## 1 Introduction  
The rapid development of attosecond physics, including the subject of high-order harmonic generation [1; 2; 3; 4; 5], ionization [6; 7; 8; 9; 10], target excitation [11; 12; 13], etc., has allowed us to probe ultrafast dynamics in atoms and molecules with unprecedented temporal and spatial resolutions. Recently, high-order harmonic (HH) generation driven by circularly polarized laser fields has been a hot topic due to its potential application in the generation of circularly polarized attosecond pulses [14; 15; 16; 17], which is a new tool for controlling and imaging ultrafast dynamics, such as charge transfer and migration and the generation of attosecond quantum electron currents for ultrafast magneto-optics.  
A well-established mechanism for HH generation is semiclassical recollision [18; 19], where the HH generation process consists of three steps: firstly an atom or molecule emits its electron to a continuous state; secondly the electron is accelerated in the laser field; and thirdly the accelerated electron recombines with the parent ion and a high energy photon is radiated, which is called HHs. Both experimental and theoretical investigations show that the harmonic efficiency is very sensitive to the polarization of the driving pulse [20; 21; 22; 23; 24; 25; 26]. In other words, the harmonic emission driven by a circularly polarized laser field is significantly suppressed compared with that driven by a linearly polarized laser field. The underlying mechanism is only those electrons which can return to the parent ion core are responsible for HH generation. However, in a circularly polarized field, the ionized electrons are transversely accelerated by the driving field, consequently missing the core [27; 28; 29; 30]. In previous investigations, it has been shown that an initial transverse velocity can compensate the transverse drift induced by the circularly polarized laser field. Hence the electron trajectories with an initial transvers velocity can lead to the electron return and HH generation [27; 28; 29; 30]. Whereas, the discussion on the factors leading to the electron return and HH generation driven by circularly polarized laser pulse is incomplete.  
In this paper, we study the influence of the waveform of driving field on high-order harmonic (HH) generation from atoms driven by circularly polarized laser pulses. It is found that the electron trajectories without an initial transverse velocity can also revisit the parent ion. Both the time-dependent Schrodinger equation (TDSE) simulation and the classical trajectory analysis show that the positive temporal gradient of the electric field amplitude is a key factor that makes the electron return to the parent ion possible. Moreover, the larger temporal gradient of the field amplitude is, the more electron trajectories can revisit the parent ion. Correspondingly, the harmonic yield is enhanced. This is confirmed by the pulse-duration dependence of the harmonic yield driven by a circularly polarized laser field. The classical trajectory analysis also shows that the maximum kinetic energy of the return electron, which agrees well with the harmonic cutoff position, is generally gained after multiple revisits. Our results provide a new way of controlling the HH emission in a circularly polarized laser field.