Abstract: Generalizable Neural Radiance Fields (GNeRF) are recognized as one of the most promising techniques for novel view synthesis and 3D model generation in real-world applications. However, like other generative models in computer vision, ensuring their adversarial robustness against various threat models is essential for practical use. The pioneering work in this area, NeRFool, introduced a state-of-the-art attack that targets GNeRFs by manipulating source views before feature extraction, successfully disrupting the color and density results of the constructed views. Building on this foundation, we propose IL2-NeRF(Iterative $L_2$ NeRF Attack), a novel adversarial attack method that explores a new threat model(in the $L_2$ domain) for attacking GNeRFs. We evaluated IL2-NeRF against two standard GNeRF models across three benchmark datasets, demonstrating similar performance compared to NeRFool, based on the same evaluation metrics proposed by NeRFool. Our results establish IL2-NeRF as the first adversarial method for GNeRFs under the $L_2$ norm. We establish a foundational $L_2$ threat model for future research, enabling direct performance comparisons while introducing a smoother, image-wide perturbation approach in Adversarial 3D Reconstruction.