Diffuse synchrotron radio emission has been observed in a number of cool-core clusters on scales comparable to that of the cooling region. These radio sources are called `mini-halos'. In order to understand their origin, which is still unclear, joint radio and X-ray statistical studies of large cluster samples are necessary to investigate the radio mini-halo properties and their connection with the cluster thermodynamics. We here extend our previous explorative study and investigate the perspectives offered by surveys in the radio continuum with LOFAR and SKA, in particular examining the effect of the intra-cluster magnetic field in the mini-halo region for the first time. By considering the minimum flux detectable in radio surveys and exploiting the $P_{radio}-L_X$ correlation observed for known mini-halos, we estimate the detection limits achievable by future radio observational follow-up of X-ray cluster samples, such as HIFLUGCS and eROSITA. This allows us to estimate the maximum number of radio mini-halos that can potentially be discovered in future surveys as a function of redshift and magnetic field strength. We show that future radio surveys with LOFAR and SKA1 (at 140 MHz and 1.4 GHz) have the potential to discover ~1,000-10,000 radio mini-halo candidates up to redshift z=1. We further note that future SKA1 radio surveys at redshift z>0.6 will allow us to distinguish between different magnetic fields in the mini-halo region, because higher magnetic fields are expected to produce more powerful mini-halos, thus implying a larger number of mini-halo detected at high redshift. For example, the non-detection with SKA1 of mini-halos at z>0.6 will suggest a low magnetic field (B < few $μ$G). The synergy of these radio surveys with future X-ray observations and theoretical studies is essential in establishing the radio mini-halo physical nature. [abridged]
A "MeerKAT-meets-LOFAR" Study of 2A 0335+096: Discovery of a Complex 500 kpc Radio Halo in a Disturbed Cool-Core Cluster
Astronomisches Institut der Ruhr-Universität Bochum（波鸿鲁尔大学天文研究所）；Ruhr Astroparticle and Plasma Physics Center（鲁尔天体粒子与等离子体物理中心）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）；INAF – IASF Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano（意大利国家天体物理研究所-米兰空间天体物理学和宇宙物理学研究所）；Institute for Computational Cosmology, Department of Physics, Durham University（杜伦大学物理系计算宇宙学研究所）；INAF – Istituto di Radioastronomia（意大利国家天体物理研究所-射电天文学研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）；Thuringer Landessternwarte（图林根州立天文台）
The Large-Scale Structure of the Universe through the SKA lenses
University of Bologna（博洛尼亚大学）；Manipal Academy of Higher Education（马尼拉高等教育学院）；University of Hamburg（汉堡大学）；MIT Art, Design and Technology University（麻省理工学院艺术、设计与技术大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；University of Tartu（塔尔图大学）；National Astronomical Observatory of Japan（日本国立天文台）
Radio Halos in Galaxy Clusters as unveiled by the SKA telescope
Indian Institute of Technology Indore（印度理工学院印多尔分校）；Rhodes University（罗德岛大学）；Naval Research Laboratory（海军研究实验室）；National Centre for Radio Astrophysics, Tata Institute of Fundamental Research（国家射电天体物理中心，塔塔基础研究所）；University Catholic of Lyon- University of Lyon（里昂天主教大学-里昂大学）；National Tsing Hua University（国立清华大学）；Leiden University（莱顿大学）
The SKA View of Cool-core Clusters: Evolution of Radio Mini-halos and AGN Feedback
Naval Research Laboratory（海军研究实验室）；Université de Montréal（蒙特利尔大学）；SKAO, SKA-Low Science Operations Centre（平方公里阵列望远镜组织，SKA低频频段科学运营中心）；University Catholic of Lyon- University of Lyon（里昂天主教大学-里昂大学）
The topology of the magnetic field in Abell 2255 out to its virial radius. Results from the LOFAR Galaxy Cluster Ultra-Deep Field
INAF - IRA（意大利国家天体物理研究所-博洛涅分院）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）；Institute for Advanced Study（普林斯顿高等研究院）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；Center for Astrophysics Harvard & Smithsonian（哈佛&史密森尼天体物理中心）；Department of Astronomy, University of Wisconsin-Madison（威斯康星大学麦迪逊分校天文学系）；ASTRON, the Netherlands Institute for Radio Astronomy（荷兰射电天文研究所）；Hamburger Sternwarte, Universität Hamburg（汉堡大学汉堡天文台）；INAF - IASF Milano（意大利国家天体物理研究所-米兰天文物理研究所）
Investigating the radio emission in the Perseus cluster with LOFAR sub-80 MHz LBA
INAF – Istituto di Radioastromia（意大利国家天体物理研究所射电天文学研究所）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）；Université Laval（拉瓦尔大学）；Dunlap Institute for Astronomy and Astrophysics, University of Toronto（多伦多大学邓普天文学与天体物理学研究所）；Università di Bologna（博洛尼亚大学）
