Yu.G. Shafer Institute of Cosmophysical Research and

Aeronomy of SB RAS

Transparency of a magnetic cloud boundary

for cosmic rays

I.S. Petukhov, S.I. Petukhov23rd European Cosmic Ray Symposium

(and 32nd Russian Cosmic Ray Conference)Moscow, Russia, July, 3 – 7, 2012

The interplanetary counterpart of a Coronal Mass Ejection (ICME) exert on the greatest impact on condition of the near-Earth space and cause the most powerful geomagnetic storms. In general ICME has a complicated structure: 1) the shock front is outer boundary of disturbance, 2) the compressed solar wind located behind the shock front, 3) CME, 4) a magnetic cloud is an important part of the CME.

Real Scheme

We propose to use as one a kinematic model, because:

1) the effect of force-free magnetic field is small

2) the kinetic energy of the flow is much higher than thermal energy

It is accepted relatively the magnetic cloud: at the initial moment the magnetic cloud has the shape of a torus; the axis of the torus locates in the plane of the solar equator; the magnetic field components of the torus satisfy solution Miller G, Turner L (1981 Phys, Fluids 24 363); the extension of the torus in its motion is the radial flow;

X

Z

Θ φ

r

Sun Earthcross section of the torus

Heliocentric coordinate system

The velocity of Lagrangian particles are distributed linearly over a distance of up 600 km/s to 400 km/s. Location of the CR source in front of the torus is given by the radius vector begining from the center of the torus and continuing from the torus border to a distance 0.5 Larmor radius of the particle.

t=0 is moment of time, when forward

part of magnetic cloud boundary

arrive to Earth's orbit

Position for six hours before, twelve and

eighteen, respectively.

Transparency - the part of particles entering into the magnetic cloud

Ek=10 GeV Ek=30 GeV

phi angle of the initial point of the trajectory of the cosmic rays

Chance to get inside the magnetic cloud is maximum for particles with an angle phi equal to pi. This is explained by the fact that even a particle moving away from the torus are reflected from the magnetic plug and come back to it.

Transparency of the particles with high energies is less because their Larmor radius is larger.

X

YAllocate part of the torus and calculate a number of cosmic rays of several energies coming into the torus.

The particle flux increases with time, while the spectrum of cosmic rays entering at the torus is softer compared with the spectrum of cosmic rays in interplanetary space.

This calculation performed for the magnetic cloud in the form of a vertical torus, which is located in the plane XOZ.

Visible difference to one cross section leads to this result …

Thin lines represent calculation for the horizontal torus, thick ones for the vertical torus.

The spectrum of cosmic rays in a vertically oriented torus is softer than in interplanetary space, but harder than one in the horizontally oriented torus.

The calculations showed a weak dependence of the results on the magnitude of the magnetic field in the torus and the type of magnetic structure

Our calculations showed that in the magnetic cloud will be form the softer spectra of cosmic rays than in the interplanetary medium

Subsequently

developed model allows to determine the dependence of the spectrum of cosmic rays in the field disturbance on the properties of the magnetic field of a magnetic cloud and on its orientation in interplanetary space, as well as to determine the dynamics of cosmic ray intensity in the vicinity of the disturbance.

Conclusions