Electromagnetic Waves Dispersion and Interaction of an Annular Beam-Ion Channel System in Plasma Waveguide

<div>In annular beam case, there is no coupling between the TM modes and ES waves in weak ion channel case. The inner and outer radius of the annular beam are taken as <svg height="8.8423pt" id="M171" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 51.5725 8.8423" width="51.5725pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z" id="g113-98"></path></g><g transform="matrix(.013,0,0,-0.013,10.212,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,21.475,0)"><path 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Advances in Mathematical Physics

fig14

Figure 14

Figure 14: Electromagnetic Waves Dispersion and Interaction of an Annular Beam-Ion Channel System in Plasma Waveguide 