<p>This article presents a theoretical study of the excitation of the terahertz field by the relativistic non-linear interaction between the laser beam and ripple plasma under the influence of the transverse magnetic field (a magnetic field perpendicular to the direction of propagation of the laser beam). The novelty in this study is the use of a non-Gaussian mode, which is a hollow Gaussian laser beam (HGLB) with different orders (n = 0, 1, 2), which self-focusing within the plasma and then this interaction generates terahertz waves. A mathematical model was derived to describe the Self-focusing process of HGLB and the generation of terahertz waves by this non-linear interaction. The MATLAB program was used to perform a theoretical simulation of the Self-focusing process of HGLB, the terahertz field excitation, the power spectrum of the terahertz wave, and the effect of some parameters on them. A terahertz beam was generated with a frequency of 7.12 THz and a conversion efficiency 0.07.</p>