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Circular synthetic aperture radar (CSAR) has the potential to form 3D images with single-pass single-channel radar data, which is very time-efficient. This article proposes a volumetric neural renderer that utilizes CSAR 2D amplitude images to reconstruct the 3D power distribution of the imaged scene. The innovations are two-fold: Firstly, we propose a new SAR amplitude image formation model that establishes a linear mapping relationship between multi-look amplitude-squared SAR images and a real-valued 4D (spatial location (<i>x</i>, <i>y</i>, <i>z</i>) and azimuth angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>) radar scattered field. Secondly, incorporating the proposed image formation model and SAR imaging geometry, we extend the neural radiance field (NeRF) methods to reconstruct the 4D radar scattered field using a set of 2D multi-aspect SAR images. Using real-world drone SAR data, we demonstrate our method for (1) creating realistic SAR imagery from arbitrary new viewpoints and (2) reconstructing high-precision 3D structures of the imaged scene.