The chemical functionalization of two-dimensional materials is an effective method for tailoring their chemical and electronic properties with encouraging applications in energy, catalysis, and electronics. One exemplary 2D material with remarkable properties, graphene, can be exploited for hydrogen storage and large on/off ratio devices by hydrogen termination. In this work, we describe a promising plasma-based method to provide high hydrogen coverage on graphene. A low pressure (∼10 mtorr) discharge generates a fine-tunable low-temperature hydrogen-rich plasma in the applied radial electric and axial magnetic fields. Post-run characterization of these samples using Raman spectroscopy and X-ray photoelectron spectroscopy demonstrates a higher hydrogen coverage, 35.8%, than the previously reported results using plasmas. Plasma measurements indicate that with the applied magnetic field, the density of hydrogen atoms can be more than 10 times larger than the density without the magnetic field. With the applied electric field directed away from the graphene substrate, the flux of plasma ions towards this substrate and the ion energy are insufficient to cause measurable damage to the treated 2D material. The low damage allows a relatively long treatment time of the graphene samples that contributes to the high coverage obtained in these experiments. [Display omitted] [ABSTRACT FROM AUTHOR]