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IMF Prediction with Cosmic Rays
THE BASIC IDEA: Find signatures in the cosmic ray flux that are
predictive of the future behavior of the interplanetary magnetic field• High-energy cosmic rays impacting Earth have passed through and interacted with
the IMF within a region of size ~1 particle gyroradius – They should retain signatures related to the characteristics of the IMF
• Neutron monitors respond to ~10 GeV protons – These protons have a gyroradius ~0.04 AU, corresponding to a solar wind transit time of ~4 h
• Muon detectors respond to ~50 GeV protons – Gyroradius is ~0.2 AU, corresponding to a solar wind transit time of ~20 h
• The method can potentially fill in the gap between observations at L1 and observations of the Sun
Spaceship Earth
Spaceship Earth is a network of neutron monitors strategically deployed to provide precise, real-time, 3-dimensional measurements of the cosmic ray angular distribution:
• 11 Neutron Monitors on 4 continents
• Multi-national participation: – Bartol Research Institute,
University of Delaware (U.S.A.)– IZMIRAN (Russia)– Polar Geophysical Inst. (Russia)– Inst. Solar-Terrestrial Physics
(Russia)– Inst. Cosmophysical Research and
Aeronomy (Russia)– Inst. Cosmophysical Research and
Radio Wave Propagation (Russia)– Australian Antarctic Dvivision– Aurora College (Canada)
SPACESHIP EARTH VIEWING DIRECTIONS
FOR A GALACTIC COSMIC RAY SPECTRUM
Circles denote station geographical locations. Average viewing directions (squares) and range (lines) are separated from station geographical locations because particles are deflected by Earth's magnetic field.
• 9 stations view northern mid-latitudes• 2 stations (TH, BA) view northern high latitudes• 2 stations (MC, MA) view southern hemisphere
TheInstrument
is theArray
IMF PREDICTION WITH COSMIC RAYSMethod 1: Predictive Digital Filters
• “X” represents a time series of input parameters extending from the present time t to a time in the past NΔt.
• The input is used to predict an output “B” at some time in the future t+mΔt.
• Filter coefficients An are determined by chi-square minimization applied to a set of test data.
• We will use hourly data, Δt = 1 h. This is appropriate in light of the large gyroradii of the cosmic rays under consideration.
Basic Input for Method 1:Cosmic Ray Intensity Corresponding
to a Certain Direction in Space
• The cosmic ray “sky” will be divided up into a number of patches
• A trajectory code will be used to correct for bending of particle trajectories in the geomagnetic field, yielding the “asymptotic direction”
This is how we defined the patches:
• Central patch is Sunward direction• Black Dots show the actual distribution of station viewing
directions at 10:00 UT on 1/1/2006
N
S
Anti-Sunward
Anti-Sunward
Data Pre-processing
cos )(sinsin )(cossin )()()( 0 ttttItI zyxfiti
To select the intensity variation that would be sensitive to the IMF,we subtract isotropic component and 12 hour trailing-averaged anisotropyfrom observed NM intensity
12
1,,,,
02
)(12
1)(
)cos )(sinsin )(cossin )()(()(t
tzyxzyx
zyxobsi
obsi
t
ttttIItI
where I0 and ξ are determined for each hour from the following best fit function
Data Pre-processing
Observed intensity
After subtract isotropic component
And after subtract 1st order anisotropic component
Data during GLE is removed
Predict IMF from NM data
nn t
tn
t
tnnorm BtB
ttBtB
Nt 1
2obsobs
1
2predobs )( 1
1 )()(
1
ii IX jiji IIX ,
Input X: NM intensity at i-th patch or deviation between i-th and j- th patch
Then output B is compared with 6 types of IMF data
))1()()(( ,,,,, tBtBtdBdBdBdBBBB zyxzyx
and determine the coefficient An that minimize following normalized chi-square
)( )(0
c
N
nn AtntXAtmt
B
I,j =1,10
norm ~1: bad prediction <1: better prediction
tn:number of the data in each year
Norm. chi-square
Color map shows the value of normalized chi-square for the prediction of Bz and dBz at the example for year 2006, m=1 and N=5 (predict 1h prior IMF from past 5h NM data)
i
j
input X1
From input X1,2
Norm. chi-square for each sector
Away sector
Toward sector
IMF PREDICTION WITH COSMIC RAYSMethod 2: Based on Quasilinear Theory
(QLT)
ENSEMBLE-AVERAGING DERIVATION OF THE BOLTZMANN EQUATION:
START WITH THE VLASOV EQUATION
The equation is relativistically correct
ENSEMBLE AVERAGETHE VLASOV EQUATION
SIMPLIFY THE ENSEMBLE-AVERAGED EQUATION WITH A TRICK
For gyrotropic distributions, only ψ1 matters!
SUBTRACT THE ENSEMBLE-AVERAGED EQUATION FROM THE ORIGINAL EQUATION
… THEN LINEARIZE
Why “Quasi”–Linear? 2nd order terms are retained in the ensemble-averaged equation, but dropped in the equation for the fluctuations δf
AFTER LINEARIZING, IT’S EASY TO SOLVE FOR δf BY THE METHOD OF CHARACTERISTICS
In effect, this integrates the fluctuating force backwards along the particle trajectory.
“z” here is the meanField direction, NOTGSE North
This is like tomography,but using a helical “lineof sight”
L = RL, = V / RL, = cos()RL : Larmor radius ( ~ 0.1AU )V : Particle speed ( ~ c ) : Particle pitch angle
z : Distance along IMF ( = 0 )t : Time ( = 0, t = 1 hour ) : Gyrophase
))]}1((sin())(sin(1(
))1((sin())(sin(1[(
))]1((cos())(cos(1(
))1((cos())(cos(1[({
)1(2
11)()()(
20
tPP
tPPA
tPP
tPPA
f
Bttftftf
xx
yyy
xx
xxx
fit this function to the cosmic ray flux (change from past t),and get 4 parameters Ax, Ay, Px, Py
Model function
From the determined parameters Ax, Ay, Px, Py, magnetic fielddisturbance is reproduced with
And then, compare them to observed IMFafter converted them from field coordinate to GSE coordinate
Method 1 fit to all 11 stations data at time t
Method 2 fit to selected1 station data of continuous past 4 hour (t-3,t-2,t-1,t)
11~1 ),1()()( itftftf iii
ttfff iii ~3 ),1()()(
Two Method to predict dB
Method 1 Method 2 (McMurdo)
Corr. Coefficient for dBz