Critica ensity(1 FIGURE 53.1 The phase space for the superconducting alloy niobium-titanium. The material is superconducting inside the volume of phase space indicated. 53.2 General Electromagnetic Properties The hallmark electromagnetic properties of a superconductor are its ability to carry a static current without any resistance and its ability to exclude a static magnetic flux from its interior. It is this second property, known the Meissner effect, that distinguishes a superconductor from merely being a perfect conductor (which conserves the magnetic flux in its interior). Although superconductivity is a manifestly quantum mechanical phenomenon, a useful classical model can be constructed around these two properties. In this section, we will outline the rationale for this classical model, which is useful in engineering applications such as waveguides The zero dc resistance criterion implies that the superelectrons move unimpeded. The electromagnetic energy density, w, stored in a superconductor is therefore μlH 2 where the first two terms are the familiar electric and magnetic energy densities, respectively. (Our electromag netic notation is standard: E is the permittivity, u, is the permeability, E is the electric field, and the magnetic lux density, B, is related to the magnetic field, H, via the constitutive law B=H, H )The last term represents the kinetic energy associated with the undamped superelectrons' motion(n* and v, are the superelectrons density and velocity, respectively). Because the supercurrent density, J,, is related to the superelectron velocity y J, = nav,, the kinetic energy term can be rewritten J where a is defined as (534) e 2000 by CRC Press LLC© 2000 by CRC Press LLC 53.2 General Electromagnetic Properties The hallmark electromagnetic properties of a superconductor are its ability to carry a static current without any resistance and its ability to exclude a static magnetic flux from its interior. It is this second property, known as the Meissner effect, that distinguishes a superconductor from merely being a perfect conductor (which conserves the magnetic flux in its interior). Although superconductivity is a manifestly quantum mechanical phenomenon, a useful classical model can be constructed around these two properties. In this section, we will outline the rationale for this classical model, which is useful in engineering applications such as waveguides and high-field magnets. The zero dc resistance criterion implies that the superelectrons move unimpeded. The electromagnetic energy density, w, stored in a superconductor is therefore (53.2) where the first two terms are the familiar electric and magnetic energy densities, respectively. (Our electromag￾netic notation is standard: e is the permittivity, mo is the permeability, E is the electric field, and the magnetic flux density, B, is related to the magnetic field, H, via the constitutive law B = moH.) The last term represents the kinetic energy associated with the undamped superelectrons’ motion (n* and vs are the superelectrons’ density and velocity, respectively). Because the supercurrent density, Js , is related to the superelectron velocity by Js = n*q*vs , the kinetic energy term can be rewritten (53.3) where L is defined as (53.4) FIGURE 53.1 The phase space for the superconducting alloy niobium–titanium. The material is superconducting inside the volume of phase space indicated. w n m v o s = + m + 1 2 1 2 2 2 2 eE H2 * * n m s s * * 1 2 1 2 2 2 v Ê Ë Á ˆ ¯ ˜ = LJ L = ( ) m n q * * * 2