Fractal reconnection at the Earth’s magnetopause and associated

ionospheric convection.

Gary Abel, Iain Coleman, Mervyn Freeman and Gareth Chisham

British Antarctic Survey

MRT Workshop 9th -10th August 2004

A quote from the classic Dungey [1961] paper

“A steady laminar flow will be assumed here for simplicity, but it should be noted that large variations of the field were detected by Pioneer I” … “The connection between the neutral points (reconnection) and the auroras (convection) is obvious in this model, but it remains to study … the effect of turbulence.” Dungey [PRL 1961].

• We commonly model dayside reconnection in terms of a uniform IMF phase front draped across the magnetopause by a laminar hydrodynamic flow.

• Such models naturally give rise to large-scale, spatially coherent reconnection structures on the magnetopause and in ionospheric convection.

• The draped IMF is in reality highly disordered, and not well described by laminar models.

• What is the implication of this at the magnetopause and in the ionosphere?

Introduction

Antiparallel Reconnection with Perfect Draping

The clock angle of the magnetosheath B-field is everywhere equal to the upstream IMF clock angle of 135°. The antiparallel reconnection regions

are shown in black

Fractal anti-parallel reconnection

• Magnetosheath is noisy• Difference between upstream measured clock angle and sheath

clock angle has standard deviation of around 40º

But!!!

Fractal anti-parallel reconnection

Perfect Draping White (gaussian) Noise Draping

• Adding significant amounts of gaussian noise breaks down the structure of the reconnection regions.

• This is because gaussian noise is spatially uncorrelated.

• It may be more reasonable to model the “noisy” part of noisy draping as fractal turbulence, rather than gaussian white noise.

• In the following slides, a random fractal of power spectrum –5/3 is added to the magnetosheath field, such that the standard deviation of the clock angle is similar to that in the gaussian case.

The Trouble with Gaussian Noise

Fractal anti-parallel reconnection

Perfect Draping Red Noise Draping

Gaussian (White) Noise

Fractal Noise

Time Series of Reconnection Sites with Fractal Turbulence

• Fractal turbulence is correlated on large spatial scales.

• Thus, it preserves the antiparallel reconnection structures of the laminar model to far greater extent than gaussian noise can manage.

• However, further structure is introduced to magnetopause reconnection sites.

• Is this structure reflected in ionospheric convection?

The Importance of Fractal Turbulence

Investigate spatial structuring of ionospheric flows using structure function analysis

• Structure function analysis using SuperDARN radar.

• Radar measure LOS component of convection velocity.

• Use Halley meridional beam – ranges 10 to 65.

• 1997 – 2001.

• Calculate <|v(r+l)-vr|m>, m=1,2,3, l=1,2,… 55

• Precondition data so we only include fluctuations of ±1

Poleward of Open/Closed Field Line Boundary -

Nightside

Slope = 0.81

Slope = 0.57

Slope = 0.30

)(P ss lvl

Summary and Conclusions

• M-I system is a complex system driven by a complex driver.

• In order to fully understand the system we must understand the fractal nature.

• Our simple model suggests that a fractal solar wind can give rise to structured reconnection on the magnetopause while maintaining spatially large scale features.

• Observations in the ionosphere show the fluctuations in convection velocity are consistent with such a model.