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### M-I Coupling Scales and Energy Conversion Processes

MPE-JUB Symposium on Auroral Physics and Plasma Boundary Analysis

MPE, 01- 05 July 2013

Gerhard Haerendel

Max Planck Institute for Extraterrestrial Physics

04 July 2013

Four Scales ?

The internal plasma dynamics in the magnetosphere can generate intrinsic scales, such as dipolarization fronts or possibly the transverse scales of bursty bulk flows. Such scales are either not impressed on the ionosphere or modified by M-I coupling. Other scales, like the width of the oval convection, are determined by the amount of energy injected during a substorm.

When e.m. energy flowing into the ionosphere is subject to a conversion process, another type of intrinsic scales is produced: M-I coupling scales.

Observationally there seem to be four major scales:

- Broad inverted V‘s
- Active auroral arcs
- Alfvénic arcs
- Cold plasma striations

M-I coupling scales

Broad Inverted V‘s

Lyons [1980] suggested that broad inverted V‘s are due to potential drops between source and ionosphere:

leading to an intrinsic scale, linv, sometimesnamed M-I coupling scale, which is of the order of a few 100 km.

This scenario implies afrozen-field relation between source and ionospheric load with energy supplied only from within the current circuit. It would be exhausted within a few Alfvénic transit times.

[Borovsky 1993]

A static model isnot appropriate for auroral arcs. Energy supply from either kinetic or magnetic energy imply dynamic processes, induction electric fields, and Alfvén waves.

Broad inverted-V‘s are composed of several narrow ones [Sakanoi et al. 1995].

Normalized potential drops of 22 inverted-V‘s [Sakanoi et al. 1995].

M-I coupling scales

M-I Coupling and Scale Separation

The transport of energy by Alfvén waves requires at least one reflection.

In the reflection process, there occurs a scale separation into reflected, transmitted, and absorbed waves. The reflection coefficient, R, depends on the transverse scales, [Vogt and Haerendel 1998]:

with the transient scale length:

Since RwSP >> 1, the reflection coefficient is small when , i.e. when wave impedance and effective field-parallel resistance are matching. The downflowing energy is almost completely absorbed.

Much shorter wavelengths are reflected from the acceleration region and much wider ones reflected from the ionosphere. This leads to scale separation, since reflected waves maintain the energy in the generator, while scales near lt allow energy dumping.

M-I coupling scales

Auroral Arcs

The width of auroral arcs isessentially determined by the transient scale length. The underlying impedance matching must be completed within very few reflections, since arcs move with little indication of reflections.

K can vary by almost two orders of magnitude, but not fully independent of the variation of Rw, since both contain the source density.

The particle energy is derived from the release of shear stresses or erosion of free magnetic energy.

M-I coupling scales

Corrected Arc Width

The transient scale length, λt, does not contain the contribution of the ionosphere. In a quasi-stationary situation, the total converted energy flux is derived from the release of magnetic shear stresses:

and converted by the auroral particle acceleration and by dissipation in

the ionosphere: with

With: , , and

one gets a more general expression,

which includes the Pedersen current of the overarching current system.

The contribution of the ionosphere to dumping of the total released energy requires a smaller auroral contribution, i.e. a lower arc width.

M-I coupling scales

Alfvénic Arcs

Alfvénic arcs are characterized bybalanced FACs,strongly structured electric fieldsand e.m. fluctuations of~ 1Hz frequency, ion conics below ~100 eV, andfield-parallel, cool electrons up to several 100 eV.The latter properties point to a near-Earth particle source, i.e. in the topside ionosphere.

They typically precede the poleward expanding arcs during substorm breakup.

The presence of high-frequency magnetic fields of order 1 Hz suggests the existence of transverse and dissipative structures of the order of the electron inertial length,

i.e. ~ 1 km, appear to be created, e.g. by non-linear interactions or multiple reflections in the ionospheric Alfvén resonator[Seyler 1990; Lysak and Song 2002].

M-I coupling scales

Scale Breaking of Alfvénic Arcs

Energies and angular distributions of the particle fluxes point to a near-Earth origin.

While the energy is dominantly deposited in the topside ionosphere, currents close at least partially through the lower ionosphere.

At low altitudes, the ratio of magnetic and

electric perturbation fields,

is found close to the expected Pedersen conductivity, . At high altitudes it is

like the Alfvén wave impedance: i.e. one sees propagating waves.

By depositing their energy in small-scale structures the magnetospheric flows decouple from the lower ionosphere and achieve a high mobility.

M-I coupling scales

Plasma Cloud in the Magnetosphere

A barium plasma cloud released at 5 RE in 1971 broke into several streaks with different mass content but near-equal transverse scale of, about 1 km, if projected to the ionosphere. There were no signs of reflection.

Separation in longitude found consistent with constant acceleration.

M-I coupling scales

Absence of Reflections

The observed absence of sign of reflections at the ionosphere was surprising in the light of the theory of Scholer [1970]. Dependent on the ratio, τA/τ0, the velocity should have changed significantly, even reversed within about 15 Alfvenic transit times, τA, which was of the order of 10 sec.

The theoretical coupling time, , derived from the

observed brigthness distribution, was ~105 sec.

M-I coupling scales

Decoupling by Scale Breaking

Transverse electric convection fields with scales below about 1 km are strongly attenuated and the Pedersen conductivity is reducedbecause of the non-negligible parallel resistivity [Farley, 1959; Scholer, 1970]. A scale leading to:

implies perfect matching of incoming energy flux and ionospheric dissipation, i.e. vanishing reflection coefficient:

Haerendel and Mende [2012] could explain the observed coupling time of the barium streaks to the ionosphere and the absence of observed reflections by scale breaking in the initial acceleration phase.

Effective over normal Pedersen conductivity [Scholer 1970]

M-I coupling scales

Summary

The scale-defining process is the matching between the e.m. energy inflow and its conversion into particle energy or heat.

There are three scales related to three different conversion processes.

- Post-accelerationof magnetospheric electrons above the ionosphere plus ionospheric dissipation
- Energy conversion in the topside ionosphere by breaking into electron inertial scales
- Energy consumption by ohmic and ion-neutral losses in the E/F-regionbywave breaking into scales ofreduced Pedersen conductivity

The scales are chosen so as to optimize the energy dumping to the ionosphere

M-I coupling scales

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