D. B. Melrose

Electron-cyclotron masers as the source of certain solar and stellar radio bursts

The theory of electron-cyclotron masers as they might apply in the astrophysical context is developed, and it is suggested that such masers provide an explanation for the very bright emission known to be associated with certain kinds of radio bursts observed on the Sun and other stars. Some of the observed properties of solar and stellar radio bursts that seem to require amplification of the radiation are summarized, including millisecond solar spikes, RS CVn binaries, and flares on M dwarf stars. Recent developments in the theory of electron-cyclotron masers are summarized and the current theory is applied to electrons with a loss cone anisotropy, estimating the growth rate and saturation levels. In the interpretation of solar microwave spikes and RS CVn binaries, the mechanisms of gyromagnetic absorption, maser at the second harmonic, polarization, and angular distribution are examined in the light of the theory.

The emission mechanisms for solar radio bursts

Emission mechanisms for meter-λ solar radio bursts are reviewed with emphasis on fundamental plasma emission.The ‘standard’ version of fundamental plasma emission is due to scattering of Langmuir waves into transverse waves by thermal ions. It may be treated semi-quantitatively by analogy with Thomson scattering provided induced scattering is unimportant. A physical interpretation of induced scattering is given and used to derive the transfer equation in a semi-quantitative way. Solutions of the transfer equation are presented and it is emphasized that ‘standard’ fundamental emission with brightness temperatures ≫109 K can be explained only under seemingly exceptional circumstances.Two alternative fundamental emission mechanisms are discussed: coalescence of Langmuir waves with low-frequency waves and direct conversion due to a density inhomogeneity. It is pointed out for the first time that the coalescence process (actually a related decay process) can lead to amplified transverse waves. The coalescence process saturates when the effective temperature Tt of the transverse waves reaches the effective temperature Tl of the Langmuir waves. This saturation occurs provided the energy density in the low-frequency waves exceeds a specific value which is about 10-9 of the thermal energy density for emission from the corona at ≈100 MHz. It is suggested that direct emission has been dismissed as a possible alternative without adequate justification.Second harmonic plasma emission is discussed and compared with fundamental plasma emission. It also saturates at Tt ≈ Tl, and this saturation should occur in the corona roughly for Tl ≳ 1015 K. If fundamental plasma emission is attributed to coalescence with low-frequency waves, then for Tl ≳ 1015 K the brightness temperatures at the two harmonics should be equal and equal to Tl. This offers a natural explanation for the approximate equality of the two brightness temperature often found in type II and type III bursts.Analytic treatments of gyro-synchrotron emission are reviewed. The application of the mechanism to moving type IV bursts is discussed in view of bursts with ≳ 1010 K at 43 MHz.

The emission and absorption of waves by charged particles in magnetized plasmas

A semiclassical theory describing the emission and absorption of waves is applied to the interaction of charged particles with waves in magnetized plasmas. Spontaneous emission of all cold plasma wave modes is calculated in detail. The method gives the absorption coefficient for the waves and a diffusion equation in momentum space for the particles describing the effects of the induced processes.Coefficients describing the systematic change of particle parameters follow from the diffusion equation. Applications of astrophysical interest are outlined.

Rotational effects on the distribution of thermal plasma in the magnetosphere of jupiter

The consequences of the assumption that the magnetosphere of Jupiter corotates with the planet are examined. It is found convenient to divide the magnetosphere into two regions. The inner region is qualitatively similar to the magnetosphere of the Earth provided that the ratio of the scale height to the radius of Jupiter is much less than 112. The outer region is dominated by rotational effects. It is expected to be slightly flattened, with a density falling off as Br−1. The velocity distribution of the plasma becomes increasingly anisotropic with increasing distance. The corotating magnetosphere breaks up as a result of electrostatic microinstabilities at 7–8 radii, well inside the boundary with the solar wind.

Quadrupolar Magnetic Reconnection in Solar Flares. I. Three-dimensional Geometry Inferred from Yohkoh Observations

We analyze the three-dimensional geometry of solar flares that show so-called interacting flare loops in soft X-ray, hard X-ray, and radio emission, as previously identified by Hanaoka and Nishio. The two flare loops that appear brightest after the flare are assumed to represent the outcome of a quadrupolar magnetic reconnection process, during which the connectivity of magnetic polarities is exchanged between the four loop footpoints. We parameterize the three-dimensional geometry of the four involved magnetic field lines with circular segments, additionally constrained by the geometric condition that the two pre-reconnection field lines have to intersect each other at the onset of the reconnection process, leading to a 10 parameter model. We fit this 10 parameter model to Yohkoh Soft and Hard X-Ray Telescopes (SXT and HXT) data of 10 solar flares and determine in this way the loop sizes and relative orientation of interacting field lines before and after reconnection. We apply a flare model by Melrose to calculate the magnetic flux transfer and energy released when two current-carrying field lines reconnect to form a new current-carrying system in a quadrupolar geometry. The findings and conclusions are the following. (1) The pre-reconnection field lines always show a strong asymmetry in size, consistent with the scenario of newly emerging small-scale loops that reconnect with preexisting large-scale loops. (2) The relative angle between reconnecting field lines is nearly collinear in half of the cases, and nearly perpendicular in the other half, contrary to the antiparallel configuration that is considered to be most efficient for magnetic reconnection. (3) The angle between interacting field lines is reduced by ≈10°-50° after quadrupolar reconnection. (4) The small-scale flare loop experiences a shrinkage by a factor of 1.31 ± 0.44, which is consistent with the scaling law found from previous electron time-of-flight measurements, suggesting that electron acceleration occurs near the cusp of quadrupolar configurations. (5) The large-scale loop is found to dominate the total induction between current-carrying loops, providing a simple estimate of the maximum magnetic energy available for flare energy release because of current transfer, which scales as ΔEI ≈ 1029.63(r2/109 cm)(I2/1011A)2 (with r2 the curvature radius and I2 the current of the large-scale loop) and is found to correlate with observed flare energies deduced from soft X-ray and hard X-ray fluxes. Most of the energy is transferred to small-scale loops that have one-half of the large-scale current (I1 = I2/2). (6) The quadrupolar reconnection geometry provides also a solution of Canfields dilemma of the offset between the maximum of vertical currents and the HXR flare loop footpoints. (7) The quadrupolar geometry provides not only a framework for interacting double-loop flares, but it can also be considered as a generalized version of (cusp-shaped) single-loop flares.

Relativistic Plasma Emission and Pulsar Radio Emission: A Critique

Relativistic plasma emission due to a beam instability in the polar cap regions is examined critically as a pulsar radio emission mechanism. Wave dispersion in the pulsar plasma is discussed, based on the use of a relativistic plasma dispersion function. The growth rate for the beam instability is estimated in the rest frame of the plasma for parallel Langmuir waves, L-O mode waves, and oblique Alfven waves. The first two of these imply frequencies that are much higher than the observed frequencies for plausible parameters, suggesting that they are not viable as pulsar radio emission mechanisms. Growth of Alfven waves requires that the beam speed equal the phase speed of the Alfven waves, and this condition cannot be satisfied within the light cylinder, except for an extremely high energy beam. It is suggested that either the plasma parameters in the source region are quite different from what is currently considered plausible or the emission mechanism does not involve a beam instability. Alternative pulsar radio emission mechanisms should be explored further.

Plasma Emission Processes in a Magnetoactive Plasma

Plasma emission (i.e. emission at about the plasma frequency and twice this frequency) is treated taking into account the effects of the magnetic field on the electron plasma waves, on the conversion processes, and on the escaping radiation. The expected degrees of polarization of the fundamental and second harmonic are calculated in the weak field limit. The results are used to estimate the magnetic field strength B at the 80 MHz level from the observed polarization of type III bursts; the result B < 0·04 G is smaller than previous estimates. The possible importance of electron-cyclotron waves in an application to type I bursts is noted.

Large-Amplitude, Pair-creating Oscillations in Pulsar and Black Hole Magnetospheres

A time-dependent model for pair creation in a pulsar magnetosphere is developed in which the parallel electric field oscillates with large amplitude. Electrons and positrons are accelerated periodically, and the amplitude of the oscillations is assumed to be large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at N± E/(8πmec2Γthr), where E0 is the parallel electric field in the charge-starved initial state and Γthr is the Lorentz factor for effective pair creation. The frequency of oscillations following the pair creation burst is given roughly by ωosc = eE0/(8mecΓthr). A positive feedback keeps the system stable, such that the average pair creation rate balances the loss rate due to pairs escaping the magnetosphere.

Second harmonic electromagnetic emission via Langmuir wave coalescence

The coalescence of Langmuir waves to produce electromagnetic waves at twice the plasma frequency is considered. A simplified expression for the rate of production of second harmonic electromagnetic waves is obtained for a broad class of Langmuir spectra. In addition, two different analytic approximations are considered. The validity of the commonly used head‐on approximation is explored, in which the two coalescing Langmuir waves are assumed to approach from opposite directions. This approximation breaks down at low Langmuir wavenumbers, and for narrow Langmuir wave spectra. A second, more general, approximation is introduced, called the narrow‐spectrum approximation, which requires narrow spectral widths of the Langmuir spectra. The advantages of this approximation are that it does not break down at low Langmuir wavenumbers, and that it remains valid for relatively broad Langmuir wave spectra. Finally, the applicability of these approximations in treating harmonic radiation in type III solar radio bursts...

Resonant scattering of particles and second phase acceleration in the solar corona

AbstractEffective acceleration of particles by hydromagnetic turbulence requires that the particles be scattered at a rate ν comparable with the frequency ω of the turbulence. The only effective scattering process is due to resonant wave-particle interactions. The resonant waves are HM waves for ions with β≫βA(βc = particle speed, βAc = Alfvén speed) and for electrons with γβ ⩾ 43β0(β0 ≈ 43βA), and are whistlers for electrons with β0 ≪ γβ≲ 43β0. The resonant waves can be generated by an anisotropic distribution of particles provided that the anisotropy factor A exceeds a threshold anisotropy A0 ≈ βA/β for HM waves and A0 ≈ β02/β2γ for whistlers. Turbulence with relative magnetic amplitude ɛ causes acceleration at a rate {ie0353-02} provided the following conditions are satisfied: (a) β ≫ βA for ions, β ≫ β0 for electrons; (b) ɛ ≫ A0; (c) n1/ne≲ω/gWi or n1/ne ≫(ω/Ωi) (γβ/43β0)2 for scattering by HM waves or whistlers respectively (n1 = number density of accelerated particles, Ωi = ion gyrofrequency).The injection energy for electrons (β > β0) implies that second phase acceleration can be operative for electrons resulting from first phase acceleration (energies ⩽ 40 keV) only in regions with Alfvén speed ⩽ 3 × 103 km s−1 (βA ≲ 102). Acceleration on a time scale of a few minutes can result from turbulence with typical periods in the range 0.1 s to 10 s, whose presence is indicated by pulsations of metre-wave continuum radiation.