Investigation of the confinement of high energy non-neutral proton beam in a bent magnetic mirror

By using the Particle-In-Cell(PIC) simulation method, we study how the proton beam is confined in a bent magnetic mirror. It is found that the loss rate of the charged particles in a bent mirror is less than that in the axi-symmetric mirror. For a special bent mirror with the deflection angle of the coils $\alpha=45^{\circ}$, it is found that the loss rate reaches maximum value at certain ion number density where the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency. In addition, the loss rate is irrelevant to the direction of the proton beam. Our results may be helpful to devise a mirror. In order to obtain the least loss rate, we may choose a appropriate deflection angle, and have to avoid a certain ion number density at which the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency.