Ion pickup by a monochromatic low-frequency Alfv6n wave, which propagates along the background magnetic field, has recently been investigated in a low beta plasma （Lu and Li 2007 Phys. Plasmas 14 042303）. In this paper, the monochromatic Alfven wave is generalized to a spectrum of Alfven waves with random phase. It finds that the process of ion pickup can be divided into two stages. First, ions are picked up in the transverse direction, and then phase difference （randomization） between ions due to their different parallel thermal motions leads to heating of the ions. The heating is dominant in the direction perpendicular to the background magnetic field. The temperatures of the ions at the asymptotic stage do not depend on individual waves in the spectrum, but are determined by the total amplitude of the waves. The effect of the initial ion bulk flow in the parallel direction on the heating is also considered in this paper.
With one-dimensional （l-D） hybrid simulations we investigate the nonlinear evolu- tion of the ion cyclotron waves excited by the H＋ and He2＋ temperature anisotropies, and analyze the evolution by using the wavelet analysis method. The results show that the proton cyclotron waves with the dominant frequency higher than the helium gyro-frequency （ΩHe = 0.5Ωp, with Ωp and ΩHe the proton and helium gyro-frequencies respectively ） are firstly excited, and then the helium cyclotron waves with the dominant frequency lower than the helium gyro-frequency are excited. The relation of our simulation results to the BIF（bifurcated） （there are two peaks in the wave spectrum： one above and one below ΩHe） and CON（continuous） （continuous spectrum from 0.1 Ωp to 1.0 Ωp） wave spectra observed in the magnetosheath are discussed.
