Terahertz (THz) gyrotron with broadband tuning capability is attractive for advanced applications, such as dynamic nuclear polarization enhanced nuclear magnetic resonance (DNP-NMR). However, it is challenging to realize broadband continuous frequency tuning (CFT) in a conventional open cavity, in which the quality ( $Q$ ) factor scaling law results in abrupt axial-mode $Q$ -factor differences and narrow tuning range because of power switch off during higher order axial mode transition. In this paper, a novel cavity scheme based on formation of a local field is proposed to break the $Q$ -factor scaling law and expand the CFT band. The field shaping with a local standing-wave formation is constructive in enhancing the $Q$ factor of high-order axial modes in a low- $Q$ open cavity, which obviously extends the CFT band and simultaneously reduces ohmic loss. Besides, a nonlinear up-tapered section of a parabolic-tapered waveguide is applied to reduce the power fluctuation in the axial mode transition process. In the preliminary design, a CFT band wider than 2 GHz with a minimum output power of 1 W is theoretically demonstrated in the TE8,2 mode 0.33-THz second-harmonic DNP-gyrotron with an ultralow voltage of 2.1 kV via magnetic field tuning.