P. 1

n Typical magnetic field diagnostics developed for fusion relevant high-temperature (low- beta) plasmas devices, measure higher fields above 1k Gauss
n Axial magnetic field inside an FRCs is low, goes to zero (at null- point) and reverses direction
Typical Field Lines in a FRC
x˙ ˙ + 2 ω L ( x˙ × B ) + γ x˙ + ω 2 x = − e E | B | 0 m
Measurement of Magnetic Null and Field Reversal in FRC Plasmas using the Hanle Effect
Motivation & Introduction
n C-2U achieved sustained, beam-driven advanced FRCs. However, all evidence related to field-reversal was indirect.
n Having a direct and local measurement of field-reversal in C-2W is very desirable
n Such measurements will also show any separate “branches” of field configuration in operation space, and may be useful for feedback control
n In addition of being local and direct, diagnostic must also be non-perturbative
Hanle Effect for Low or Null Field
Measurement Schemes for FRC
Measurement of Hanle Signal in Lab
n Hanle effect can provide measurement of low magnetic field, including position and shape of axial-field null location.
n Hanle Effect is widely used to measure low magnetic fields on the Sun and stellar plasmas
Magnetic Field Measurement on Sun using Hanle Effect
ΔEB >ΔEnat ~!/τ _I i M=-i
HMI Magnetic Field Color Table
triplet (Fig. 1). The last two panels of Fig. 2 display STEREO
n Signal saturates at higher magnetic field, but can still
Hanle Field, B Han
The line of sight magnetic field color table is designed to visually show structure at both high and low field values.
Field strengths <24 G are shades of gray. Positive Field Values are green and blue3.0 Negative field values are yellow and red.
Weak field regions appear mostly yellow or green. Increasingly positive values 10 range from dark green to bright green at 236G. Negative values move from bright yellow to orange at -236G.
There is a sharp discontinuity in color at 236G. 20
Positive or negative polarity sunspots and other strong field regions will 10
appear blue or red with dark umbrae.
0 30
Fig. 1. Peak intensity map of the He I 1083.0 nm triplet emission profile. 25
us to know its position on the solar disk and the angle θ between our LOS and the solar radius vector through the observed point (hereafter the local solar vertical). This light scattering angle is necessary to properly invert the Stokes profiles (see Sect. 4). In this case, θ ≈ 70◦, on average. The exact values of the θ angle at each pixel of the TIP-II slit is taken into account in the anal- ysis of the profiles with HAZEL. We can also calculate the real height h over the solar surface from the apparent height h′ as (see Fig. 3 from Merenda et al. 2006):
B= Han
mcA e ul
2eg L
for some useful lines in FRC plasma
0 30
1215.34 53.4 6560.93 7.7
20 10
D. Orozco Suárez et al.: The magnetic fiel0d vector config2u0ration of a sol4a0r prominence 60
Fe XII 195 Å and He II 304 Å observations. The prominence can be clearly seen in absorption (i.e., as a filament), which allows
Self Illumination Illustration
There are 254 defined colors symmetrically arranged around the zero point.
The 127 positive include 2 darkening gray, 18 brightening green, and 110 darkening blue. 40
The 127 negative include 2 brightening gray, 18 darkening yellow, and 107 darkening red.
Nominally, each color spans a range of ~11.81 G and the color table extends from -1500 to 1500 G. 20 chromosphere. In the intensity map, we cannot distinguish finer
30 20 10
0 20 40 60
details within the prominence such as threads, even though the
He 1083.0 nm peak intensity
because they lie within the solar disk. The shape resembles the
The prominence is seen as a bright structure against a dark background. The lower dark part corresponds to the solar limb. The top-left arrow
points to solar North. The deprojected height (see Sect. 2) above the solar surface is shown on the right axis. The data was taken 20 M1a5y
2011 at 9:44 UT and finished at 11:15 UT on the same day.
reduction process included dark-current, flat-field, and fringes
R +h′ ⊙
correction, as well as the polarimetric calibration. To improve
β ∼ 17
is the angle that the prominence forms with the merid-
the signal to noise ratio the data were down-sampled spectrally
and spatially along the slit direction, yielding a final spectral and spatial sampling of 4.4 pm and 0′.′51, respectively. 110
0s NN
The observed prominence can be seen in Fig. 1, were the 90
with a map of the photospheric magnetic flux. They show that in the right hand side (solar west) of the prominence, positive po- larity flux dominates the photosphere. This information will help us determine the chirality of the filament, once we have inferred the magnetic field vector in the prominence body.
We classify the observed prominence as of quiescent type, meaning that it is located outside active regions. Quiescent prominences are often characterized as sheets of plasma stand- ing vertically above the PIL and showing prominence threads. When these threads are vertically oriented, quiescent promi- nences are often classified as the hedgerow type. The attained spatial resolution in TIP-II observations prevented us from re- solving any prominence small-scale structures. However, we do see strands in the EUV images. At high latitudes, these show motions that are mainly parallel to the solar limb, similar to those described by Chae et al. (2008). At low latitudes, the motions seem to be perpendicular to the limb and are typi- cal of interactive hedgerow prominences (Pettit 1943; Hirayama 1985). The long-term evolution of the prominence can be seen in an SDO/AIA Fe XIV 211 Å movie available in the online edi- tion along with Fig. 2. In the movie, the evolution of the fine- scale structures can be very well appreciated. Interestingly, at 16:30 UT (5 h after the TIP-II observation) and for no apparent reason, the prominence begins to rise and erupts (not shown in the movie). This prominence may be similar to the one observed
X-axis represents the position along the slit and the Y-axis is 80
the scanning direction. The right axis shows the deprojected height over the solar surface. The more vertical appearance7o0f
the prominence on both sides of the observed FOV (hereafter,
prominence feet), which are connected to each other with a
more diffuse horizontal filamentary structure (hereafter, promi- 50
nence body) shape the prominence as loop-like structure. The
feet show more He I peak intensity signal than the prominence
30 20 body. They may be connecting the prominence body with the
data were obtained during good seeing conditions.
To put the TIP-II observations in context, we ma-2d0e
use of data provided by the extreme ultraviolet light tele-
scope (AIA; Lemen et al. 2012) onboard NASA’s Solar
Dynamics Observatory (SDO; Pesnell et al. 2012), the
Solar Terrestrial Relations Observatory (STEREO-B) Extreme
UltraViolet Imager (Kaiser et al. 2008), and the Big Bear Solar
Observatory (BBSO) high-resolution Hα filter (Denker et al.
1999). Figure 2 displays maps of the prominence as seen in the
FeIX 171 Å, FeXIV 211 Å, and HeII 304 Å AIA band passes
(top panels). The AIA spatial resolution is about ∼1.6. The
white box outlines the TIP-II field-of-view, thus our observa-
0 20 40 60
tions sampled the central p[arctsoefc]the prominence as seen in these
Prominence body
prominence as seen in the peak intensity of the He I 1083.0 nm
h= ◦ −R⊙. cos(90 −θ)
Impurity Ion
Wavelength B Hanle
In Fig. 3 we sketch the geometry of the prominence. In particu-
lar, we show a top view of the prominence using STEREO-B
contour lines (right side). The filament has a length of about
138′′ (∼100 Mm) and a width of 15′′. The angle between the
LOS and the long axis of the prominence is α = 90◦ + β, where
ian, measured counterclockwise. In the right hand side of Fig. 3,
we define the reference system with the Y and Z-axis contained
in the sky-plane. Finally, SDO/HMI magnetograms provided us
n Vector components of the field
can also be estimated by using
multiple resonance radiation-
lines with different sensitivities
(say,B/B ~1andB/B ≫1). HH
This will help measuring both axial and azimuthal magnetic field simultaneously
De-excitation Rate or
Einstein Coefficient, A ul
~ (Lifetime, t)
p= Radial View sensitivity:
n Laboratory experiments confirm and match the theoretical understanding
Comparison of measured signal with predicted signal
n n
Described by Wilhelm Hanle in 1924
De-polarization of scattered resonant-line radiation in presence of magnetic field
An external illumination source, e.g., Laser, of selected wavelength is injected radially in the FRC
External Illumination Illustration
n Experiments with Hanle signal were done in the lab with DC discharge for comparison with theory
n Neon discharge was used with magnetic field varying from +26 Gauss to -26 Gauss
n Self illumination scheme is used in which a part of discharge illuminate other part.
n Stokes vectors are measured. Typically normalized U and V
Experimental Setup
Quantum mechanically, this is the effect due to coherent superposition of degenerate Zeeman sublevels (No field, B=0)
Degeneracy lifted with magnetic field and coherence decreases
1+6(B/B )2 H
Asymmetric self-illumination of axial-null location, from the FRC itself, may be sufficient for the observation of Hanle effect without the need of an external source
The polarization signal will peak along the whole axial-null circle, with polarization directed toward the azimuthal direction, providing an image of the whole null circle simultaneously. And, hence a direct measurement of FRC location and shape, based on internal magnetic structure
⎛3p cos(α )⎞
⎛3p cos(α )⎞
Us /Ii =⎜ 0 2 ⎟sin(2β−α2) α =tan−1(2B/B )
provide field direction
Deepak K. Gupta1, K. Nordsieck2, R. Ignace3, J. Kinley1, M. Nations1 and the TAE Team
1TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2Department of Astrophysics, University of Wisconsin, Madison, WI
3Department of Physics, East Tennessee State University, Johnson City, TN
THE HANLE EFFECT APPLIED TO MAGNETIC FIELD DIAGNOSTICS 393 Pz and without magnetic field the polarization direction should lie along Px. In
Linearly polarized signal only
at and near null location will be N observed, proving the radial position of axial null location
Classically treated as a
fact, the classical oscillator vibrating along Px and damped by its lifetime ~- is
subject to the Larmor precession oJ = (e/2m)B around the magnetic field direction. damped harmonic oscillator,
with light scattered partly
The combination of the damping and the Larmor precession is the Hanle effect.
By using the equivalent quantum language, this can be described by identifying the classical oscillator with a normal Zeeman triplet (J = 1 ~ J = 0). The energies
isotropically and partly
dipole-like of the Zeeman sublevels are shown in Figure 2. The ground state is not split and
Change in the rotation of polarization provides magnetic field direction
Change in Rotation of Polarization:
α = arctan(2B / BH ) / 2 Axial View sensitivity:
has an infinite lifetime, whereas the three Zeeman sublevels M = 0 + 1 of the excited
state are broadened by the lifetime r. The direction of the magnetic field being the
quantization axis Pz, the incident radiation scattered along direction Pz is equivalent
N Rs
to a portion of a beam of energy hu and electric vector ex=-(1/~/2)(e+-e_) in
the usual classical description. It corresponds to the photon of state vector ]ex)=
-(1/,/-2)(1~+)- [~-)) of the standard representation. Immediately after absorption at time t = O, the excited atomic state is a linear combination of its eigenstates ]JM) and reflects that of the incident photon:
HanleRatio,H≈ωL /Aul ≈B/Aul
I~b(t=O)}-II, 1}-11,-1).
Owing to its natural damping and as a consequence of its interaction with the magnetic field, the atom evolves in its excited state until time t where the photon
1+ 4(B / B
StimulatedSignalfor Axial and Radial View
Radial View Magnetic Field
Axial View
is emitted:
) p = 1+ 2(B / BH )2
10(t)) -,/,r be
Ix, 1)-e+i~
Qs /Ii =−⎜ 0 ⎝3+p0 ⎠
⎝3+p0 ⎠ 2 H Stokes Parameter U/I
[arcsec] [arcsec] [arcsec]
Suárez , A&A 566, A46 (2014)
Field azimuth [degree]
Field inclination [degree]
Field strength [Gauss]
Deepak K Gupta, Tri Alpha Energy, Inc., “Measurement of magnetic null and field reversal in FRC plasmas using the Hanle effect ” BP11.00049 ; 59th Annual Meeting of the APS-DPP, October 23 - 27, 2017 • Milwaukee, Wisconsin
n Field Sensitivity: Hanle signal is sensitive to low magnetic for !ow magnetic fie~ds,
D. Orozco Suárez et al.: The magnetic field vector configuration of a solar prominencefield strength only. (B = BHan at Hanle Ratio, H = 1)
Fig. 2. Lower and upper levels that result in a Zeeman triplet. Note overlapping of excited sublevels
1031.9 35.5 303.78 855.1
4685.70 27.3 1238.8 29.1
2 ⎟cos(2β−α2) Stokes Parameter Q/I
n Hanle effect may provide a non-perturbative diagnostic to measure the low magnetic field in an FRC plasma, including the position and shape of zero axial magnetic-field (null) location
n Diagnostics can be extended to measure the vector magnetic field using multiple lines, and is in design with this configuration on C2-W
n Technique of measuring low or null magnetic field is not limited to FRC only. It is applicable to other laboratory plasmas with low magnetic-field conditions such as magnetic cusps
Height (Mm)