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Electromagnet design and characterization for magnetic tweezers application
1. IntroductionRecent demands have made electromagnets an attractive option for force generation to the
molecules attached to the superparamagnetic particles. Magnetic tweezers is an important
application in which particles are exposed to an external magnetic field via alternating current
applied to the electromagnet coil. Main objective of the study is to design and build an
electromagnet system for magnetic tweezers application to exert a force up to 100 pN. This will
allow us to study the neuronal growth cone using magnetic particles. Considering the design
constraints, our area of interest for applying force is 500x500 m2 300 m below the tip of the
magnet. It is necessary to understand the distribution of magnetic force inside a particular area of
interest which depends on the geometry and material properties of electromagnet. In general, a
force on a magnetic particle can be given by: =
. Where
is the induced magneticmoment per unit volume and is the magnetic field gradient. It is clear from the equation that
magnitude of the pulling force is directly proportional to the magnetic field gradient and therefore it
is important to optimize the shape of the magnet to achieve the highest possible field gradient in the
area of interest. In order to complete this goal, we will decide it into three sub goals as follows:
1) Use Comsol software to carry out simulations to predict and design geometry of the magnetalignment that will produce the magnetic field gradients that can hopefully produce forces that
can achieve up to 100 pN using finite element analysis method.
2) Machine and assemble the magnetic design created from the simulations and also to set up theentire apparatus along with minichiller for cooling, automated motorized stage control and
automated power supply control using the computer.
3) 3D magnetic field characterization for the designed electromagnet using Hall-probe magneticsensor to understand the available magnetic field gradient in the vicinity of the electromagnet.
Our final design will be composed of an Electromagnet with its transparent plastic housing
held by the three-dimensionally operated mount with a linear motor control base capable of
manoeuvring in the horizontal direction. The sole purpose of this movement is to achieve our
desired distance from the area of interest to the tip of the electromagnet. The design also contains a
minichiller which pumps water in and out using a set of tubing controlling the temperature inside
the housing of electromagnet. It also facilitates us to use high currents up to 6 A on the designed
electromagnet eliminating the risk of overloading the magnet. Our electromagnet is hooked to the
DC power supply which is connected to the computer which allows us to control the desired current
value going to our electromagnet for the definite time. Lastly, the whole set-up was fixed on to the
microscope stage to control and record the position of the electromagnet movement on micron
level. A hall probe sensor was placed near the tip of the electromagnet and magnetic field in all
three dimensions was calculated. After the introduction, this report includes materials specifications
in chapter 2 followed by both simulated and experimental results in chapter 3 and conclusion in
chapter 4.
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2. Materials:This section of the report includes the materials and equipment used for in the
electromagnet development and field characterization.
With the goal of achieving high force experimentally, we selected a single tip geometry for detailed
analysis of magnetic field distributions. As starting point of our simulations, we chose hiperco 50A
ferromagnetic core alloy with a radius of 60
2.1. Ferromagnetic core
The electromagnet for magnetic tweezers usually consists of a solenoid with a cylindrical
high permeability core. High permeability core is required because it exhibits magnetic properties
superior to those of other commercial iron-cobalt soft magnetic alloys. Hiperco 50A alloy is an
iron-cobalt-vanadium soft magnetic alloy possessing high magnetic saturation (24 kilogauss), high
D.C. maximum permeability, low D.C. coercive force, lower thermal conductivity and low A.C.
core loss. [from datasheet]. It is a best suited material primarily for magnetic cores in electricalequipment requiring high permeability at high magnetic flux densities providing high saturation
field strength. Table 1 provides some D.C. magnetic properties of Hiperco 50A alloy.
Saturation Magnetization 24200 Gauss
Maximum Permeability 10000
Coercive force 0.4 Oersteds
Coercive force 31.83 A/m
Table 1: Hiperco 50A typical DC magnetic properties.
2.2. Copper coil solenoid and its cylindrical housingElectromagnet was fabricated using copper wire diameter of 0.5 mm with the coil and core
properties listed in detail in the next section. It was then fitted in a vacuum tight plastic housing. It
has a 5 mm diameter hole on the front of housing giving access to the tip of the electromagnet and
two small holes which facilitates input current to the copper coil. On the sides of the wall of the
housing, it is connected to the minichiller tubing providing water in and water out functionality,
2.3. Minichiller
It is necessary to control our electromagnet with higher current values to get higher
magnetic field gradient around the tip. Higher current leads to higher temperature. Hence, to control
the temperature, minichiller from Huber is used which controls the temperature ranging from -10 Cto 20 C with maximum allowable pump pressure be 0.2 bar.
2.4. Power supply
To drive the electromagnet with continuous DC current, a Kikusui PWR800L DC power
supply have been used in this study. It facilitates a constant current mode. A manual control is often
inconvenient, hence a USB power controller PIA4850 is used with a USB interface. PIA4850 is
connected to the computer via USB cable and to the power supply via TP bus. Lastly, the power
supply is operated using WAVY software which is a sequence creation utility allowing us to design
the desired waveform, edit it and store it for the future use with just a mouse click.
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2.5. Hall effect Gaussmeter
A gaussmeter from Lakeshore namely 475 DSP gaussmeter has been used to measure the
magnetic field produced by the electromagnet in our experiment. It works on the principle of Hall-
effect where a semiconductor material changes its voltage which is directly proportional to the
magnetic flux density passing through it. This gaussmeter has resolution of 0.2 mG having higherDC accuracy of 0.05 % detect small changes in the magnetic field. It can detect magnetic field
ranging from 35 mG to 350 kG.
3. ResultsIn this chapter of the report, magnetic field simulations in Comsol and experimental
characterizations with Hall effect sensor of the electromagnet are briefly elaborated.
3.1. Theoretical simulations in Comsol
In order to design the electromagnet with the goal of achieving high forces of up to 100pN
in accessible configurations, we opted for finite element analysis of single tip geometry for detailedanalysis of magnetic field distributions using Comsol software. The geometry of the ferromagnetic
core of the electromagnet as well as coil configuration strongly affects the produced magnetic field
around the tip. Figure 3.1 below shows a simple geometrical view of the Comsol simulation design.
Figure 3.1: Geometry of the designed Electromagnet in Comsol with coil and core
parameters listed in table 2.
As a starting point of our simulations, an electromagnet with Hiperco 50A alloy core with a
radius of 5 mm, length of 60 mm and maximum relative permeability of 10000 was chosen. The
core was excited by 1700 turns of copper wire of 0.5mm in diameter, cylindrically surrounded
around the core. To avoid any thermal damage of the core, core and coil were separated by a
distance of 1 mm. Finally, whole geometry was tilted to 28 degrees to match with the hypothesised
design. The design of an electromagnet has been numerically optimized based on the finite element
analysis in Comsol software. Several geometrical configuration of different size of ferromagnetic
core and solenoid were calculated and the best configuration was chosen to be used for the
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experimental purpose. To summarize, table 2 enlists finalised core and coil parameters for the
electromagnet.
Copper coil parameters:
Inner diameter 7 mmOuter diameter 24 mm
Length 50 mm
Copper wire dia. 0.5 mm
Number of Turns 1500
Hiperco 50 core parameters:
Core diameter 5 mm
Length 60 mm
Tip angle 15
Flat tip diameter 0.860 mmRelative permeability 10000
Table 2: List of all parameters used in Electromagnet
After defining the geometry, calculations to find the magnetic field near the tip of the
electromagnet were performed considering the direct current of different magnitudes. A direct
current of 1 A was applied to the electromagnet of figure 1, which produces a current density of J=
4E6 A/m2. Figure 3.2 shows the magnetic flux density surface plot for the defined geometry and
applied current value and arrows in the figure emphasizes the normalised magnetic field
distribution is symmetric around the ferromagnetic core reaching the magnetic field of 1225 G at
200 m away and 300 m below the tip.
Figure 3.2: Magnetic field density with arrows representing the direction of the normalilsed
magnetic field.
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Next, magnetic field density around the tip was calculated for 2000 m away from the tip
(X axis) and 1400 m below the tip (z axis) with the help of a plotting tool in Comsol. Please
kindly note that due to the geometrical restraint of the core tip all the measurements are 200 m
away and 300 m below the tip centre. In other words, origin of the coordinates (0, 0) is actually
(200 m, 300 m) in Cartesian coordinate system, as emphasised in figure 3.3.
Figure 3.3: Schematics of the positions on x- and z- coordinates from the tip centre.
Moreover, the positions, used for the measurements of magnetic field, on x- axis were 0,
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.25, 1.5, 1.75 and 2 mm and 0, 0.1, 0.3, 0.6, 1, 1.4 mm in
z- axis. Figure 3.4 shows the magnetic field density plots for the enlisted positions in x- and z-
coordinates representing a nonlinear relationship between magnetic field and distance. It is clearthat magnetic field is high near the tip and it decreases as we move away from the tip and after
certain value below the tip, magnetic field is homogeneously distributed in the x-coordinate. In
figure 4.4, magnetic field simulation shows that maximum field of 1225 Gauss can be achieved for
input direct current of 1 A. Also, magnetic field value decreases to the value of 605 Gauss and 510
gauss at 1.4 mm below the tip and 2 mm away the tip respectively.
In addition, magnetic field gradient from the simulated results were calculated in matlab.
Magnetic field Data at different positions was exported from Comsol as a file with comma
separated values. After that, exported data was interpolated using a polynomial fit of forth order in
order to calculate a smooth magnetic field gradient curve. Figure 3.5 represents magnetic fieldgradient curve for different positions for the same values listed in the above section. Magnetic field
gradient is inhomogeneous near the tip and it becomes homogeneous as we go away as well as
below the tip.
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Figure 3.4: a) Magnetic field density Bx in different locations on x-coordinates for
several z planes and b) Magnetic field density Bz in different locations on z-coordinates for
several x planes.
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Figure 3.5: a) Magnetic field gradient dBx/dx in different locations on x-coordinates
for several z planes and b) Magnetic field gradient dBz/dz in different locations on z-coordinates for several x planes.
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3.2. Experimental result:
After designing the coil, the designed configuration was given to the mechanical shop for
manufacturing purpose where a copper wire of 0.5 mm diameter was wounded for 1700 turns
around a mettalic rod. Due to manual winding, original solenoid had less number of turns than used
for the theoritical simulations. Later, the copper windings were glued together using a hightemperature adhesive and metallic rod was taken away sparing a hollow space of 7 mm diameter
inside the solenoid. Then, hiperco 50A ferromangetic core was placed inside the solenoid leaving
air gap between the solenoid inner surface and the core. Lastly, the electromagnet set up was
assembeled inside the microscope cage as explained in the second chapter.
Initially our coil was driven with different Direct current magnitudes and the magnetic field
near the tip of the ferromagntic core was measured using the Hall-probe sensor. Figure below
shows the magnetic field at 700 m away from the tip for different current ranging from 0.1 to 5A.
Figure: 3.6: Magnetic field relationship for different current values.
It is clear from the figure above that the currents produce a linear magnetic field until the
range of 1 A. Increasing the current to higher magnitude magnetic field varies non linearly. Anonlinear relationship for higher currents results from the fact that Hiperco 50A is made up of
ferromagnetic material which starts approaching its magnetic saturation.
As discussed in detail, magnetic field of designed electromagnet was measured using the
Hall probe sensor at several locations on x, y and z. To understand the magnetic field gradient
behaviour of the electromagnet, magnetic field was measured for 2000 m away on x- coordinate, -
1000 to 1000 m on y-coordinate and 1400 m in z-coordinate was measured.
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Figure 3.7: Three dimentional magnetic field Bx characterization for different x and y
positions at 400 m below the tip.
Three dimensional graph representing the magnetic field distribution around the z plane
shows that the field is symmetric around the y axis, highest at the centre and gradually decreasing
as the tip moves away on each side. This plot also explains the electromagnet field behaviour in x-
coordinate. As expected, it is highest reaching the value of around 1200 at 200 m away from the
tip. An exponential decrease in the magnetic field could be also noticed as the tip of the magnet
moves away from the electromagnet. Furthermore, magnetic field in the figure below has been
plotted at 0 on the y coordinate for different positions on x and z coordinate to compare it with the
simulated magnetic field for the comparison purpose.
To compare the simulated results with the experimental results, magnetic field was
measured for the same positions as it was simulated for. At the tip, Hall probe sensor measured the
magnetic field of 1200 Gauss and 900 gauss in horizontal and vertical coordinates respectively.
From the figure 3.8, it is clear that magnetic field decreases gradually as we go away from the tip
but after a certain distance below the tip, magnetic field value Bzbecomes homogeneous. Also,magnetic field gradient from the experimental data at different positions were processed using the
same method of interpolation order in order to calculate a smooth magnetic field gradient curve.
Figure 3.9 represents magnetic field gradient curves for different positions for the same values
listed in the above section. Magnetic field gradient is inhomogeneous near the tip and it becomes
homogeneous as we go away as well as below the tip. Different peak of magnetic field gradient for
different positions is a result of combined error due to incident angle of 28 degrees and manual
operation for translation on z- coordinate.
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Figure 3.8: Experimental results. a) Magnetic field gradient Bx in different locations
on x-coordinates for several z planes and b) Magnetic field gradient B z in different locations
on z-coordinates for several x planes.
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Figure 3.9: Experimental results. a) Magnetic field gradient dBx/dx in different
locations on x-coordinates for several z planes and b) Magnetic field gradient dB z/dz in
different locations on z-coordinates for different x planes.
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3.3. Measuring the magnetic field at the area of interest
As mentioned in the introduction, our area of interest for generation of the magnetic force
on the particles is 500x500 m2, 300 m below the tip of the magnet. To compare the magnetic
field and field gradient in that region, both simulated and experimental results have been drawn in a
single graph representing field distribution in x coordinate for z plane at 300 m, 600 m and 900m below the tip.
Figure 3.10: Simulated (red line) and experimental (black line) Magnetic field Bx for a) 300
m, b) 600 m and c) 900 m.
As shown in figure 3.10, there is a close comparison between the experimental and
simulated results. Visible difference between the curves at different positions is due to the manual
handling of the z axis as well as the possible human error while winding the copper coil.
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Figure 3.11: Simulated (red line) and experimental (black line) Magnetic field dBx/dx for
different positions on x and measured for a) 300 m, b) 600 m and c) 900 m below the
tip.
4. Conclusions
In this report, development of a new type of magnetic tweezers have been introduced that enables
the exertion of high forces on magnetic beads and simultaneous control of the direction of this force due to
high magnetic field gradient in the horizontal direction and homogeneous magnetic field in vertical
direction. Experimental results show that field gradients of 70 T/m can be achieved with the fabricated
magnetic tweezers. These results are in agreement with theoretical simulations carried out in Comsol. Based
on these calculations, it is predicted that with this magnetic tweezers forces of 30 to 50 pN can be achieved.
Furthermore, this electromagnet is going to be used for nuoronal growth cone pulling experiments.
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