Magnetic Helicity

1
Magnetic Helicity

• Magnetic helicity measures
• intrinsic properties of flux tubes
• (shear, linking, kinking
• twisting handedness)
• It is defined by a volume integral
• where A is the vector
  potential
• and B is the magnetic
  field
• Magnetic helicity is a conserved quantity even
  
• in resistive MHD (Berger, 1984)
• Methods to measure magnetic helicity on the Sun
• are only 3-4 years old.
• We are one of the pioneer groups, who can do
  it!

2
Why is helicity interesting?

• Helicity can be traced as the magnetic field
• emerges through the photosphere
• fills the corona
• erupts as a coronal mass ejection (CME)
• reaches the Earth as a magnetic cloud
• Helicity accumulation is the key to CMEs
• reaching a stability threshold of helicity
  is emerging as an
• underlying cause of CMEs
• Helicity output is the key to the solar dynamo
• puts constraints on the dynamo models
  taking into account
• the conservation of helicity

3
How can helicity change?
In a given volume, change of magnetic helicity
can be written

(Berger Field, 1984)
advection term
shear term
twisted flux emergence (increase) ejection via
CMEs (decrease)
horizontal photospheric motions
twisting
braiding
shearing
emergence
4
Helicity injection to the corona
Chae, 2003
Green et al, 2002
Photospheric helicity injection Local
Correlation Tracking methods LCT has intrinsic
problems
Coronal helicity Computed from
magnetic extrapolation models matched with
observed loops
5
Our project
To develop new methods for measuring the
inflow of helicity through the photosphere using
SOHO/MDI magnetograms helicity
increase in the corona using coronal models and
images To develop methods for magnetic
helicity measurements using vector
magnetograms present methods use only the
line-of-sight component of the magnetic
field, since Blos 5 G, while Btrans 200 G
To get prepared for Solar-B, which will provide
us with greatly improved magnetic field
measurements and coronal images
6
Helicity Solar-B
SOT/FPP (0.25, 164x164, Blong 1-5 G,
Btrans 30-50 G) Measurements of helicity
inflow through the photosphere using full
vector magnetograms of high resolution
XRT EIS ( STEREO) Modelling of coronal
loops, of a large range of T Measuring the
increase of helicity in the corona ?
establishing a the limit of stability ?
eventually CME forecast (CME identification
with STEREO)
7
Solar-B Instruments

• Solar Optical Telescope (SOT)
• 0.25 spatial resolution optical telescope
• Focal Plane Package (FPP) vector
• magnetograph spectrograph
• fov 164x164, Blong1-5 G, Btrans30-50 G
• temp. res.5 min. detailed Stokes profiles
• X-ray telescope (XRT)
• -- 2 spatial resolution, 2 sec. cadence
  full-disc and partial frame
• EUV imaging Spectrometer (EIS)
• -- in imaging mode temporal res. 3-10 s
  fov 4x4

8
Helicity injection via footpoint motions

• Helicity generation rate by footpoint motions
  can be understoodas the summation of the rotation
  rate of all the individual elementary flux pairs
  weighted by their magnetic flux (Berger, 1986).
• We can separate the helicity generated by the
  differential
• rotation (a shear flow) into two terms
  
• Twist and writhe helicity have opposite signs,
  while their magnitudes are similar ? they
  partially cancel
• (Démoulin et al, 2002).

9
Helicity Solar B

• Please use this template to produce your RG panel
  slides
• Use sub-bullets for effect
• Dont alter the style
• Be concise

Add your own text boxes if needed
For example, as labels
10
Computation of magnetic helicity generated by
differential rotation
We consider the first term (effect of horizontal
motions) which shows that the helicity
generation rate can be understood as the
summation of the rotation rate of all the
individual elementary flux pairs weighted by
their magnetic flux (Berger, 1986).
Differential rotation time-independent shear
flow. We can separate the helicity generated by
the differential rotation into two terms

Twist and writhe helicity have opposite
signs, while their magnitudes are similar ?
they partially cancel (Démoulin et al, 2002, SP).
11
Relative magnetic helicity

• Computation of helicity is physically
  meaningful when B is fully contained inside V
  (since A ? A ??), when field lines cross the
  boundary (Bn ? 0 on S around V, solar case) a
  relative magnetic helicity can be computed
• B0 has the same Bn distribution on S as
  B.
• The helicity is measured relative to that of
  the
• potential field.
• Hr is gauge invariant (Berger Field,
  1984 Field
• Antonsen 1985).