results for the calculated current density vector field are presented for an x-z-plane through the thrusters centerline (y ¼ 0) in Fig. 10. Presentation of all results obtained would be outside of the scope of this paper. Plots show the current density distribution between 1 and 6 ms, i.e. for the first half cycle of the discharge. Arrows indicate the 2D-vector direction. The magnitude of the current density is illustrated by a color map. As predicted from the magnetic field, the data clearly indicates the breakdown and subsequent begin of the discharge pulse near the PTFE surface. The current carrying hot zone then advances into the interelectrode gap without losing cohesion and stays within 40 mm of the propellant at all times. It is interesting to note, that no separation of the current carrying zone is visible [15]. Instead, the current zone recedes towards the propellant surface as the pulse progresses. It is therefore concluded from the data, that the presence of a moving current sheet is highly unlikely and not supported by the data. It is noted here, that the streamline patterns between the measurement points are purely qualitative in nature and do not represent actual experimental data. To compare the visual plasma phenomena to the calculated current density, time correlated shots of the discharge channel were taken with the DICAM-2. The shots are presented in Fig. 11 and show little congruence with the current density plots. The plasma formation and subsequent light emission does not appear to be linked to the path of the discharge current. Any attempt to deepen the understanding must therefore first deal with the origins
Fig. 10. Current density plots at y ¼ 0 for the first half cycle of the discharge.
Fig. 9. Magnetic field for 7 positions along the thruster discharge channel centerline, distance from PTFE in mm.
of light emission and the underlying physical implications to explain the observations from an empirical point of view. To support the absence of a link, the location and presence of excited carbon C2 and carbon ions Cþ near the cathode during the € nherr using first 12 ms of the discharge has been confirmed by Scho wavelength filtered high-speed-camera imaging [16]. Both species were detected concentrated mainly in the region 1 in Fig. 2. They
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Fig. 11. Side view shots of the discharge channel for the first half cycle of the discharge, plasma flowing from left to right.
were not detected in the discharge path found by the inductive €nherr, it probes. While no distinct current sheet was found by Scho is suggested that the plasma is created in the current, not downstream of it. This supports the idea of an intermittent region as the plasma origin, indicated in Figs. 1 and 11 with lower light emission as the plasma is only created there. The lack of ability of the current to create carbon ions after 5 ms, and a mere thermal acceleration of neutrals is also mentioned. This is supported by the fading current at 6 ms in Fig. 10 and absence of light emission visible in Fig. 11. While these results provide spatial information, particle densities are also investigated for ADD SIMP-LEX by emission spectroscopy and MacheZehnder interferometry in literature [17]. Both diagnostic approaches yield matching results. The electron density is found to be about 1017 cm3 at 1300 V discharge voltage, which allows for classification of the plasma as a thermal lowtemperature plasma. Maximum ionization levels found are carbon ions Cþþ and fluorine ions Fþ. The idea that the current zone only expands to a fraction of the electrode length would leave the rest of the electrodes to charring and sputtering depending on the form of the electric and magnetic field. This can be observed on the electrode tips of ADD SIMP-LEX, which show respective patterns. It also points toward better understanding the possible impact of field-shaping, to optimize the electrode shape and to minimize its length. The path and interactions of particles must hence be clear first, to then link it to the formation and shape of the electric and magnetic fields. Depending on acceleration in the electric field and deviation in the magnetic field, a particle will leave or will not leave the discharge chamber. Examination of Fig. 11 suggests that the light emission is the result of accelerated heavy particle interactions, most likely with neutrals. Ions emitted from the anode either exit the thruster or collide with the cathode. The dark area near the anode (see also Fig. 2) supports this idea, since no ions return to the anode [16] and therefore no interactions occur and no emission is detected. The bright area near the cathode is assumed to be created due to particle impacts, which cause electrode material to be ejected. When the ejected particles collide with incoming ions, more emission could be detected. In this case, the moving of the high emission zone near the cathode can be caused by the increasingly bent paths of the ions between anode and cathode. Instead of a moving sheet, data hints towards an outburst of a plasma, conceivable as a pulsed sweep of plasma wind. It should be noted, that the thrust vector would vary over time under such conditions. In turn, better coordination of early strong acceleration by the electric field and matching deviation of the plasma during a pulse promises gains in thrust efficiency and evaluation of the level of optimization of a thruster. To investigate the reliability of the data, the computed current density was integrated over the z ¼ 0 mm x-y-plane grid area between the electrodes. In theory, the resulting current integral signal should show the same qualitative behavior in time as the current measurement signal from a HoKa current sensor of one of the thruster's capacitors. The magnitudes of the current signals' amplitudes cannot be compared, as the few measurement points in the time frame of this work offer insufficient grid resolution. The diagram in Fig. 12 shows two graphs for comparison of the measured and grid-integrated current signals of the ADD SIMP-LEX thruster. The experimental data, acquired by a custom made HoKacurrent monitor [18] on the terminal of a capacitor, is indicated by the fine line. Signals show remarkably good agreement in time for the first peak. A discrepancy between the two signals occurs after 8 ms leading to mismatch of the second peaks. This can partly be explained by an unwanted energy exchange between the thruster's
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found to match in time for the first discharge peak only. The second peak shows a delay. Although absolute values for the current cannot be compared, the ratios of the first to second current peaks also match, indicating feasibility of the presented analysis and diagnostics. Although the maturity of the inductive probes at IRS is high, future efforts have to include an increase in the resolution of available empirical data of ADD SIMP-LEX. Further, introduction of a calibration of the inductive probes with sinusoidal signals of magnitudes comparable to the PPT is required to increase the MatLab™ calculation accuracy. The presented analysis can be considered a first step and needs confirmation from other sources of information. To further clarify the impact of the intrusive probe on the thruster discharge behavior, thrust measurements with the probe have to be compared to nominal thruster operation. Further experimental investigations should focus on higher spatial grid fidelity of the particle densities and magnetic field measurements inside of the discharge channel of ADD SIMP-LEX to complement and confirm the theories of this work. This is challenging due to the need to better resolve the discharge with the spectrometer. Fig. 12. Comparison of current signals from a single capacitor current measurement and MatLab™-integration of the current density.
Acknowledgments
front and back capacitors, causing an internal current flow. This energy exchange would not be present in the field between the electrodes and consequently only be detected by the current sensor, not the inductive probe. The ratios of 1st to 2nd peak amplitude match very well, even for a low measurement point grid resolution. This supports feasibility of the comparison analysis approach in Fig. 12.
The authors gratefully acknowledge funding by the German Aerospace Center and German Federal Ministry of Economics and Technology under contract number 50-RS-1002.
5. Conclusion The presented data was used to analyze the dynamic discharge current and its self-induced magnetic field in an iMPD Pulsed Plasma Thruster. (1) It is found that the concept of a detached current sheet that accelerates down the electrodes (slug-model) as a modeling approach is not supported. Hence, the current is unlikely to act like a magnetic pressure plasma ejector piston, pushing the plasma with its sheet surface. A suggestion for an appropriate treatment is the emanation of the pulsed plasma from an intermittent region expanding and contracting within range of the PTFE-surface. (2) High-Speed-Camera shots revealed three recurring zones between the electrodes. Light emission is found unlikely to be linked to the discharge current distribution. Any attempt to explain the observations must include ion particle energy, momentum exchange and movement trajectory, as well as the distribution of the inherent electric and magnetic vector fields to investigate ion bombardment of the cathode. (3) A three dimensional curl calculation of magnetic field measurements revealed the current density vector field. The 2D-current density plots are derived using a MatLab™-program. The plots show a strong concentration of the main current within 4 cm of the PTFE-surface. The magnitude of the derived current density of 104 A/m2 is lower than expected. (4) The inductive probes and measurement apparatus performed well, but indicate potential for further improvement. The miniaturization must be enforced to mitigate the probe impact, increase spatial resolution and foster the setup of probe arrays for faster data acquisition. The grounding of the probe must be improved to prevent noise from the discharge to be reflected on the probe and cause signal distortion. This can be implemented together with an optical data transfer interface, which is already successfully employed for current sensors. (5) Comparison of the empirically and semi-empirically determined discharge current is
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Please cite this article in press as: Lau M, Herdrich G, Plasma diagnostic with inductive probes in the discharge channel of a pulsed plasma thruster, Vacuum (2014), http://dx.doi.org/10.1016/j.vacuum.2014.07.023