Although the jet phenomenon has been discovered for more than 100 years, extensive studies on jets began merely more than 50 years ago getting benefit from an unprecedented development of radio telescope. It is generally believed that the magnetic field plays an important role in the jet process. The radial dynamic equilibrium of a magnetically dominated jet is controlled by the so-called "pulsar" equation (force-free condition applies). This equation, established in 1960s, is not easy to be solved even by numerical method since it is highly nonlinear and has a singularity.

Undoubtedly, the rapid development of numerical simulation has significantly improved our understanding of the jet physics. However, the “complexity” of numerical simulation makes it harder to quantitatively duplicate accumulated observations.

Inspired by the numerical simulation, the researchers separate the “pulsar” equation into rotating and non-rotating terms, and find that each of the two-term equations can be solved analytically, and the two solutions match each other very well.

Based on this general approximate solution, an analytical jet model is built, which quantitatively measures all properties of a magnetically dominated jet. Therefore, the process of jet launching, acceleration and collimation can be described. For example, the model analytically measures the jet acceleration from non-relativistic to relativistic.

Qualitatively, the magnetic field behaves like a rigid wire, and the plasma fluid can hardly move across the magnetic field lines (frozen) and it behaves like beads slide freely along the direction of magnetic field lines.

At the beginning of jet formation, the celestial object drags the magnetic field lines rotating, which can “throw out” the frozen plasma by centrifugal force. At this stage, the magnetic field is poloidal dominated, and jet fluid motion is toroidal dominated.

As the jet propagates outward, the magnetic field gets weak, and the magnetic pressure gradient force will accelerate the jet fluid. As the magnetic field energy is gradually transformed into the jet kinetic energy, the magnetic field lines will be twisted. After crossing a characteristic surface known as “Alfven surface”, the twisted magnetic field becomes toroidal dominated, and the jet fluid motion becomes poloidal dominated.

This analytical solution is consistent with known theoretical results and numerical simulations, and can be applied to interpret main observations of jet in active galactic nuclei, gamma-ray bursts and pulsars, such as jet configuration, acceleration, polarization, stratification, periodical variability, etc. The model also predicts more abundant phenomena, waiting for future observational tests. This solution helps to understand and validate simulations as well.