Dipole Magnetic Field Geometry Research Articles

Ionospheric Alfvén resonator and aurora: Modeling of MICA observations

AbstractWe present results from a numerical study of small‐scale, intense magnetic field‐aligned currents observed in the vicinity of the discrete auroral arc by the Magnetosphere‐Ionosphere Coupling in the Alfvén Resonator (MICA) sounding rocket launched from Poker Flat, Alaska, on 19 February 2012. The goal of the MICA project was to investigate the hypothesis that such currents can be produced inside the ionospheric Alfvén resonator by the ionospheric feedback instability (IFI) driven by the system of large‐scale magnetic field‐aligned currents interacting with the ionosphere. The trajectory of the MICA rocket crossed two discrete auroral arcs and detected packages of intense, small‐scale currents at the edges of these arcs, in the most favorable location for the development of the ionospheric feedback instability, predicted by the IFI theory. Simulations of the reduced MHD model derived in the dipole magnetic field geometry with realistic background parameters confirm that IFI indeed generates small‐scale ULF waves inside the ionospheric Alfvén resonator with frequency, scale size, and amplitude showing a good, quantitative agreement with the observations. The comparison between numerical results and observations was performed by “flying” a virtual MICA rocket through the computational domain, and this comparison shows that, for example, the waves generated in the numerical model have frequencies in the range from 0.30 to 0.45 Hz, and the waves detected by the MICA rocket have frequencies in the range from 0.18 to 0.50 Hz.

Magnetospheric resonances at low and middle latitudes

AbstractWe present results from a numerical study of structure and dynamics of dispersive Alfvén waves in the near‐Earth magnetosphere containing proton radiation belt (near L = 1.5 dipole magnetic shell). The interest in this problem is motivated by numerous observations of magnetic oscillations with frequencies in the range of 0.1–4.0 Hz detected on the ground at low and middle latitudes. In a number of studies these oscillations interpreted as shear Alfvén waves standing inside the so‐called ionospheric Alfvén resonator. We present results from two‐dimensional, time‐dependent simulations of the reduced two‐fluid MHD model performed in the dipole magnetic field geometry with the realistic parameters of the magnetospheric plasma. These simulations show that these pulsations can be produced by the fundamental mode of the global field line resonator, spanning the entire magnetic field line in the low or middle magnetosphere. Simulations also show that even the waves with the highest considered frequencies (2.44 Hz) are not trapped inside the ionospheric resonator. Therefore, if these waves will be generated by some ionospheric source, then they can reach the equatorial magnetosphere and interact with energetic protons in the proton radiation belt.

Feedback instability analysis for dipole configuration with ionospheric and magnetospheric cavities

[1] Linear eigenmodes of ionospheric feedback instability in the dipole magnetic field geometry are investigated by considering the ionospheric and magnetospheric resonant cavities with inhomogeneous Alfven velocity profiles. The two-field reduced magnetohydrodynamic model is used to describe shear Alfven wave dynamics, associated with auroral arcs, in a strongly nonuniform magnetic flux tube. Linear properties of ionospheric cavity modes (eigenfrequency and eigenfunctions) are examined for a wider parameter range than the previous works. It is found that several harmonics, denoted by the mode numbers of n = 3, 6–7, 10–11, …, are trapped in the cavity region, and their magnetic fluctuations have a large amplitude at the ionosphere, leading to a high growth rate. By steepening a gradient of the Alfven velocity on the magnetospheric side, the properties of ionospheric cavity modes are fully dismissed from these low n harmonics, although their growth rates remain small positive values. On the other hand, the fundamental field line resonant mode (n = 0) has a high growth rate with a large amplitude of magnetic fluctuations at the ionosphere owing to the magnetospheric cavity. Possible spatial and temporal scales of auroral arcs and ULF wave resonances in a realistic situation are discussed.

Excitation of the ionospheric Alfvén resonator from the ground: Theory and experiments

[1] We report results from numerical and experimental studies of the excitation of ULF shear Alfvén waves inside the ionospheric Alfvén resonator (IAR) by heating the ionosphere with powerful HF waves launched from the High Frequency Active Auroral Research Program (HAARP) facility in Alaska. Numerical simulations of the two-fluid MHD model describing IAR in a dipole magnetic field geometry with plasma parameters taken from the observations at HAARP during the October–November 2010 experimental campaign reveal that the IAR quality is higher during nighttime conditions, when the ionospheric conductivity is very low. Simulations also reveal that the resonance wave cannot be identified from the magnetic measurements on the ground or at an altitude above 600 km because the magnetic field in this wave has nodes on both ends of the resonator, and the best way to detect IAR modes is by measuring the electric field on low Earth orbit satellites. These theoretical predictions are in good, quantitative agreement with results from observations: In particular, (1) observations from the ground-based magnetometer at the HAARP site demonstrate no significant difference in the amplitudes of the magnetic field generated by HAARP in the frequency range from 0 to 5 Hz, and (2) the DEMETER satellite detected the electric field of the IAR first harmonic at an altitude of 670 km above HAARP during the heating experiment.

Propagation of whistler mode waves with a modulated frequency in the magnetosphere

This paper presents results from experimental and numerical studies of the propagation of whistler mode waves in the Earth's magnetosphere. An experiment conducted at the High Frequency Active Auroral Research Program (HAARP) on 16 March 2008 demonstrates that ionospherically generated waves with particular frequency‐time formats are amplified on their pass from HAARP to the conjugate location in the South Pacific Ocean more efficiently than waves with a constant frequency. Numerical simulations of a one‐dimensional electron magnetohydrodynamics (MHD) model in the dipole magnetic field geometry reveal that the amplification takes place more efficiently when the frequency of the whistler mode waves (in the frequency range from 0.5 to 1.0 kHz) changes in the equatorial magnetosphere with the rate from 0.25 to 0.47 kHz/s. The maximum amplification occurs when this rate is 0.33 kHz/s and no/very little amplification is observed when this gradient is equal to 0 or when it is larger than 0.78 kHz/s.

Coupling between density structures, electromagnetic waves and ionospheric feedback in the auroral zone

This paper presents results from a numerical study of nonlinear interactions between ultra‐low‐frequency (ULF) electromagnetic waves and the magnetospheric‐ionospheric plasma at high latitudes. The study is motivated by observations of density cavities in the ionosphere in regions of downward field‐aligned current adjacent to auroral arcs. The role of active ionospheric feedback in the development of intense, small‐scale electromagnetic waves with frequencies of 0.1–1 Hz is considered, together with the effects of the waves on the ion dynamics. The numerical results are based on a reduced two‐fluid MHD model that self‐consistently describes shear Alfvén waves, ion parallel dynamics, and effects of ionospheric E‐region activity and magnetosphere‐ionosphere feedback instability. Numerical simulations performed in dipole magnetic field geometry with realistic parameters of the ambient plasma show that, under some conditions, ionospheric feedback gives rise to intense ULF electromagnetic waves, which, via the ponderomotive force, produce density cavities in the bottomside ionosphere (between the E‐ and F‐region peaks) and an associated upwelling of the topside ionosphere. The simulated magnitude and spatial and temporal scales of the cavities match the corresponding parameters of cavities observed with ground‐based radars.

Störmer theory applied to magnetic spacecraft shielding

The existence of a toroidal region from which charged particles are excluded was demonstrated by Störmer (1955) for a dipole magnetic field geometry. Using a standard numerical code to trace the trajectories of particles in a magnetic field, we find excellent agreement with the predicted region for a variety of particle energies and masses. The ability of magnetic fields to shield certain regions from energetic particles, such as galactic cosmic rays (GCRs), has led to the suggestion that certain magnetic field configurations could be used to shield the occupants of a spacecraft from the harmful effects of GCRs during interplanetary space travel. In particular, systems involving a deployed superconducting coil of wire that extends well beyond the dimensions of the spacecraft have been proposed as a viable solution to shielding GCRs. The correct use of the analysis by Störmer (1955) requires that the radius of such a coil be much smaller than the dimension of the region being shielded. Alternatively, it is shown that the energy of the particles shielded from a given region decreases as the radius of a coil with a constant magnetic moment increases. The reality is that large magnetic fields, and thus currents, are necessary to adequately shield GCRs, neither of which are provided by deployed magnetic shields.

Computing magnetospheric mass density from field line resonances in a realistic magnetic field geometry

Ultra‐low‐frequency (ULF) field line resonances can be used to infer the mass density along magnetospheric magnetic field lines. By specifying how mass density is distributed along the magnetic field (usually a power law as a function of distance from the Earth) and a dipole magnetic field geometry, the MHD standing wave equation can be analytically solved and mass density inferred from observed field line eigenfrequencies. However, the geometry of the Earth's magnetic field can deviate significantly from a dipole, even at relatively low L shells and on the dayside magnetosphere. This study investigates the importance of including a realistic magnetic field geometry when computing plasma mass density from observed field line eigenfrequencies. A generalized version of the toroidal mode MHD standing wave equation is solved using the Tsyganenko (2002a, 2002b) empirical magnetic field model (T01). The results are compared to those found using a dipole. We find that assuming a dipole magnetic field geometry results in an overestimation of mass density. The overestimation is larger for more disturbed levels of geomagnetic activity. Our results have important implications for the inference of heavy ions in the magnetosphere. Namely, an increase in heavy ion concentration as a result of enhanced geomagnetic activity will be exaggerated unless the proper magnetic field geometry is taken into account when calculating mass density from field line eigenfrequencies.

The Radio Spectrum of TVLM 513‐46546: Constraints on the Coronal Properties of a Late M Dwarf

We explore the radio emission from the M9 dwarf TVLM 513-46546 at multiple radio frequencies, determining the flux spectrum of persistent radio emission, as well as constraining the levels of circular polarization. Detections at both 3.6 and 6 cm provide a spectral index measurement α (where Sν ∝ να) of -0.4 ± 0.1. A detection at 20 cm suggests that the spectral peak is between 1.4 and 5 GHz. The most stringent upper limits on circular polarization are at 3.6 and 6 cm, with V/I < 15%. These characteristics agree well with those of typical parameters for early- to mid-type M dwarfs, confirming that magnetic activity is present at levels comparable with those extrapolated from earlier M dwarfs. We apply analytic models to investigate the coronal properties under simple assumptions of dipole magnetic field geometry and radially varying nonthermal electron density distributions. Requiring the spectrum to be optically thin at frequencies higher than 5 GHz and reproducing the observed 3.6 cm fluxes constrains the magnetic field at the base to be less than about 500 G. There is no statistically significant periodicity in the 3.6 cm light curve, but it is consistent with low-level variability.

Harmonic structure of field line eigenmodes generated by ionospheric feedback instability

Ionospheric feedback instability generates field line eigenmodes under favorable conditions of low ionospheric conductivity and high electric convection. A numerical study has been performed using a two‐dimensional model in dipole magnetic field geometry that includes active ionospheric feedback and shear Alfvén wave dynamics of the magnetospheric response. Strong parallel inhomogeneities of the magnetospheric parameters included in the numerical model permit the simultaneous development of local ionospheric resonator modes (fast feedback) trapped between the ionosphere and Alfvén speed maximum above it and field line eigenmodes (slow feedback) that stand along the entire magnetic field line between two conjugate ionospheres. Fourier analysis of the numerical solution has been used to investigate the relative contribution of fast and slow feedback in the global dynamics of magnetosphere–ionosphere coupling. While many harmonics of the global magnetospheric resonator can be simultaneously generated by the ionospheric feedback instability, all modes above the fundamental eigenmode are strongly suppressed by Alfvén wave dispersion. The numerical results suggest that ionospheric feedback is a generating mechanism for the formation of narrow field line resonances.

The dynamics of current carriers in standing Alfvén waves: Parallel electric fields in the auroral acceleration region

The acceleration of current carriers in an Alfvén wave current system is considered. The model incorporates a dipole magnetic field geometry, and we present an analytical solution of the two‐fluid equations by successive approximations. The leading solution corresponds to the familiar single‐fluid toroidal oscillations. The next order describes the nonlinear dynamics of electrons responsible for carrying a few μAm−2 field aligned current into the ionosphere. The solution shows how most of the electron acceleration in the magnetosphere occurs within 1 RE of the ionosphere, and that a parallel electric field of the order of 1 mVm−1 is responsible for energising the electrons to 1 keV. The limitations of the electron fluid approximation are considered, and a qualitative solution including electron beams and a modified E∥ is developed in accord with observations. We find that the electron acceleration can be nonlinear, (ve∥∇∥)ve∥ &gt; ωve∥, as a result of our nonuniform equilibrium field geometry even when ve∥ is less than the Alfvén speed. Our calculation also elucidates the processes through which E∥ is generated and supported.

Dispersive width of the Alfvénic field line resonance

The results from a numerical investigation of the dependence of the eigenfrequency and structure of Alfvénic field line resonance (FLR) layers on the dispersion of the resonant Alfvén waves are presented. The investigation is based on the linear, reduced, two‐fluid MHD‐kinetic model considered in the dipole magnetic field geometry with a realistic distribution of the background plasma parameters along the entire auroral flux tube. It is shown that (1) dispersion of the small‐scale Alfvén wave due to the finite electron inertia (inertial dispersions) decreases the eigenfrequency of the Alfvénic FLR and broadens the FLR layer in the direction along the transverse gradient in the background Alfvén speed; (2) dispersion of the wave due to the finite plasma temperature (kinetic dispersion) increases the FLR eigenfrequency and broadens the resonance layer in the opposite direction; and (3) on the field line where the effect of the kinetic dispersion balances the effect of the inertial dispersion, the eigenfrequency becomes independent of the transverse wavelength of the resonant wave. As a result, a FLR occurring on such a particular field line develops fields and currents with smaller transverse scale sizes and larger amplitudes than FLRs on field lines where inertial and kinetic dispersions are not in a balance.

Three‐dimensional simulations of the ionospheric plasma transport in the presence of the structured field‐aligned flows

Recent observations from the Preja and FAST satellites as well as earlier observations from OGO 5, Heos 2, and DE 2 indicate the presence of fine structures in the field‐aligned plasma flows. We have simulated the effects of such structures on ionospheric plasma transport processes, using our three‐dimensional large‐scale, multimoment, multifluid model. The model solves the continuity, momentum and double adiabatic energy equations with anisotropic ion temperatures in the field line coordinates from 1500 km to 10 RE. It includes important physics of the ionosphere‐magnetosphere coupling region, such as the mirror force and generalized ambipolar electric field in a dipole magnetic field geometry. Freja satellite observations of the structured field‐aligned currents were used as input parameters in the simulation. It has been shown that in the presence of the field‐aligned current filaments with sufficiently small transverse scale sizes, the transverse transport can play a dominant role in the overall plasma response processes in the ionosphere‐magnetosphere coupling region. For example, the local changes in parallel flow velocity due to transverse transport, l min after the structured field‐aligned current application, may be &gt; 30%. The plasma response time due to transverse transport has been found to be shorter than that due to parallel transport. The difference is more pronounced at higher altitudes.

A Geometrical origin of the Pulsar Core and Conal Emissions

We have analysed the dipole magnetic field geometry for the general case of an oblique rotator and have found that open field lines which define the polar cap divide into two branches (Kapoor and Shukre 1996) which appear naturally relevant for distinguishing the core and conal emissions. The polar cap shape is actually determined by a quadratic equation having two roots leading to two values of the polar angle,θ+andθ−with respect to the magnetic axis for a given azimuth φ. For the north pole bothθ+andθ−branches are shown as polar plots in Fig. 1 for various inclination angles α and a typical pulsar period. The discussion of pulsar polar caps hitherto (e.g. Biggs 1990) had not distinguished between theθ+and theθ−solutions. The region defined by theθ+solution is completely contained inside the polar cap. It has a peculiar triangular shape whose lowest vertex is always on the magnetic axis. This naturally suggests an identification of theθ+and theθ−regions with the core and conal emission zones.

Resonant Alfvén waves on auroral field lines

It is shown that resonant Alfvén waves on dipole magnetic field geometry and plasma distributions suitable for auroral field lines can be conveniently treated in the theory of Mathieu functions. Resurgent interest in invoking large‐scale Alfvén waves to structure some elements of auroral electrodynamics calls for interpretation of measured perpendicular electric and magnetic disturbance fields in terms of Alfvén waves. The ability to express the resonant eigenmodes in closed form in terms of Mathieu functions allows for convenient tests of the Alfvén wave structuring hypothesis. Implications for current vector electric and magnetic disturbance measurements are discussed.