ALBERT

Notes: Abstract A general scheme is established to examine any magnetohydrodynamic (MHD) configuration for its acceleration potential including the effects of various types of plasma waves. The analysis is restricted to plasma waves in a magnetic field with electron cyclotron frequency less than, but comparable to, the electron plasma frequency (moderate field). The general role of electron plasma waves is examined in this paper independent of a specific MHD configuration or generating mechanism in the weak turbulence limit. The evolution of arbitrary wave spectra in a non-relativistic plasma is examined, and it is shown that the nonlinear, process of induced scattering on the polarization clouds of ions leads to the collapse of the waves to an almost one-dimensional spectrum directed along the magnetic field. The subsequent acceleration of non-relativistic and relativistic particles is considered. It is shown for non-relativistic particles that when the wave distribution has a negative slope the acceleration is retarded for lower velocities and enhanced for higher velocities compared to acceleration by an isotropic distribution of electron plasma waves in a magnetic field. This change in behavior is expected to affect the development of wave spectra and the subsequent acceleration spectrum.

Notes: Abstract The observations of type-III solar radio bursts are briefly reviewed to set requirements on a model for their interpretation. The most important of these requirements is that the source must be an electron stream which is in a state of continuous quasilinear relaxation and which initially must have a nearly monotonically decreasing velocity distribution. The problem of constructing a model is broken into three parts: (1) The plasma wave source which depends on the interaction of the electron stream with electron plasma waves. (2) The radiation source which depends on the interaction of plasma waves and transverse electromagnetic waves or in a magnetized plasma the ordinary and extraordinary modes of magnetoionic theory. (3) The propagation of radiation between the source and the observer which depends on the transmission of radiation through a scattering refracting absorbing magnetized plasma. Progress on a model for the plasma wave source is reviewed and it is concluded that no existing models are adequate. The equations which would lead to an adequate model are written down, but not solved. These include, in addition to collisional damping, Landau damping both by the exciting stream and the background plasma, and spontaneous and induced processes for a three-dimensional distribution of plasma waves. Possible limitations to a quasilinear approach such as pile-up of plasma waves and nonlinear effects are considered. Processes which affect the gross structure of the source such as electron trajectories in coronal streamers and electron scattering by inhomogeneities are reviewed. Progress on the radiation source is considered both in the absence and presence of a magnetic field. At high frequencies (e.g., 80 MHz) observations of radiation near the fundamental and second harmonic of the plasma frequency allow a unique determination of source size and the energy density in plasma waves within the uncertainties of geometry by source ray tracing. This determination is extremely critical because the fundamental must be amplified and thus production of the fundamental is effectively a much more highly nonlinear process than production of the second harmonic. At low frequencies (e.g., 500 kHz) the second harmonic is shown to be dominant because amplification of the fundamental becomes an inefficient process. Calculations of scattering of radiation in a random medium are reviewed. It is concluded that these are adequate at high and low frequencies, but have not been carried out properly at intermediate frequencies where amplification of the fundamental may still be present. It is shown in particular that when scattering is taken into account at high frequencies all observations can be explained by isotropic emission near the second harmonic. At low frequencies the nature of the scatterers is determined by source occultations unlike the case at high frequencies where these are free parameters. This fact allows the possibility of determining true source sizes at low frequencies by subtracting out the contribution due to scattering. A mechanism for producing the possibly observed linear or highly elliptical polarization of type-III bursts, which must be imposed far from the source due to Faraday rotation, is reviewed. Finally, the questions of what remains to be done and what we can hope to obtain upon completion of this work are briefly considered.

Notes: Abstract The processes by which streams of charged particles become charge and current neutralized in the corona are investigated. It is shown that a large amplitude plasma wave, which is related to precursor phenomenon in type III bursts and possibly plasma radiation from type IV bursts, will be excited at the head of the stream. The energy extracted from the stream to produce this plasma wave is computed and used to set conservative upper limits on the densities of possible excitors for type III bursts. For electron streams the density n s 〈 10−5 n e, where n e is the density of the background plasma. For proton streams n s 〈 1.8 × 10−2 n e. The energy extracted from the stream is also used to set upper limits on the lifetimes of relativistic electrons ‘stored’ in the corona and it is concluded that for n e 〉 102 cm−3 this loss must be taken into account. Since electron streams cannot produce their own stabilizing ionacoustic waves because they would violate the condition n s 〈 10−5 n e, other mechanisms for producing ion-acoustic waves in the corona are examined. Another stabilization mechanism due to velocity inhomogeneity is investigated.

Notes: Abstract Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain 〉 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.

Notes: Abstract Both individual and collective motions of electron and proton streams in the current sheet which is thought to exist near the center of a coronal streamer are considered. Unlike previous analyses, closed field lines which must exist when finite conductivity is taken into account as well as a B ø field due to solar rotation are present. It is shown on the basis of individual particle motions that neither electrons nor protons could move in most of the sheet in the manner required to explain type III bursts since they are effectively tied to the closed field lines. The possibility that the stream could collectively drag the closed field lines out with itself is considered. It is shown that impossibly high densities are required for electron streams and improbable densities for proton streams. Thus the particles responsible for type III bursts cannot travel in the densest part of a coronal streamer, but presumably travel close to this region. Moreover, the current sheet cannot act as a channeling agent to help explain the transverse coherency of type III burst sources.

Notes: Abstract The procedure developed in Smith (1974) to model the radiation source for type III bursts is modified to include scattering of radiation in the source itself. Since the inhomogeneities in the source must have the same statistical properties as the inhomogeneities used in tracing radiation from the source to the observer, these two parts of the type III problem are no longer uncoupled. Thus we use inhomogeneities consistent with the scattering inhomogeneities of Steinberg et al. (1971) and Riddle (1974) and apply the procedure to an archetype ‘fundamental-harmonic’ pair observed at Culgoora on 28 September, 1973 at 0319 UT. We find that it is impossible to model this burst with a source which is homogeneous in the sense that every part of the source has the same energy density in plasma waves. The density inhomogeneities in the source severely hamper amplification of the supposed fundamental. Possible ways out of this dilemma are discussed, including second harmonic pairs and a source with an inhomogeneous distribution of plasma waves. It is concluded that none of the possibilities are completely satisfactory to explain present observations and suggested that critical observations are missing.

Notes: Abstract The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W p . The source size and W p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω p )/P(2ω p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W p = 10−6.52 erg cm−3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W p = 10−6.3 erg cm−3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.

Notes: Abstract The possibility is investigated that the plasma turbulence used in many recent models of the primary energy release and acceleration in solar flares should be detectable by radiation near the fundamental and second harmonic of the plasma frequency. Formulae are derived for fundamental emission due to the combination of ion-acoustic and Langmuir plasma turbulence and for second harmonic emission due to the combination of two Langmuir waves. These results are applied to recent primary energy release and acceleration models which shows that either such radiation should be detectable and possibly distinguishable with suitable microwave interferometers or that its absence places fairly stringent constraints on the possible level of Langmuir or Langmuir and ion-acoustic waves in these models.

Notes: Abstract The two major candidates for proton acceleration in impulsive γ-ray producing flares, shock and stochastic acceleration, are considered in light of recent observations of mass motions and turbulence in flares. Starting with the basic problem of energies required, energy storage and the currents which must be involved, it is concluded that the primary energy release must occur close to the temperature minimum region. It is shown that energy can propagate upwards in the form of fast magnetosonic waves which become evanescent in the transition region, converting a large fraction of their energy to mass motions and turbulence. Present observations are mostly of rather coarse (7000 km) spatial resolution and it is quite possible that significantly higher velocities than those observed were present. Using the results of recent simulations of parallel shocks and the well tested theory of Lee (1983) for parallel shock acceleration in the interplanetary medium, it is shown that shock acceleration is a viable candidate at velocities slightly higher than present observations. It is also shown that shocks must be driven by a mass of material which would be visible in coronal lines such as Caxix for them to be energetically important in proton acceleration. Stochastic acceleration is examined using the hypothesis that there is an equipartition of energy between observed turbulence and magnetic field fluctuations. It is shown that this is a viable acceleration mechanism within a large range of presently observed turbulence provided that the above equipartition hypothesis is valid and the turbulent elements are of small scale (1–200 km). Since turbulence is observed in many flares without any evidence of γ-rays, one of the above conditions must not be satisfied in general. It is concluded that although present observations favor stochastic acceleration, no definitive conclusion can be made without higher spatial resolution observations and additional theoretical work.

Notes: Abstract Observations of some type III radio bursts in the hectometer and kilometer wave range are compared with theoretical predictions. It is shown that the burst emission must be near the plasma frequency in the region between 10 R ⊙ and 50 R ⊙ in order to be consistent with the observed steep rise in brightness temperature for these bursts. The results of Fainberg, Malitson et al., and Haddock and Alvarez are discussed and compared with the interpretation of emission near the plasma frequency.