G. Li(1), Y. Yan(2), B. Miao (3), G. Qin (4)

1) Dept. of Physics and CSPAR, University of Alabama in Huntsville, AL 358992) Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, China3) School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China4) Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, China

Magnetic networks on the photosphere

and fluxtubes in the solar wind and their effects on the transport of SEPs

magnetic network on the solar surface

Hinode/SOT vector magnetogramCa II image

MDI 2004 and 2005 within 15 degrees of the solar ecliptic.

We use the middle part of the MDI plot for a period of Carrington Rotation (27.2753 days)

Example of MDI for a Carrington Rotation.

2005-0104

2005-0704

Threshold=30No dilation Threshold=15

Dilate 2X4Ca II image Original

Threshold=30No dilation

Threshold=15Dilate 2X4

Ca II image Original

Counting the Supergranules

R sun ~ 0.75 * 10^6 km

size of super granule l ~ 3*10^4 km

one solar rotation ~ 27 days

=> (2 pi Rsun/l) / (27 days *24 hours)

~ 5 / day

Fix at a point in space, counting boundaries:

Rotation of the Sun changes longitudinal structures to radial structures

Interplanetary imprint of Supergranule

What could be these structures?

Bruno et al, 2001Borovsky, SHINE 2006

Flux tubes in the solar wind can be originated

from the Sun!

Current sheets are the boundaries!

Complications from MHD turbulence

Numerical simulations suggest that coherent structures such as “current sheets” can be generated as the results of the non-linear interaction term in “NS” equation.

Zhou et al 2004 Chang et al 2004

f ~ (/) / [(T-)/]

f: frequency of large angle changes between B(t) and B(t+

T: total measurement interval

: measurement interval

f scale with

: measurement resolution

t

Finding a current sheet

T

2

Current sheets

Li 2008

Ulysses Observations

McComas et al 1998

They are everywhere

1997

A B

Miao et al. 2010

Current-sheet example – class A

Miao et al. 2011

Gradual change of angle

Perhaps reconnection

Current-sheet example – class B

One-peak event Two-peak event

Sharp change of angle

One-peak event -- Flux tube crossing

Two-peak event -- Flux tube dangling

Two-peak event -- Flux tube dangling

As the lag increases, the two peaks get closer, till they touch, and then separate again

The history of magnetic field

Similar to magnetic holes identified previouslyTsurutani et al. (2005)

A hedogram movie

Do the numbers match?• If sharp change, one-peak events ==>

boundaries of flux tubes, and are rooted at the solar surface,

We expect to see approximately equal number of supergranules and one-peak C/S event.

For the month of 2004 – 01, we find ~ 100 one-peak event, fewer than 10 two-peak events.

Daily number of Supergranules in 2004

Daily number of Supergranules in 2005

 

N15 0 S15

2004 1196 1010 1123

2005 1156 943 1097

The Results

Match nicely with the C/S data!

So current sheets are copious in the solar wind...

Will they affect the transport of energetic particles?

Parker's transport equation

Gleeson & Axford 1967

In conservation form:

S: current in r spaceJ: current in p space

Diffusion coefficient

No explicit magnetic field dependence.Effect of (turbulent) magnetic field comes through diffusion coefficient.•Diffusion is assumed implicitly in all directions, therefore both the parallel and the perpendicular directions.

Diffusion, sub-diffusion and super-diffusion

z Diffusion: rdiff(t)=(x2+y2+z2)1/2~ t1/2

Super-diffusion r(t) > rdiff

Diffusion is widely used in astrophysics and space physics!

x

y

Sub-diffusion r(t) < rdiff

The sum of a series random variables is itself a random variable with a Gaussian distribution, irrespective of the shape of the original distribution, if the following is satisfied:

If the individual R.V. has finite expectation µ and variance σ > 0.

Why Diffusion: Central Limit Theorem

Is diffusion a good approximation?Depends on turbulence geometry

2D turbulence is proposed to account for discrepancy between QLT and observed mean free path of cosmic ray.

Slab geometry:Slab geometry: wave vector parallel to the mean magnetic field

2D geometry: 2D geometry: wave vector perpendicular to the mean magnetic field

Belcher, 1971

Bieber et al., 1994Alfven waves

Competing view: Do we need significant 2D turbulence or is Alfven wave turbulence enough?

Sub (compound) diffusion for a slab turbulence

If slab geometry only, then only gets sub-diffusion

Compound diffusionWhat happened:

Having ptcls tightly tie to field lines violate the “randomness” assumption of “CLT”.

== > Compound diffusion

If slab turbulence gives sub-diffusion, then 2D turbulence must be introduced if Parker's transport equation is correct.

Is there an alternative?

Effects of current sheets on the transport of energetic particles

Toy model: a cellular solar wind.If plasmas come in as many parcels with local magnetic field orientated different from the background magnetic field, and having a local turbulence, how energetic particle will respond to it?

Local magnetic field

Qin and Li ApJL, (2008)

What is the effect of having flux tubes in the solar wind on energetic particle transport?

Running Diffusion Coefficient --- Kubo's formula

Perpendicular direction

Parallel direction

< ... > is the ensemble average

current sheet: from sub-diffusion to diffusion

Pure slab turbulence in individual cell.

== >

large scale perpendicular diffusion is recovered.

As long as magnetic wall exists (whatever its origin), 2D turbulence is not necessary for having a perpendicular diffusion.

Diffusion Sub-diffusion

What is next?

Sectors in the heliosheath

Work in progressFlorinski et al 2011

Question: what is the response of energetic particles to these ordered current sheets?