Analytical solution for minimum length MHD ACCELERATOR with constantpressure.

Abstract

Fig. 3b Emission curves on trajectory E = 0.05, A = 0.009, 1) shell height 10,000 km, 2) shell height 20,000 km, 3) shell height 30,000 km.along the other two trajectories of Fig. 1. We can conclude then that there is discrimination only when the spacecraft is near the apex of the shadow or near its edge. Though this result could have been anticipated, it is felt to be of value to exhibit it quantitatively. In this exploratory study we have ignored complications introduced by centers of activity and ray structure. The sun lacks heliocentric symmetry and this will make interpretation more difficult. A helpful feature is that the emission from a complex distribution may be expressed as the sum of emissions from its parts; with a knowledge of the locations on the sun of bright regions, a set of integrals [Eq. (1) ] could be summed to improve the theoretical model.The important question of how much EUV radiation is scattered by the Earth's atmosphere to the observation point from the occulted part of the chromosphere will be examined in later work. However, a rough overestimate, considering scattering to occur in a uniform belt of upper atmosphere 100 miles thick in which the scattering efficiency is 100%, shows that this scattered radiation can compete with direct coronal light only if all but 10 ~4 of the chromospheric emission is eclipsed. This strongly indicates that the Earth is a good occulting disk in the EUV. SummaryFlight of spacecraft-borne instruments into the Earth's shadow is proposed as a method for obtaining source distributions of ultraviolet and x-ray emission in the corona and chromosphere. Typical trajectories are found to give durations of many hours and distances of a few hundred thousand kilometers within the shadow. The variation of chromospheric emission along these trajectories is studied for three simple source models; good discrimination between the three sources is obtained along trajectories the entry and exit points of which are farthest toward the end of the shadow. Discrimination is possible between several emission lines originating at altitudes above the photosphere differing by less than 10,000 km.Nomenclature P = density u = velocity along x axis A = duct area P -pressure J = current density B = magnetic induction a_ = electric conductivity E -electric field R = gas constant T = temperature x = duct length 7 = specific heats ratio (3 = E/UB p' = dp/du Subscripts 1 = conditions at inlet section 2 = conditions at outlet section R ECENTLY, J. H. Drake, 1 H. Mirels, and others 2 -3 presented minimum length solutions for crossed field accelerators without plasma temperature variation in the longitudinal direction. Although this requirement insures that added electrical energy appears as kinetic and not as thermal energy, we would recall that the constant temperature MHD accelerator is not the only approach to the problem of accelerating conducting flows by means of crossed magnetic and electric fields. Both experimental and theoretical investigations by K. Burkhard and others 4 and by ...