Acceleration of acrs at a blunt termination shock 2 d simulations
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● V-1. SHINE Nova Scotia, August 2009. ● V-2. Acceleration of ACRs at a Blunt Termination Shock: 2-D Simulations. J. K ό ta University of Arizona Tucson, AZ 85721-0092, USA Thanks: J.R. Jokipii, J. Giacalone. Difference between 1 & 2 D Shocks.

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Acceleration of ACRs at a Blunt Termination Shock: 2-D Simulations

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● V-1

SHINE Nova Scotia, August 2009

● V-2

Acceleration of ACRs at a Blunt Termination Shock: 2-D Simulations


University of Arizona

Tucson, AZ 85721-0092, USA

Thanks: J.R. Jokipii, J. Giacalone

Difference between 1 & 2 D Shocks

● Are Anomalous Cosmic Rays (ACRs) indeed accelerated at the solar wind termination shock (TS) ?

Likelyyes but

● Bluntness of TS counts

● Topology between shock & field Lines counts (cannot be modeled in 1 D)

● Model still qualitative

Do not consider other important effects, like dynamical variations

Voyager-1 fooled us with (1) “anti-sunward” precursor anisotropiesSolution: field line intersects the TS multiple times.

Multiple intersection explains precursor anisotropies

and ….



Displacement of the ‘nose’ helps

Voyagers fooled us with(2) spectra did not unfold at crossing the TSSolution: field lines .….?

ACR fluxes continued

to increase into the


● Temporal variaton

(Florinski Zank,2006)

● Magnetic topology

(McComas & Schwadron,

Kόta & Jokipii)

● Combination of the two?

Can be a direct result of 2D topology

Could have been foreseen (Kόta & Jokipii, 2004)

McComas and Schwadron (2006)

Blunt Shock

Injection & Acceleration at Flanks

Short time for


Kóta and Jokipii, 2004

2D simulation of Blunt TS (offset circle)- no latitudinal motion -

This Simulation: Shock & Injection stronger at nose, weaker toward tail

More TSP at nose (injection profile)

Less ACRs at nose (global feature)

2 D simulation (offset circle) cont’d

Simulated spectrum

unfolds gradually

Nose-tail asymmetry

Controlled by κ┴

ACR flux continues

to increase beyond TS

Tracing back ACRs

  • Solve Parker’s equation “backward”, with the solar wind blowing inward. What we obtain is the “chance” function which is to be convolved with injection.

  • Inward wind advects trajectories back to the TS, where pseudo-particles cool-down to injection energy.

  • Ideally suited for GCRs (all trajectories leave sooner ot later the heliosphere. More cumbersome for ACRs

”Backward tracing” starting w5 MeV ACR 10 AU off the TS

5 MeV

Cooled down to 100 keV

Starting energy 5 MeV

Chance to become 5 MeV ACR10AU off the shock



acceleration cooling

Nose (V-1)

Flank 60 West

Age distibution

ACRs are `older’ deeper in the HS




Reverse method w larger κ Forward method w smaller κ


  • ACRs are best accelerated if injected at front (more time for acceleration)

  • Birthplace at Nose: Likely most of all ACRs (even those in tail) were injected at front.

  • Nursery toward Flanks: TSP seen by Voyagers is the seed population of MeV ACRs. TSPs moving toward flanks during further acceleration.

One word on Precursor Events:Possible scenarios for Voyager

  • Scenario (M* ) is more efficient to accelerate energetic particles

  • Voyager precursor events may have been associated with configuration M*


Less efficient- More efficient

> <




● Magnetic field lines cross the blunt TS multiple times. This explains upstream anisotropies and :

● Two-population spectrum: ACRs start as TSPs at the nose and move toward the flanks during acceleration. Appear still modulated at the TS, and continue to increase into the heliosheath.

● 2-D Shock differs from 1-D shock (topology)

● Dependence on parameters (κ) still need to be explored .

Global features are insensitive injection profile

  • The distribution & spectrum of MeV ACRs turn out largely insensitive to the injection-profile along the shock.

  • Lower ACR intensity is obtained at the nose even if

    - injection rate and/or shock ratio is higher at nose

    Reason: unfavourable topology (natural cold spot)

  • To trace the history of ACRs we perform a “backward“ simulation. The solar wind is reversed and a pseudo ‘testparticle’ is released from the point of observation. What we obtain is the Green-function or chance of injected particle to become ACR

Illustrative example of 2-D shock- field/shock angle alternates -



Along shock front



Distance from shock

Global structure along shock front

organized by magnetic field

Motivation: where is the source?is history repeating itself ?Do we need a new paradigm ? Likely not

ACR fluxes continued to increase beyond TS

Source outside


V. Hess 1912

Voyager-1 December 2004

Similar result from V-2 (2007)

Global structure of Heliosphere

VLISM: partially ionized


0.1/cc μG B ?




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