Editing Josephson effect (section)

==Josephson penetration depth==
The Josephson penetration depth characterizes the typical length on which an externally applied [[magnetic field]] penetrates into the [[long Josephson junction]]. It is usually denoted as <math>\lambda_J</math> and is given by the following expression (in SI):

:<math>\lambda_J=\sqrt{\frac{\Phi_0}{2\pi\mu_0 d' j_c}},</math>

where <math>\Phi_0</math> is the magnetic flux quantum, <math>j_c</math> is the [[critical supercurrent density]] (A/m<sup>2</sup>), and <math>d'</math> characterizes the inductance of the superconducting electrodes<ref>{{cite journal |last1=Weihnacht |first1=M. |year=1969 |title=Influence of Film Thickness on D. C. Josephson Current |journal=Physica Status Solidi B |volume=32 |issue=2 |page=169 |bibcode=1969PSSBR..32..169W |doi=10.1002/pssb.19690320259}}</ref>

:<math>
  d'=d_I 
  +\lambda_1 \tanh\left(\frac{d_1}{2\lambda_1}\right)
  +\lambda_2 \tanh\left(\frac{d_2}{2\lambda_2}\right),
</math>

where <math>d_I</math> is the thickness of the Josephson barrier (usually insulator), <math>d_1</math> and <math>d_2</math> are the thicknesses of superconducting electrodes, and <math>\lambda_1</math> and <math>\lambda_2</math> are their [[London penetration depth]]s. The Josephson penetration depth usually ranges from a few [[Micrometre|μm]] to several mm if the critical current density is very low.<ref>{{cite book |last1=Buckel |first1=Werner |last2=Kleiner |first2=Reinhold |title=Supraleitung |date=2004 |publisher=Wiley-VCH Verlag GmbH&Co.KGaA |location=Tübingen |isbn=3527403485 |page=67 |edition=6.}}</ref>