Long Josephson junction

(Redirected from Swihart velocity)

In superconductivity, a long Josephson junction (LJJ) is a Josephson junction which has one or more dimensions longer than the Josephson penetration depth . This definition is not strict.

In terms of underlying model a short Josephson junction is characterized by the Josephson phase , which is only a function of time, but not of coordinates i.e. the Josephson junction is assumed to be point-like in space. In contrast, in a long Josephson junction the Josephson phase can be a function of one or two spatial coordinates, i.e., or .

Simple model: the sine-Gordon equation

edit

The simplest and the most frequently used model which describes the dynamics of the Josephson phase   in LJJ is the so-called perturbed sine-Gordon equation. For the case of 1D LJJ it looks like:

 

where subscripts   and   denote partial derivatives with respect to   and  ,   is the Josephson penetration depth,   is the Josephson plasma frequency,   is the so-called characteristic frequency and   is the bias current density   normalized to the critical current density  . In the above equation, the r.h.s. is considered as perturbation.

Usually for theoretical studies one uses normalized sine-Gordon equation:

 

where spatial coordinate is normalized to the Josephson penetration depth   and time is normalized to the inverse plasma frequency  . The parameter   is the dimensionless damping parameter (  is McCumber-Stewart parameter), and, finally,   is a normalized bias current.

Important solutions

edit
  • Small amplitude plasma waves.  
  • Soliton (aka fluxon, Josephson vortex):[1]
 

Here  ,   and   are the normalized coordinate, normalized time and normalized velocity. The physical velocity   is normalized to the so-called Swihart velocity  , which represent a typical unit of velocity and equal to the unit of space   divided by unit of time  .[2]

References

edit
  1. ^ M. Tinkham, Introduction to superconductivity, 2nd ed., Dover New York (1996).
  2. ^ J. C. Swihart (1961). "Field Solution for a Thin-Film Superconducting Strip Transmission Line". J. Appl. Phys. 32 (3): 461–469. Bibcode:1961JAP....32..461S. doi:10.1063/1.1736025.