  We used 2D coupled sine-Gordon equations combined with 3D heat diffusion
equations to numerically investigate the thermal and electromagnetic properties
of a $250 \times 70\,\mu\mathrm{m}^2$ intrinsic Josephson junction stack. The
700 junctions are grouped to 20 segments; we assume that in a segment all
junctions behave identically. At large input power a hot spot forms in the
stack. Resonant electromagnetic modes, oscillating either along the length ((0,
$n$) modes) or the width (($m$, 0) modes) of the stack or having a more complex
structure, can be excited both with and without a hot spot. At fixed bath
temperature and bias current several cavity modes can coexist in the absence of
a magnetic field. The (1, 0) mode, considered to be the most favorable mode for
THz emission, can be stabilized by applying a small magnetic field along the
length of the stack. A strong field-induced enhancement of the emission power
is also found in experiment, for an applied field around 5.9 mT.
