Physics
Meissner Effect
The Meissner Effect is a phenomenon in which a superconductor expels all magnetic fields from its interior when it is cooled below a certain temperature, known as the critical temperature. This effect is due to the formation of superconducting currents that flow on the surface of the material, creating a magnetic field that cancels out any external magnetic field.
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12 Key excerpts on "Meissner Effect"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner Effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner Effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided where H is the magnetic field and λ is the London penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H c . Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H c 1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength H c 2 , superconductivity is destroyed.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ magnetic field is applied to a conductor, it will induce an electric current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner Effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner Effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided where H is the magnetic field and λ is the London penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H c . Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner Effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner Effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided where H is the magnetic field and λ is the London penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H c . Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of super-conducting material containing no field. In Type II superconductors, raising the applied field past a critical value H c 1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ magnetic field is applied to a conductor, it will induce an electric current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner Effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner Effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided where H is the magnetic field and λ is the London penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H c . Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of super-conducting material containing no field.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner Effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner Effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided where H is the magnetic field and λ is the London penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H c . Depending on the geometry of ________________________ WORLD TECHNOLOGIES ________________________ the sample, one may obtain an intermediate state consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H c 1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large.
- David C. Jiles(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
φ passing through the material because by the Faraday-Lenz law of electromagnetic induction they would set up an induced current. In a perfect conductor this induced current should produce an opposing flux change which exactly counteracts the flux change producing it. In fact, the situation is quite different inside a superconductor in its superconducting state. The magnetic flux ∅ is zero, except for a thin boundary layer at the surface. (We must note immediately that this condition is not exactly fulfilled in the mixed state because of the prescence of normal material.) The Meissner Effect does, however, demonstrate that the superconducting state is something more than just a state with perfect conductivity, since the exclusion of flux is an additional property that a merely resistanceless material would not possess.Figure 13.4 Diagram showing the expected behaviour of a ‘perfect conductor’ in the presence of a field.13.2.5 Surface currents and the Meissner Effect
How can we explain the Meissner Effect?When a superconductor is cooled in a magnetic field persistent currents arise on the surface of the material at the critical temperature and these circulate so as to exactly cancel the flux density inside. The surface supercurrents are determined only by the strength of the external prevailing magnetic field.Figure 13.5 Equivalent behaviour of a superconductor (compare with Fig. 13.4 ) which exhibits the Meissner Effect or flux exclusion.The emergence of the surface currents when a material is cooled through its superconducting transition lies beyond the concept of ‘perfect’ conductivity. In order not to get an infinite current density, these surface currents must exist over a finite depth. In fact, the surface currents decay exponentially with depth, and this means that the magnetic field does penetrate at the surface of the superconductor to some extent. This is expressed by the penetration depth λ. Typical penetration depths in superconductors are 10−8 m. Some values are shown in Table 13.2
eBook - PDFSuperconductivity
Theory and Applications
- Adir Moyses Luiz(Author)
- 2011(Publication Date)
- IntechOpen(Publisher)
8 Foundations of Meissner Superconductor Magnet Mechanisms Engineering Jose Luis Perez-Diaz and Efren Diez-Jimenez Dpt. Ingeniería Mecánica – Universidad Carlos III de Madrid Spain 1. Introduction It has long been known that a repulsive force arises between a magnetic field (generated, for instance, by a permanent magnet - PM) and a superconductor –Sc (Arkadiev, 1947). This force is due to the repulsion of the magnetic field away from the superconductor – the Meissner Effect. Type I superconductors only can be in the Meissner state, which means that a magnetic field will be always expelled from the superconductor, independently of its poles orientation. Nevertheless, type II superconductors may be in two different states: first, provided the magnetic field is low enough, they are at a Meissner state similar to type I superconductors. In this Meissner state they absolutely expel the magnetic field and prevalent repulsive forces appear. Second, for magnetic fields larger than the so-called First Critical Field H C1 , the magnetic flux penetrates the superconductor creating a magnetization which contributes to an attractive resulting force. This second state is known as mixed state. In 1953 Simon first tried to make a superconducting bearing (Simon, 1953) using superconductors in the mixed state.The first engine using a superconducting bearing was made in 1958 (Buchhold, 1960). After the discovery of high critical temperature superconductors (Bednorz & Müller, 1986), the Meissner repulsive force has become a popular way of demonstrating superconducting properties (Early et al., 1988).For calculating forces between a magnet and a superconductor it is necessary to have models that describe both the flux penetration state and the Meissner state repulsion. The first one can be solved by using conventional methods to compute forces between magnetic elements and magnetized volumes. However, for the Meissner state the question has remained open until these last years.
eBook - PDF- Steven M. Girvin, Kun Yang(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
A discussion of the microscopic theory of superconductivity is deferred to Chapter 20 . 19.1 Thermodynamics In 1933 Meissner and Ochsenfeld discovered that weak magnetic fields are expelled by supercon-ductors. This perfect diamagnetism , now known as the Meissner Effect , is intimately related to the perfect conductivity, as can be seen from the Maxwell equation ∇ × E = − 1 c ∂ B ∂ t . (19.1) In a perfect conductor, the electric field must vanish (at least in the limit of zero frequency where the inertia of the carriers can be neglected) since otherwise infinite current would flow. But this means that the magnetic flux density cannot change with time. Thus, if a perfect conductor at B = 0 is subjected to an applied field, the flux is unable to penetrate into the sample. Conversely, if a perfect conductor already contains a finite flux density, it cannot be removed. 550 19 SUPERCONDUCTIVITY: PHENOMENOLOGY It is indeed observed that a superconductor initially at B = 0 does not allow the penetration of a weak applied field. However, superconductivity is much more than simply perfect conductivity. A sample in the normal state at high temperatures and having an applied field does something very strange when it is cooled below the critical temperature for the onset of superconductivity. The flux does not stay trapped inside the sample as would be expected for the case of perfect conductivity. Instead, the flux is actually expelled from the sample. Thus the system arrives at the same final state irrespective of whether the field is applied before or after the temperature is lowered. This tells us that a superconductor with the flux expelled is in an equilibrium thermodynamic phase. It costs free energy to expel the magnetic flux against the applied magnetic pressure. Nevertheless, the system is willing to pay this price because it can gain the energy of condensation into the superconducting state.
eBook - PDFMagnetic Materials
Fundamentals and Applications
- Nicola A. Spaldin(Author)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
The science of superconductivity is extremely rich, and the details are beyond the scope of this book. However, in the remainder of this chapter we will give a brief overview of some of the fundamentals. 4.5.1 The Meissner Effect If a metal such as lead, which is normally diamagnetic, is cooled in a magnetic field, then at some critical temperature, T c , it will spontaneously exclude all magnetic flux from its interior, as illustrated in Fig. 4.3. If B = μ 0 (H + M) = 0, then M = −H, and χ = M/H = −1 (in SI units). And the permeability μ = 1 + χ = 0, so the material is impermeable to the magnetic field. T c is also the temperature at which the material undergoes the transition to the superconducting state. The exclusion of flux is called the Meissner Effect [14], and is the reason that superconductors are perfect diamagnets. The circulating currents which (by Lenz’s law) oppose the applied magnetic field are able to exactly cancel the applied field because the resistivity is zero in the superconducting state. This is the reason that the exclusion of flux coincides with the onset of superconductivity. 44 Diamagnetism 4.5.2 Critical field Even below T c , the superconducting state can be destroyed if a high enough field is applied. The field which destroys the superconducting state at a particular tempera- ture is called the critical field, H c . At lower temperatures, the critical field is higher, and by definition it is zero at T c because the superconducting state is destroyed spontaneously. If the superconductor is carrying a current, then the field produced by the circulating charge also contributes to H c . Therefore there is a maximum allowable current before superconductivity is destroyed. The critical current depends on the radius of the conductor and is a crucial factor in determining the technological utility of a particular superconducting material. 4.5.3 Classification of superconductors Superconductors can be classified as type I or type II.
eBook - PDFCritical Currents and Superconductivity
Ferromagnetism Coexistence in High-Tc Oxides
- Samir Khene(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
In the international system, the magnetic field B (in teslas) which prevails in the material is given by the following relation: B = µ 0 (H + M) (1.2) where M is the magnetization of the sample in A/m, H the field of excitation in A/m and m 0 the magnetic permeability of the vacuum. The Meissner state corresponds in the case where B = 0 leading to M = – H : the diamagnetism is therefore perfect until the critical field B C above which the material becomes normal, so M = 0 (see Fig. 1.2). Superconducting State 7 T K ( ) B T ( ) Normal State B T c ( ) Meissner State B = 0 0 T c r = 0 r > 0 B c (0) Figure 1.1. Phases diagram of a type-I superconductor. Superconducting state –M(A/m) 0 B c B T ( ) Normal state Meissner state r = 0 = 0 B Figure 1.2. Magnetization as a function of the magnetic field of a type-I superconductor. The Meissner state is characterized by a perfect diamagnetism. 3.2. Type-II Superconductors A type-II superconductor has two critical fields, the lower critical field B C 1 and the upper critical field B C 2 . For magnetic fields lower than B C 1 , the type-II superconductor behaves like a type-I superconductor below B C : it totally expels the magnetic flux (see Fig. 1.3). –M(A/m) Superconducting state Normal state B = 0 Mixed state B C B T ( ) 0 r = 0 = 0 state B Meissner B C 1 B C 2 Figure 1.3. Magnetization as a function of the magnetic field of a type-II superconductor. In the mixed state, the Meissner Effect is partial. 8 Critical Currents and Superconductivity For fields higher than B C 2 , the sample becomes normal. For fields between B C 1 and B C 2 , the magnetic flux partially penetrates into the sample in the form of very thin microscopic tubes called “vortices” (see Fig. 1.4). The material is then in a superconducting state called “mixed state”; the vortices are arranged according to a triangular configuration of Abrikosov 11 (see Fig. 1.5). Each vortex contains only one quantum of flux F 0 = 2.067 × 10 –15 Wb.
eBook - PDF- Tao Xiang, Congjun Wu(Authors)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
A superconductor has two characteristic electromagnetic features, namely zero direct current resistance and perfect diamagnetism. Zero resistance means that superconductors are ideal conductors, and there is no energy loss during electric energy transport using superconducting transmission lines. Moreover, supercon- ductors are more than just ideal conductors. More fundamentally, superconductors 1 2 Introduction to Superconductivity exhibit perfect diamagnetism which expels magnetic flux lines from the interior of superconductor. The external magnetic field can only penetrate into supercon- ductors within a short length scale near the surface called the penetration length. The perfect diamagnetism of superconductivity was discovered by W. Meissner and R. Ochsenfeld in 1933. It is also called the Meissner Effect [11]. The Meissner Effect is not a consequence of zero resistance but an independent fundamental property resulting from the phase coherence of superconductivity. The Meissner Effect distinguishes a superconductor from an ideal normal conduc- tor in their responses to an applied magnetic field. If a magnetic field is applied to a normal metal, Faraday’s law, or Lentz’s law, says that a screening eddy current is induced to expel the magnetic flux. However, due to the existence of resistance, the induced eddy current dissipates and eventually decays to zero, allowing the magnetic field to penetrate into the interior of the conductor. On the other hand, if the magnetic field is applied to an ideal conductor or a superconductor at low temperatures, as there is no resistance in either case, a persistent eddy current exists which expels the magnetic field from within the bulk. Now if the temperature is raised so that both systems return back to their normal metallic states, the magnetic field penetrates to the bulks again. So far we have not seen any difference between a superconductor and an ideal conductor.
eBook - PDF- Joseph Callaway(Author)
- 2013(Publication Date)
- Academic Press(Publisher)
7.8 Superconductivity 689 This relation describes freely accelerating electrons. Note that at T = 0, (7.8.94) implies that (μολ 2 ) 1 = Ne 2 /m. (7.8.99) This is exactly the value to be expected from a simple kinetic derivation of (7.8.98). From a microscopic point of view, we may describe a persistent current as modifying the basic pairing of electrons in a superconductor. Thus instead of combining k Î and — k j , we pair k + q/2 | with — k + q/2 [ . The same value of q will be used for all pairs. A state of the entire system with some q ^ 0 is metastable. Individual particle scattering could tend to change the value of q for a single particle, but is ineffective in changing q for the entire system. Hence, q is in fact unchanged, and currents flow without resistance. 7.8.7 Flux Quantization One of the remarkable phenomena associated with the superconducting state is the quantization of magnetic flux through a superconducting ring. This effect was originally suggested by London (1950) and Onsager (1954). The first observations were made by Deaver and Fairbank (1961) and by Doll and Nabäuer (1961). The basic quantum unit of flux is φ 0 = h/2e. The effect is closely related to the Meissner Effect and gives clear evidence for the pairing of electrons in a superconductor. It should be emphasized that flux quantization is determined by the properties of superconductors and is not the result of some new physical principle concerning electromag-netic fields. We present first the simple argument of London (1950) and Onsager (1961). Consider a ring of superconducting material such that some flux passes through the center. At a distance greater than the penetration depth λ in the material of the ring, the Meissner Effect implies that the magnetic field B vanishes. However, the vector potential A will not vanish. This follows since the flux Φ through the ring is Φ = f BdS = f V X A-dS = Φ A-dl (7.8.100) in which the line integral runs along any path inside the superconductor which goes around the hole. On the other hand, the current density in the presence of a vector potential A is proportional to the average of p — gA, in which q is the charge of the particles which carry the current. The current will be confined to the surface of the ring and
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