Report on Electromagnet Field Characterization

7/29/2019 Report on Electromagnet Field Characterization

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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.

Report on Electromagnet Field Characterization

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