Alanko, K

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29th International Cosmic Ray Conference Pune (2005) 2, 5356The role of drifts in the galactic cosmic ray transportK. Alanko , I.G. Usoskinand K. Mursula (a) Department of Physical Sciences, P.O. Box 3000, University of Oulu, Finland(b) Sodankyl¤a Geophysical Observatory (Oulu unit), P.O. Box 3000, University of Oulu, FinlandPresenter: K. Alanko (katja.alanko@oulu.fi), fin-alanko-K-abs1-sh32-posterWe have earlier presented a 2D-axisymmetric model of the transport of galactic cosmic rays in the heliospherewhich is based on the stochastic simulation technique and allows us to study different aspects of cosmic raymodulation process separately. In addition to the basic modulation effects (convection, adiabatic cooling bythe solar wind, scattering on magnetic inhomogenities), our model also includes particle drift along the wavyheliospheric current sheet whose tilt angle can be varied.Here we present our first results from a refined modelling of the current sheet drift. The drift effect isshown to play an important role in the modulation process and should be included in any detailed calculationsof cosmic ray transport. We visualize the drift effect by presenting the particles’ streaming in the heliospherefor both positive and negative polarity periods.1. IntroductionWhen galactic cosmic rays enter the heliosphere, both their flux and energy are modulated due to their interac-tion with the heliospheric magnetic field and solar wind. Modulation is effective for particles with  100 GeVenergy, for higher energies the heliosphere is almost transparent. We have earlier presented a 2D-axisymmetricmodel of the heliospheric transport of cosmic rays, which included the basic modulation processes: convectionby the solar wind, adiabatic cooling by the expansion of the heliospheric magnetic field and scattering on theinhomogenities of the heliospheric magnetic field [1]. Drifts were not included in that study.The solar magnetic field points outward in one hemisphere and inward in the other. The magnetic field has aspiral structure due to solar rotation. The heliospheric current sheet (HCS) is created in the interface of theoppositely oriented magnetic field sectors. Due to the gradients of the magnetic field around the sheet and thereversal of the direction of the magnetic field from one side of the sheet to the other the particles experience aneffective drift along the sheet. The direction of the particle drift depends on the polarity of the solar magneticfield which changes every 11 years. During positive/negative polarity periods, positively charged particles driftoutward/inward, respectively.The HCS drift effect has been proposed long time ago [2]. Here we perform a detailed study of particle stream-ing due to this drift. We study the transport of cosmic rays through the heliosphere by stochastic simulation,i.e., we send test particles from the heliospheric boundary and follow their path in the heliosphere step by step.With simulations of millions of particles we are able to model the drift pattern of particle velocities in theheliosphere.First we consider the flat HCS. The equation of averaged drift velocity is then as follows:	 ﬀﬂﬁﬃ (1)where "!$#&%('' )+*,'.-0/21!435!$#6%ﬀ*87:9;=<?>)+*A@,54 K. Alanko, I. G. Usoskin and K. Mursula is the cosine of the particle’s pitch angle, ﬀ is the phase of the particle’s Larmor rotation, 9  is particle’sdistance from the current sheet and;B<is particle’s Larmor radius andis particle’s velocity. Here we assumethe form of the Parker spiral for the heliospheric magnetic field and an infinitely thin current sheet.Figure 1. a) Average current sheet drift velocity relative to particle’s velocity. Our calculation (grey line) and calculationby [3] (black line). b) Drift vectors for a 2 GeV particle at CEDGF tilt angle current sheet and DHF azimuth angle.From Eq. 1 we get the relation between drift velocity and particle’s velocity as a function of 9 HI;	<. Figure1a shows that our calculation for the flat current sheet drift agrees well with earlier calculations [3]. Note thatdrift velocity goes to zero if particle’s distance from the sheet is more than two Larmor radii.We can approximate the result for the flat sheet in Figure 1a as follows:	*KJML JNJONP79;<>RQﬂSJTLU$JONO79;<>*VJML WX$YT79;<>ZSJML W0[[J(2)We can use Eq. 2 in the case of a wavy sheet. Although a wavy sheet is a 3D-problem we will study it in a2D-model with heliospheric distance \ and polar angle ] as coordinates. First we calculate the drift velocityfor all azimuth angles separately and then average the result. For a given position and energy of the particle,we find its Larmor radius and distance to the sheet. We assume the sheet to be locally flat and apply Eq. 2 tocalculate particle’s relative drift velocity at position ^_\ , ]N` near the sheet whose tilt angle is a and azimuth angleb. Figure 1b shows the drift velocity vectors for the case a dcJAeand fixed azimuthbJ0e. The figure showshow the drift area around the sheet is thinner in inner heliosphere, where the magnetic field strength is higherand particle’s Larmor radius smaller. After averaging the result overbwe find that the latitudinal componentof the total current sheet drift is negligibly small so the drift can be approximated to be radial.Adding this effect to the basic 2D model [1], we combine all the modulation processes. We trace a large set oftest particles from the heliospheric boundary to the Earth’s orbit. As a result we get the streaming patterns ofcosmic ray particles in the heliosphere.The role of drifts in the galactic cosmic ray transport 552. DiscussionFigure 2 shows the streaming patterns for 2 GeV protons during positive and negative polarity periods with tiltangle of the sheet a H[Ne. Here we show streaming of only those particles which finally reach the Earth’sorbit.Figure 2. Streaming pattern for 2 GeV particles during a) positive polarity, b) negative polarity period inside 90 AU. Thethick line denotes the tilt angle of the sheet.Figure 2 depicts a clear difference in particle behavior during the two polarity periods. During the positivepolarity period particles tend to avoid the tilt cone. Particles make large latitudinal excursions and reach theEarth’s orbit at 1AU mainly from the polar regions. The particle motion is mainly diffusive. During negativepolarity period streaming from polar regions is again clearly shown, but there’s also another streaming pattern:particles at lower latitudes tend to move first towards the tilt cone and then drift nearly radially along the sheettowards the Sun. The drift effect clearly dominates and we see a very organized streaming pattern.The magnitudes of the average drift velocities for a 2 GeV particle are of the order ofJTL JT	*ZJTL JN[/ , so theyare relatively small compared to particle velocity fJTL gO/ and to the drift velocities in a flat sheet shown inFigure 1a. For a wavy sheet there are many particles inside the tilt cone that are far away from the sheet itselfand do not feel the drift effect. This makes the average drift velocity lower. Figure 3 shows two examples ofhow the HCS drift velocity relative to particle’s velocity changes over polar angle and radial distance from theSun. It is seen that the relative drift velocity is larger for lower tilt angles. The drift velocities are lowest in theequatorial plane and tend to increase towards the edges of the tilt cone.3. ConclusionsThe result of Figures 2a and 2b show that the current sheet drift clearly has an important role on the solarmodulation of galactic cosmic rays. Particle behavior is very different in different polarity periods. Duringpositive polarity period particles make large latitudinal excursions and reach the Earth’s orbit from the polarregions. During negative polarity particles reach the Earth also from equatorial plane drifting along the HCS.Further studies should be done to estimate the HCS drift effect in different modulation conditions.56 K. Alanko, I. G. Usoskin and K. MursulaFigure 3. Average current sheet drift velocity for 2 GeV particles for a) h2i F tilt angle of the sheet b) i F tilt angle of thesheet4. AcknowledgementsWe thank G.A. Kovaltsov for useful comments and Finnish Academy of Science and Letters, Vilho, Yrjo¨ andKalle Va¨isa¨la¨ foundation and the Finnish graduate school in astronomy and space physics for financial support.References[1] K. Alanko et al., Proc. of the 28th ICRC, 27, 3851 (2003).[2] see, e.g., J.R. Jokipii and B. Thomas, Astropysical Journal, 243, 1115 (1981).[3] R.A. Burger and M.S. Potgieter, Astrophysical Journal, 339, 501 (1989).

The role of drifts in the galactic cosmic ray transport

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