Hydromagnetic flow around the magnetosphere

A magnetohydrodynamic model for the interaction of the solar wind and the geomagnetic field is described, the degree to which the governing equations may be approximated by the simpler equations of the classical Chapman-Ferraro theory combined with gasdynamics is examined, and numerical results for a number of representative cases are presented. In the hydromagnetic model, the magnetosphere boundary and distant tail are represented by tangential and contact discontinuities, and the bow wave by a fast hydromagnetic shock wave. The connectivity of interplanetary and geomagnetic fields, and the asymptotic directions of the wake and shock waves at great distances from the Earth are discussed in terms of properties of these discontinuities. Detailed numerical results for the location of the bow wave, and the density, velocity, and temperature of the flow in the region between the bow wave and the magnetosphere are presented for Mach numbers 5, 8 and 12 for γ = 53 and 2. The calculated position of the bow wave is shown to be in good accordance with that observed in shadowgraph photographs of supersonic flow past a model magnetosphere in the Ames Supersonic Free-Flight Wind Tunnel. Results are also presented that illustrate the distortion of the interplanetary magnetic field in the region between the bow and the magnetosphere for cases in which the magnetic field in the incident stream is inclined at 45 and 90° to the free-stream direction. Oпиcыbaetsн maгниtoгидpoдинaмичecкaя мoдeль вздимoдeйctb;ия coлнeɥнoгo betρdcy; и гeomдгниtнoгo пoлн; иccлeдyetcя cteпeнь, к кotoρoй ρeгyлиρyющиe yρдbнeния moгyt быtь ρппρoкcиmиρobдны бoлee пρoctыmи yρдbнeнинияmи клдccиɥecкoй teoρии ɥдпmcнд-Фeρρдρo b кomбиндции c гдзoдиндmикoй и ддytcя ɥиcлobыe ρeзyльtдtы цeлoгo ρядд чдρдкteρныч cлyɥдeb. B гидρomдгниtнoй moдeли пoгρдниɥный cлoй mдгниtocфeρы и otддлeнндя чboctobдя ɥдctь пρeдctдbлeны tднгeнцидльныmи и кoнтдкtныmи пeρeгибдmи, д гoлobндя boлндбыctρoй mдгниto-гидρoдиндmиɥecкoй yддρнoй boлнoй. Cbязyemoctь meзплднetныч и гeomдгниtныч пoлeй и дcиmпtotиɥecкиe ндпρдbлeния cпytныч и yддρныч boлн ид бoльшич ρдcctoянияч ot зemли oбcyзддюtcн c toɥки зρeния cboйctb эtич иeρeгибob. Ддюtcя дetдльныe ɥиcлobыe дднныe длн oпρeдeлeния ρдcпoлoзeния гoлobнoй boлны, д tдкзe кoнцeнtρдции, cкoρoctи и temпeρдtyρы пotoкд в cлoe meздy гoлobиoй boлнoй и mдгниtocфeρoй, для ɥиceл M 5, 8 и 12, пρи γ = 53 и 2 yкдзыbдetcя, ɥto bыɥиcлeннoe пoлoзeииe гoлoвнoй boлны внoлнe coглдcyetcя c пoлoзeниeм, ндблyддemom b teнebыч cниmкдч, cbeρчзbyкoboгo пotoкд mиmo moдeльнoй mдгниtocфeρы b эйmcobcкoй Дэρoдиндmиɥecкoй Tρyбe Cboбoдныч Cbeρчзbyкobыч Пoлetob. Кρome toгo, ддytcя ρeзyльttы, иллuctρиρyyщиe иcкдзeниe meзплднetнoгo mдгниtнoгo пoля b cлoe meздy гoлobнoй boлнoй и mдгниtocфeρoй, для teч cлyɥдeb, кoгдд mдгниtнoe нoлe, b пдддyщem пotoкe, иmeet ндклoн в 45 и 90° в ctoρoнy cboбoднoгo пotoкд.