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 methods for magnetic helicity measurements
• 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”, 164”x164”, Blong= ± 1-5 G, Btrans= ± 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: 164”x164”, Blong=1-5 G, Btrans=30-50 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: 4’x4’

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
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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).