fluxgate magnetometer-based determination of ion ...

SP2018_00026

FLUXGATE MAGNETOMETER-BASED DETERMINATION OF ION BEAM CURRENT SEVILLE, SPAIN / 14 – 18 MAY 2018 (1)

(2)

(3)

Chris Volkmar , Christopher Geile , Andreas Neumann , Klaus Hannemann

(4)

(1)- (4)

German Aerospace Center, Institute of Aerodynamics and Flow Technology, Spacecraft Department, Bunsenstrasse 10, 37073 Goettingen, Germany (1) (2) (3) (4) Email: [email protected], [email protected], [email protected], [email protected]

KEYWORDS: Electric propulsion testing, ion beam measurement, fluxgate magnetometer, zero flux direct-current current transformer

measurement studies, but could lead to wrong conclusions if the integral beam current delivered by the thruster is of particular interest. To quantify the mentioned effects, the Faraday cup calibration function, including angle dependence, has to be known. The calibration function f relates the Faraday cup collector current Icol to its input current Iin:

ABSTRACT: A comprehensive approach to measure DC ion beam currents generated by electric space thrusters by means of the fluxgate methodology is proposed. Beam currents in the typical range for electric thrusters can be measured with high resolution. A detailed SPICE (Simulation Program with Integrated Circuit Emphasis) model to assist during hardware development is furthermore introduced. The model is verified by experiments conducted on a prototype hardware version of the proposed sensor in air, simulating the ion beam by a current-carrying wire. 1.

f =

I col I in

(1)

The input current has to be obtained very accurately to thoroughly analyze the calibration function. In this paper, we show the development steps, including the basic concept (Sect. 2), a (preliminary) design (Sect. 3), and a proof of principle (Sect. 4), of a device to determine this current, based on the fluxgate magnetometer methodology [7]. Since this methodology is based on an electrical transformer capable of measuring DC currents, it is often referred to as (zero flux) direct-current current transformer (DCCT) [8-12].

INTRODUCTION

There is a wide spectrum of electric propulsion testing procedures and equipment [1]. It spans from basic plasma characteristics, using different probes or spectroscopic methods to obtain a deeper understanding of the underlying physics of the discharge [2, 3], to devices with focus on the thruster assembly performance, such as thrust balances and power meters [4, 5]. The ion beam, or plume, is often of special interest since it exhibits very useful information on the thruster propulsive performance, e.g. thrust vector, composition of the ion beam, and the ion energy distribution function (IEDF).

Those devices have been used since many years at particle accelerators, with CERN leading the way. There are many studies available concerning these sensors. However, usually accelerator ion beam energies are orders of magnitude higher than those associated with electric propulsion and they show low angle divergence. Due to less pronounced space-charge effects, this typically results in very narrow ion beams in accelerators, whereas electric propulsion plumes are comparably highly divergent. This has to be taken into account as a constraint for the development and the placement of the sensor inside the plume.

Most beam diagnostics have in common that the beam ions are captured by a Faraday cup [6]. An equivalent electron current can be measured if the cup is biased and, if gridded, suppressed, to dispose of secondary electrons which may be generated. Gridded Faraday cups additionally offer the feature of energy selective filtering, enabling the upper mentioned determination of the IEDF: This assembly is often referred to as Retarding Field Energy / Potential Analyzer (RFEA / RPA).

2.

CONCEPT

The fundamental functionality of fluxgate magnetometers and DCCTs is nested in the nonlinear magnetization curve of ferromagnetic materials. This otherwise unwanted effect is here used for very accurate DC current determination.

The downside of a gridded Faraday cup is the inherent loss of transparency the grids impose on the ion beam. Additionally, due to the often large aspect ratio of axial length to diameter, Faraday cups exhibit substantial angle dependence. This may seem advantageous when performing thrust

As can be seen in Fig. 1, the DCCT is basically given by two magnetic cores that are magnetized by a modulated signal source; in this case a sine wave generator. The modulation windings are 1

Figure 2. Schematic of the proposed sensor system The total error ∆I is a function of the mismatch of the magnetic cores and, more importantly, the parasitic characteristics and the noise level of the electrical circuit elements used. Said circuit elements have to be, therefore, chosen very carefully after thorough assessment of their relevant specifications.

Figure 1. Conceptual design of a DCCT (reproduced from [13])

The electrical circuit of the proposed sensor system consists of the before mentioned magnetic cores, a modulator stage, an integrator, an actuator for the compensation current, and a microcontroller, which is driven in closed-loop mode. A schematic of the circuit is shown in Fig. 2.

reversed, so that a phase shift of exactly 180° between the modulation signals at the two cores is achieved. The modulation signal is adapted to the cores’ material in a way that it can sufficiently saturate the cores. The resulting magnetic flux densities B also have opposing directions. A sense winding, which is wrapped in the same direction on both cores, is used to read out the superimposed induced voltage. This voltage will be zero as long as the magnetic fluxes cancel each other, provided the cores show identical magnetic properties. If a DC current offsets both cores simultaneously, the magnetic hysteresis of both cores is shifted towards the positive or negative saturation area, depending on the sign of the current. This leads to the situation that the magnetic fluxes do not exactly cancel each other and thus, induce a net voltage. The induced voltage waveform has a fairly high bandwidth due to the nonlinear behavior of the magnetic hysteresis. In this work, the resulting signal shows a bandwidth of several hundred kHz, making an elaborate electrical sensing circuit necessary in order not to lose any valuable information. However, there have been attempts to only work with the second harmonic since it shows a strong spectral peak and is proportional to the DC offset within the magnetic cores [14, 15].

The closed-loop mode is achieved by the feedback line, as indicated in Fig. 2. When the magnetic cores (referred to as DCCT in the figure, including some electronics like differential amplifiers) exhibit net magnetic flux due to DC ion beam current, the induced voltage is integrated with a small time constant. This stable voltage (Vint) is converted to a digital signal, in our prototype case, with a 12 bit analog-digital converter (ADC). The microcontroller then compares this value, which is proportional to the magnetic flux, with a set point voltage (Vset), which is typically 0 V but may be set to any value up to 3.3 V. The difference of the signals is fed to a proportional-integral (PI) controller which tends to minimize this difference by triggering the actuator stage. First, the resulting digital compensation signal is converted to an actual analog voltage VDAC with a 12 bit digital-analog converter (DAC), and is in turn used to drive a current Icomp through the cores; in opposite direction to the ion beam current. The compensation current is driven through a precision resistor R. Its value is obtained simply by applying Ohm’s law:

The induced voltage is the figure of merit for a controller circuit, often described as the demodulator, which is in turn used to drive a current through a wire going through both cores, compensating the original input current offset. When the controller reaches stationary behavior, both currents are within the accuracy thresholds ∆I of the system. The compensating current Icomp is, therefore, an indirect measure of the input current or, in this case, the ion beam current:

= I b I comp ± ∆I

I comp =

VDAC R

(3)

The PI controlling scheme used needs some constants as input parameters. They are currently hardcoded, but will be passed to the controller using a serial interface connection in the future. The controlling algorithm is constituted by a proportional part that computes the response of the controller as a linear function of the deviation of the control variable Vint to the set point variable

(2)

2

Figure 3. Simplified circuit diagram of the current sensor system Vset as well as an integral part that sums up all the past deviations. The feedback signal is thus given by:

implies that the driving voltage at the DCCT induces magnetic flux with several harmonics, depending on the input current. This does not only have an effect on the induced voltage but also on the driving voltage, making it a self-consistent problem. The Chan model takes this very thoroughly into account, which will be shown in the next section.

VDAC ( ti ) = kP Vint ( ti ) − Vint ( ti −1 )  + i

+ kI ∑ Vint ( tn ) − Vint ( tn −1 ) 

(4)

n =1

The constants kP and kI are used to adjust and optimize the control precision and are obtained by heuristic testing following the approach of Chien, Hrones, and Reswick [16], which is based on the findings of Ziegler and Nichols [17]. The scheme in Eq. (4) differs slightly from common PI control schemes because it is implemented on a digital architecture, which offers some flexibility in contrast to analog systems; e.g., kP and kI can be adjusted independently. The time steps ti resemble the discrete sampling points of the DAC. 3.

In order to have the Chan model work properly, the magnetic characteristics of the used cores have to be known. The cores used in this work (VITROVAC 6025 Z) have been used in other attempts as well [11, 15], especially for devices measuring high-energy ion beams at particle accelerators like CERN [8, 9]. The cores exhibit very important features for the proposed kind of sensor type; i.e., very high permeability in linear mode (around 150,000), high saturation flux density (0.6 T) low coercivity (5-10 A/m), and high temperature stability. Those parameters are enabled by amorphous Co-based nanocrystalline ferromagnetic stacked strips and a corresponding specialized manufacturing process, resulting in a soft-magnetic alloy with rectangular hysteresis loop. More information can be found in a technical note from the manufacturer Vacuumschmelze GmbH [19].

PRELIMINARY DESIGN

A simplified circuit diagram of the current version of the sensor system is shown in Fig. 3. This schematic resembles the basis of a complex SPICE model used for simulations prior to and during hardware prototype design (Virtual Prototyping).

A circuit for characterization of the cores has been assembled, following the idea shown in Fig. 4.

The circuit consists mainly of the upper mentioned modular functions; i.e. modulator, nonlinear transformer, demodulator, and the feedback system including the controller. For the simulations, libraries of the actual operational amplifiers used in the hardware version have been compiled and parameterized. Furthermore, a nonlinear inductor model introduced by Chan [18] has been incorporated in the transformer model in order to correctly account for hysteresis effects. The important thing is to take the mutual interconnection of primary (modulator) and secondary (demodulator) circuit into account. This

Figure 4. Magnetic hysteresis characterization circuit 3

Here, the magnetic hysteresis is obtained with AC signaling, canceling magnetic biasing effects. The induced voltage at the transformer’s secondary is integrated at the capacitor C. With this functionality, and under consideration of Faraday’s law of induction together with Ampère’s law applied to a toroidal magnet core, the magnetic field strength and the magnetic flux density can be expressed by:

H (t ) =

N1 vR ( t ) lm R1 1

B (t ) = −

R2 C vC ( t ) N 2 AFe

(5) Figure 6. Validation of the SPICE model

In these equations, N1 and N2 denote the transformer’s primary and secondary windings, respectively, lm the mean length for magnetic field lines inside the rectangular toroidal core, and AFe the effective area the magnetic field lines pass through. The circuit values and elements are arranged as depicted in Fig. 4. The voltages vR1 and vC are obtained with an oscilloscope in x/y mode, offering direct visualization of the hysteresis. The magnetic hysteresis for one of the cores used is shown in Fig. 5. A slight offset on both axes can be observed, which is caused by the signal generator. However, the values for saturation flux density Bsat and coercivity Hc can still be found easily by taking the mean value of the respective absolute quantity, e.g. Hc = ( H c 1 + H c 2 ) 2 ≈ 6.4 A m and, following the

amplifiers (lower kHz range) are abundantly available. The SPICE model has been used to determine the necessary amplification factors, protective circuits, filtering stages, etc. Additionally, tests of different controlling parameters in order to reach optimal control accuracy have been carried out with aid of the model. The model has been validated by experiments. It is crucial for the nonlinear part of the model to work properly, in order to account for all the physical effects that occur within the magnetic cores. Therefore, the validation has been performed by comparing the voltage waveforms across one of the inversely wound coils. As shown in Fig. 6, nearly perfect agreement can be observed. The nonlinearity of the driving voltage is caused by the magnetic hysteresis and the mutual inductance. Based on the agreement, it can be concluded that, in the experiment, the cores show at least very similar magnetic characteristics because in the SPICE model, the measured data of one core has been used to parameterize both cores.

same procedure with the saturation flux density values, Bsat ≈ 0.57 T. Those values correspond nicely to the datasheet values. It was additionally found that they do not exhibit any frequency effect in the single and double digit kHz range. With the cores’ data obtained, the SPICE model can be formulated and parameterized accordingly. The modulator frequency is fixed to 10 kHz in order to keep core losses [19] and losses in the wires caused by the skin effect low. Additionally, low-noise and highly accurate power audio

4.

PROOF OF PRINCIPLE

In this section, the functionality of the sensor is assessed. For this assessment, the simulation results obtained by the SPICE model are used to parameterize the controller of the hardware prototype heuristically. A systematic investigation of the control path has yet to be performed, including a system identification, linearization of the plant, and determination of stable control parameters. The accuracy obtained via the SPICE model of the sensor is depicted in Fig. 7. As can be seen, an optimal set of control parameters was apparently found, judging from the transient behavior of the compensation current. However, there is a deviation of approx. 3 µA observable. Since the operational amplifiers used are parameterized with realistic values (including stray

Figure 5. Magnetic hysteresis of one of the used VITROVAC 6025 Z cores 4

Figure 7. Transient behavior of the compensation current obtained by the SPICE model capacitances), this error is assumed to be caused by offsets in the circuit. The aspired experimental resolution of 2.4 µA which is determined by the quantization of the DAC lies on the order of the deviation.

Figure 8. Prototype of the proposed sensor and experimental setup for validation defined manner. The radiator shown in the picture is attached to the hi-fi amplifier. This device generates losses around 1 W. The integral power consumption of the sensor is well below 2 W, most importantly located around the hi-fi generator. The cores’ secondary only generates heat at the shunt resistors the compensation current is driven through. However, even for the highest compensation current of 10 mA, the power loss lies in the double-digit mW range. Hence, no special thermal issues for the secondary circuit elements are anticipated.

With help of the simulation, an online logging of important voltages and currents had been enabled, which delivered very useful insight into the internal state of the sensor system. Especially, transients could be identified and handled properly. Those transients are usually generated by the nonlinearity caused by a) the hysteresis loop, b) the differential amplifier, and c) nonlinear protective circuit elements, such as (Zener) diodes. It is crucial to monitor and understand those signals in order to prevent particular circuit elements, e.g. operational amplifiers, from taking damage or, in the worst case, being destroyed. Unfortunately, there is no thermal model implemented yet. However, since the transients are well understood (and filtered, if necessary), and due to low supply current, the hardware is assumed to be at room temperature while being operated. Nevertheless, since the preliminary tests have been conducted outside the vacuum, with convectional thermal transport enabled, special care has to be taken when testing inside a vacuum chamber.

The prototype results for test currents in the range 5 mA – 50 µA are shown in Fig. 9. Currently, only relative measurements can be performed due to low-frequency drift of the reference voltage. This drift has to be examined in more detail, but is believed to originate from either thermal effects within the cores or low-frequency interference from the power supply. In either case, it is highly probable that this kind of disturbance is coupled galvanically. To address this phenomenon, meaningful EMC studies of the sensor have to be

To ultimately show the proof of principle and thus the proper function of the developed sensor, the ion beam current has been simulated by a conducting wire, driven by a highly accurate current supply. The experimental setup is shown in Fig. 8. The electrical components used are ready for operation in vacuo; in particular, special capacitors had to be chosen for this purpose. Furthermore, wide ground planes have been constructed to facilitate thermal management under vacuum conditions. The cores have been arranged loosely without any fixation during the initial experiment, as can be seen in the picture. Currently, a tubular fixture device is being developed to house the cores in a

Figure 9. Delta measurement results on a log scale ordinate 5

Figure 10. Relative error of the sensor

Figure 11. Calibration curve of the sensor

conducted. However, a digital calibration of the set point value prior to each measurement might facilitate the process.

The next steps include testing inside a vacuum chamber with an electric thruster delivering the current to be measured. For this, the actual sensor comprised by the magnetic cores has to be shielded against electrons and electromagnetic radiation. There is no special treatment for thermal management anticipated due to large ground planes at the PCB and low power operational amplifiers used.

Despite the obvious low-frequency drift, the measurement results look quite promising. As can be seen, even the lowest current generated has been resolved properly. Additionally, the noise level lies in the double-digit µA range, as depicted in terms of the relative error in Fig. 10. Quantitatively, the absolute error detected is 12 µA, which limits the resolution of the DAC (2.4 µA) drastically.

6.

1. Goebel, D. M. & Katz, I. (2008). Fundamentals of Electric Propulsion: Ion and Hall Thrusters, John Wiley & Sons, Hoboken, New Jersey, USA.

The sensor shows a very linear behavior until the measured current approaches the absolute error. This behavior is shown in Fig. 11 in terms of a calibration curve. 5.

REFERENCES

2. Chabert, P. & Braithwaite, N. (2011). Physics of Radio-Frequency Plasmas, Cambridge University Press, Cambridge, UK.

CONCLUSION

3. Lieberman, M. A. & Lichtenberg, A. J. (2005). Principles of Plasma Discharges and nd Materials Processing, 2 ed., John Wiley & Sons, Hoboken, New Jersey, USA.

In this paper, we presented the development stages of a current sensor based on the fluxgate methodology to measure ion beam currents generated by electric thrusters. In this respect, we do not aim to measure the integral current delivered by a thruster, which easily might be on the order of several A. Instead, we focus on accurately measuring small currents on the order of some µA up to some mA. Those currents are locally present in the far field downstream the plume of electric thrusters.

4. Neumann, A. (2017). DLR electric propulsion test facility, JLSRF 3, A108. 5. Volkmar, C., Geile, C. & Hannemann, K. (2018). Radio-Frequency Ion Thrusters— Power Measurement and Power Distribution Modeling, J. Propul. Power, accessed April 2, 2018. doi: https://arc.aiaa.org/doi/abs/10.2514/1.B3686 8

The fluxgate methodology offers this kind of accuracy. However, as can be seen in our preliminary experiments, in order to fully utilize the resolution of the sensor, internal and peripheral effects causing electromagnetic or thermal interference have to be studied in more detail. Particularly, the magnetic cores seem to exhibit a thermal effect which is not fully understood until now. Additionally, the actual prototype shows a low-frequency drift which may be generated by the voltage supply powering the sensor. It may as well be caused by thermal effects.

6. Bundesmann, C. et al. (2017) Advanced Electric Propulsion Diagnostic Tools at IOM, Procedia Eng. 185, 1-8. 7. Primdahl, F. (1979). The Fluxgate Magnetometer, J. Phys. E: Sci. Instrum. 12, 241-253.

6

8. Unser, K. (1981). A Toroidal DC Beam Transformer with High Resolution, IEEE Trans. Nucl. Sci. 28(3), 2344-2346. 9. Oldier, P., Ludwig, M. & Thoulet, S. (2009). The DCCT for the LHC Beam Intensity Measurement. In Proc. DIPAC’09 Conference, Geneva, Switzerland. 10. Zhao, Z. et al. (2010). Measurements and Calculation of Core-Based B – H Curve and Magnetizing Current in DC-Biased Transformers, IEEE Trans. Appl. Supercond 20(3), 1131-1134. 11. Soliman, E. et al. (2014). Sensor Studies for DC Current Transformer Applications. In Proc. IBIC2014, Monterey, California, USA. 12. Callegaro, L., Cassiago, C. & Gasparotto, E. (2015). On the Calibration of Direct-Current Current Transformers (DCCT), IEEE Trans. Instrum. Meas. 64(3), 723-727. 13. Forck, P. (2011). Lecture Notes on Beam Instrumentation and Diagnostics – Joint University Accelerator School. Gesellschaft fuer Schwerionenforschung (GSI), Darmstadt, Germany. 14. Chao, A. W., Mess, K. H., Tigner, M. & Zimmermann, F. (2013). Handbook of nd Accelerator Physics and Engineering, 2 ed., World Scientific Publishing Company, Singapore. 15. Nair, S. et al. (2015). Design of DC Current Magnetic Sensor for Measurement of Beam Currents in Accelerators, IJERT 4(5), 13491353. 16. Chien, K. L., Hrones, J. A. & Reswick, J. B. (1952). On the Automatic Control of Generalized Passive Systems, Trans. ASME 74, 175-185. 17. Ziegler, J. G. & Nichols, N. B. (1942). Optimum Settings for Automatic Controllers, Trans. ASME 64, 759-768. 18. Chan, J. H. et al. (1991). Nonlinear Transformer Model for Circuit Simulation, IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 10(4), 476-482. 19. Technical Note Pk-002 (1998). Tape-Wound Cores for Magnetic Amplifier Chokes VITROVAC 6025 Z. Vacuumschmelze GmbH, Hanau, Germany.

7