In neutral beam injection (NBI), which is a primary auxiliary heating method for tokamak plasmas, the negative hydrogen ion source (NHIS) functions as a critical front-end component governing neutral beam quality. The performance of NHIS remains a key challenge. This work presents a three-dimensional (3D) fluid model, which is developed for a double-driver NHIS to simulate and optimize surface-generated negative hydrogen ion density. A comparison of plasma parameters between the NHIS with Cs and without Cs shows that surface generation yields negative ion density one order of magnitude higher than volume generation. However, the presence of the magnetic filter field induces asymmetry in negative ion density within the extraction region. To improve this asymmetry, two approaches are proposed: 1) increasing the power of one of the drivers and 2) adding a spacer plate to the expansion region. After increasing the power of Driver I from 50 to 56 kW, the H^– density asymmetry at the y = 25 cm intercept on the xy-plane (z = –22 cm) decreases from 0.04 to 0.01, and the value of H^– density increases. Following the addition of a spacer plate, the H^– density asymmetry further decreases to 0.004, but the value of H^– density also shows a significant reduction. Finally, adding a magnetic shield to the back plate of the expansion region further optimizes H^– density from 1.48×10¹⁷ m^–3 to 2.50×10¹⁷ m^–3, yielding a 69% increase downstream. This is because increased plasma transport into the expansion region enhances the dissociation rate of H₂ molecules, thereby yielding more H atoms. The attenuation of the magnetic filter field in the driver region after adding a magnetic shield also enhances the symmetry of the H^– density.