We used one-dimensional coupled sine-Gordon equations combined with heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a 300 $\mu \mathrm{m}$ long intrinsic Josephson junction stack consisting of $N=700$ junctions. The junctions in the stack are combined with $M$ segments where we assume that inside a segment all junctions behave identically. Most simulations are for $M=20$. For not too high bath temperatures there is the appearance of a hot spot at high-bias currents. In terms of electromagnetic properties, robust standing-wave patterns appear in the current density and electric field distributions. These patterns come together with vortex/antivortex lines across the stack that correspond to $\pi$-kink states, discussed before in the literature for a homogeneous temperature distribution in the stack. We also discuss scaling of the thermal and electromagnetic properties with $M$, on the basis of simulations with $M$ between 10 and 350.

• Received 27 November 2014
• Revised 5 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.104513