Lixian Yang, Si Liu, Zhonglei Gao, Hongming Yang, Xiongjun Shang, Yang Gao, Fuliang Xiao
{"title":"Statistical Analysis of Nonlinear Interactions Between Chorus and Electron Cyclotron Harmonic Waves","authors":"Lixian Yang, Si Liu, Zhonglei Gao, Hongming Yang, Xiongjun Shang, Yang Gao, Fuliang Xiao","doi":"10.1029/2025JA034027","DOIUrl":null,"url":null,"abstract":"<p>Nonlinear wave-wave interactions are crucial for extending wave frequency ranges and redistributing energy, thereby influencing the magnetospheric dynamics. The interactions between chorus and electron cyclotron harmonic (ECH) waves can generate the ECH sidebands. Statistical analysis of Van Allen Probes data shows that these interactions primarily occur in the region of <span></span><math>\n <semantics>\n <mrow>\n <mi>L</mi>\n </mrow>\n <annotation> $L$</annotation>\n </semantics></math> = 5.0<span></span><math>\n <semantics>\n <mrow>\n <mi>–</mi>\n </mrow>\n <annotation> $\\mbox{--}$</annotation>\n </semantics></math>6.0 and MLT = 23<span></span><math>\n <semantics>\n <mrow>\n <mi>–</mi>\n </mrow>\n <annotation> $\\mbox{--}$</annotation>\n </semantics></math>09 near the equator <span></span><math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mrow>\n <mo>|</mo>\n <mi>M</mi>\n <mi>L</mi>\n <mi>A</mi>\n <mi>T</mi>\n <mo>|</mo>\n <mo><</mo>\n <mn>5</mn>\n <mo>°</mo>\n </mrow>\n <mo>)</mo>\n </mrow>\n <annotation> $(\\vert \\mathrm{M}\\mathrm{L}\\mathrm{A}\\mathrm{T}\\vert < 5{}^{\\circ})$</annotation>\n </semantics></math>. As the AE index increases, the ECH sidebands occur over a wider region and their intensity grows. Moreover, the root-mean-square (RMS) amplitude of the ECH sideband <span></span><math>\n <semantics>\n <mrow>\n <mfenced>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>S</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n </mfenced>\n </mrow>\n <annotation> $\\left({E}_{\\mathrm{S}\\mbox{-}\\text{RMS}}\\right)$</annotation>\n </semantics></math> is roughly in proportion to the square root of the product of that of the chorus <span></span><math>\n <semantics>\n <mrow>\n <mfenced>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>C</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n </mfenced>\n </mrow>\n <annotation> $\\left({E}_{\\mathrm{C}\\mbox{-}\\text{RMS}}\\right)$</annotation>\n </semantics></math> and ECH <span></span><math>\n <semantics>\n <mrow>\n <mfenced>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>E</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n </mfenced>\n </mrow>\n <annotation> $\\left({E}_{\\mathrm{E}\\mbox{-}\\text{RMS}}\\right)$</annotation>\n </semantics></math> waves. For over <span></span><math>\n <semantics>\n <mrow>\n <mn>95</mn>\n <mi>%</mi>\n </mrow>\n <annotation> $95\\%$</annotation>\n </semantics></math> of samples, the ratio <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>S</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n <mo>/</mo>\n <msqrt>\n <mrow>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>C</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n <mo>∗</mo>\n <msub>\n <mi>E</mi>\n <mrow>\n <mi>E</mi>\n <mo>-</mo>\n <mtext>RMS</mtext>\n </mrow>\n </msub>\n </mrow>\n </msqrt>\n </mrow>\n <annotation> ${E}_{\\mathrm{S}\\mbox{-}\\text{RMS}}/\\sqrt{{E}_{\\mathrm{C}\\mbox{-}\\text{RMS}}\\ast {E}_{\\mathrm{E}\\mbox{-}\\text{RMS}}}$</annotation>\n </semantics></math> ranges from <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <msup>\n <mn>0</mn>\n <mrow>\n <mo>−</mo>\n <mn>1.6</mn>\n </mrow>\n </msup>\n </mrow>\n <annotation> $1{0}^{-1.6}$</annotation>\n </semantics></math> to <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <msup>\n <mn>0</mn>\n <mrow>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n </msup>\n </mrow>\n <annotation> $1{0}^{-1}$</annotation>\n </semantics></math>. Using the typical parameters, we find that the ECH sidebands can effectively extend the energy range of resonant electrons down to <span></span><math>\n <semantics>\n <mrow>\n <mo>∼</mo>\n </mrow>\n <annotation> ${\\sim} $</annotation>\n </semantics></math>10 eV. This study reveals the global distribution of chorus-ECH interactions and the energy conversion efficiency in this nonlinear process.</p>","PeriodicalId":15894,"journal":{"name":"Journal of Geophysical Research: Space Physics","volume":"130 6","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geophysical Research: Space Physics","FirstCategoryId":"89","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1029/2025JA034027","RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
Nonlinear wave-wave interactions are crucial for extending wave frequency ranges and redistributing energy, thereby influencing the magnetospheric dynamics. The interactions between chorus and electron cyclotron harmonic (ECH) waves can generate the ECH sidebands. Statistical analysis of Van Allen Probes data shows that these interactions primarily occur in the region of = 5.06.0 and MLT = 2309 near the equator . As the AE index increases, the ECH sidebands occur over a wider region and their intensity grows. Moreover, the root-mean-square (RMS) amplitude of the ECH sideband is roughly in proportion to the square root of the product of that of the chorus and ECH waves. For over of samples, the ratio ranges from to . Using the typical parameters, we find that the ECH sidebands can effectively extend the energy range of resonant electrons down to 10 eV. This study reveals the global distribution of chorus-ECH interactions and the energy conversion efficiency in this nonlinear process.
非线性波波相互作用对于波频率范围的扩展和能量的重新分配至关重要,从而影响磁层动力学。电子回旋谐波(ECH)与副歌波之间的相互作用可以产生电子回旋谐波的边带。对Van Allen探测器数据的统计分析表明,这些相互作用主要发生在赤道附近的L $L$ = 5.0 - $\mbox{--}$ 6.0和MLT = 23 - $\mbox{--}$ 09区域(| M L A T | &lt;5°)$(\vert \mathrm{M}\mathrm{L}\mathrm{A}\mathrm{T}\vert < 5{}^{\circ})$。随着声发射指数的增加,高强边带出现的范围越来越广,强度也越来越大。而且,ECH边带的均方根(RMS)振幅es - RMS $\left({E}_{\mathrm{S}\mbox{-}\text{RMS}}\right)$大致与合唱振幅乘积的平方根成比例E E E - RMS $\left({E}_{\mathrm{C}\mbox{-}\text{RMS}}\right)$和ECH E E - RMS$\left({E}_{\mathrm{E}\mbox{-}\text{RMS}}\right)$波浪。95岁以上 % $95\%$ of samples, the ratio E S - RMS / E C - RMS ∗ E E - RMS ${E}_{\mathrm{S}\mbox{-}\text{RMS}}/\sqrt{{E}_{\mathrm{C}\mbox{-}\text{RMS}}\ast {E}_{\mathrm{E}\mbox{-}\text{RMS}}}$ ranges from 1 0 − 1.6 $1{0}^{-1.6}$ to 1 0 − 1 $1{0}^{-1}$ . Using the typical parameters, we find that the ECH sidebands can effectively extend the energy range of resonant electrons down to ∼ ${\sim} $ 10 eV. This study reveals the global distribution of chorus-ECH interactions and the energy conversion efficiency in this nonlinear process.