Characteristics Of The Dispersion Relation And Gyroresonance Of Right-handed Low Frequency Electromagnetic Waves In Earth’s Magnetosphere

Fast magnetic wave,a kind of right-handed low-frequency electromagnetic wave,is widely found in the space plasma.Its frequency is higher than the proton cyclotron frequency,lower than the low mixing frequency.It spreads in the area of L=9-2 nearing the magnetic equatorial plane within 10°,which is different from the fast magnetic wave in the magnetic fluid mechanics.Far away from the magnetic equatorial plane area,the probability of appearance of fast magnetic waves are very low and the same is true of its intensity.In recent years,observations and numerical simulations show that fast magnetic waves can effectively affect the dynamic process of high-energy charged particles in the radiation zone.Under different magnetic layer conditions,fast magnetic waves are likely to accelerate the high energy electrons from about 100,000 electron volt to several million electron volt,which may lead to the loss of throwing angle of the high-energy electrons in the radiation zone and can cause the scartting of the throwing angle of several thousand electron volt energy protons,making themrapidly settle into the atmosphere and form proton aurora.Therefore,the instability,propagation characteristics and global distribution of fast magnetic waves have attracted more and more researchers’ interest.In this paper,the influence of the Stix notations D,S,its positive and negative orientation on the refractive index are mainly analyzed for three different plasma space environments and two special plasma composition ratios.And then,the dispersion curve and the minimum resonance energy curve of fast magnetic waves are calculatedin two different cases(complete dispersion relationship and high density approximate dispersion relation).We found a characteristic of the fast magnetic waves’s dispersion relationship:when the plasma background parameters ρ ≥ 1,the refractive index in both cases is almost the same.At the same time,ρ≤0.1,the refractive index increases with almost no change in the propagation angle of the wave in the case of high density approximation.In the complete dispersion relation,the refractive index increases not only with the enhancement of the magnetic activity,but also with increase of the propagation angle increase.This shows that the fast-wave propagation of the oblique propagation cannot adapt to the high geomagnetic activity in the case of high-density approximation,which is found to be different from that of single-ion plasma.The description of the plasma space environment is an important factor in determining the dispersion characteristics of fast magnetic waves.Then we calculated and analyzed the characteristics of the minimum resonance energy curves of the three ions.The results show that the minimum resonant energy curves of these three ions are basically the same in the same environment,but different in the minimum resonant energy.However,for the analysis of the change trend,the minimum resonance energy curve of all bands increases with the increase of the frequency for the resonance order,indicating that there is the minimum resonance energy of fast magnetic waves in a wide range of wave frequencies,But with the increase in the spread of the angle,there will be a gradual decline in the trend,especially at that time,the minimum resonance energy values from the quantitative level can be quickly reduced to a few,and the minimum resonant energy cannot be seen in this wave range in the case of high density approximation,which also demonstrates that high density approximation cannot accommodate this strong geomagnetic activity.