Search for a TeV gamma-ray halo of Mkn 501

For distant extragalactic sources of gamma-rays in the PeV (10(15) eV) ener gy range, interactions of the gamma rays with intergalactic diffuse radiati on fields will initiate a pair cascade. Depending on the magnetic fields in the vicinity of the source, the cascade can either result in an isotropic halo around an initially beamed source or remain more or less collimated. D ata recorded by the HEGRA system of imaging atmospheric Cherenkov telescope s are used to derive limits on the halo flux from the AGN Mrk 501. This is achieved by comparing the angular distribution of TeV gamma-rays during the 1997 burst phase - where direct photons should dominate with the distribut ion during the 1998/99 quiescent state, where a steady-state halo contribut ion should be most pronounced. The results depend on the assumptions concer ning the angular distribution of the halo; limits on the halo flux within 0 .5 degrees to 1 degrees from the source range between 0.1% and 1% of the pe ak burst flux.