  It is known that a gas of electrons in a uniform neutralizing background can
crystallize and form a lattice if the electron density is less than a critical
value. This crystallization may have two- or three-dimensional structure. Since
the wake field potential in the highly-nonlinear-broken-wave regime (bubble
regime) has the form of a cavity where the background electrons are evacuated
from and only the positively charged ions remain, it is suited for
crystallization of trapped and accelerated electron bunches. However, in this
case, the crystal is moving relativistically and shows new three-dimensional
structures that we call relativistic Wigner crystals. We analyze these
structures using a relativistic Hamiltonian approach. We also check for
stability and phase transitions of the relativistic Wigner crystals.
