Abstract The Parker Solar Probe (PSP) provides us with an unprecedentedly close approach to the observation of the Sun and hence the possibility of directly understanding the elementary process that occurs on the kinetic scale of particles' collective interaction in solar coronal plasmas. We report a type of weak solar radio burst (SRB) that was detected by PSP when it passed a low-density magnetic channel during its second encounter phase. These weak SRBs have a low starting frequency of ∼20 MHz and a narrow frequency range from a few tens of MHz to a few hundred kHz. Their dynamic spectra display a strongly evolving feature of the intermediate relative drift rate decreasing rapidly from above 0.01 s⁻¹ to below 0.01 s⁻¹. Analyses based on common empirical models of solar coronal plasmas indicate that these weak SRBs originate from a heliocentric distance of ∼1.1–6.1 R _S (the solar radius), a typical solar wind acceleration region with a low-β plasma, and that their sources have a typical motion velocity of ∼v _A (Alfvén velocity) obviously lower than that of the fast electrons required to effectively excite SRBs. We propose that solitary kinetic Alfvén waves with kinetic scales could be responsible for the generation of these small-scale weak SRBs, called solitary wave radiation.