We calculate and compare the temporal growth rate and the number of e-folding growths for the following wave modes due to a loss-cone-driven cyclotron maser: fundamental x, o, and z modes and second harmonic x and o modes. The dominant mode of the maser should be the fastest growing mode for a saturated maser and should be the mode with the greatest number of e-folding growths for an unsaturated maser; this mode is the fundamental x mode for mp/•e < 0.3, the z mode (or perhaps the fundamental o mode) for 0.3 < mp/•e < 1.0, and the z mode (or perhaps t•e second harmonic x mode) for 1.0 < mp/•e < 1.3. We discuss the effect of cyc16tron damping by thermal electrons on the growth. Numerical calculations show that the effect is important only when the ratio of the mean energies of the thermal and maser emitting electrons exceeds 0.1-0.2. An analytic expression for the damping rate is derived and is used to show that some earlier treatments of cyclotron damping greatly overestimate the effect for loss-cone-driven maser emission. These results, when applied to AKR, imply that only either the fundamental x mode (for mp/•e < 0.3) or the z mode (for mp./•e 5 0 3) is produced directly by maser emission. We suggest (1) that an o mode component in AKR might be due to partial reflection of x mode radiation incident onto sharp overdense plasma intrusions of the kind observed in the auroral cavity and (2) that a second harmonic component can be produced by coalescence of two z mode waves. 1. 1984; Benson and Akasofu, 1•84]. We argue here that the latter component, which is restricted to•betwcen •2e ' and the upper hybrid frequency zs z mode radiation generated by the process discussed by Hewitt et al. [1983]. In section 2 we discuss the criterion for the dominant mode of a loss-cone-driven maser, and suggest that this is the x mode for mp/•e < 0.3 and the z mode for 897 898 Melrose et al.: Cyclotron Masers in Different Modes I o -• •
We examine the gyroresonance condition to determine which electrons can resonate with a specific electromagnetic wave (given m and kll) and find that for each gyroresonance harmonic the resonant electrons lie on an ellipse in v 1 -vii space. The growth rate for a given wave due to a given distribution f of electrons involves an integral around the 'resonant ellipse.' Using a contour plot of f in vñ -vii space and a set of drawn ellipses, one can identify which waves grow fastest and which electrons contribute to the growth. We find that for •f/•v i > 0 at small vñ there always exist rapidly growing waves with Palmadesso et al.,
Electron-cyclotron instabilities may be classified in two ways depending on whether the relativistic correction to the gyrofrequency is important (class S) or not (class N), and whether the instability mechanism is of a maser type (class M) or due to bunching (class B). Renewed interest in class SM has followed the Wu and Lee application of it to the interpretation of terrestrial kilometric radiation. The maser is assumed to be driven by a one-sided loss-cone distribution of electrons. This mechanism seems particularly favourable for the interpretation of certain planetary, solar and stellar radio emissions.The loss-cone driven SM instability is explored in detail here through numerical calculations of the growth rate and the development of a semi-quantitative theory for the maser mechanism. The numerical calculations are for a hot Maxwellian distribution with a hole in pitch angle IX; the distribution falls off with pitch angle inside the loss cone IX > 1X0 (> tn) as a power of a sine function of 1X-1X0. It is assumed that the dispersive properties of the waves are determined by a cold plasma (with frequency rop) and only emission in the x mode and the 0 mode above their respective cutoff frequencies is considered. The semi-quantitative theory involves the parameters 1X0 and the characteristic range of IIX -lXo lover which the distribution falls off inside the loss cone !!.IX, the energy tmv~ and the number density nH of the energetic electrons, and the ratio rop/Q., with Q. the electron-cyclotron frequency.The maser emission is possible at all harmonics s = 1,2, ... An application of the mechanism to the interpretation of the Jovian decametric radio emissions is outlined.
A new, simple, and exact method is given for calculating the reaction matrix G in a twoparticle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrodinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based-on the Hamada-Johnston potential are used in a shell-model calculation of 4=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operafors. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed.
Ground-based observations of Jupiter’s decametric radio emission (DAM) have been reviewed by Ellis (1965), Warwick (1967, 1970) and Carr and Gulkis (1969). A startling feature of DAM is the modulating effect of Io, and interpretation of the Io effect has dominated theoretical discussions of DAM until quite recently, specifically until the fly-by s of Voyagers 1 and 2. The Voyager data showed that the DAM appears as nested arcs in the frequency-Jovian longitude plane (Warwick et al. 1979, Boischot et al. 1981). The interpretation of this arc structure has been of primary theoretical interest over the past two years. The most widely adopted explanation is that the emission from each point is confined to the surface of a hollow cone (Goldstein and Thieman 1981). This idea is not new: emission on the surface of a cone was discussed by Ellis and McCulloch (1963); Dulk (1967) derived detailed parameters for the cone (half angle 79° width 1°) from the occurrence pattern of DAM; and Goldreich and Lynden-Bell (1969) presented a theoretical interpretation of it. More recently Goldstein et al. (1979) used observational data on the Jovian magnetic field in deriving properties of the required emission cone. It seems that one requires the properties of the emission cone to vary with position in the Jovian magnetosphere to account for the nested arc pattern (Goldstein and Thieman 1981; Gurnett and Goertz 1981).
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