Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias cur rent and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results are in terms of elliptic functi ons for the case of inline geometry, and are in agreement with the numerica l calculations, explaining also the strong hysteretic phenomena typically s een in the calculation of the maximum tunnelling current. This suggests a d ifferent experimental approach based on the use, instead of the external ma gnetic field, of the modulus of the elliptic function or the related quanti ty the total magnetic flux to avoid hysteretic behaviour and unfold the ove rlapping I-max (H) curves.