  Magnetic monopoles, if they exist, would be produced amply in strong magnetic
fields and high temperatures via the thermal Schwinger process. Such
circumstances arise in heavy ion collisions and in neutron stars, both of which
imply lower bounds on the mass of possible magnetic monopoles. In showing this,
we construct the cross section for pair production of magnetic monopoles in
heavy ion collisions, which indicates that they are particularly promising for
experimental searches such as MoEDAL.
