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
29th ICRC, Pune, India, August 6, 2005 SH-34
Global structure of Heliosphere
GCR
ACR SEP
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
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.)
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
ACR drift for A< 0 (1980-1990) (Cummings – Jokipii)
Model simplified – major simplification in topology
Re-acceleration of GCR at the TS
Re-acceleration
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
Schematic Heliosphere
outw
ard
inward
bi[polar
bipol
ar
HCS may mitigate the effect of magnetic wall ?
Mapping the heliosphere: fold around poles
Θ,Φ footpoints - ψ=cosθ
inward
outw
ard
Θ=0
Θ=π
Mapping the heliosphere into T,θ,(Φ)
unipolar out
unipolar in
bip
ol
arSW
T=
0
equatorSP
T: transit timeΘ-Φ: footpoints
SW: uniform in T-direction
B in Φ-direction
Magnetic field
• General Formulation of Heliospheric Field:
Bi = B(θ,T)o εijk sinθ θ,j T,k
Θ,Φ: Footpoints of StreamlinesT: transit time from footpoint
● No θ component in B (+)● θ,Φ no longer orthogonal (-)● Boundary conditions change● Test particles only !
θ,j = ∂θ/∂xj
+ deal with singularities
Parker’s equation rewritten in general coordinates:
ii x /
}/)(}{{}{/ pFpVgFVFgtFg jjijij
i
g
2fpF
gbgbb kijkA
ijjiij /
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
How to condense into 2-D ?
o Heliosphere 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
}/{// FVgxFgxtFg ijiji
}/)(}{/{ pFpxVg jj
+
i,j=1,2
“average” κ
“average” V
Summary/Conclusions
o Topology of field lines: polar lines never connect to heliopause – important difference for A>0
o HCS connects from the equator to the heliopause, which might(?) reduce the effect of the magnetic wall
o Quantitative work still to come
Thank you
Motto:
● “Make everything as simple as possible, but not simpler “
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
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