Gelsenkirchen University of Applied Sciences, Energy Institute, Germany. 4. French-German Research Institute of Saint Louis (ISL), France. Abstract. An array ...
MANGANITE SENSORS ARRAY FOR MEASUREMENTS OF MAGNETIC FIELD DISTRIBUTION O. Liebfried3, S. Balevičius1,2, S. Bartkevičius2, M.J. Löffler3, J. Novickij1,2, M. Schneider4, V. Stankevič1,2, N. Žurauskienė1,2 1 Vilnius Gediminas Technical University (VGTU), Lithuania 2 Semiconductor Physics Institute (PFI), Lithuania, 3 Gelsenkirchen University of Applied Sciences, Energy Institute, Germany 4 French-German Research Institute of Saint Louis (ISL), France Abstract An array consisting of four magnetic field sensors made from thin polycrystalline La0.83Sr0.17MnO3 film was used for measurement of magnetic field distribution inside the bore of multi-layer coil during electromagnetic launching of Cu hollow cylinder. The magnetic field distribution along the axis of the bore at different time points during movement of the cylinders was simulated and then compared with experimental results. Both simulation and testing demonstrated the same behaviour of the complicated magnetic field distribution.
INTRODUCTION Recently the interest in pulsed technologies, such as electromagnetic launchers, magnetocumulative generators, electromagnetic forming systems increased due to their possible applications in industry [1,2]. During the operation of these devices, extremely high pulsed magnetic fields with amplitudes up to 50 T are generated. However, measurement of such high magnetic fields is a very complicated technical task because the amplitude and direction of the magnetic field changes simultaneously. The existing high pulsed magnetic field measurement methods using B-dot, Hall or magnetooptical sensors are applicable in case of known magnetic field direction. The accuracy of these methods is low when the direction of magnetic field is not determined in advance or it is changing during an experiment. For this reason the development of sensors able to measure the magnitude of magnetic fields independently on their direction is of importance for scientists and engineers. Since the discovery of colossal magnetoresistance (CMR) in manganites, it was suggested to use this phenomenon for high magnetic field measurements. It was demonstrated that La0.83Sr0.17MnO3 thin polycrystalline films can be used for pulsed magnetic field measurements with amplitudes up to 50 T [3]. Moreover, it was demonstrated [4] that the magnetic field response of these sensors does not depend on the orientation of the sensor to magnetic field direction and measurements of magnitude of pulsed magnetic field with unknown direction can be carried out by B-scalar-sensor. In this work we demonstrate how array consisting of several manganite based B-scalar CMR-sensors can be used for measurement of pulsed magnetic field
distribution inside a coil-gun during electromagnetic launching of nonmagnetic conductive hollow cylinders.
EXPERIMENTAL The magnetic field sensors were prepared using polycrystalline La0.83Sr0.17MnO3 (LSMO) films grown on lucalox substrates by means of the Metal Organic Chemical Vapour Deposition (MOCVD) technique. The technologies used to grow these films are described in more detail in [5]. Lucalox substrates, with thickness of 0.4 mm and dimensions 25 x 25 mm2, were used to take advantage of their low dielectric constant and polycrystalline structure. The thickness of these films was about 400 nm. The sensors were fabricated using a conventional integrated circuit processing technique. Electrical contacts were made by thermal deposition of Ag, using a Cr sub-layer, followed by standard negative photolithography. The distance between the contacts was 50 µm. After removing the photoresistive mask, the contacts were annealed in O2 atmosphere at 420 °C for 20 min. The substrate was cut into pieces 0.5 mm long and 1 mm wide. Therefore, the active area of the sensor was 500 x 50 μm2. Then the samples were soldered to wires bifilarly twisted in the direction perpendicular to the surface of films and covered by epoxy. The resistance of these sensors was about 5 kΩ. During measurements, the sensor was connected in series to a ballast resistor of 3.6 kΩ and voltage source of 1.48 V. The resistor, battery power supply, and voltage stabilizer were mounted in a box. Testing and calibration of the CMR-sensors were performed using a high magnetic field generator developed at the Vilnius High Magnetic Field Centre [6]. Pulsed magnetic fields were generated by a multiple winding coil with 13 windings in each of 4 layers, outer diameter of 38 mm, length of 50 mm, and inner diameter of 18 mm. For mechanical stability the coil was fixed by a metallic case of 60 mm length, 36 mm inner and 58 mm outer diameter. Pulses used for testing and calibration were half-period sinusoidal pulses with amplitudes up to 20 T and duration of 600 µs. A loop sensor with an integrator was used to calibrate the magnetic field sensor (it’s calibration was performed by using the optical Faraday method, as well as by measuring the current in the magnetic coil [4]). The loop sensor was positioned in
the centre of the coil at the same place as the CMRsensor. Therefore, the calibration of the CMR-sensor was performed in a homogeneous pulsed magnetic field. Due to the small size of the sensor, it was obvious to produce an array of sensors, limited by inputs of further measurement devices, for measuring of magnetic field distributions. In this case, 4 sensors were positioned in a flexible tube in distances of 5 mm each to the other and fixed by customary glue. In order to protect the sensor from high frequency noise, the flexible tube together with the sensors array and twisted wires were coated by a wire screen. To measure the distribution of magnetic field dynamic, the sensor array was positioned on the centerline inside the coil. The positions of the sensors along the axis were definite with an accuracy of 1 mm. As a projectile a copper hollow cylinder of 8.8 mm length was used. Fig . 1 describes a longitudinal section of the arrangement. The sensor array (1) is placed in a tube made of Textolite (4), which holds the copper ring (2). The tube (7) directed ring (2) to move along the xdirection and defined its starting position. Fig. 2 shows a schematic diagram of the experimental setup and measurement equipment. The high magnetic field generator with the main components (capacitor, thyristor and coil) is triggered by a single pulse produced by a function generator. After ignition the thyristor connects the capacitor to the coil. The duration of 600 µs of the trigger signal is equivalent to the duration of the positive current pulse. The trigger signal also triggered the oscilloscope, which is used for visualization of the signal measurement by means of CMR-sensor. For data storage, the oscilloscope output was connected to a personal computer (PC). The acceleration of the metallic projectile along x-
Figure 2: Schematic diagram of the experiment and measurement equipment. direction was realized using magnetic field pulses having about 600 µs in duration and amplitudes up to 10 T.
THEORY In order to check the experimental results corresponding simulations were carried out. In a first step the currents in the coil, its casing and in the projectile were calculated. Subsequently the magnetic induction at the positions of the sensors was calculated. To calculate the current distribution in the projectile and in the metallic casing, a discretization was made: Projectile and casing were split into some small rings with square cross section, which are positioned at zero clearance to each other (see Fig. 1). The length of the edges of the square cross sections was chosen to be smaller than the AC skin depth. In radial direction projectile and casing were divided into two layers (see Fig. 1). After discretization the arrangement can be described by a system of magnetically coupled conductive rings. The coil itself was described by one circuit. According to [7] the complete system can be depicted with u (t ) = M ( x (t )) ⋅
r d r d i (t ) + ( R + M ( x (t ))) ⋅ i (t ) dt dt
(1)
R is a matrix, where Ri,i represents the ohmic resistivity of the ith ring and Ri,j=0 Ω else. M ( x(t )) is a matrix with Mi,i as the self-inductivity of the ith ring and Mi,j= Mj,i as the mutual inductivity between the ith and the jth ring. r u (t ) and i (t ) are vectors describing voltages and currents of all circuits. x(t) describes the position of projectile. Eq. (1) can be written as Figure 1: Longitudinal section of the electromagnetic coil launcher. 1 – sensor array; 2 – projectile; 3 – flexible tube; 4 – carrying tube; 5 – coil; 6 – case; 7 – stopper. All dimensions in mm.
u (t ) = M ( x(t )) ⋅
d r i (t ) + dt
(2)
r d M ( x) d (R + ⋅ ( x(t ))) ⋅ i (t ) dx dt
Here d M ( x ) / dx is the matrix of gradients of mutual inductivities. The mutual inductivities and their gradients between all circuits were calculated according to [8] for different positions in x-direction. For faster computation the resulting functions were approximated by simpler functions. Fig. 3 shows the interpolation functions of mutual inductivities and their gradients between two rings of the projectile and the coil. The acceleration a of the projectile with mass m is given by the propelling force between the currents of projectile rings, the coil, and the casing. Due to rotational symmetry, the force acts in x-direction. It is described by r d M ( x) r F = m ⋅ a = i1 ⋅ ⋅ i2 dx
(3)
The sum of all forces acting on the single projectile rings gives the resulting force acting on the projectile. The equation a (t ) =
d d2 v (t ) = 2 x(t ) dt dt
(4)
The calculation of the currents was accomplished applying Mathematica 5.2. Geometrical parameters as shown in Fig. 1 were used. Instead of an elliptic cross section of the coil winding a circular form with a radius of 1.41 mm was chosen resulting in the same area as in reality. It is assumed, that the conductivity of the coil windings and the projectile is 56·106 S/m, for the casing 5·106 S/m. The projectile mass of 3.7 g was calculated assuming a density of 8930kg/m3. Other constants for wires and facilities in the electric circuit were assumed with R0 = 0.1 mΩ and L0 = 20 nH. The used Pulsed Power Generator includes a Capacity of 2240μF. For calculation of the magnetic induction the law of Biot-Savart was applied resulting in the contribution of the nth ring given in cylindrical coordinates by [8] B n (t ) = 2 µI k ⋅ ∆x b 2 + r 2 + ∆x n 2 2 n ⋅ n ⋅ − K (k n ) + ⋅ E (k n ) 2 2 2π (b − r ) + ∆x n br 3 (5) 0 µI k n ⋅ ∆x n b 2 − r 2 − ∆x n 2 2 2 ⋅ ⋅ K (k n ) + ⋅ E (k n ) 3 2π (b − r ) 2 + ∆x n 2 br
[
]
with k n 2 = 4 b r / (b + r )2 + ∆xn 2 K and E are complete elliptic integrals of the first and of the second kind. a is the radius of the ring whose centreline coincides with the x-axis. ∆xn and r are the axial respectively the radial distance between the nth ring and the point of interest. The superposition of all B n gives the complete magnetic field at any point of the arrangement.
completes the equation system.
RESULTS a)
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Figure 3: Mutual inductivity (a) and its gradient (b).
Two types of experiments were accomplished. The purpose of the first experiment was to measure the axial distribution of the magnetic field in the coil with fixed copper projectile. The second experiment was carried out with a moving projectile. Here, the axial distribution of the magnetic induction during its motion was of interest. Fig. 4 shows the response of two sensors positioned at distances of 7.5 mm from the centre of the coil. One of the sensors was located inside of the projectile whereas the second one was located in a distance of 9.5 mm from the projectile. The projectile length was 8.8mm. The edge of the projectile was placed in a distance of 2 mm from the center of coil. The positions of the sensors are shown in the inserted sketch of Fig. 4 . The obtained results are compared with the calculations. Good agreement between both has to be stated. Fig. 5 shows the results obtained with the moving projectile. The graphs show the axial distribution of magnetic induction at different time points. The straight lines represent the result of the calculations, the points represent experimental data from different experiments. The sensor array consisted of four sensors. Hence to obtain the complete field distribution on the axis of the
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t [µs] Figure 4: Run of magnetic field pulse with and without fixed projectile. coil, four experiments were made at same experimental conditions. After each experiment the array of sensors was displaced by a distance of 15 mm. Therefore, the position of the first sensor of the subsequent experiment coincides with the position of the fourth sensor in the previous experiment. The different results obtained with each experiment are represented by other symbols. Inside the coil the projectile moved to the right side (Fig. 1). During all experiments the capacitor was initially charged to 1 kV. Fig. 5a shows the axial magnetic field distribution 50 µs after current ignition. This corresponds to the increasing part of magnetic field pulse (see Fig. 4). The curve has a minimum which coincides with the center of projectile. The second graph (Fig. 5b) shows the distribution of magnetic field after 250 µs. At this time the induction reaches its maximum. In the next graph (Fig. 6c) the result at decreasing magnetic field at 500 µs can be seen. Now the magnetic field is trapped inside the projectile resulting in a local maximum of the magnetic induction. A similar curve results from the fourth (Fig. 5d) graph where at t=700 µs the coil current is switched-off by the thyristor. At this time the magnetic field is maintained by eddy currents in the projectile and in the casing. A very high gradient of magnetic induction is observed at the edge of the projectile: here, sensors of smaller size will be required for more precise measurements.
DISCUSSION AND CONCLUSION A CMR-sensor array was used to investigate the dynamics of a complicated magnetic field distribution. The experimental results fit very well with the theoretical results: After current switch-off by the thyristor at 600 µs the “tail” of the magnetic field pulse is observed (see Fig. 4). The remaining magnetic flux is maintained by the electric currents induced in the casing (first curve) and projectile
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x [cm] Figure 5: Axial distribution of magnetic field at different moments of time with a moving projectile. Lines are calculated results; four kinds of symbols display measured results of four experiments under same conditions but with replaced sensor array (see text). (second curve). Furthermore the maximum of the magnetic induction inside the projectile is shifted in time and reduced in amplitude compared to the magnetic field outside the projectile. This is due to the induction of an eddy current in the projectile shielding the projectile’s interior against the intruding magnetic field. By its ohmic resistivity the eddy current is damped allowing the magnetic field to penetrate into the projectile. At decaying primary magnetic field the field inside the projectile is trapped by its eddy current. At switch-off of the current the magnetic field inside the coil is maintained by the eddy current in the casing. The eddy current in the projectile tries to keep the magnetic flux inside the projectile stable. Due to ohmic damping of the eddy currents the magnetic fields inside the projectile and inside the coil decrease exponentially. Small derivations between the calculation and the measurement appeared because in the calculation effects like friction and heating were neglected and because the measurement tolerance of the position of the sensors and of the projectile was restricted to 1 mm. Furthermore the precise reproduction of the same magnetic fields during several experiments was restricted by the possibility to
adjust the initial experimental parameters (especially charging voltage of the capacitor). Fig. 5 shows the distribution of the magnetic field along the coil axis at different time instants. It is possible to identify the motion of the projectile by comparing the local maxima/minima of the magnetic induction inside the projectile. The results from four different experiments are in excellent agreement with the calculations although the magnetic field distribution is complicated. This work demonstrates the abilities of the Vilnius High Magnetic Field Centre and its partners to measure and to calculate highly complicated magnetic field distributions of high amplitudes inside axially symmetric electrical systems.
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[4]
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[8]
B.Vengalis, N.Žurauskienė and L.L.Altgilbers, “Manganite Based Strong Magnetic Field Sensors Used for Magnetocumulative Generators”, Materials Sci. Forum, 384-385 (2002) 297. S. Balevičius, N. Žurauskienė, V. Stankevič, S. Keršulis, J. Novickij, L. L. Altgilbers, F. Clarke, “High Pulsed Magnetic Field Sensor Based on LaCa-Mn-O Thin Polycrystalline Films “, Acta Physica Polonica A 107 (2005) 207. A.Abrutis, V.Plausinaitienė, V.Kubilius, A.Teišerskis, Z.Saltytė, R.Butkute, J.P.Senateur. “Magnetoresistant La1-xSrxMnO3 films by pulsed injection metal organic chemical vapor deposition: effect of deposition conditions, substrate material and film thickness“, Thin Solid Films 413 (2002) 32. J.Novickij, S.Balevičius, N.Žurauskienė, P.Cimmperman, L.L.Altgilbers, “Compact system for pulsed high magnetic field generation”, EPPS 2002, Saint Louis, IEE Proceedings, p.30. M.J.Loeffler, “Pulsed Power Technology – Part1”, University of Applied Sciences Gelsenkirchen, Germany, Sep.2005 W.R.Smythe, “Static and dynamic electricity”, ISBN 0-89116-916-4
