The work of [3] assessed the performance comparison between beam hopping systems and the non-hopped systems in Ka-band, which demonstrated that beam hopping can improve the utilization rate of system resources. The work of [10] intended to dynamically schedule the time slot number of each beam to realize the long-term delay fairness in a beam hopping system. The work [11; 12; 13; 14; 15] proposed a framework based on deep reinforcement learning (DRL) for dynamic resource allocation in beam hopping satellite systems with complicated calculation methods. Moreover, European Telecommunications Standards Institute (ETSI) published DVB-S2X standards [16] to support beam hopping. The work of [17; 18] introduced the super-frame structure in Appendix E of DVB-S2X, and also discussed the feasibility of engineering realization. The work of [19] investigated potential synergies of non-orthogonal multiple access (NOMA) and beam hopping for multi-beam satellite systems. Moreover, the work of [20; 21; 22] employed precoding to suppress co-channel interference in a beam hopping system. However, most of these previous works assumed constant channel quality during beam hopping transmission, which is too idealistic in a real satellite communication system. An HTS usually employs Ka or Q/V frequency band to obtain more spectrum resource and achieve broadband transmission. Therefore, channel attenuation especially time-varying rain attenuation in such high frequency band becomes a major factor that dynamically affects channel quality, which should not be ignored [23; 24]. To overcome these limitations, this paper studies dynamic beam hopping time slots allocation method under the effect of time-varying rain attenuation. Firstly, a beam hopping system model as well as rain attenuation time series based on Dirac lognormal distribution are provided. On this basis, the genetic algorithm (GA) [25] for beam hopping is proposed by considering uneven traffic demand and changeable spectrum efficiency. Simulation results show that, compared with conventional methods, the proposed algorithm can dynamically adjust time slots allocation to meet the non-uniform traffic requirements of each beam under the effect of time-varying rain attenuation and effectively improve system performance. Moreover, the reasons for adopting GA for beam hopping under rain environment are as follows. It is noticed that some of the current research interest is focused on applying reinforced learning algorithms for pursuing superior performance. However, except for the high complexity and long processing delay, the reinforced learning algorithm needs a mass of sample data to learn for a certain environment. It may not be suitable for the issue discussed in this paper, since the rain environment is changeable during BH transmission and different beams may be under different rainfall intensities. This problem is avoided by adopting GA. Comparing with the complicated reward function of DRL, the fitness function of GA is easily obtained and suitable for different rainfall environments. Therefore, GA is employed for beam hopping under the rain environment to achieve both better performance and lower algorithm complexity. The main contributions and innovations of this paper are as follows:  
(1) Without the assumption of constant rain attenuation, different beams may suffer different rain attenuations which are also time-varying. Consequently, this situation will bring different and time-varying spectrum efficiency for each beam during the transmission. It makes the design of beam hopping transmission plan become a complicated two-dimensional time-space optimization problem. In this context, this paper introduces genetic algorithm to solve the joint optimization problem. Moreover, in order to validate the proposed algorithm performance, rain attenuation time series based on Dirac log-normal distribution are provided to simulate the rainfall environment.