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 The Instrument is the Array

IMF PREDICTION WITH COSMIC RAYS Method 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 A n 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 To select the intensity variation that would be sensitive to the IMF, we subtract isotropic component and 12 hour trailing-averaged anisotropy from observed NM intensity where I 0 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 1 st order anisotropic component Data during GLE is removed

Predict IMF from NM data 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 and determine the coefficient A n that minimize following normalized chi-square I,j =1,10  norm ~1: bad prediction <1: better prediction t n :number of the data in each year

Norm. chi-square Color map shows the value of normalized chi-square for the prediction of B z and dB z at the example for year 2006, m=1 and N=5 (predict 1h prior IMF from past 5h NM data) i j input X 1 From input X 1,2

Norm. chi-square for each sector Away sector Toward sector

IMF PREDICTION WITH COSMIC RAYS Method 2: Based on Quasilinear Theory (QLT)

ENSEMBLE-AVERAGING DERIVATION OF THE BOLTZMANN EQUATION: START WITH THE VLASOV EQUATION The equation is relativistically correct

ENSEMBLE AVERAGE THE VLASOV EQUATION

SIMPLIFY THE ENSEMBLE-AVERAGED EQUATION WITH A TRICK For gyrotropic distributions, only ψ 1 matters!

SUBTRACT THE ENSEMBLE-AVERAGED EQUATION FROM THE ORIGINAL EQUATION … THEN LINEARIZE Why “Quasi”–Linear? 2 nd 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 mean Field direction, NOT GSE North This is like tomography, but using a helical “line of sight”

L =  R L,  = V / R L,  = cos(  ) R L : Larmor radius ( ~ 0.1AU ) V : Particle speed ( ~ c )  : Particle pitch angle z : Distance along IMF ( = 0 ) t : Time ( = 0,  t = 1 hour )  : Gyrophase

fit this function to the cosmic ray flux (change from past  t), and get 4 parameters A x, A y, P x, P y Model function From the determined parameters Ax, Ay, Px, Py, magnetic field disturbance is reproduced with And then, compare them to observed IMF after 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) Two Method to predict dB

Method 1 Method 2 (McMurdo)

Corr. Coefficient for dBz