  We study gravitational waves generated by the cosmological magnetic fields
induced via bubble collisions during the electroweak (EW) and QCD phase
transitions. The magnetic field generation mechanisms considered here are based
on the use of the fundamental EW minimal supersymmetric (MSSM) and QCD
Lagrangians. The gravitational waves spectrum is computed using a
magnetohydrodynamic (MHD) turbulence model. We find that gravitational wave
spectrum amplitude generated by the EW phase transition peaks at frequency
approximately 1-2 mHz, and is of the order of $10^{-20}-10^{-21}$; thus this
signal is possibly detectable by Laser Interferometer Space Antenna (LISA). The
gravitational waves generated during the QCD phase transition, however, are
outside the LISA sensitivity bands.
