Outline

1
An Empirical Phase-Space Analysis of Ring-Current
Dynamics Solar Wind Control of Injection and
Decay
Paul OBrien and R. L. McPherron UCLA/IGPP tpoiii_at_
igpp.ucla.edu

• Outline
• Introduction and Review
• Data Analysis
• Linear Phase-Space Trajectory
• Decay Depends on VBs
• Physical Interpretation
• Position of Convection Boundary
• Conclusions

2
Meet the Ring Current

• During a magnetic storm, Southward IMF reconnects
  at the dayside magnetopause
• Magnetospheric convection is enhanced hot
  particles are injected from the ionosphere
• Trapped radiation between L 2-10 sets up the
  ring current, which can take several days to
  decay away
• We measure the magnetic field from this current
  as Dst

March 97 Magnetic Storm
Recovery
100
0
Dst (nT)
-100
-200
Injection
-300
91
92
93
94
95
96
97
98
99
Pressure Effect
10
VBs (mV/m)
5
0
91
92
93
94
95
96
97
98
99
60
40
Psw (nPa)
20
0
91
92
93
94
95
96
97
98
99
Day of Year
3
DDst Distribution (Main Phase)
No Data
DDst ? Q - Dst/t
Median Trajectory
No Data
4
Motion of Median Trajectory
VBs 0
VBs 1 mV/m
VBs 2 mV/m
VBs 3 mV/m
VBs 4 mV/m
VBs 5 mV/m
As VBs is increased, distributions slide left and
tilt, but linear behavior is maintained.
5
The Trapping-Loss Connection

• The convection electric field shrinks the
  convection pattern
• The Ring Current is confined to the region of
  higher nH, which results in shorter t
• The convection electric field is related to VBs

t Decreases
Larger VBs
6
Fit of t vs VBs

• The derived functional form can fit the data with
  physically reasonable parameters
• Our 4.69 is slightly larger than 1.1 from Reiff
  et al.

?
7
How to Calculate the Wrong Decay Rate

• Using a least-squares fit of DDst to Dst we can
  estimate t
• If we do this without first binning in VBs, we
  observe that t depends on Dst
• If we first bin in VBs, we observe that t depends
  much more strongly on VBs
• A weak correlation between VBs and Dst causes the
  apparent t-Dst dependence

8
Summary

• Dst follows a first order equation
• dDst/dt Q(VBs) - Dst/t(VBs)
• Injection and decay depend on VBs
• Dst dependence is very weak or absent
• We have suggested a mechanism for the decay
  dependence on VBs
• Convection is brought closer to the exosphere by
  the cross-tail electric field

9
Phase Space Trajectories
Simple Decay
Oscillatory Decay
Dst(t)
Dst(t)
Variable Decay
Dst(tdt)-Dst(t)
Dst(tdt)-Dst(t)
Dst(t)
Dst(tdt)-Dst(t)
10
Q is nearly linear in VBs

• The Q-VBs relationship is linear, with a cutoff
  below Ec
• This is essentially the result from Burton et al.
  (1975)

11
Speculation on t(VBs)
The charge-exchange lifetimes are a function of L
because the exosphere density drops off with
altitude t is an effective charge-exchange
lifetime for the whole ring current. t should
therefore reflect the charge-exchange lifetime at
the trapping boundary

• A cross-tail electric field E0 moves the
  stagnation point for hot plasma closer to the
  Earth. This is the trapping boundary (p is the
  shielding parameter)
• Reiff et al. 1981 showed that VBs controlled the
  polar-cap potential drop which is proportional to
  the cross-tail electric field

12
Neural Network Verification
DDst NN(Dst,VBs,)

• A neural network provides good agreement in phase
  space
• The curvature outside the HTD area may not be real

Neural Network Phase Space
0
High Training Density
-50
Dst
-100
-150
-25
-20
-15
-10
-5
0
5
10
15
DDst
13
Small Big Storm Errors

• More errors are associated with large VBs than
  with large Dst

14
Details of Model Errors in Simulated Real-Time
Mode
ACE availability was 91 (by hour) in 232 days
Predicting large Dst is difficult, but larger
errors may be tolerated in certain applications
15
Calculation of Pressure Correction

• So far, we have assumed that the pressure
  correction was not important.This is true because

But now we would like to determine the
coefficients b and c. We can determine b by
binning in DP1/2 and removing Q(VBs)
We can determine c such that Dst decays to zero
when VBs 0
16
Small Big Storms
17
Comparisons to Other Models
ACE Gap
AK2 is the new model, Kyoto is the target, AK1 is
a strictly Burton model, and UCB has slightly
modified Q and t. AK2 has a skill score of 30
relative to AK1 and 40 relative to UCB for 6
months of simulated real-time data availability.
These numbers are even better if only active
times are used.