Propagation of cosmic rays in the Solar system Charged cosmic ray nuclei entering the Solar system have to overcome the magnetic field that is carried by the solar wind. The solar wind is an outflow of material from the Sun that was predicted by L. Biermann. The magnetic field structure was explained in 1958 by Parker. The magnetic field frozen in the ionized material and is expanding away from the Sun. In the vicinity of the Earth the solar wind velocity is between 300 and 600 km/s which corresponds to an average kinetic energy of 500 MeV/particle. The magnetic field strength is about 3x10-5 G which is about 40 times lower than the kinetic energy of the solar wind particles. The Parker spiral has two components: radial and azimutal
Swarthmore/ Newark neutron monitor data. The modulation of the galactic cosmic rays particles in the solar system was first observed as an anti-correlation of the neutron monitors data with the sunspot numbers on the Sun. The sunspot number, which measures the number of active regions on the Sun, has roughly an 11 year cycle, ½ of the magnetic cycle on the Sun. There is 1 2 yrs delay after the sunspot number changes.
There is a standard spherically symmetric model of solar modulation (Gleeson & Axford) that accounts for -- cosmic ray diffusion through the magnetic field carried by the solar wind -- the convection by the ouward motion of the solar wind -- the adiabatic deceleration of the galactic cosmic rays in this flow The diffusion coefficient used is k = C0 R where R is the particle rigidity. The solar wind speed is 400 km/s. The solar modulation parameter r1rh (v/k) dr. The data is best fit with MeV. For r1 = one AU and rh (radius of the heliosphere of 50 AU. Current data suggests the heliospheric radius is significanly bigger (a factor of 2?). In this force field approximation the solar modulation is expressed in terms of this single parameter. A particle of energy EIS in interstellar space would reach Earth with E = EIS - Z
The flux of particles of this energy and type is related to the Interstellar flux IS as Comparison of the proton flux measured above 20 GeV with the LEAP experiment with solar modulation using 200, 400, 600, 800 and 1,000 MeV. The values used today are between 400 MeV at solar minimum to 1400 MeV for solar maximum. The decrease of the particle flux is three times higher than the decrease of the energy of the individual particles.
Galactic cosmic ray modulation in different parts of the Solar system. (H. Moraal) The solid lines show the numerical solutions, while the dashed lines show the force field solutions at different distances from the Sun. The end of the heliosphere here is at 90 AU. The solutions for different distances are shown divided by 101/2.
There are significant indications that positively and negatively charged particles modulate in different ways and in different solar polarities. One indication is the different shape of the neutron monitors counts as a function of the solar polarity. Direction of the solar magnetic field during different solar polarities, Cosmic ray particles generally gyrate around the magnetic field lines in the Solar system.
Regions of outward and Inward polarities are separated by the current sheet which is shown here in 3D. The combination of solar rotation and radial flow of the solar wind creates this complicated shape of the current sheet. All graphs on black are by J.W. Bieber
In the presence of magnetic field charged particles move in Spiral trajectory around the magnetic field lines. The Larmor (or gyro radius) is rg = m v sin /(qb) where is the the pitch angle to the field line.
The efficient particle transport is perpendicular to the magnetic field lines. The negatively charged particles (electrons and antiprotons) drift in the opposite way. When the solar polarity reverses the drift direction also reverses.
Positive solar polarity Negative solar polarity The motion is more complicated because the current sheet is not a plane.
Long term behaviour of the neutron monitor data during different solar polarity periods. Note also the time delay that varies between a fraction of an year to two years.
Intensity of protons and antiprotons In different solar polarities as Calculated by Bieber et al.
The BESS detector Detection of protons and antiprotons in the BESS 1999 and 2000 flights. Antiprotons are bend by the magnets in the opposite way which results in negative rigidity.
Comparison of the BESS and other measurements to calculations of the fluxes for positive Solar polarity.
Comparison of the measurements in different Solar polarity to predictions of different solar modulation models. The interstellar fluxes (LIS) do not depend of the Solar polarity but the modulation does.
In spherically symmetric models the modulation does not depend on the solar polarity but fitting the detected fluxes requires different parameter.
Ratio of the positron to the electron fluxes measured by the PAMELA experiment. The lines are the solar modulated fluxes calculated by Bieber et al. The paper is not published Yet so I cannot give you more details about it.
Geomagnetic field effects: The charged particles that we detect have to also penetrate the Earth magnetic field. The geomagnetic field is an offset dipole field where the magnetic pole in the Northern hemisphere is at latitude 81 deg and longitude 84.7oW. This is actually the South magnetic pole; The North magnetic pole is close to the South rotational pole. The rigidity cutoff was calculated analytically by Stoermer as where is the particle zenith angle and B is the particle azimutal angle measured clockwise from the direction of the North magnetic pole. It includes the East-West effect: more positively charged particles come from the West at the zenith angle than from the East. It is the opposite for negatively charged particles such as electrons and antiprotons.
The geomagnetic cutoff has to be taken into account when accurate calculations are made of different particles that reach experiments on the surface of the Earth. The figure shows the zenith angle dependence of protons of different energy that can reach the atmosphere and interact in it. The calculation was made for the location of Kamiokande where the big Japanese neutrino experiment SuperK is located. Since we deal with neutrinos that reach the experiment from all direction we had to deal with the whole magnetic field of the Earth.