  First order phase transitions in the early universe can give rise to a
stochastic background of gravitational waves. A hypothetical first order
electroweak phase transition is particularly interesting in this respect, since
the signal is in the good frequency range to be detectable by the space
interferometer LISA. Three main processes lead to the production of the
gravitational wave signal: the collision of the broken phase bubbles, the
magnetohydrodynamical turbulence in the plasma stirred by the bubble
collisions, and the magnetic fields amplified by the magnetohydrodynamical
turbulence. The main features of the gravitational wave spectrum, such as the
peak frequency, the amplitude, and the slopes both at low and high wave-number
can be predicted by general arguments based on the characteristics of the
source: in particular, the structure of its space and time correlation. We find
that the gravitational wave signal from a first order phase transition
occurring at electroweak symmetry breaking falls into the LISA sensitivity
range if the phase transition lasts for about one hundredth of the Hubble time
and the energy density of the turbulent motions is about twenty percent of the
total energy density in the universe at the phase transition time.
