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.

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