The Structure of the Astron E-layer

Abstract

The structure of the field-reversing layer of circulating relativistic electrons which constitutes the plasma trap of the Astron has been calculated self-consistently using a model embodying the simplifying assumptions: (1) uniformity over an infinite length so that end-effects are absent, (2) uniformity of impressed field, i.e., no plasma diamagnetism, (3) dynamical friction from the trapped plasma but no scattering, (4) no radiative energy loss, (5) absence of instabilities, and (6) the structure can be initiated. Assumptions (1), (5), and (6) are the most questionable. In the model monoenergetic electrons appear uniformly on a cylindrical surface of radius r2 with no radial velocity, all traveling at the same polar angle. The impressed magnetic field is defined by a, the radius of the helix executed in that field. The dynamical friction is defined by the constant ν = β dγ/dt where β ≡ ν/c ≡ (γ2−l)1/2/γ and ν is proportional to plasma density. The energy degradation is slow enough for the structure to be viewed as a steady-state ensemble with the number of electrons in any small energy-momentum interval inversely proportional to the rate of slowing down there.The initial-energy range is defined by 10 ≤ P0 ≡ (γ2–1)1/2 ≤ 80. A basic parameter is G ≡ r2/a — the larger G, the tighter the electrons tend to spiral relative to the layer diameter. At any value of G greater than about 1.2, increasing the injection rate does indeed cause field reversal. An initial steep traversal through zero is followed by a region of slow increase–a quasi-plateau–as the electrons cease to penetrate to the axis and become confined to an ever-thinner layer lying inside r2. This might well constitute the working region. The useful range of G appears to be from about 1.3 to 2.5 irrespective of P0. (Beyond this the ratio of reversed to impressed field exceeds 0.75 and the mathematics produces physical unrealities.) For S, the “injection rate”, the useful range is roughly 0.8 to 1.6 at the low G and 3.8 to 4.6 at the high. For S = 2 and a plasma density of electrons of 1015, the electron injection rate is 0.32 mA/cm length of E-layer.