Cognitive radio (CR) and non-orthogonal multiple access (NOMA) have been deemed two promising technologies due to their potential to achieve high spectral efficiency and massive connectivity. This paper studies a multiple-input single-output NOMA CR network relying on simultaneous wireless information and power transfer (SWIPT) conceived for supporting a massive population of power limited battery-driven devices. In contrast to most of the existing works, which use an ideally linear energy harvesting model, this study applies a more practical non-linear energy harvesting model. In order to improve the security of the primary network, an artificial-noise-aided cooperative jamming scheme is proposed. The artificial-noise-aided beamforming design problems are investigated subject to the practical secrecy rate and energy harvesting constraints. Specifically, the transmission power minimization problems are formulated under both perfect channel state information (CSI) and the bounded CSI error model. The problems formulated are non-convex, hence they are challenging to solve. A pair of algorithms either using semidefinite relaxation (SDR) or a cost function are proposed for solving these problems. Our simulation results show that the proposed cooperative jamming scheme succeeds in establishing secure communications and NOMA is capable of outperforming the conventional orthogonal multiple access in terms of its power efficiency. Finally, we demonstrate that the cost function algorithm outperforms the SDR-based algorithm.