The paper presents a 3D numerical model of the neutron source for the transmutation of long-lived radioactive waste in spent nuclear fuel. The projected plasma type neutron source is based on the Gas Dynamic Trap (GDT) which is a special magnetic mirror system for the plasma confinement. A new improved version of the GDT type fusion neutron source is numerically simulated by use different numerical methods. New physical phenomena such as a vortex confinement, improved axial confinement, low radial transport, high etc. were included in these simulations. The experimental and theoretical foundations of these phenomena were obtained in the GDT-U experimental facility in the Budker Institute. In result the proposed neutron source has two n-zones of 2 m length with a neutron power of 1.6 MW/m and a neutron production rate up to 1.5x1018 n/s each. This source can be used for application to a fusion driven system for the burning of MA in spent nuclear fuel.