Petukhov I.S., Petukhov S.I.

Yu.G. Shafer Institute for Cosmophysical Research and Aeronomy SB RAS

21st European Cosmic Ray Symposium in Košice, Slovakia

9 - 12 September 2008

Introduction Study of cosmic rays intensity dynamics

with large-scale disturbance of solar wind is of a grate interest in connection with the possibility to use the results for prediction of interplanetary disturbances and pre-decrease of CR intensity as a precursors are revealed for a sufficiently large number of individual events.

Sun

Disturbance Shock front

Earth magnetosphereInterplanetary

magnetic field

Escaped CR from FD region

Reflected CR

UndisturbedSolar wind

Used model of the Shock:

Shock front

VsReflected CR

Escaped CR

Variation CR

Reflected CR

Escaped CR

Cosmic ray trajectories are calculated by means of numerical integration of an equation system of relativistic protons movement by the Runge-Kutta method of the forth accuracy order.

Magnetic field of quiet solar wind is of Parker type, with constant flow velocity being radial and equal 400 km/sec. Electric field of solar wind is defined using a frozen condition.

The disturbance is shock wave which given in the shape of an ellipsoid.

When calculating particle drift at the shock front, electromagnetic field in the region behind the front is determined using the Rankine-Huhoniot relation.

a) Rs = 0.5 AU; b) Rs = 0.7 AU; c) Rs = 0.9 AU

↑ - blue upwards arrow – reflected particle↓ - red downwards arrow – particle escaped

from FD region = - equal – undisturbed particle

Viewing cone connects the certain area on the magnetosphere surface by means of cosmic rays with corresponding ground detector. Position and configuration of this area depend on CRs energies, detector geographic coordinates and universal time. For determination of viewing cone CR trajectories are calculated in Earth magnetic field presented by 8-th harmonics of Tsiganenko model for 2000-th epoch.

Primary CR

Magnetospheresurface

Viewing cone

Ground detector

Earth rotation

Neutron monitors and muon detectors measure the intensity of secondary particles (neutron and muons) produced by interactions of primary cosmic rays with atoms in Earth’s atmosphere. Calculated CR intensity variation is determined by: 1) integrating on solid angle using dependence of secondary particles intensity with polar angle I=cos(Theta)^6 for neutrons or cos(Theta)^2 for muons; 2) integrating on energy using coupling coeffitiens for neutrons (Quenby-Webber coupling coefficients) or for muons

Where - differential variation; W(ε) - coupling coefficients; - geomagnetic cutoff energy.

min min

( ) ( ) ( )I I W d W d

( )I

min

PositiveApparently from comparison calculations well reproduce time sequence of CR intensity variations, measured by various detectors. Sizes of falls CR intensity, measured by detectors before shock wave arrival into an orbit of the Earth quite well correspond.

NegativeThe calculated CR intensity variations during the different moments of time for neutron monitor Norikura and muon telescop Nagoya considerably differ one from another on size, that speaks that expansion of the area of corresponding CR trajectories a magnetosphere surface in process of shock wave approach.

Absence of the calculated variation of CR intensity for the neutron monitor of station to Thule

Calculated results are in general agreement with the CR intensity variation registered by ground-level detectors. The method of CR trajectories for describing CR intensity dynamics with solar wind large-scale disturbances is useful and adequate since the mean free path is long enough for high-energy particles to carry the directional intensity information from an interplanetary disturbance to the Earth.