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.

Exact analytical calculation and numerical modelling by finite-difference time-domain method of the transient transmission of electromagnetic waves through cold plasmas

The transient transmission of an electromagnetic wave through cold, unmagnetized and collisionless plasmas is described both analytically and numerically for its normal incidence from vacuum upon a plasma half-space. Exact formulas for the electromagnetic field are written in integral forms, which are convenient for approximate analysis and comparison with the results of direct numerical simulations. The time when the plasma particle oscillations become self-consistent with the electromagnetic field can be calculated from the simplified formulas for an arbitrary distance from the plasma–vacuum interface. Special attention is paid to the formation of the electrostatic oscillation in the case when the frequency of the incident wave is equal to the plasma frequency. The amplitudes of the vanishing magnetic field and the forming electrostatic oscillation are calculated as functions of time and the distance from the plasma–vacuum interface. The formation of the electrostatic oscillation is a slow process because the electromagnetic power penetrating into the plasma tends to zero with time. The transmitted plasma electromagnetic field is also simulated by the a finite-difference time-domain (FDTD) code. The difficulties of the numerical simulation of the quasi-electrostatic field are discussed. The analytical results can be used for the validation of the FDTD codes for plasma waves.