Relativistic Landau damping of longitudinal waves in isotropic pair plasmas

Landau damping is described in relativistic electron-positron plasmas. Relativistic electron-positron plasma theory contains important new effects when compared with classical plasmas. For example, there are undamped superluminal wave modes arising from both a continuous and discrete mode structure, the former even in the classical limit. We present here a comprehensive analytical treatment of the general case resulting in a compact and useful form for the dispersion relation. The classical pair-plasma case is addressed, for completeness, in an appendix

The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journa

Collisionless Magnetic Reconnection via Alfven Eigenmodes

We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical waves are confined by the tanh^2 potential. The dynamical time scale of reconnection is the system scale divided by the eigenvalue propagation velocity of the n=1 mode. The prediction of the n=1 mode shows good agreement with the in situ measurement of the reconnection-associated Hall fields

Vlasov equation and collisionless hydrodynamics adapted to curved spacetime

The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form

A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU

(Abridged) Turbulence in the solar wind is believed to generate an energy cascade that is supported primarily by Alfv\'en waves or Alfv\'enic fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic scales $k_\perp \rho_i\gtrsim 1$. Linear Landau damping of KAWs increases with increasing wavenumber and at some point the damping becomes so strong that the energy cascade is completely dissipated. A model of the energy cascade process that includes the effects of linear collisionless damping of KAWs and the associated compounding of this damping throughout the cascade process is used to determine the wavenumber where the energy cascade terminates. It is found that this wavenumber occurs approximately when $|\gamma/\omega|\simeq 0.25$, where $\omega(k)$ and $\gamma(k)$ are, respectively, the real frequency and damping rate of KAWs and the ratio $\gamma/\omega$ is evaluated in the limit as the propagation angle approaches 90 degrees relative to the direction of the mean magnetic field.Comment: Submitted to Ap

Adiabatic nonlinear waves with trapped particles: II. Wave dispersion

A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift $\omega_{\rm NL}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $\omega_{\rm NL} \propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic $\omega_{\rm NL}(a)$ is generally nonlocal.Comment: submitted together with Papers I and II

Kinematic dynamo wave in the vicinity of the solar poles

We consider a dynamo wave in the solar convective shell for the kinematic $\alpha\omega$-dynamo model. The spectrum and eigenfunctions of the corresponding equations are derived analytically with the aid of the WKB method. Our main aim here is to investigate the dynamo wave behavior in the vicinity of the solar poles. Explicit expressions for the incident and reflected waves are obtained. The reflected wave is shown to be relatively weak in comparison to the incident wave. The phase shifts and the ratio of amplitudes of the two waves are found.Comment: 20 pages, 2 EPS figure

The chromosphere: gateway to the corona, or the purgatory of solar physics?

I argue that one should attempt to understand the solar chromosphere not only for its own sake, but also if one is interested in the physics of: the corona; astrophysical dynamos; space weather; partially ionized plasmas; heliospheric UV radiation; the transition region. I outline curious observations which I personally find puzzling and deserving of attention.Comment: To appear in the proceedings of the 25th NSO Workshop "Chromospheric Structure and Dynamics. From Old Wisdom to New Insights", Memorie della Societa' Astronomica Italiana, Eds. Tritschler et a

Converging and diverging convection around axisymmetric magnetic flux tubes

A numerical model of idealized sunspots and pores is presented, where axisymmetric cylindrical domains are used with aspect ratios (radius versus depth) up to 4. The model contains a compressible plasma with density and temperature gradients simulating the upper layer of the Sun's convection zone. Non-linear magnetohydrodynamic equations are solved numerically and time-dependent solutions are obtained where the magnetic field is pushed to the centre of the domain by convection cells. This central magnetic flux bundle is maintained by an inner convection cell, situated next to it and with a flow such that there is an inflow at the top of the numerical domain towards the flux bundle. For aspect ratio 4, a large inner cell persists in time, but for lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3 this inner convection cell is smaller, tends to be situated towards the top of the domain next to the flux bundle, and appears and disappears with time. When it is gone, the neighbouring cell (with an opposite sense of rotation, i.e. outflow at the top) pulls the magnetic field away from the central axis. As this happens a new inner cell forms with an inflow which pushes the magnetic field towards the centre. This suggests that to maintain their form, both pores and sunspots need a neighbouring convection cell with inflow at the top towards the magnetic flux bundle. This convection cell does not have to be at the top of the convection zone and could be underneath the penumbral structure around sunspots. For an aspect ratio of 1, there is not enough space in the numerical domain for magnetic flux and convection to separate. In this case the solution oscillates between two steady states: two dominant convection cells threaded by magnetic field and one dominant cell that pushes magnetic flux towards the central axis