Microwave frequency downshift in the time-varying collision plasma has been demonstrated by particle-in-cell simulations.The simulation results are consistent with the theoretical analysis,and the preconditions for mi...Microwave frequency downshift in the time-varying collision plasma has been demonstrated by particle-in-cell simulations.The simulation results are consistent with the theoretical analysis,and the preconditions for microwave frequency downshift are that the collision frequency needs to be greater than the incident wave frequency,and the plasma frequency is two times greater than the incident wave frequency.Finally,the simulation results are compared with the reported experimental results indicating good agreement.展开更多
For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the ...For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.展开更多
文摘Microwave frequency downshift in the time-varying collision plasma has been demonstrated by particle-in-cell simulations.The simulation results are consistent with the theoretical analysis,and the preconditions for microwave frequency downshift are that the collision frequency needs to be greater than the incident wave frequency,and the plasma frequency is two times greater than the incident wave frequency.Finally,the simulation results are compared with the reported experimental results indicating good agreement.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. U1706230 and51379071)the Key Project of NSFC-Shandong Joint Research Funding POW3C (Grant No. U1906230)the National Science Fund for Distinguished Young Scholars (Grant No. 51425901)
文摘For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.