% ! Real%Time)Dynamics)of)Geomagne3c) - - PowerPoint PPT Presentation

13th%Interna+onal%Conference%on%Substorms% 25829%September%2017% %Portsmouth,%New%Hampshire,%USA%

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% Real%Time)Dynamics)of)Geomagne3c) Magne3c)Storms)and)Substorms)) )

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E.)Spencer1,)W.)Horton2,)S.)Vadepu1,)) P.)Srinivas1)S.)Patra3)

1Univ of South Alabama, Mobile, USA ) 2Univ of Texas at Austin, USA 3Univ of Oslo, Oslo, Norway

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OUTLINE

Brief Description of the WINDMI Model. Substorm trigger in the model. Periodic Substorms (Sawtooth Events) - Model behavior. Isolated Substorms - Parameter values on substorm trigger.

WINDMI Model

Real-time low dimensional model for predicting substorms from ACE solar wind data Nonlinear ODE’s result from the application of conservation laws to global energy components of the system. Lumped nonlinear representation of magnetosphere. Kinetic effects are included in a simplified manner.

WINDMI Model

WINDMI Current Systems

WINDMI Model

The largest energy reservoirs in the magnetosphere-ionosphere system are: Plasma ring current energy Wrc. Geotail lobe magnetic energy Wm. The R1 FAC associated with the westward auroral electrojet. The FAC at the lower latitude closing on the partial ring current. Kinetic energy proportional to E × B perpendicular plasma flows. Kinetic energy K∥ due to mass flows along magnetic field lines. Plasma Sheet thermal energy component pcps.

WINDMI Model

Model input is Vsw and Model outputs are I1 and Wrc

L dI dt = Vsw(t) − V + M dI1 dt (1) C dV dt = I − I1 − Ips − ΣV (2) 3 2 dp dt = ΣV 2 Ωcps − u0pK 1/2

∥

Θ(u) − pVAeff ΩcpsBtrLy − 3p 2τE (3) dK∥ dt = IpsV − K∥ τ∥ (4) LI dI1 dt = V − VI + M dI dt (5) CI dVI dt = I1 − I2 − ΣIVI (6) L2 dI2 dt = VI − (Rprc + RA2)I2 (7) dWrc dt = RprcI2

2 + pVAeff

BtrLy − Wrc τrc (8)

WINDMI Physical Parameters

L 90 H Inductance of the lobe cavity surrounded by the geotail current I(t). The nominal value is L = µ0Aℓ/Leff

x in Henries where Aℓ is the lobe area and

Leff

x the effective length of the geotail solenoid.

C 50000 F Capacitance of the central plasma sheet in Farads. The nominal value is C = ρmLxLz/(B2Ly) where ρm is the mass density in kg/m3, LxLz is the meridional area of the plasma sheet, Ly the dawn-to-dusk width of the central plasma sheet and B the magnetic field on the equatorial plane. Computations of C are given in horton1996. Σ 8 S Large gyroradius ρi plasma sheet conductance from the quasineutral layer

• f height (Lzρi )1/2 about the equatorial sheet. The nominal value is Σ =

0.1(ne/Bn)(ρi /Lz)1/2. Computation of Σ is given in horton tajima. Ωcps 2.6 × 1024m3 Volume of the central plasma sheet that supports mean pressure p(t), initial estimate is 104R3

E.

u0 4e − 9m−1kg−1/2Heat flux limit parameter for parallel thermal flux on open magnetic field lines q∥ = const × v∥p = u0(K∥)1/2p. The mean parallel flow velocity is (K∥/(ρmΩcps))1/2. Ic 1.78 × 107 A The critical current above which unloading occurs. ∆I 1.25 × 105 A The rate of turn-on of the unloading function. α 8 × 1011 The geotail current driven by the plasma pressure p confined in the central plasma sheet. Pressure balance between the lobe and the central plasma sheet gives B2

ℓ/2µ0 = p with 2LxBℓ = µ0Ips. This defines the coefficient

α in Ips = αp1/2 to be approximately α = 2.8Lx /µ1/2 .

Table: WINDMI Nominal Parameters, estimated by physical considerations of the state and geometry of the nightside magnetosphere.

Model Input I

Measured Solar Wind parameters from ACE. Two functions have been found to be most useful and reliable: Input Coupling Function 1 (Rectified vBs (kV)): V Bs

sw = V0 + vswBIMF s

Leff

y

Input Coupling Function 2 (in kV)(Newell 2007): V N

sw

= V0 + νnv 4/3

sw B2/3 T

sin8/3(θc/2) (9)

Model Outputs

Outputs of the WINDMI model The outputs are the AL and Dst indices, which are compared to ground measurements. The AL index from the model is obtained from the region 1 current I1 The Dst signal from the model is partly given by ring current energy Wrc through the Dessler-Parker-Sckopke relation: DstWrc = − µ0 2π Wrc(t) BER3

E

Substorm Mechanism and Control in WINDMI Model

The trigger function controls when the substorm is initiated: Θ(u) = 1 2

• 1 + tanh

I − Ic ∆I

• (10)

The character (growth, expansion, recovery phases) is strongly controlled by the first three equations of the model: LdI dt = Vsw(t) − V + M dI1 dt (11) C dV dt = I − I1 − Ips − ΣV (12) 3 2 dp dt = ΣV 2 Ωcps − u0pK 1/2

∥

Θ(u) − pVAeff ΩcpsBtrLy − 3p 2τE (13) Parameters in red are tuned manually in this study.

October 4 2000 Sawteeth Event I

ACE data between 3-7 October 2000

October 4 2000 Sawteeth Event II

−1000 1000 2000 3000 AL and DST Index Comparison Oct 3−7 2000 −AL [nT] COR = 0.75 ARV = 0.46 Model Data 50 100 −200 −150 −100 −50 Time [Hrs] Dst [nT] ARV dst = 0.57 Model Data

See Spencer et. al. JGR 2009, Spencer et. al. JGR 2007 for details. Here Ic = 10.5MA, C = 105000 F. Using oxygen O2+ with number density 20e6 per cubic meter and magnetic field 18nT gives 107000 F.

Substorm And Pseudo-Breakup Data Set

Kalmoni et. al. 2015JA021470 use a set of Substorm and Pseudo-Breakup events to study how the growth rate of auroral beads are related to possible instability mechanisms in the near-earth plasma sheet. We used the same set of events but studied the substorm energy and triggering conditions using solar wind and IMF as drivers. 17 events. Good solar wind data for 13 events. 9 events where triggering with the model is possible. Compared model substorm trigger time against auroral

• bservations (Dotted vertical red lines in all figures).

Ω = 10000R3

E (100 X 20 X 5) for all the results.

28 November 2005 10:08 am

02 October 2008 04:29 am

• 0.2

15 March 2009 04:28 am

07 March 2010 05:15 am

Model Performance On Substorm Data

Table: WINDMI Model Triggering Conditions And Associated Parameters

Date Onset (Mdl. Onset) (∆t) Σ [S] Ic [MA] C [F] 28/03/2008 05:36 (05:32) (-4) 10 3.7 8000 28/11/2005 10:08 (10:08) (0) 10 4.4 10000 22/02/2006 06:26 (06:36) (+10) 10 3.7 5000 07/03/2007 05:50 (05:47) (-3) 10 3.4 5000 02/10/2008 04:29 (04:23) (-6) 10 4.9 10000 03/01/2009 04:36 (04:24) (-12) 5 3.5 7000 24/02/2009 07:32 (07:26) (-5) 5 2.5 8000 15/03/2009 04:28 (04:24) (-4) 10 3.7 5000 07/03/2010 05:15 (05:25) (+10) 10 3.7 5000

Parameter And Variable Values - Possible Physics

Fixing the average Bz in the central plasma sheet, the effective width Ly, and Ω, we can estimate the mass density present in the central plasma sheet from the capacitance values needed to trigger a substorm. The perpendicular vE = E × B flow velocity with B = Bz = 10nT goes as 100 km/s per 1 mV/m electric field. Need to find consistent satellite data for the average Ey or vE. From the geotail current we can track how the curvature dˆ b/ds changes during the substorm development, which is a condition for ballooning instability. We can use the critical current parameter Ic to estimate the conditions when current driven instabilities may be triggered. The pressure gradient current Ips in the model is an estimate of dp/dx, which is also related to conditions for ballooning instability.

Summary

Model is able to capture substorms. We can study onset time, possible state of magnetosphere when onset occurs. We can track intermediate variables in the model and use them as a proxy to compare with satellite data. Previously we used the AL index to train the model. This resulted in the parameters fluctuating somewhat unpredictably. Here we used the onset time as identified from auroral

• bservations to constrain the trigger mechanism in the model,

and obtained better results. Parameter and state variable values in the model give bounds for instabilities that trigger substorm onset.