Substorms: Ionospheric Manifestation of Magnetospheric Disturbances P. Song, V. M. Vasyliūnas, and J. Tu University of Massachusetts Lowell Substorms: Defined by ground observations: AE index Originated in the magnetosphere There is an ionosphere between the magnetosphere and ground Conventional (global) ionospheric models Electrostatic: B=constant Ionosphere does not “generate” waves Oscillations in the ionosphere are controlled by the magnetospheric driver Processes at the interface between magnetosphere and ionosphere Magnetospheric wave reflection Wave mode conversion: transmitted waves in the ionosphere are fast modes New M-IT models: Inductive: B changes with time Dynamic: in particular ionospheric motion perpendicular to B Multi fluid: allowing upflows and outflows of different species Wave propagation/reflection: overshoots Summary

M-I Coupling via Waves (Perturbations) The interface between magnetosphere and ionosphere is idealized as a contact discontinuity with possible small deformation as the wave oscillates Magnetospheric (Alfvenic) perturbation incident onto the ionospheric interface For a field-aligned Alfvenic incidence (for example on cusp ionosphere)  B  k, B 0 :  B in a plane normal to k (2 possible components) Polarizations (reflected and transmitted) (noon-midnight meridian) Alfven mode (toroidal mode)  B,  u  k-B 0 plane Fast/slow modes (poloidal mode)  B,  u in k-B 0 plane Antisunward ionospheric motion =>fast/slow modes (poloidal) => NOT Alfven mode (toroidal) Magnetosphere Ionosphere

Global Consequence of A Poleward Motion Antisunward motion of open field line in the open-closed boundary creates –a high pressure region in the open field region (compressional wave), and –a low pressure region in the closed field region (rarefaction wave) Continuity requirement produces convection cells through fast mode waves in the ionosphere and motion in closed field regions. Poleward motion of the feet of the flux tube propagates to equator and produces upward motion in the equator. Ionospheric convection will drive/modify magnetospheric convection

Ionosphere Reaction to Magnetospheric Motion Slow down wave propagation (neutral inertia loading) Partial reflection Drive ionosphere convection –Large distance at the magnetopause corresponds to small distance in the ionosphere –In the ionosphere, horizontal perturbations propagate in fast mode speed –Ionospheric convection modifies magnetospheric convection (true 2-way coupling)

Amplification of Magnetic Perturbation at the Ionosphere At the magnetosphere- ionosphere boundary, the boundary conditions are maintained by the incident, reflected and transmitted perturbations. The reflected perturbations have a phase reversal between dB and dV from the incident. The inertia of the ionospheric plasma minimizes the velocity change across the boundary The magnetic perturbation nearly doubles across the boundary => forming a strong current

Basic Equations Continuity equations Momentum equations Temperature equations Faraday’s Law and Ampere's Law s = e, i or n, and e s = -e, e or 0 Field-aligned flow allowed

Simplifying Assumptions (dt > 1sec) Charge quasi-neutrality –Replace electron continuity with Neglecting the electron inertial term in the electron momentum equation –Electric field, E, can be eliminated in other equations; –electron velocity will be calculated from current definitions.

Momentum equations without electric field E

1-D Stratified Ionosphere/thermosphere Equation set is solved in 1-D (vertical), assume  B<<B 0. Neutral wind velocity is a function of height and time The system is driven by a change in the motion at the top boundary No local field-aligned current; horizontal currents are derived No imposed E-field; E-field is derived. test 1: solve momentum equations and Maxwell’s equations using explicit method test 2: use implicit method (increasing time step by 10 5 times) test 3: include continuity and energy equations with field-aligned flow 2000 km 500 km

Dynamics in 2-Alfvén Travel Time x: antisunward; y: dawnward, z: upward, B 0 : downward On-set time: 1 sec Several runs were made: the processes are characterized in Alfvén time Building up of the Pedersen current Song et al., 2009

30 Alfvén Travel Time The quasi-steady state is reached in ~ 20 Alfvén time. During the transition, antisunward flow in the F- layer can be large During the transition, E- layer and F-layer have opposite dawn-dusk flows There is a current enhancement for ~10 A-time, more in “Pedersen” current Song et al., 2009

Neutral wind velocity The neutral wind driven by M-I coupling is strongest in F-layer Antisunward wind continues to increase Song et al., 2009

After 1 hour, a flow reversal at top boundary Antisunward flow reverses and enhances before settled Dawn-dusk velocity enhances before reversing (flow rotates) The reversal transition takes slightly longer than initial transition Larger field fluctuations Song et al., 2009

After 1 hour, a flow reversal at top boundary “Pedersen” current more than doubled just after the reversal Song et al., 2009

Electric field variations Not Constant! Electric field in the neutral wind frame E’ = E + u n xB Not Constant! Song et al., 2009

Heating rate q as function of Alfvén travel time and height. The heating rate at each height becomes a constant after about 30 Alfvén travel times. The Alfvén time is the time normalized by t A, which is defined as If the driver is at the magnetopause, the Alfvén time is about 1 min. Height variations of frictional heating rate and true Joule heating rate at a selected time. The Joule heating rate is negligibly small. The heating is essentially frictional in nature. Tu et al., 2011

Time variation of height integrated heating rate. After about 30 Alfvén travel times, the heating rate reaches a constant. This steady-state heating rate is equivalent to the steady-state heating rate calculated using conventional Joule heating rate J∙(E+u n xB) defined in the frame moving with the neutral wind. In the transition period, the heating rate can be two times larger than the steady-state heating rate. Heating rate divided by total mass density (neutral mass density plus plasma mass density) as function of Alfvén travel time and height. The heating rate per unit mass is peaked in the F layer of the ionosphere, around about 300 km in this case. Tu et al., 2011

Summary When the ionosphere is treated self-consistently and dynamically, it –reflects magnetospheric perturbations –oscillates at magnetospheric eigen-mode frequencies (not simply responds to magnetospheric disturbances) –forms an envelop over the eigen-mode oscillations due to constructive or destructive interference until steady state is reached. –has a transient time of Alfven times, or min –sets convection pattern with the fast mode speed The above distinct processes predict/explain –Substorm time geomagnetic measurements have intrinsic oscillations, the frequency of which is less correlated with the oscillations in the solar wind –Substorm time geomagnetic perturbations are less correlated with specific time scales of reconnection –Substorm time is about 30 min –The whole ionosphere responds to the magnetospheric changes in 1 min –During substorms, more energy is dissipated within the polar cap proper where frictional heating is the strongest, not in the auroral oval or field-aligned current sheets where convection velocity is the smallest. –The requirement for a substorm is a substantial change in the magnetospheric convection which has to be maintained, with its variations, for at least 30 min.