Levitation Experiments Using the Meissner Effect

Abstract

The phenomenon that a superconductor levitates above a magnet is called the Meissner effect. Because the superconducting state repels the magnetic field of magnets, superconductors can levitate above magnets. The Meissner effect experiments require superconductors, magnets and LN₂. The magnetic field distribution of the magnet needs to be understood to conduct a superconducting levitation experiment. The distribution of magnetic field on the single magnet is similar to a water fountain with a maximum point in the centre. It is thus difficult to levitate the superconductor above a single magnet. Of course, if the size of the magnet is quite large, the shape of the magnetic field is almost flat, so superconductors can be levitated above it. However, due to the limitation of magnetization capacity, it is difficult to manufacture magnets of several tens of centimetres or more. For this reason, we made the magnetic levitation platforms by connecting several magnets. In this chapter, we demonstrated a variety of Meissner effect experiments using the magnetic platforms.

5.1 Array of Magnets

5.1.1 Meissner Effect

The perfect diamagnetism of superconductivity was first discovered by a German physicist, Meissner [1], after whom this phenomenon, the Meissner effect, is named. The superconducting state expels not only the external magnetic field but also the magnetic field present inside the superconductor. Because of the perfect diamagnetism of superconductivity, the superconductor levitates above magnets (see Fig. 5.1).

Fig. 5.1

Meissner effect of a high-T_c oxide superconductor

High-T_c superconductors, Nd-B-Fe magnets, and LN₂ are required to conduct the Meissner effect experiments. When a superconductor is cooled below the T_c of a superconductor, the superconductor has a perfect diamagnetic nature. The boiling temperature of nitrogen is −195.8 °C (77 K). High-T_c oxide superconductors such as BSCCO [2] and YBCO [3] have a T_c higher than 77 K. Therefore, the LN₂-cooled high-T_c superconductors can be levitated above the magnet. When the state of the superconductors and the magnetic field distribution of the magnets are understood, the Meissner effect experiment can be carried out effectively.

5.1.2 Ball on a Fountain

Consider a fountain in a pond. We go to the fountain and carefully drop a small plastic ball over the fountain. What happens when we drop the ball over the fountain? The water flow of the fountain supports the ball, but gravity pulls the ball down. Most of the balls fall down. Whether a ball can float on a fountain is determined by the shape of the water flow of the fountain. If the water flow at the top of the fountain is flat in shape, the ball may float on the fountain. However, most of the water flow of a fountain has a parabolic shape with a maximum point at the centre (Fig. 5.2).

Fig. 5.2

Ball on a fountain

Let us compare the levitation of a superconductor above a magnet to the ball on the fountain. The superconductor corresponds to the ball and the magnetic field corresponds to the fountain. A superconductor with perfect diamagnetism pushes out the magnetic field of the magnet. At the same time, gravity pulls the superconductor down. The shape of the magnetic field of the magnet is similar to the water flow at the top of the fountain. Some people think that superconductors can be levitated above a magnet. Try to place a 1-cm-sized superconductor cooled using LN₂ above a single magnet with a diameter of several centimetres. Does the superconductor levitate above the magnet? The superconductor pushes the magnet and easily to falls to the floor. In the same way as the ball on the fountain, the superconductor does not levitate above a single magnet .

The reasons why superconductors cannot levitate above a single magnet is as follows. Consider two magnets with the same polarity. The two magnets push each other. Place one magnet on the floor and then try to place another one on top of it. We cannot place one magnet above another magnet, even if we try repeatedly. Likewise, a superconductor cannot be levitated above a single magnet. The superconductor cooled using LN₂ in a magnetic-field-free environment (ZFC) repels the external magnetic field regardless of the polarity of the magnet.

If the magnet is larger than a few tens of centimetres and the superconductor is about a few millimetres in size, the superconductor may float above the magnet. In this case, the magnetic field distribution of the large magnet is almost flat. However, it is difficult to manufacture such a large magnet because of the limitation of magnetisation capacity. Although it can be manufactured, the price will be very high.

5.1.3 Magnetic Platform

The magnetic platform for superconducting magnetic levitation is manufactured by connecting several magnets. Nd-B-Fe magnets with a surface magnetic field of 3000–4000 G are used to manufacture the magnetic platform for the levitation experiments. The unit of the magnetic field is Gauss (G), and there are 10,000 Gauss in 1 Tesla. Since the magnetic force of the magnet is proportional to the thickness of the magnet [4], the levitation height of the superconductor is low when the thickness of the magnet is small. We recommend the use of magnets with a thickness of 10–15 mm. If a magnet of an appropriate thickness is not available, multiple magnets in a stack are prepared. Prepare four Nd-B-Fe magnets. A disk, square, or any shape magnet can be used. The four magnets are connected together (see Fig. 5.3a). The N pole of one magnet is connected to the S pole of another magnet. Opposite polarities attract each other, so it is easy to connect the magnets. If one end of the connected magnets is the N pole, the other end becomes the S pole. If both ends are connected, the array will look like Fig. 5.3b.

Fig. 5.3

(a) Schematic of an array of four magnets for a superconducting levitation experiment, (b) Coupled magnets

As can be seen in Fig. 5.3b, there is a space in the centre of the magnetic platform. Disc-shaped magnets having a thickness of 10 mm and a diameter of 20 mm were used for the magnetic platform. If the disc-shaped magnets are replaced by square magnets, there will be no space in the centre of the magnetic platform. As long as the space is not larger than the superconductor sample, the magnetic platform can be used for the levitation experiment.

Superconductors are needed for levitation experiment. Oxide superconductors with a T_c higher than 77 K (boiling point LN₂) are suitable for the experiment using LN₂. The J_c and grain size of a superconductor are also important for determining the magnetic levitation force of a superconductor [5]. The higher the J_c of a superconductor, the greater the magnetic levitation force of the superconductor. In this experiment, MG-processed large-grain Y123 bulk superconductors with a high J_c were used. The superconductor sample that is used for the levitation experiment should be of a size similar to or smaller than the magnetic platform.

5.1.4 Levitation of Superconductors above Magnets

Figure 5.4 shows the superconducting levitation of Y123 superconductors (black disc) above the magnetic platforms made using (a) disc-shaped and (b) rectangular magnets. The superconductors were cooled to 77 K using LN₂. The diameter of the superconductor in Fig. 5.4a is about 35 mm, and the size of the magnetic platform is 40 mm. The superconductor is slightly smaller than the platform. In Fig. 5.4b, the diameter of the superconductor is 35 mm, the longer side of the magnet is 80 mm, and the shorter side is 40 mm. The magnet is larger than the superconductor. There is a space in the centre in the magnetic platform in Fig. 5.4a, whereas there is no space in the centre of the magnetic platform in Fig. 5.4b. Regardless of the presence of space in the magnetic platforms, both cases exhibit excellent superconducting levitation above the magnetic platforms. In this experiment, the levitation height is 15–20 mm.

Fig. 5.4

Superconducting levitation above magnetic platforms made using (a) Disc-shaped, (b) Rectangular magnets

5.2 Levitation Experiments Using Ring-Shaped Magnets

5.2.1 Ring-Shaped Magnets

Consider a ring-shaped magnet (Fig. 5.5). If the polarity of the upper surface of the ring-shaped magnet is N, the bottom is S. The centre of the ring-shaped magnet is a space. The magnetic force of the magnet spreads to the upper part of the ring shape. The centre of the ring is empty, but since the magnetic force of the ring potion extends horizontally and vertically, the magnetic force at the centre is not completely zero. Therefore, in the ring-shaped magnet, the magnetic force at the centre of the magnet is weaker than the magnetic force at the ring. That is, the distribution of the magnetic field of the ring-shaped magnet is similar to that of a cup.

Fig. 5.5

Ring-shaped Nd-B-Fe magnet

Superconductors in a superconducting state repel all magnetic force generated from the ring-shaped magnet. The repulsive magnetic force allows the superconductor to levitate above the magnet. However, further help beside the repulsive force is needed for the superconductor to be positioned stably above the ring-shaped magnet. The empty space in the centre of the ring plays a role. The repulsive force of the centre (space) of the ring is relatively weak compared to that of the ring. Gravity pulls the superconductor down in the centre of the ring and the magnetic force of the ring pushes the superconductor. The two forces, which are in harmony, allow the superconductor to levitate at an appropriate height above the ring-shaped magnet.

5.2.2 Levitation of Superconductors

Figure 5.6 shows the levitation of a superconductor above the ring-shaped magnet. The superconductor samples are a single grain Y123 superconductor manufactured by the TSMG process. They were cooled using LN₂. Superconductors levitate in the space above the centre of the ring-shaped magnet. The position of the superconductor can be vertical, horizontal, or inclined relative to the surface of the ring-shaped magnet. As shown in Fig. 5.6a, the rectangular Y123 superconductor is parallel to the ring-shaped magnet. The magnetic field of the magnet is parallel to the c-axis of Y123. In Fig. 5.6b, the Y123 superconductor levitates normal to the magnet. The superconductor can also be tilted to the surface of the magnet as shown in Fig. 5.6c.

Fig. 5.6

Levitation of Y123 bulk superconductors above a ring-shaped magnet, (a) Parallel, (b) Vertical, (c) Inclined to the ring surface

5.2.3 Size of Superconductors

There is a proper size of a superconductor that can be levitated above the ring-shaped magnet. If the superconductor is too small compared to the central hole of the ring-shaped magnet, it is difficult to levitate the superconductor above the ring-shaped magnet. It is also difficult to levitate the superconductor if the superconductor is too large compared to the hole. Therefore, the optimum size of the superconductor for the levitation experiment using a ring-shaped magnet should be determined.

Five Y123 superconductors of different sizes are prepared to understand the levitation performance above the ring-shaped magnet and are shown in Fig. 5.7. The Y123 superconductors were manufactured by a TSMG process. The dimensions of each specimen in descending order of diameter are as follows: (a) diameter d = 42 mm, thickness t = 13 mm; (b) d = 35 mm, t = 16 mm; (c) d = 25 mm, t = 10 mm; (d) d = 17 mm, t = 12 mm; (e) d = 8 mm, t = 7 mm.

Fig. 5.7

TSMG-processed single grain Y123 bulk superconductors

Figure 5.8 shows the single-grain Y123 bulk superconductors levitating above ring-shaped magnets. The d of sample (a) is 42 mm, which is slightly larger than the d (40 mm) of the central hole of the ring-shaped magnet. Other samples are smaller than the central hole. All samples levitate above the ring-shaped magnets, regardless of the diameter of the sample. Samples (d) and (e) are much smaller than the central hole but levitate above the space in the centre. This result indicates that there is a repulsive force that pushes the superconductor even in the central space. The repulsive force at the centre of the ring seems to be weaker than that at the ring surface. Therefore, it can be said that the magnetic force distribution of the ring-shaped magnets has a cup shape.

Fig. 5.8

Superconductors with various diameters levitating above ring-shaped magnets: (a) d = 42 mm, (b) d = 35 mm, (c) d = 25 mm, (d) d = 17 mm, (e) d = 8 mm

The same experiment shown in Fig. 5.8 was carried out using a small ring-shaped magnet with a hole diameter of 10 mm. This experiment was performed to understand the effect of the hole size on the superconducting levitation. As a result, except for the smallest sample (sample (e)), samples did not take a position above the small ring-shaped magnets . The superconductors and the ring-shaped magnets just pushed each other. They were like two magnets with the same polarity. Only sample (e) was sucessfully levitated above the centre of the small ring-shaped magnet as shown in Fig. 5.9. The diameter of sample (e) is 8 mm, which is similar to the diameter (10 mm) of the ring-shaped magnet. The result indicates that the size of the superconductor should be similar to or smaller than that of the hole of the ring-shaped magnet for superconducting levitation to take place successfully.

Fig. 5.9

Superconductor levitating above a small ring-shaped magnet

5.3 Platforms for Magnetic Levitation

5.3.1 Introduction

Superconductors can be levitated above a magnetic platform made by connecting several magnets or a single ring-shaped magnet. This is explained by the magnetic field distribution of magnets. At least four magnets are required to create the magnetic platform. If the magnetic platform for superconducting levitation is extensive, the superconductor can be reliably levitated above the platform. This time, I will introduce how to make a large-area magnetic platform using several magnets. The method of making a ring-shaped magnetic platform using disc-shaped magnets is also presented.

Figure 5.10 shows the preparation material for superconducting levitation experiments using a magnetic platform. The experimental setup consists of followings: (i) a plastic cup; (ii) non-magnetic tweezers ; (iii) LN₂; (iv) Nd-B-Fe magnets (a surface magnetic field of 3000–4000 G, a thickness of 10 mm, a diameter of 20 mm); (v) high-T_c superconductors (TSMG-processed single-grain Y123 bulk superconductors ).

Fig. 5.10

Preparation of the superconducting levitation experiments using a magnetic platform

5.3.2 Ring-Shaped Magnetic Platform

The way to create a ring-shaped magnetic platform using multiple Nd-B-Fe magnets is presented. Figure 5.11a, b show schematic drawings of magnet arrays with even and odd numbers of magnets. The number of magnets used to create the magnetic platform must be at least four and must be an even number such as six, eight, or ten. In the case of an even number, the pole of one end of the magnet array is the N pole and the pole of the other end becomes S. This allows the first magnet to be connected to the last magnet (Fig. 5.8a). If the number of magnets is odd, the polarities of the first and last magnets are the same. The two magnets push each other, so the two ends cannot be joined (Fig. 5.11b).

Fig. 5.11

Schematic drawings of magnet coupling: (a) Even number, (b) Odd number of magnets

As shown in Fig. 5.11a, the magnet of the N pole and the magnet of the S pole are combined one by one. Finally, one end of the magnet array is connected to the other end. When both ends of the magnet array are connected, the entire shape of the magnetic platform becomes a ring. The polarity sequence of the ring-shaped magnetic platform is N–S–N–S–N–S, which differs from the single polarity (N or S) of the ring-shaped magnet in Fig. 5.5.

Disc-shaped Nd-B-Fe magnets with a diameter of 20 mm and a thickness of 10 mm were used to manufacture a ring-shaped magnetic platform . The larger the number of magnets, the larger the space in the centre of the ring. If the diameter of the ring is large, large superconductors can be levitated. However, it is also necessary to recognize that the central space with weak magnetic force is widened. Figure 5.12a shows a ring-shaped magnetic platform made by connecting eight magnets. Inserting a non-magnetic plastic or wooded disc in the centre of the ring prevents the facing magnets with the same polarity from colliding (see Fig. 5.12b). On a ring-shaped magnetic platform, the polarity sequence of the surface is S–N–S–N–S–N. The sequence of magnet polarity does not influence the demonstration of superconducting levitation significantly. After a ring-shaped magnetic platform has been fabricated, the size of the superconductor to be levitated above it is determined by considering the area of the magnetic field and the size of the centre space.

Fig. 5.12

(a) Ring-shaped magnetic platform, (b) Ring-shaped magnetic platform with a plastic insert

5.3.3 Board-Like Platforms

Large-area magnetic platforms for superconducting levitation can be manufactured by connecting many small magnets. We determine the size of the magnetic platform we want to create. The number of magnets to be used is calculated. The number of magnets may vary depending on the size of the magnets. Disc type or square magnets are used. The S-pole magnet is combined with the N-pole magnet (see the schematic in Fig. 5.13a). Because the magnets with opposite polarities can be easily connected, a magnetic platform with a large area can be created in a short time. Figure 5.13b, c show large-area magnetic platforms produced by connecting disc-shaped magnets and rectangular magnets, respectively. When using rectangular magnets, there is no space between the magnets of the magnetic platform (see Fig. 5.13c). The board-type magnetic platform has a large magnetic field area, which allows the levitation of large-sized superconductors above it.

Fig. 5.13

(a) Schematics of a board-type magnetic platform, and a magnetic platform made of (b) Disc-shaped, (c) Rectangular Nd-B-Fe magnets

5.3.4 Cooling Using LN₂

MG-processed Y123 bulk superconductors are most commonly used for superconducting levitation experiments because of the large grain size and high J_c. LN₂ (77 K) is used to cool the superconductor. Since the T_c of the Y123 superconductor is 91 K, the superconductor reaches the superconducting state at a temperature 14 K higher than 77 K. Plastic cups for coffee are used as pots to cool superconductors. The superconductor is put into a plastic cup and LN₂ is poured into the cup. Plastic cups are thin and flexible, so they do not break easily in spite of repeated LN₂ pouring. Thick plastic or glass cups often break during the cooling test. Moreover, since the plastic cup is transparent, it is easy to observe the situation that occurs inside it.

Figure 5.14 shows a plastic cup used for cooling superconductors and LN₂ bottles (thermos). The cup contains a superconductor. It is convenient to transfer the amount of LN₂ required for the experiment from a large capacity LN₂ container to a thermos . The lid of the thermos should always be open. After the lid of a thermos has been closed and the thermos has been left for a long time, the gas (nitrogen) pressure in the bottle increases and the thermos may explode.

Fig. 5.14

(a) Plastic cup and thermos , (b) LN₂ being poured into a plastic cup to cool a superconductor

Figure 5.15 shows top views of the plastic cups into which LN₂ is poured: (a) the view after LN₂ has been poured into the cup, and (b) the view after the superconductor has completely cooled. There is a superconductor in the cup. When LN₂ is poured into a plastic cup, the LN₂ boils violently and many bubbles form due to the temperature difference between the superconductor and LN₂ (Fig. 5.15a). Then it is necessary to wait for the superconductor to cool down. As the superconductor is cooled to 77 K, bubble generation is significantly reduced (Fig. 5.15b).

Fig. 5.15

Top views of plastic cups (a) During cooling, (b) After cooling

As a plastic cup containing LN₂ is left in the air for a long time, the moisture in the air freezes on the surface of the cup, forming a frost (see Fig. 5.16a). The superconductor cooled to 77 K is transferred from the plastic cup toward the magnet using plastic forceps. The superconductor is moved over the magnet (Fig. 5.15b). In this experiment, we used a ring-shaped magnetic platform made by connecting six magnets. The superconductor is placed in the centre of the platform, as shown in Fig. 5.16b.

Fig. 5.16

(a) Holding a superconductor with tweezers, (b) Moving a superconductor to a magnetic platform

5.3.5 Levitation above Ring-Shaped Platforms

Ring-shaped magnetic platforms were made by connecting several disc magnets. Figure 5.17 shows a superconductor levitating above a magnetic platform made by connecting (a) four, (b) six, and (c) eight magnets. The levitation height of the superconductors above platform (a) is larger than 20 mm (see Fig. 5.17a). The size of the superconductor is slightly smaller than the magnetic platform. For platforms (b) and (c), the levitation height of the superconductor is smaller than that for platform (a) (Fig. 5.17b, c). As the number of magnets used to produce the platform increases, the space in the centre of the platform becomes large. The magnetic forces of the platform are generated from the individual magnets. The superconductor repels the magnetic force and levitates above the platform. Therefore, as the area of the superconductor facing the magnet increases, the repulsion of the superconductor increases. As a result, the superconductor levitates high above the platform. By adjusting the size of the superconductor and the number of magnets, the levitation height of the superconductor can be maximized.

Fig. 5.17

Superconductor levitating above a ring-shaped magnetic platform made by connecting (a) Four, (b) Six and (c) Eight magnets

5.3.6 Levitation above Board-Type Platforms

A large-area magnetic platform was produced by connecting twelve magnets with a diameter of 20 mm. The magnetic platform has a long side of 80 mm and a short side of 60 mm. The MG-processed Y123 superconductor with a diameter of 35 mm was used for the levitation experiment. The superconductor was cooled using LN₂. Figure 5.18 shows the superconductors levitating above the board-type magnetic platform. Because the size of the magnetic platform is large, there are several places available for demonstrating superconducting levitation on the platform. The superconductor can be levitated above the right side of the magnetic platform (Fig. 5.18a) or above the left side (Fig. 5.18b).

Fig. 5.18

Superconductor levitating above (a) Right side, (b) Left side of a board-type magnetic platform

Figure 5.19 shows other examples of superconducting levitation above the board-type magnetic platform. Two rectangular Y123 superconductors were cooled using LN₂ and then placed above the magnetic platform at the same time. One superconductor levitates above the left side of the platform and the other above the right side (Fig. 5.19a). This board-type magnetic platform has a wide magnetic field area , so several superconductors can be levitated simultaneously.

Fig. 5.19

(a) Levitation of two superconductors above a board-type magnetic platform, (b) Superconductors in a normal state

As the superconductor comes into contact with the atmosphere for a longer time, the superconductor temperature becomes higher than the T_c of Y123 and the superconducting state changes to the normal state. A superconductor in a normal state cannot push the magnetic force, so the superconductor goes down to the magnetic platform (Fig. 5.19b). Due to the temperature difference between the air and the superconductor, small droplets of water are formed around the superconductor and are converted to frost (ice) at the surface of the superconductor.