Saunderson E, 1 and Gouws D 2 South African National Space Agency, Hermanus, Western Cape, 7200, South Africa

Transcription

1 SpaceOps Conferences 28 May - 1 June 2018, 2018, Marseille, France 2018 SpaceOps Conference / Evaluation of the effect of ambient temperature variation on the calibration of a Large Helmholtz Coils System, employed for the calibration of space qualified magnetometers Saunderson E, 1 and Gouws D 2 South African National Space Agency, Hermanus, Western Cape, 7200, South Africa Large 3-axes Helmholtz Coils are used as research as well as calibration equipment for the calibration of magnetic instruments. Systems containing magnetic sensors can be inserted into the coil and the magnetism of the system or dynamic platform can be measured for compensation in hardware or software. A Large Helmholtz Coils system (average sidelength 2.4 m) is located at the SANSA (South African National Space Agency), Space Science facility in Hermanus, South Africa. The facility is also an INTERMAGNET (International Real-time Magnetic Observatory Network) Magnetic Observatory (HER), therefore the area is magnetically clean and quiet to observatory standards. At SANSA Space Science the Large Helmholtz Coils are used regularly for the calibration of space qualified magnetometers. Predetermined magnetic fields are created in 3 axes in the center of the coils by application of predetermined currents to the coils. However, coil non-orthogonality errors, orientation of the coil relative to the ambient magnetic field, coil levelling errors and fluctuations in the ambient magnetic field have to be compensated for. Thus the coils system has to be adjusted and calibrated annually to absolute magnetic field standards. Since the accuracy of the magnetic sensor calibration is directly dependent on effectiveness and accuracy of the coil calibration procedure, the coil calibration needs to be executed with the highest possible precision. At SANSA this calibration was executed annually using a laborious manual process requiring various magnetic observatory equipment and specialized staff. Man-hour cost is significant and the coils system is non-operational for at least a week, adding loss of possible income to the cost of calibration. A new semi-automatic method could be executed by a less-experienced person using less demanding equipment, with only 6 hours downtime. The new semi-automatic calibration procedure has proven to be relatively repeatable; however, there remains a major uncertainty in terms of the stability of the generated field due to the possible variation in the ambient temperature during calibration and subsequent use. Therefore, the aim of this study was to evaluate the new semi-automatic calibration procedure in terms of repeatability to determine the effect of variations in the ambient temperature on the calibration constants of the coil. Evaluations were executed in autumn ambient temperatures at the location in South Africa. The calibration procedure was executed 50 times spanning a temperature range of 14 ⁰C to 25 ⁰C inside the building (12 ⁰C to 30 ⁰C degrees outside). Analysis of the coil constants have shown that the coil constants exhibit change of ~1.4 nt/⁰c at nt applied field. This is significant as magnetic sensors are often calibrated up to nt, and moreover, the magnetometer calibrations are not specifically executed at the same temperature as coil calibration. A method of compensating for temperature dependence of the coils, or significant temperature insulation of the building, will have to be investigated in the near future. 1 Specialist Engineer, South African National Space Agency, esaunderson@sansa.org.za 2 Specialist Scientist, South African National Space Agency, dgouws@sansa.org.za 1 Copyright 2018 by South African National Space Agency. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

2 I. Nomenclature B = magnetic flux density in Tesla, T µ 0 = free air magnetic permeability [4πx10-7 Henry/m] I = electrical current in Ampere, A n = number of windings L = side length of the Helmholtz coil system, m a = perpendicular distance from the center of the Helmholtz coils to the plane of each coil, m B x, B y, Bz = applied fields in the H (X), D (Y), and Z coils of the Helmholtz system, nt I x, I y, I z = applied currents in the H (X), D (Y), and Z coils of the Helmholtz system, ma C x, C y, C z = coil constant of the H (X), D (Y), and Z coils of the Helmholtz system, nt/ma X 0, Y 0, Z 0 = H (X), D (Y) and Z coil offsets, nt B m = 3-axes magnetic field measured at the center of a 3-axes Helmholtz coil, nt B coils = 3-axes applied magnetic field in the coils, nt B geo adj = 3-axes adjusted ambient geomagnetic field in real time, nt B 0 = 3-axes coil offsets, nt v 1, v 2, v 3 = non-orthogonal angles of a 3-axes Helmholtz system, degrees β = Levelling angle in the North-South direction, degrees γ = Levelling angle in the East-West direction, degrees = Helmholtz coil system orientation angle with respect to True North, degrees α 0 II. Introduction Large 3-axes Helmholtz coils are used very effectively as research equipment, as well as calibration equipment for the calibration of magnetometers, magnetic sensors and electronic compasses. Parameters of these sensors that are most often evaluated are linearity, noise, gain and electronic offsets. Given adequate size of the coils a system containing a magnetic sensor can be inserted into the coil and the magnetism of the system or dynamic platform can be measured and compensated for in the hardware or software of the system. Fig. 1 Outline of a 3-axes Helmholtz coils indicating the center area that adheres to 99.99% uniformity. Helmholtz coils systems are capable of supplying predetermined magnetic fields in 3 axes by compensating for coil non-orthogonality errors, orientation of the coil relative to the ambient magnetic field, coil levelling errors and fluctuations in the ambient magnetic field. To accomplish this, the coils system itself needs annual setup, and thereafter calibration to absolute magnetic field standards. At the Space Science facility of SANSA (South African National Space Agency), this calibration was, until recently, executed annually using a very laborious manual process requiring various magnetic observatory equipment and experienced staff for the magnetic measurements required for the calibration process. The total manhours required for the measurements and data reduction was around 60 hours. Furthermore, the coils system is nonoperational for at least a week. A new semi-automatic method was evaluated recently. This method can be executed by a less-experienced person using less demanding equipment and can be completed in a tenth of the time compared to the manual 2

3 procedure. However, a major uncertainty remains in terms of the stability of the generated field as a function of ambient temperature. The new procedure will be used to determine the effect of the ambient temperature on the calibration constants of the coil, and the correction thereof if necessary. For a single axis Helmholtz coil [1] the flux density at the center is given by: B= π 2 4µ InL ( L + 4 a ) ( L / 2+ a ) (1) This can be expanded to a 3-axes system for creating a uniform field at the center of the system. For calibration of sensors a 3-axes system is required with a uniformity of 99.99% or better. This equates to a sphere with a diameter of ± 10% of the side length of the coil system. III. SANSA Large Helmholtz Coils system The SANSA Space Science directorate in Hermanus, South Africa, is the authoritative South African institute for calibrating magnetic compasses, magnetometers and many other systems containing magnetometers. For this purpose, extensive use is made of Helmholtz coils to generate a uniform magnetic field as calibration reference. As magnetometers and compasses have a vital role in the operation of subsea, sea, air or space platforms for navigation, orientation, scientific or other purposes, their calibration is essential and must be accomplished as accurately as possible. A set of Large Helmholtz Coils (Fig. 2(a)) are located in the non-magnetic Calibration hut (Fig. 2(b)) on the premises of SANSA Space Science, which also houses an INTERMAGNET (International Real-time Magnetic Observatory Network ) Magnetic Observatory designated as HER, and the area is magnetically clean to magnetic observatory standards. The physical parameters of the SANSA 3-axes coil are shown in Table 1. (a) (b) Fig. 2 (a) 3-axes Large Helmholtz Coils system located in the (b) Non-magnetic Calibration hut Table 1 Physical parameters of the Large 3-axes Helmholtz Coils system at SANSA Coil axis Side length, mm Separation, mm No. of windings Total resistance Conductor X (H) Ω Ø1.0 mm Cu, enamel insulation Y (D) Ω Ø1.0 mm Cu, enamel insulation Z Ω Ø1.0 mm Cu, enamel insulation 3

4 IV. Helmholtz Coils as calibration facility Magnetic sensors at SANSA are calibrated by characterizing their response to a known external magnetic field, as generated in the Helmholtz coil system. For any desired field to be generated in the coil system, the required current to be applied in the coils is calculated from various different measured or calculated variables. These currents are converted by the AMES (Automatic Magnetometer Evaluation System) system to relevant voltages which are applied in the coils as currents. Magnetometer calibration parameters are typically estimated by means of spherical harmonic analysis by correlating magnetometer outputs to the desired (applied) magnetic field. The AMES system, which controls the Large Helmholtz Coils, includes the 3 sets of orthogonal coils, 3 calibrated 1 Ohm sensing resistors, 3 KEPCO high current power supplies, a Keysight 34972A Data Acquisition Unit with & 34902A Multiplexer modules, and a PC with custom developed software, as shown in Fig. 3. (a) (b) (c) Fig. 3(a) KEPCO high current power supplies, (b above) KEYSIGHT 34972A Data Acquisition Unit with & 34902A Multiplexer modules, (b below) and c) custom developed Labview software The PC and power supplies are located in a separate building 30 m from the Calibration hut containing the coils, to reduce magnetic influences. As the geomagnetic field changes during calibration of instruments, the applied magnetic fields in the coils are corrected in real-time for any fluctuations of the ambient geomagnetic field. Information to this end is received from the INTERMAGNET Observatory HER located 50 m from the Calibration hut. The AMES system is a closed loop control system. The current through the coils are monitored across calibrated 1 Ohm resistors in order to determine the final applied fields. Magnetic fields up to nt can be applied in the coils system, but under normal conditions magnetometers and magnetic systems require calibration only up to nt. The magnetic field measured by a 3-axes magnetometer centered and aligned in a 3-axes Helmholtz coil system, is given by: B m = B coils+b geo_adj+b 0 (2) To be able to apply any desired field in the coils, the required currents have to be calculated from: ( _ 0) I = M B B B (3) 1 a c d geo adj and then applied via the AMES system, where M c is the calibration matrix:. Cx Cy sinυ1 Cz sinυ2 cosυ3 Mc = 0 Cy cosυ1 Cz sinυ2 sinυ Cz cosυ 2 (4) 4

5 V. Calibration of the Helmholtz Coils Annual calibration of the Large Helmholtz Coils is necessary to ensure the accurate application of magnetic fields within the Helmholtz Coils. A calibration model was developed with estimated coil calibration parameters which provide the means to generate any desired magnetic field in SANSA s Large 3-axes Helmholtz Coils by sufficiently compensating for parameters such as coil non-orthogonality errors, coil orientation in the ambient magnetic field, coil levelling errors and fluctuations in the ambient magnetic field. Two important factors influencing the modelling of the magnetic field observed by a magnetic sensor placed in the coil system are the coil system non-orthogonality (v1, v2, v3) and its physical orientation in the Earth's magnetic field (α 0 ). Further influencing factors are pillar differences, coil levelling effects (β, γ) and the fluctuations in the ambient field necessitating real time calculations. For many years a manual procedure of coil calibration was employed, where all the above mentioned parameters and errors were determined by hand. This procedure is slow, but nevertheless very accurate, summing up to a few days of work and therefore labour intensive and costly. The first step is the manual levelling of the Z (vertical) coil using a QHM (quartz horizontal intensity magnetometer) and Askania circle (Fig. 4(a)) with large non-magnetic adjustment tools. Thereafter the H (X) and Z coil constants are calculated by applying certain currents and measuring the response of an Overhauser absolute magnetometer (Fig. 4(b)), whereas the D (Y) coil constant is determined with the use of a DI-fluxgate magnetometer (Fig. 4(c)). Non-orthogonal angles between the H (X), D (Y), and Z coils are determined with the DI-fluxgate magnetometer. As the DI-fluxgate magnetometer has an accuracy ±0.2 nt, this error with respect to the nt field gives an angle error of 2" (seconds of arc). The angle between two orthogonal components needs two measurements and therefore the error in the measurement of an angle between two components is less than ±5" (seconds of arc). Pillar differences between the pillar in the center of the Helmholtz coils and the pillar where the HER Observatory geomagnetic measurements are taken, as well as baseline values, are determined with the Overhauser and DI-fluxgate magnetometers, with an average value of 0.03⁰ and a maximum absolute offset (corrected) of 0.7⁰. (a) (b) (c) Fig. 4 (a) QHM mounted on an Askania circle (b) Overhauser absolute magnetometer (c) DI-fluxgate magnetometer Final parameters of the Helmholtz Coil calibration can be applied as follows: Bx Cx Cy sinυ1 Cz sinυ2 cosυ3 I x cosβ 0 sinβ Bx X 0 B = 0 C cosυ C sinυ sinυ I + sinβ sinγ cosγ sinγ cosβ B + Y y y 1 z 2 3 y y 0 B 0 0 C cosυ I cosγ sinβ sinγ cosγ cosβ B Z z m z 2 z z geo _ adj 0 (5) The above order also reflects the order of importance of the parameters. The coil constants have the largest effect, as they result directly in the applied currents and therefore in the size of the field. Coil offsets, which are 5

6 usually small, represent unaccounted effects (e.g. temperature dependence) and inadverted model errors that result in offsets (biases) present in each coil. The manual calibration has certain shortcomings, of which the time spent on the calibration is the main problem, however, the repeatability of the process as well as the temperature dependence of the result is hard to investigate given a procedure that takes a week to execute. VI. Automatic calibration procedure An automatic procedure was developed, based on spherical harmonic analysis as adapted from [3] and [4]. This procedure takes less than an hour to execute, and calculates all the calibration parameters, except the coil orientation angle with respect to True North, α 0. However, the automatic procedure is based on initial data from the manual procedure, therefore can not be used as standalone method, but may be used as a quick verification of the system or confirmation of the system status. A set of random magnetic field vectors are created within the Helmholtz Coils, and measured with an absolute Overhauser magnetometer. Spherical harmonic analysis and the Levenberg-Marquardt algorithm are used to calculate the so-called calibration matrix M c, as well as other parameters. The greatest advantage of this procedure is the amount of time spent on it (1 hour) compared to the manual method (4-5 days). Beneficial to the accuracy of the obtained data is the fact that the applied magnetic vectors use a wide range of the coil s capability whereas the manual method only use positive fields in the H and Z coils, neglecting more than half of its range. Furthermore, repeatability of the process, as well as dependency of the coil parameters on various external factors, can be investigated with ease in a short time period. VII. Calibration Matrix M c and temperature variation A major uncertainty in the stability of the generated field is the possible dependence on the ambient temperature. The automatic procedure is well adapted to determine the effect of the ambient temperature on the calibration constants of the coil, as many repetitions of the calibration could be executed in a single working day. The matrix M c plays a central role in the calibration, has the largest influence on the accuracy of the applied fields relative to the other parameters, and therefore it was decided to use this matrix for the temperature dependence investigation. Assume the coils have coil constants C x, C y, and C z respectively and currents I x, I y, and I z are applied in the [C x, C y, C z ] triad, then: B =M.I (6) coils Due to physical constraints on the construction of the coils, the coils are not exactly orthogonal to one another, and the small non-orthogonality angles v1, v2, v3 exists. c Fig. 5 Non-orthogonality angles of Helmholtz configuration 6

7 Bx Cx Cy sinυ1 Cz sinυ2 cosυ3 I x B = 0 C cosυ C sinυ sinυ I y y 1 z 2 3 y B 0 0 C cosυ I z coils z 2 z (7) For the SANSA Large Helmholtz Coils parameters are typically: C x = C y = C z = v 1 = -155 sec of arc v 2 = 5 sec of arc v 3 = -6 sec of arc VIII. Test setup and analysis of measurements The measurement campaign was launched to include a variety of ambient temperature conditions during the early autumn in South Africa. The calibrations were executed over 7 non-consecutive days, with outside temperatures ranging from 12 C to 30 C. The ambient temperatures inside the hut during the calibrations varied between 14 C to 25 C effectively, as the Calibration hut housing the coils is temperature insulated to a certain extent. The instrument setup was undisturbed for the length of the calibration evaluation. The Overhauser magnetometer was set up in the center of the Helmholtz coils and tuned to nt. A specific set of random vectors ( nt ± 4000 nt) were applied repeatedly, 50 tests in total. Each test consists of 200 random vectors, with a 5 second delay after application of the field until measurement of the Overhauser and coil currents. All calibrations were executed remotely; therefore the hut remained closed for the duration of the calibrations. Automatic correction was made in the AMES system for changes in the local geomagnetic field during the calibrations. The Data Acquisition Unit for the coils currents has a measuring accuracy of 2.2 µv or 2.2 µa. IX. Results of temperature dependency tests In total, 50 calibrations were executed to represent temperatures over a spread of 11 ⁰C. The SANSA Space Science facility is located in a relatively temperate climate along the South-Western coast of South Africa at a latitude of 34.5⁰ South, therefore the temperatures reached is representative of most daytime temperatures within the insulated coil hut over the course of a year. The criteria used for evaluation are the elements of M c, specifically the coil constants C x (H coil constant), C y (D coil constant), and C z (Z coil constant). The off-diagonal elements of M c were also investigated, however, did not show any significant temperature dependence. Fig. 6 Experimental variation of coil constants with ambient temperature Fig. 6 shows the variation of the three coil constants of the Large Helmholtz Coils with variation in ambient temperature. The ambient temperature is the temperature measured inside the hut, in fact, directly adjacent to the coils. The outside temperature variations were at least 3 to 5 degrees warmer or colder at the extremes. It can be seen clearly that all three coils show an inverse sensitivity to ambient temperature. At a maximum applied field of nt the effective applied field in the H coil varies with 1.2 nt/⁰c, which represents a 0.002% error per ⁰C. For similar maximum applied fields in the D and Z coils, the effective applied fields in the D and Z coils vary with 1.4 nt/⁰c and 1.3 nt/⁰c respectively, representing errors of % and 7

8 0.0022% per ⁰C, respectively. Thus, given an 11 ⁰C ambient temperature change, errors of 13.2 nt to 15.4 nt would be measured at applied fields of nt, representing total errors up to 0.026%. X. Discussion of results and recommendations The measurements in the previous section have shown that an inverse relationship between coil constants and temperature variation exists within the Large Helmholtz Coils system. Depending on the accuracy of a magnetic instrument inserted into the coils for calibration, this effect could be negligible or significant. In practice, should the Large Helmholtz Coils be calibrated at an ambient temperature of 14 ⁰C during the winter, but used at an ambient temperature of 25 ⁰C during the summer, a potential inaccuracy of up to 15 nt may exist for maximum applied fields of nt. In the absence of corrective measures, it would be recommended that the coils should be calibrated at an average temperature around 18 ⁰C to 20 ⁰C to minimize possible errors. Furthermore, care should be taken to apply the coils at ambient temperatures as close as possible to the calibration temperature, thus calibrations of magnetic equipment should take place during midday in the winter, and early morning in summer time. However, these measures would be restrictive to research and commercial use. Improvement in the temperature insulation of the Calibration hut should also be considered if practically possible. A better solution would be correction of the coil constants for ambient temperature. Although the source of the temperature variation has not been investigated, it could be assumed that the temperature sensitivity could be due to the change in resistance of the copper wire with ambient temperature and/or the linear expansion of the physical aluminum coils with ambient temperature. However, the AMES system supplies constant current to the coils, which is measured directly for feedback purposes, therefore, a change in resistance would effect a change in voltage, but not current. A linear relationship exists between current and applied field according to Eq. (1), thus a change in resistance would not effect a change in applied field as the current is constant. Linear expansion of the aluminum structure of the Large Helmholtz Coils is another possibility. Given the linear expansion coefficient of (m/m⁰c) for aluminum, the side length of the H coil would increase with 0.7 mm from m to m for an increase in ambient temperature of 11 ⁰C. According to Eq. (1) the applied field would then decrease with ~7 nt. Similarly, for the D and Z coils the decrease in applied field due to linear expansion of the aluminum would also both be ~7 nt. These changes in applied field would account for half of the effective change measured in this study via the coil constants. The decrease in field due to linear expansion would be a quantity that could be measured, modelled and simulated, and consequently it would be possible to correct the coil constants with a calculated factor for use at different temperatures other than the calibration temperature. Independent temperature insensitive magnetometers could be used to verify results. One could theorize further that the temperature of the aluminum could additionally be elevated due to heat dissipation of the windings; however, further studies would be necessary. It is therefore recommended that the correction of the coil constants for ambient temperature should be investigated to improve accuracy of the Large Helmholtz Coils system. References [1] Pramanik, A., Electromagnetism: Theory & Applications, 2 nd ed., Phi Learning PVT. Ltd, New Delhi, 2009, Chap. 7, ISBN: [2] Jankowski, J., Sucksdorff, C., Guide for Magnetic Measurements and Observatory Practice, International Association of Geomagnetism and Aeronomy (IAGA), NOAA Space Environment Center, Boulder CO, 1996 [3] Merayo, J.M.G., Brauer, P., Primdahl, F., Petersen, J.R., Nielsen O.V., Scalar Calibration of Vector Magnetometers, Measurement Science and Technology, Vol 11, 2000, pp [4] Risbo T., Brauer, P., Merayo J.M.G, Nielsen O.V., Petersen. J.R., Primdahl, F., Olsen, N., Oersted Calibration Mission: The Thin Shell Method and Spherical Harmonic Analysis, in Ground and In-Flight Space Magnetometer Calibration Techniques, vol. ESA SP-490, 2002 (in press) 8