  Josephson junctions fabricated on the surface of three-dimensional
topological insulators (TI) show a few unusual properties distinct from
conventional Josephson junctions. In these devices, the Josephson coupling and
the supercurrent are mediated by helical metal, the two-dimensional surface of
the TI. A line junction of this kind is known to support Andreev bound states
at zero energy for phase bias \pi, and consequently the so-called fractional ac
Josephson effect. Motivated by recent experiments on TI-based Josephson
junctions, here we describe a convenient algorithm to compute the bound state
spectrum and the current-phase relation for junctions with finite length and
width. We present analytical results for the bound state spectrum, and discuss
the dependence of the current-phase relation on the length and width of the
junction, the chemical potential of the helical metal, and temperature. A
thorough understanding of the current-phase relation may help in designing
topological superconducting qubits and manipulating Majorana fermions.
