Small scale Alfvénic structures
First working team meeting at ISSI, Bern, 24-28 March, 1998

Summary of the meeting.
The meeting started with a welcome speech and an introduction to ISSI activities presented by Bengt Hultqvist, director of ISSI. The participants made a review of the observations and theories related to small scale Alfvénic structures in the magnetosphere and in the laboratory plasma. By small scale it is meant  here structures with perpendicular width on the order of few electron skin depths in the ionosphere (100-1000 m).

The participants agreed that:

• Alfvén waves and structures with short perpendicular wavelength represent challenging and not yet resolved problem in the magnetospheric physics, which is of fundamental importance for transfer and dissipation of the solar wind energy throughout the magnetosphere.
• Laboratory experiments performed in the parameter regime encountered in space provide complementary information needed to understand the space measurements and to check validity of theoretical models.
• Clarification of SKAW terminology is needed: The structures observed on Freja are clearly IAW (Inertial Alfvén Wave) structures with thickness of a few electron skin depth. Although they show sometimes fine features on a shorter scale comparable to the ion gyroradius - the use of SKAW term is missleading.
• The next meeting will be held in October 1998.

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1. Observations and Measurements

1.1. Optical Observations of Discrete Structures (T. Trondsen material, presented by KS).
Participants would like ground based observers to address the following topics:
(a) Time scales related to discrete structures: frequency, growth and decay times.
(b) Typical shapes and distortion patterns. Evolution in time, motion in space.
(c) Correlate optical structures with satellite measurements.

1.2. Satellite measurements

1.2.1. Freja observations (h=1200-1700 km) (K. Stasiewicz, J.-E. Wahlund)
Freja observations published in several articles can be summarized as follows:
(a) magnetic structures (100-1000 m) with gradients equivalent to currents of 50-300 mA/m²
(b) associated density depletions up to 50%
(c) electric field amplitude consistent with e/b=V_A.
(d) large parallel electric fields.
(e) accelerated electron fluxes (bursts)
(f) presence (in the vicinity) of perpendicularly accelerated ions (conics)
(g) signatures of the kinetic effects at smaller scales corresponding to ion gyroradius (ca 20 m).
(e) Integrated hot electron current much smaller than the magnetometer current (cold electrons are main current carriers?)
(f) Broadband waves in the vicinity of Alfvénic structures

Problems/tasks:
- Separation between spatial and temporal variations, what is the wave frequency?
- How deep are plasma cavities?  how often associated with IAW?
- The measurements indicate E_// which is sometimes much larger (tens of mV/m) than expected from an Alfvén wave relation (tens of mV/m). Is this related to anomalous resistivity, electrostatic structure within IAW, or it is an instrumental effect?
- How the ions are energized?
- electron acceleration by AW: spatial/temporal relations between suprathermal electron bursts and current channels.
- are small scale bursts temporary or narrow stationary structures?
- higher frequency emissions inside the structures
- Energy flux: particles energy and EM fields energy (Poynting flux)

1.2.2. Observations by Fast (h=400-4000 km) (C. Chaston)
(a) At lower altitudes (h=1500 km) density and electromagnetic structures similar to those on Freja (only few preliminary findings).
(b) Apparently electrostatic character of the observed structures at higher altitudes (h=4000 km).
(c) Large scale inverted-V structures consistent with electrostatic potential integrated along the trajectory.
(d) Integrated hot electron current consistent with magnetometer current (hot electron are current carriers!)

Problems/tasks:
- Why the ion beam energy is often larger than the potential below the satellite?
- Errors in the potential integration caused by wave electric fields
- Find out whether small magnetic field component can be explained by high Alfvén speed (i.e. very low density)
- typical electron density in large scale cavities 1 cm^-3 at 4000 km compared with 1000 cm^-3 at Freja altitude (1500 km) indicates strong parallel density gradient. Implications for theoretical models: wave reflections, mode conversions?
- What is relation between large scale cavities observed on Fast (Viking) and Alfvénic structures observed at lower altitudes.

1.2.3. Observations on POLAR (4-8 Re) (presented by K. Stasiewicz)
(a) In the cusp and in the night side auroral oval strong structuring of the magnetic field: compressional and shear like.
(b) Extreme magnetic structures in the outer cusp and near the magnetopause (very small B).

Problems/tasks:
- check mapping of the structures along the field lines
- compute EM energy flow, try to combine different altitudes: i.e. Polar ->Fast (Viking) -> Freja.

1.3. Laboratory experiments at UCLA (J. Maggs)
(a) Small scale Alfvén waves studied in the inertial and kinetic plasma regime: (V_th/V_A)²=0.2-8.
(b) Propagation of single frequency Alfvén waves launched from disk exciters with skin depth scale size observed and theoretically modeled in both inertial and kinetic regimes. Verification of the spreading of energy across field lines.
(c) Impressive 3D tomography of currents associated with a propagating AW.
(d) Drift Alfvén waves and inertial Alfvén waves are observed to grow spontaneously in pre-existing magnetic field aligned density striations. These fluctuations exhibit an eigenmode structure with the primary frequency determined by the length of the striation. The properties of the fluctuations are well explained by a full electromagnetic description.

Problems/tasks:
- Experimentally investigate the effects of smaller ion gyroradius to electron inertial lengths by going to larger electron inertial lengths.
- Launch waves using a phased array in both the perpendicular and parallel directions. Look for Alfvén wings.
- Launch waves from a disk antenna using a pulse as input signal.
- Look for focusing from Alfvén lens effect by heating the center of the plasma.
- Model compressionally driven field line resonance.
- Test predictions of full electromagnetic theory for a striation with Freja parameters.

2. Theoretical Models

2.1. Inertial Alfvén Waves

P. M. Bellan
Cone pattern excited by an impulse. Inertial Alfvén waves propagate in a plasma having b < m_e/m_i and form Alfvén cones when excited by a localized source oscillating as exp(-iwt). If the source is a temporal pulse, then the source will excite a family of nested, coaxial cones so that observers at different locations will intercept different members of the family of cones and see different frequencies. The structure resulting from this superposition of cones could explain ground observations attributed earlier to field line resonances and would require an impulsive source in the magnetotail at 100-200 Re.

Ponderomotive Force of Inertial Alfvén wave  is shown to be dominated by Ez²/w². The parallel electric field Ez is simply related to the parallel current by Ez/w~Jz so cavities due to ponderomotive force should occur at locations where Jz² is large. Freja data allows estimation of Jz by interpreting apparent magnetic oscillations in the spacecraft frame as convective motion across magnetic gradients. The density cavities predicted from the measured Jz² are coincident with the observed cavities and have the right order of magnitude.

Alfvén Wave radiation. Collisionless reconnection requires some sort of energy sink to provide an effective resistivity. This resistivity relates the electric field associated with flux annihilation to currents associated with change in magnetic topology. Reconnection in a low beta plasma involves formation of an x-point in the plane perpendicular to the main Bz field. Comparison of the magnetic geometry before and after formation of the x-point shows that the change in magnetic geometry is associated with a transient field-aligned current at the x-point. In resistive reconnection, actual Spitzer resistivity provides an electric field Ez =hJz along the transient current and Ez represents the rate at which flux is annihilated. If the plasma is collisionless, then h is essentially zero so that flux cannot be annihilated. A new model is proposed to provide the effective resistivity needed for Collisionless reconnection. Unlike past models for reconnection, it is stressed that the reconnection region is of finite axial extent so that the transient field-aligned current is also of finite axial extent. It is argued that the longest reasonable length h for this current filament is h=v_At_reconnection . The length could not exceed this, because then all elements of the antenna would have to act in synchronism (assumed) without being able to communicate with each other (information can only propagate at the Alfvén velocity). The finite length field-aligned current has precisely the geometry required for the excitation of Alfvén waves so it can be considered as an antenna radiated a pulse of Alfvén waves (either inertial or kinetic depending on the plasma beta). The radiation represents a real power loss from the antenna which is manifested as a radiation resistance experienced by the antenna current. The radiation resistance results from retarded time effects on the E.J power relation describing each element of the antenna. The retarded time means that the field calculated at any element is a sum of contributions to the vector potential from the currents in other elements, evaluated with time retardation taken into account. Without time retardation, the electric field is always reactive, but with time retardation, the electric field has an in-phase component resulting in real power loss. The retarded time involves the Alfvén velocity; i.e., the contribution from each element must be evaluated at the time t-d/v_A where d is the distance to the element. The entire radiated power from the antenna can be calculated from the Poynting flux of a surface enclosing the antenna. By choosing an appropriate surface, the calculation becomes feasible and the radiated power is proportional to the square of the antenna current. Writing P=I²*R allows determination of the effective antenna resistance. Assuming the antenna radius is of the order of a l_perp of the Alfvén wave (inertial or kinetic as appropriate) and the length is of the order of the Alfvén parallel wavelength, allows evaluation of the effective resistivity associated with the antenna region. It is found for many situations of interest that this effective resistivity is adequate to provide the anomalous resistivity required for magnetic fields to diffuse a distance equal to the thickness of the antenna (i.e., the thickness of the current filament) in the time assumed for the reconnection. Thus, it is proposed that radiation of Alfvén waves is intrinsic to reconnection and provides the power loading required for reconnection in many collisionless situations.

Tasks:
- Determine the relevance of finite source dimensions to the excitation of pulsed Alfvén cones.
- Provide the IAW equations in dimensionless form.
- Examine ponderomotive effects in sheet geometry as well as cylindrical.
- Relate the experimental results of M. Ono (Phys. Rev. Letter, vol. 42, p.1267, (1979)) which describe inertial cones and Landau damping to IAW issues.
- Consider self-consistent models for the ponderomotive force where the IAW propagation is affected by the density cavity dug by the IAW. For example, ducting might occur where an intense IAW is trapped within its own cavity.
- Calculate the signature (feather patterns) of the electric and magnetic fields observed by a spacecraft transiting an IAW cone with different impact parameters.
- Consider the effect of second harmonics associated with IAW nonlinearities. Do these generate new cones with different angles?
- Make a statistical study of the density cavities and Jz² measurements from Freja data to see if the depth of the cavities is statistically proportional to Jz².

2.2. Kinetic effects in AW with small cross-field scale sizes

J. Maggs
Transition between the inertial and kinetic regime:
Using the full plasma dispersion function in the description of the electron dynamics changes wave dispersion at large values of k_perpd_e, so that the resonance cone behavior of the inertial Alfvén wave is modified. This effect leads to the conclusion that only a limited range of perpendicular wave numbers can be trapped as required for the field line resonance concept. Also at values of k_perpd_e larger than three wave dissipation is important.

Heated ions play an important role in forming density cavities. The parallel electric field of the Alfvén wave and its low frequency lead to generation of electron streams with speeds faster than the thermal speed. This process triggers the Buneman instability, heats the electrons and generates spatially localized electric fields near the lower hybrid resonance frequency. The process of transit time acceleration leads to strong ion heating, expelling ions from the localized electric field region so that a density cavity is subsequently produced.

Tasks:
- Investigate the role of wave frequency on the process of density channel formation. The time for electron acceleration in the higher frequency waves (i.e., waves with frequencies near 10 Hz) may not be sufficient to trigger the Buneman instability

C. Seyler:
Stringer diagram for normal modes indicates that the linear waves of greatest interest are on the intermediate frequency branch and correspond to ratios of kz/kx smaller than the square root of the mass ratio. In this range, the electrostatic potential response is ion polarization at large scales (AW) and ion Boltzmann at scales smaller than the ion gyroradius corresponding to slow ion acoustic waves (SIA). This has been used as a diagnostic for SIA wave detection and for the identification of the characteristic IAW large amplitude spike as an ion Boltzmann response to a steepened density gradient. Clarification of SKAW terminology is needed: It is a short wavelength ion Boltzmann response feature occurring frequently on the top of, but not to be confused with a larger IAW structure.

Compressible solitary wave solutions are only possible only in the kinetic regime at scales smaller than the ion acoustic gyroradius and not at the inertial electron length. Nonlinear wave steepening appears to be an important mechanism in determining waveform morphology, shorter scale wave emission as well as in producing suprathermal electron bursts. Kinetic effects associated with steepening of AW were shown to lead to emission of meter to 10 meter scale SIA waves. These waves can only exist in a hot ion environment. The features of suprathermal electron bursts can only be reproduced by one-dimensional oblique kinetic simulations if a hot ion background is assumed.

Numerical solutions for IAW cones including density variations and parallel advective nonlinearity show some of the characteristic electric and density features of Freja IAW and SKAW. At this point in time, a self-consistent formation of a density cavity has not been found. But this is a very preliminary result.

Tasks:
- Two-dimensional, non-linear x-z simulations of IAW. Two types of simulations are planned. Alfvén wing emission from a zero frequency drifting potential disturbance and a stationary source of non zero frequency which generates Alfvén cones. Two dimensions are necessary in order to allow for different ratios of kz/kz. Further tests for possible self consistent cavity formation will also be performed.
- Three dimensional simulations to determine if Alfvén vortices can form from IAW emission from magnetospheric source/boundary condition. The model is capable of examining patchy reconnection and its possible influence on IAW structure. Simulated satellite cuts through the simulation can be compared to B-field feather plots/hodograms which suggest multidimensional structure in the observations.

2.3. Dispersive Field Line Resonances

A. Streltsov
Formation and spatial structure of small scale field line resonance (FLR) layers formed by shear Alfvén waves standing along auroral magnetic field lines between ionospheres are presented. Current model written in dipole magnetic field geometry includes full ion Larmour radius correction, which makes it suitable for investigation of extremely narrow (up to several hundreds meters at the ionospheric altitudes) electromagnetic structures. The results show that: hot magnetospheric ions significantly retard the development of parallel electric field in dispersive Alfvén waves; a fundamental FLR with eigenperiod ~90 s, forming near L=7.5 can contract to a transverse scale sizes about 800 m and produce parallel potential drop up to 2 kV between ionosphere and ~3-4 Re altitude. Introduction of the anomalous resistivity in the model allows to extend obtained results on observed auroral structures with significantly large transverse scales. The model with anomalous resistivity shows an impressive accuracy when was used to model set of FAST observations.

Tasks:
- By using basically the same numerical code (just adjusted for the geometry and background parameters),  model some basic events observed in experiments on LAPD.
- Investigate different possible mechanisms leading to the same effects as anomalous resistivity.
- Model/reproduce several other experimental data sets from FAST and FREJA satellites.

Problems:
- Some ground based observations (Samson et al., 1991) show the ULF pulsation with period of 300-600 s, which cannot be explained by the presented model for FLR.

P. Bellan : The field line resonance problem is revisited using cold 2-fluid theory with finite me and finite Ez. Box geometry is used with a density gradient in the x direction, and prescribed ky and kz. It is shown that the Poynting flux is conserved everywhere, including at the Alfvén layer so that there cannot be any accumulation of energy at the Alfvén layer. The x component of the Poynting flux involves two terms. One term is the product of Ey and Bz and corresponds to the fast (MHD) mode. The other term is the product of Ez and By and corresponds to the IAW mode. Ideal MHD neglects the IAW mode, because ideal MHD invokes Ez=0. A manipulation of the wave equations shows that the sum of the two terms is a constant and shows that there cannot be any accumulation of energy. If the IAW term is neglected as in ideal MHD, then it appears that there will be an accumulation at the Alfvén layer. Taking the IAW term into account shows that incident fast wave power is either mode converted or reflected, but cannot resonantly build up at the Alfvén layer.
 
 

2.4. Alfvén solitons and vortices

O. Pokhotelov
Introduced the reduced 2D non-linear MHD equations which describe the propagation of solitary Alfvén structures in inhomogeneous magnetospheric plasma. In contrast to the 1D case these equations contain the non linearity in the form of Jacobian (vector non linearity). The theoretical treatment was carried out both in inertial and kinetic type regimes and the equations under study are assumed to be valid both for relatively low and high altitudes. Similar to the case of Hasegawa-Mima equation these non-linear equations have a stationary solutions of Larichev-Reznik type, e.g. dipole solutions or solutions in the form of a vortex streets. The temporal evolution of the initial perturbations governed by these non-linear equations are also studied in a simplified case of convective cells when the dependence of the perturbations along the external magnetic field is illuminated. It is demonstrated that various forms of auroral structures (e.g., folds, spirals and vortex chains) may be obtained as a result of numerical simulation of non-linear equations for convective cells. The initial data on observations of 2D solitary Alfvén structures on board the IC-Bulgaria 1300 were presented which are in a qualitative agreement with the theory under study.

Problems:
- It is unclear what kind of non-linear phenomena are involved in the transition region.
- What kind of acceleration process are involved in the creation of a precursor in particle measurements.

Tasks:
- It is necessary to carry out a detailed comparison of the predictions of non-linear theory with the existing satellite data (Freja, Polar).
- Study the role of ponderomotive forces accounting for the effects of self-action and divergence of the ambient magnetic field.
- Modify  the theory of feedback resonance.