We study the properties of the Sydney University Molonglo Sky Survey (SUMSS) 843 MHz radio active galactic nuclei (AGNs) population in galaxy clusters from two large catalogues created using the Dark Energy Survey (DES): similar to 11 800 optically selected RM-Y3 and similar to 1000 X-ray selected MARD-Y3 clusters. We show that cluster radio loud AGNs are highly concentrated around cluster centres to z similar to 1. We measure the halo occupation number for cluster radio AGNs above a threshold luminosity, finding that the number of radio AGNs per cluster increases with cluster halo mass as N proportional to M-1(.2 +/- 0.1) (N proportional to M-0.(68 +/- 0.34)) for the RM-Y3 (MARD-Y3) sample. Together, these results indicate that radio mode feedback is favoured in more massive galaxy clusters. Using optical counterparts for these sources, we demonstrate weak redshift evolution in the host broad-band colours and the radio luminosity at fixed host galaxy stellar mass. We use the redshift evolution in radio luminosity to break the degeneracy between density and luminosity evolution scenarios in the redshift trend of the radio AGNs luminosity function (LF). The LF exhibits a redshift trend of the form (1 + z)(gamma) in density and luminosity, respectively, of gamma(D) = 3.0 +/- 0.4 and gamma(P) = 0.21 +/- 0.15 in the RM-Y3 sample, and gamma(D) = 2.6 +/- 0.7 and gamma(P) = 0.31 +/- 0.15 in MARD-Y3. We discuss the physical drivers of radio mode feedback in cluster AGNs, and we use the cluster radio galaxy LF to estimate the average radio-mode feedback energy as a function of cluster mass and redshift and compare it to the core (<0.1R(500)) X-ray radiative losses for clusters at z < 1.
