The conditions for the existence of the electric field opposite to the current along the magnetic field lines in the thin plasma

The flow of the current along the magnetic field lines in the thin plasma directed opposite to the electric field is considered. The particles moving to the equatorial plane are supposed to have mirror points above the region of absorption (the ionosphere) and the particles moving to the ionosphere are supposed to have mirror points below the region of absorption. The current, therefore, flows. The functions of the distribution of the electrons and ions are considered to be mono-energetic. The energies of the electrons and the ions and their densities on the boundary of absorption are estimated for the potential difference and for the current density which are typical for the auroral field lines.     

The role of electrostatic instabilities in the critical ionization velocity mechanism

The role of electrostatic instabilities in the critical ionization velocity mechanism is investigated. The analysis is based on the theory developed by Sherman, which interprets Alfvén's critical velocity in terms of a circular process. This process involves the acceleration of electrons by a two-stream instability modified by the presence of a magnetic field. A general expression for the energy and momentum of ions and electrons associated with an electrostatic mode is derived in terms of the plasma dielectric constant. This is used in the case of the modified two-stream instability to determine the distribution of energy between ions and electrons. An extrapolation from the linear phase then gives an estimate of the energy delivered to the electrons which is compared to that required to ionize the neutral gas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Multicomponent theory of buoyancy instabilities in magnetized plasmas: the case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.     

On the acceleration of solar-flare charged particles in a collapsing magnetic trap with an electric potential

We consider the kinetic problem of charged-particle acceleration in a magnetic trap with converging magnetic mirrors. We show that for a positive electrostatic potential of the trap plasma relative to the mirrors, the efficiency of confinement and acceleration increases for electrons and decreases for ions.     

Electron acceleration in an array of auroral arcs

Energy spectra of electrons encountered on a rocket flight across an array of auroral arcs are employed to test three related models of electron acceleration. All three are based on a potential difference existing between the source plasma in the magnetosphere and the observation point in the ionosphere. One of the models provides a satisfactory fit to the observed spectra. Two alternative mechanisms are suggested to explain this model. The first possibility is a time-varying potential difference, which results in the accelerated electrons being observed with a statistical distribution of energy gain. The second possibility, which results in the same energy gain distribution, is a constant potential difference operating in conjunction with plasma instabilities generated by the accelerated beam. The energy gain distribution in the second case is therefore a consequence of a constant potential difference and a variable energy loss. In addition it is suggested that electrostatic waves generated by the instabilities could accelerate ambient plasma to suprathermal energies. Application of the model to the complete data set yields a continuous record of the parameters defining the acceleration and source plasma across the array of arcs. Reference is also made to an acceleration mechanism involving resonance with electrostatic waves.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

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.     

Simulation studies of electron acceleration by ion ring distributions in solar flares

Using a 2 1/2-D fully relativistic electromagnetic particle-in-cell code (PIC) we have investigated a potential electron acceleration mechanism in solar flares. The free energy is provided by ions which have a ring velocity distribution about the magnetic field direction. Ion rings may be produced by perpendicular shocks, which could in turn be generated by the super-Alfvénic motion of magnetic flux tubes emerging from the photosphere or by coronal mass ejections (CMEs). Such ion distributions are known to be unstable to the generation of lower hybrid waves, which have phase velocities in excess of the electron thermal speed parallel to the field and can, therefore, resonantly accelerate electrons in that direction. The simulations show the transfer of perpendicular ion energy to energetic electrons via lower hybrid wave turbulence. With plausible ion ring velocities, the process can account for the observationally inferred fluxes and energies of non-thermal electrons during the impulsive phase of flares. Our results also show electrostatic wave generation close to the plasma frequency: we suggest that this is due to a bump-in-tail instability of the electron distribution.     

MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

Waves in cosmic magnetic structures taking into account the anisotropic plasma pressure

This paper provides an analysis of magneto-sonic eigenwaves travelling in magnetic plasma structures based on the Chew-Goldberger-Low approximation, for which the plasma kinetic pressure is different along and across the magnetic field. The anisotropy does not lead to the emergence of new modes. The dependence of phase velocities of the waves, trapped by a single magnetic surface, on the pressure anisotropy is investigated. For a magnetic slab with field-free surroundings, the dispersion relations for the eigenwaves are obtained. The pressure anisotropy may change dispersion relations of such modes significantly. In particular, backward waves are possible in the case of strong anisotropy. The dependences of the thresholds for the mirror and hose instabilities on the system parameters are obtained. In particular, hose and mirror instabilities of such waves are absent for some wave number regions. The results are used to obtain the eigenwave characteristics in coronal loops and chromospheric flux tubes.     

Magnetically trapped particles in the lower solar atmosphere

The trapping of energetic electrons and protons in a simple, arched magnetic field imbedded in the lower solar atmosphere was considered. The lifetime of electrons with kinetic energies up to about 1.5 MeV was found to be completely determined by the motion of the mirror points, provided the gyro-synchrotron loss can be neglected. The same motion also influences the lifetimes of more energetic electrons, up to 10 MeV. This was not found to be the case for protons in the range from 1 MeV to 100 GeV. Some fluid and streaming instabilities were also considered; they pull the particles upward, raise their mirror points, and increase their lifetime. The emission of gyro-synchrotron radiation and bremsstrahlung in this model has been related to observations. Using the duration of non-thermal X-ray peaks given by Kane (1969), the altitude of injection of energetic particles was estimated.     

Plasma emission and the decimetre portion of type-IV solar bursts

An attempt is made to account for the decimetre portion of the Type-IV solar radio bursts by plasma emission. Non-thermal electrons (E ～ 500 keV) trapped in a magnetic mirror (IV_dm, burst source) having loss-cone gap distribution excite plasma waves which are transformed into transverse waves through non-linear scattering by ions. A good agreement was reached between the calculated spectrum and the observed fluxes for the event of 1972 August 2. A distribution of the number of non-thermal electrons with height, and a total number of 10³², were obtained. Also it was found that the Langmuir waves can accelerate some background thermal electrons to the MeV range.     

Energy Gain of Positive Ions in Solar Polar Coronal Holes

We have investigated heating of solar polar coronal holes and acceleration of fast solar wind by means of lower hybrid (LH) waves. A three-fluid Maxwell model comprising electrons, protons, and α-particles is employed at around two solar radii heliocentric distance, where wave dissipation starts to be dominated by collisionless processes. We suggest specific wavenumber ranges corresponding to LH as well as stochastic instabilities and find that these instabilities may bring about a significant energy gain in positive ions.     

Electromagnetic Models of Compact Radio Sources and Circular Polarisation

An electromagnetic model of relativistic jets is outlined. It is suggested that these jets be interpreted as current flows and that they owe their persistence and collimation to the pinching action of the magnetic field. Such structures are unstable and it is suggested that the nonlinear development of these instabilities involves the formation of an electromagnetic turbulence spectrum. This turbulence may be responsible for the acceleration of relativistic electrons and positrons. It may also provide the electromagnetic field in which these electrons and positrons radiate. Some mechanisms through which circular polarisation may be created in this environment are outlined.     

Electron acoustic double layers in a plasma with a <Emphasis Type="Italic">q</Emphasis>-nonextensive electron velocity distribution

Electron-acoustic double-layers (EA-DLs) are addressed in a plasma with a q-nonextensive electron velocity distribution. The domain of their allowable Mach numbers depends drastically on the plasma parameters and, in particular, on the electron nonextensivity. As the electrons evolve far away from their thermodynamic equilibrium, the negative EA-DLs shrinks and may develop into compressive EA-DLs. Our results may be relevant to the double-layers observed both in the auroral region and the plasma sheet of Earth’s magnetosphere (during enhanced magnetic activity). These DLs associated parallel electric fields are thought to be responsible for particle (electrons and ions) acceleration. Furthermore, our theoretical analysis brings a possibility to develop more refined theories of nonlinear cosmic DLs that may occur in astrophysical plasmas.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

Plasma instability in relativistic jets

Based on the Maxwel-Vlasov equations, we consider the possible generation mechanisms of hard emission through the growth of plasma instabilities in a relativistic jet composed of electrons and protons. The accelerated material of the jet moves by inertia. When a small difference arises between the electron and proton velocities (which may result from the interaction of jet material with background plasma or from the acceleration mechanism) plasma instabilities can grow. The particle distribution functions, which were initially delta functions both in angle and in energy, transform into complex angular and energy dependences. In this case, the probability of collisions between high-energy particles in the jet increases, resulting in hard gamma-ray emission.     

Field-aligned currents and auroral acceleration by non-linear MHD waves

This paper examines the consequences of the assumption that substorm-associated growth of magnetosphere-ionosphere current systems is triggered by the incidence, on the ionosphere, of a large amplitude Alfvén wave generated in the distant magnetotail. It is pointed out that there is a large body of evidence suggesting that, in the acceleration region near 1 R_E, one is likely to find a major discontinuity in mass density. Following the approach of Cohen and Kulsrud (1974) who studied the steepening of large amplitude hydromagnetic waves into shocks, we demonstrate that the character of the background plasma and magnetic field in the auroral acceleration region near 1 R_E can be ideal for the generation of MHD shocks and that these shocks can lead to the acceleration of ions and electrons as reported by investigators using S3-3 satellite data.     

Loop heating by D.C. electric current and electromagnetic wave emissions simulated by 3-D EM particle code

We have shown that a current-carrying plasma loop can be heated by magnetic pinch driven by the pressure imbalance between inside and outside the loop, using a 3-dimensional electromagnetic (EM) particle code. Both electrons and ions in the loop can be heated in the direction perpendicular to the ambient magnetic field, therefore the perpendicular temperature can be increased about 10 times compared with the parallel temperature. This temperature anisotropy produced by the magnetic pinch heating can induce a plasma instability, by which high-frequency electromagnetic waves can be excited. The plasma current which is enhanced by the magnetic pinch can also excite a kinetic kink instability, which can heat ions perpendicular to the magnetic field. The heating mechanism of ions as well as the electromagnetic emission could be important for an understanding of the coronal loop heating and the electromagnetic wave emissions from active coronal regions.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.