1. Drift Effects if the 22-year Solar Cycle of Cosmic Ray Modulation
35th ICRC Busan Korea, July 14, 2017
Drift Effects if the 22-year Solar Cycle of Cosmic Ray Modulation
József Kóta
The University of Arizona, Tucson, AZ
w. thanks to J.R. Jokipii, J. Giacalone, F. Fraschetti
Supported by NASA Grant NNX16AB77G

2. Prelude 40 years ago: Motto:
“Make everything as simple as possible, but not simpler “
Voyager 2 & 1 launched
Theory of diffusive shock acceleration
Particle Drift’s role in cosmic ray transport (Jokipii et al) met some initial resistance

3. - Outline - Particle drifts: how they appear in Parker’s Equation
Role of latitudinal diffusion & tilted HCS is decisive. The tilted HCS reduces drift effects – without scaling down drift artificially at solar maximum
A ‘hoop model’ to simulate the solar cycle variation of GCRs due to variation of the tilt angle of the heliospheric current sheet (HCS).
Few words about drifts at the Heliopause

4. Parker Equation:
If scattering is frequent enough to maintain quasi-isotropy, then the particles phase space density, f (xi,p,t) obeys
Source/Loss
Where is convection and energy change ?

5. Parker ‘s Equation continued
Drifts affect energy change indirectly via changing GCR’s path
Advection, V, and energy loss (~divV) are hidden absorbed into a 4x4 “diffusion tensor” K*.
In General: reversible motion appears in the anti-symmetric part (imaginary eigenvalues)

6. Parker Equation: identical, more convenient form
Drifts can be
handled by a matching cond. or be made
finite & gradual
Matching condition: the same for HCS and shocks
No need to be afraid
of infinitely fast drift
Drift term includes advection, + 4th component

7. Interplay of Drift & Perp. Diffusion
The inverse of the diffusion tensor appears !! !!
Large perp diffusion kills drift
& so does a wavy current sheet

8. 22 year Sunspot Cycle: another early signature of drift
A<0 – peak
peak
flat
peak
flat
A>0 – flat
Explained by particle drifts

9. 2.5 D Simulations in a ‘Hoop Model’
To capture the 3-D HCS in 2-D requires compromise
The change of the tilt angle introduces a meriodional HMF component
Both these problems can be avoided if we conveniently omit the radial component of the HMF
Filed lines become rings, the waviness is kept in the form of time-dependence
Co-rotating HMF:

10. 22 year cycle: tilt of HCS is the only variable parameter
Simulated 22 year
peak - flat - peak cycle .
Solar Minima at: t=0, A<0 t=11, A> t=22 A<0
Note the difference between t=0 and t=22

11. From A<0 Minimum to A>0 Minimum
A<0 Solar Min.
Solar Max
Spherical, no drift effect

12. Voyager-1 at the Heliopause
2012: V1 crossed the HP
The step-like increase of GCRs at the HP is a surprise, no consensus explanation.
The question arises if V1 crossing is “typical”
V2 may help to answer
GCR e
ACR
GCRs show a step-like increase
ACRs vanished almost instantly

13. Drifts in the Heliosheath: two models of heliotail
Conventional model
elongated tail
Croissant (Opher & Drake)
Toy-model (Drake et al, 2015)
Field lines are stretched & sectors are compressed New mode of GCR transport (Florinski)
Less distorted field structure

14. Drift Pattern near and at the HP (toy-model)
Outward drift at polar lines
Poleward drift at the TS
Drifts along the HP are likely – what is their effect?
Can the wavy HCS help GCRs to penetrate deep into the heliosphere ?
Opposite
sector

15. Summary
Large-scale particle drifts and advection are equally important. They can be treated in the same way. Drift causes energy change indirectly
Latitudinal diffusion is critical in determining the magnitude of drift effects. Either fast latitudinal diffusion or a wavy HCS will mitigate drift effects (drift shuts down itself automatically at solar maximum conditions)
The role of drift near the HP is an open and intriguing question.

16. Motto: ● “Make everything as simple as possible, but not simpler “
You must remember this
A drift is just a drift
Just one of the drifts
Fundamental things apply
As time goes by

17. Sector Structure in the Heliosheath
The flux of few hundred MeV GCRs showed and almost step-like increase at the HP,
This could be interpreted in terms of very small perpendicular diffusion.
It is conceivable that HCS near the HP plays a role providing “cracks” for GCR inflow (?)
It will be interesting to see if V-2 sees the same step-like jump at the HP.
opposite
sector
Potentially
fast inflow
of GCRs

18. Predicted ACR Anisotropies at V1 & V2 in the Heliosheath (2)

19. Predicted ACR Anisotropies for V1 & V2 (3)

20. 22 year Solar Cycle: dependence on latitudinal diffusion
Smaller diffusion higher peak, larger diffusion smaller peak at A<0

21. Contribution of HCS tilt & diffusion in the weaker B to the record high 2009 GCR flux
HCS tilt only
Faster diffusion + HCS tilt

22. Last Solar Minimum: GCR at record level (Mewaldt et al)
MeV/n
Fe at ACE
Black: prediction from earlier cycle
GCR increase is the result of :
decreasing B
decreasing tilt ?

23. How about Anomalous CRs?
ACRs are high, but not record-setting (Leske, Mewaldt et al).
Why are not ACRs at record level?
Faster diffusion at the TS gives less efficient acceleration (Moraal & Stoker). Detailed modeling still needed.

24. Parker Equation: traditional form
Drift becomes infinite at HCS. This is not inconsistency.
Parker’s equation does not contain the particle velocity.
It is a diffusion equations, which represents the limit taking v →∞ , and λ→ 0 (keeping v*λ finite).
Breaks down if gyro-radius larger than relevant scales (higher moments of the distribution are important). .