1. The Evolution of the Heliospheric Current Sheet and its Effects on Cosmic Ray Modulation József Kóta and J.R. Jokipii The University of Arizona Tucson, AZ 85721-0092 USA kota@lpl.arizona.edu 29 th ICRC, Pune, India, August 6, 2005 SH-34

2. Global structure of Heliosphere GCR ACRACR SEP

3. Magnetic wall Based on 2-D Flow Simulation ( Florinski, Izmodenov) Wall Pile-up of field lines near the Heliopause builds magnetic wall Cosmic rays find hard to penetrate into the Heliosheath through the magnetic wall (?) “Polar line” does not connect to Helio- pause

4. Motivation A large part of cosmic ray modulation occurs in the heliosheath Particle drifts are important in the cosmic-ray transport, but their role in the heliosheath has not been investigated thoroughly To explore the role of drift in the heliosheath we consider otherwise simplified models (test particle etc.)

5. Parker Equation Diffusive transport equation of energetic charged particles: - assumes near isotropic distribution Diffusion (anisotropic) Drift Convection Cooling/ Acceleration Source Related to regular gyro- motion Polarity/charge dependent

6. ACR drift for A< 0 (1980-1990) (Cummings – Jokipii) Model simplified – major simplification in topology

7. Re-acceleration of GCR at the TS Re-acceleration

8. Spiral Field beyond the Termination Shock – contn’d Solar wind & field lines are deflected toward the heliotail Sun TS Sun IS Wind Sun IS Wind

9. Schematic Heliosphere outward inward bi[polarbipolar HCS may mitigate the effect of magnetic wall ?

10. Mapping the heliosphere: fold around poles Θ,Φ footpoints - ψ=cosθ inward outward Θ=0 Θ=πΘ=π

11. Mapping the heliosphere into T,θ,( Φ) unipolar out unipolar in bipolar SW T=0 equator SPSP T: transit time Θ- Φ: footpoints SW: uniform in T-direction B in Φ- direction

12. Magnetic field General Formulation of Heliospheric Field: B i = B(θ,T) o ε ijk sinθ θ, j T, k Θ,Φ: Footpoints of Streamlines T: transit time from footpoint ● No θ component in B (+) ● θ,Φ no longer orthogonal (-) ● Boundary conditions change ● Test particles only ! θ, j = ∂θ/∂x j + deal with singularities

13. Parker’s equation rewritten in general coordinates: Identical equation for notations: volume element Diffusion convection cooling/acceleration & drift Diffusion tensor: Metric tensor non-diagonal - can be ugly i,j=1,2,3

14. How to condense into 2-D ? oHeliosphere is inherently 3-d even for a flat current sheet. One way to proceed is o Assume F=F(T,θ) – these are magnetically connected. Then average the 3-D equation + i,j=1,2 “average” κ “average” V

15. Summary/Conclusions oTopology of field lines: polar lines never connect to heliopause – important difference for A>0 oHCS connects from the equator to the heliopause, which might(?) reduce the effect of the magnetic wall oQuantitative work still to come Thank you

16. Motto: ● “Make everything as simple as possible, but not simpler “

17. Cosmic-ray gradients for A>0 and A<0: Flat HCS vs Wavy HCS Reacceleration Flat HCS: large θ gradient Wavy HCS: small θ gradient Reacceleration at TS