Ignace-ASP2019-poster

Motivation & Introduction
n Direct and local measurements of internal magnetic field are highly desirable in TAE’s fusion plasma experiments to characterize the magnetic field profile and directly measure the presence of field reversed configuration.
n Such measurements will show separate branches of magnetic field configurations, including cusp, mirror, etc.
n With real time measurements of internal magnetic field, a feedback control system can be deploy for plasma control.
n Diagnostic must also be non-perturbative (no probes). n Typical magnetic field
2TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
Magnetic Field Measurement on Sun using Hanle Effect
3Department of Astrophysics, University of Wisconsin, Madison, WI
Self Illumination in Cylindrical
Laser Illumination in Cylindrical Geometry
n Consider a laser that shines along the diameter of the plasma.
n Scattered light is measured along axial (top) and radial (side) views
B=B Case z0
Hanle Effect for Low and Null Magnetic Field
n The Hanle effect, described by Wilhelm Hanle in 1924, refers to how a magnetic field modifies the polarization from resonance line scattering.
n In a classical description of resonancescatteringthat treatstheatomasadamped harmonic oscillator, the oscillating electron experiences precession in the presence of a magnetic field.
n This precession alters the distribution of scattered light withdirectionaswellasthe degree of polarization of the scattered light.
n At larger field strengths excess of BHan , Zeeman effect dominates.
2
Non-Perturbative Measurements of Low and Null Magnetic Field in High Temperature Plasmas Using the Hanle Effect
Richard Ignace1, Deepak Gupta2, and Kenneth Nordsieck3
1Department of Physics, East Tennessee State University, Johnson City, TN
HMI Magnetic Field Color Table
body
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.
20
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
44
30
(hereafter the local solar vertical). This light scattering angle is necessary to properly invert the Stokes profiles (see Sect. 4). In
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
http://jsoc.stanford.edu/data/hmi/images/latest/
-10
solving any prominence small-scale structures. However, we do
* Gupta, DK, et.al., B
October 23 - 27, 2017 • Milwaukee, Wisconsin
ab
ove
th
en
oi
,
P
U/ a
1
1
0
20
30
20
cos ↵
Self Illumination Illustration
10
10
details within the prominence such as threads, even though the
nences are often classified as the hedgerow type. The attained
1
0
30
see strands in the EUV images. At high latitudes, these show
N N 3E (1 + cos2 ↵ ) N N
n Hanle effect is widely used to measure low magneti
1 1
.
se
lev
s
a
0
0
el.
Th
efi
4
r
e
p
r
p
o
s
9
,
5
ts
are
go
o
d in
Sto
kes
Ih,oa
rnd-lik V/I, and the residuals are very small. Profiles in case (b) corre-
9
t
A
h
/I, u
n
n
l
M
e
e
Q
eT
es
d
f
g fro
m
the
inve
30
20 10
Fe XII 195 Å and He II 304 Å observations. The prominence can
n Consider a long cylinder plasma
Limb
0 Spicules
D. Orozco Suárez et al.: The magnetic fiel0d vector config2u0ration of a sol4a0r prominence 60 [arcsec]
thin, no radiative transfer.
at each pixel of the TIP-II slit is taken into account in the anal-
height h over the solar surface from the apparent height h′ as (see
n Axial observation of signal.
spond to a point where the Stokes U/I and V/I signals are barely ◦ ◦ † ◦ of a coronal cavity right above the prominence (Régnier et al.
cylindrical radius.
NN
above the noise level. The fit in Stokes Q/I is good. Case (c) rep- 2011).
Individual He I 1083.0 nm triplet emission profiles recorded in 58
3E(13cos' ) 1 B
0
3E (1 + cos ↵ ) 1 p = 2 1 2
resents an infrequent pixel where the Stokes V/I signal shows -horizontal (Dextral) 6.9 77.0 49.0 In the H image (bottom left panel), the prominence body
B
Axial;
net circular polarization. Again, the fits are good except for ◦
is seen in emission outside the solar disk while the prominence
profiles are normalized to their maximum peak value (first col-
-horizontal (Sinistral – 180 ) 6.4 Stokes V/I. The version of HAZEL we applied neglects atomic ◦
orientation and possible correlations between the magnetic field
5
8+E (13cos ↵ )
and the velocity gradients along the LOS . Cases (a) and (c) are in the Hanle saturation regime, B > 10 G. In the same panels we show both the quasi-vertical and quasi-horizontal solutions, i.e., one solution and its corresponding 90◦ ambiguous solution. We pay attention to the difference between the two fits: it is neg- ligible and at the noise level which means that the Stokes Q/I,
A46, page 3 of 12
8+E (13cos ↵ ) 12
U/I,andV/Iprofilesareindistinguishablefortwodifferentmag- The field strength, inclination, and azimuth maps of the n Field Sensitivity: “Hanle field” B , defined by the ratio of
22
constrain the field strength, but constrain the field direction.
Han prominence obtained from the analysis of the Stokes profiles netic field orientations. Two compatible solutions are found not with HAZEL and corresponding to two compatible solutions via
B
5
the Larmor preceGiven that the fractional number of pixels showing anomalous ◦
ssional rate for the elec
r
the
Stokes V profiles is very small, we do not find it justified to increase correspond to a solution where the inclination of the field vec-
9
the complexity of our model assumptions. tor is almost perpendicular to the local vertical (quasi-horizontal
radiative rate of the line transition (i.e. Einstein A-value), is
= 0 Polarization; p =
3E1(1 3cos2'B) 2
A46, page 9 of 12 the scale at which magnetic fields will alter the resonance
scattering line polarization.
n Hanle signal is sensitive to lower magnetic field strengths.
(B~BHan).Signalsaturatesathighermagneticfield,butcan stillprovidefielddirection.
B=0 B=B1 >0
B=B >B 21
B=B >B 32
B=0
8+E1(13cos 'B) 3E1(1 3cos2'B)
€
Impurity Ion
D-I
D-I O-V O-VI He-II He-II N-V
Wavelength (A)
1215.34 6560.93 2781.0 1031.9 303.78
BHanle (Gauss)
53.4 7.7 11.4 35.5 855.1
j ,whichin-turn B
BHan
=
e 2egL
ul
m c A
Han
for some
and 0,0.5,1.0 Angle of the
polarization, aP
relates directly to
e
rsio
t
t
i
0
am
bigu
ity
are
di
spla
yed in Fig. 8. The left hand panels
For no poloidal field, cos# B
n of
the ob
n
h1
a. pS eu
o
n
t
g
o
dm)msat
e otfur
Hanle Field, B
useful lines in FRC plasma
2 2
r r uy c
st.he
top
(se
ro
D. Orozco Suárez et al.: The magnetic field vector configuration of a solar prominence
He 1083.0 nm peak intensity 66 Prominence
r disk.
prominence as seen in the peak intensity of the He I 1083.0 nm
Fig. 1. Peak intensity map of the He I 1083.0 nm triplet emission profile. 25
Fig. 3 from Merenda et al. 2006): R +h′
JJ
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
⊙
h= −R⊙. (1)
B
NN
B
12 􏰂3E􏰃 E=1.0
more diffuse horizontal filamentary structure (hereafter, promi- 50
✓◆
nence body) shape the prominence as loop-like structure. The
3E 4E
feet show more He I peak intensity signal than the prominence
p
those described by Chae et al. (2008). At low latitudes, the motions seem to be perpendicular to the limb and are typi-
1
2
2
2 top2
body. They may be connecting the prominence body with the
B=B Case
top
=
2
chromosphere. In the intensity map, we cannot distinguish finer
z0
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 20 Solar Terrestrial Relations Observatory (STEREO-B) Extreme UltraViolet Imager (Kaiser et al. 2008), and the Big Bear Solar
Observatory (BBSO) high-resolution H filter (Denker et al. α
p= cosα 8+E1(13cos ↵2) J J Axial; top 4−E 2
10 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
tion along with Fig. 2. In the movie, the evolution of the fine-
scale structures can be very well appreciated. Interestingly, at
fields strength and direction on the Sun.
polarization before depolarization.
B
4 − E1
1
0
m
′′
(top panels). The AIA spatial resolution is about ∼1.6. The
16:30 UT (5 h after the TIP-II observation) and for no apparent
✓◆ 3E
E1=0.75 2 E =0.5 2
white box outlines the TIP-II field-of-view, thus our observa-
serv
f
t
o
t
ed
St
oke
In this case, it can be seen as a large and dark envelope with a 2012).
Therotationisafunctionof
8+E1(1−3cos α2)
3E (1 + cos ↵ )
h
suinlt
e
A
s profi
les
wit
h the HAZEL code. Each
=
Quasi- B[G] θB[] χB[] χ []
2
h
e
4685.70 27.3 1238.8 29.1
c
in an SDO/AIA Fe XIV 211 Å movie available in the online edi- side
2
P
S
D
P
e ar
ws
in F
...
J J
N N0
B
B (r)=B tanh((r r )/(r r)) zz0 0
n High field strengths (saturated limit) yields the largest amplitude changes across the null point.
2
3 E ( 1 + c o2 s α )
1
70
n The top view combined with the side view (assuming axisymmetry) uniquely determine the scattering volume, and hence B field.
0
spatial resolution in TIP-II observations prevented us from re-
reason, the prominence begins to rise and erupts (not shown in filters (see Fig. 1). In the 171 Å and 211 Å filters, the promi- by Athay et al. (1983), which also erupted shortly after the ob-
0 20 40 60 0 20 40 60
n Similar measure [arcsec] tions sampled the central p[arctsoefc]the prominence as seen in these the movie). This prominence may be similar to the one observed
1
✓
◆
e
n The polarization position angle is ◦ nence is seen as a dark absorption against a bright background. servations. The eruption is slow and lasted 15 h until 21 May
cos2 ↵ p =
n
t
o
s
o
r
F
R
C
p
l
g.8. F
column represents one of the two 90 ambiguous solutions, quasi-horizontal (left) and quasi-vertical (right). As in Fig. 1, the black bottom
Fi
a
m
a
s
p
Radial; pside = p =
3E 4 E
E =0.25 1
It looks like a sheet made of strands, forming arc structures. In at 7:00 UT. Remarkably, we have detected apparent spiraling
3E (1 + cos α ) 1 1 4E2 2
top
2
* Gupta, Deepak K., Review of Scientific Instruments, 87 (2016) 11E526
This filter shows radiation coming from plasma at log T = 4.7. sit-and-stare slit observations and TIP-II (Orozco Suárez et al.
R
R
1
1
(aUbl-
top right panel). These “horns” may be indicating the presence 3. Analysis of the polarization signals
-
ig.
2,
P
this quiescent prominence are shown in Fig. 4. The Stokes I 1 0 8
only for two different magnetic field orientations but also for two different field strengths as seen in the Stokes U/I legend. Only in case (c) do the Stokes V/I fits differ, both of them fitting the profile within the noise level of the data.
- vα e r t i c a l ( S i n i s t r a l ) 1 1 . 7 1 3 6 . 0 − 1 . 5
77.0 − 49.0 feet are see-nveinrtiacabls(oSripntiisotrna,l h–e1n8c0e )darker 7th.8at the3s3u.8rroun1d.i2ngs,
156
1u06mn). They show the fine structure of the He I 1083.0 nm
2
Geome
hape
triplet (Fig. 1). The last two panels of Fig. 2 display STEREO
because they lie within the sola
The s
resemble
s the
be clearly seen in absorption (i.e., as a filament), which allows
us to know its position on the solar disk and the angle θ between
B=0
our LOS and the solar radius vector through the observed point
NN
N NN
this case, θ ≈ 70◦, on average. The exact values of the θ angle
N JJR
ysis of the profiles with HAZEL. We can also calculate the real
try
Richard Ignace (ETSU), Deepak Gupta, (TAE Tech.) et.al., “Non-Perturbative Measurements of Low and Null Magnetic Field in High Temperature Plasmas Using the Hanle Effect ” UP10.00155 ; 61st Annual Meeting of the APS Division of Plasma Physics • October 21-25, 2019 • Fort Lauderdale, FL
Radial;
[arcsec]
[arcsec] [arcsec] [arcsec]
Suárez , A&A 566, A46 (2014)
Field azimuth [degree]
Field inclination [degree]
Field strength [Gauss]
[arcsec]
with uniform emissivity. Optically
Height (Mm)
diagnostics developed for fusion relevant high-temperature (low- beta) plasmas devices, measure higher fields above 1 kiloGauss.
n Axial magnetic field inside an FRCs is low, goes to zero (at null- point) and reverses direction.
the scanning direction. The right axis shows the deprojected height over the solar surface. The more vertical appearance7o0f
larity flux dominates the photosphere. This information will help us determine the chirality of the filament, once we have inferred
Typical Field Lines in a FRC
60
i
236G.
Positive or negative polarity sunspots and other strong field regions will appear blue or red with dark umbrae.
′′ 110
of symmetry. Peaks toward edge due to maximum
0 30
138
′′ ′′
(∼100 Mm) and a width of 15 . The angle between the
n Position along a curve in p versus p corresponds to the
0
20
10
0
30
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.
100 90
ded
us
B
correction, as well as the polarimetric calibration. To improve
s
the signal to noise ratio the data were down-sampled spectrally
ian, measured counterclockwise. In the right hand side of Fig. 3, we define the reference system with the Y and Z-axis contained
side
field strength of the scattering
volume.
and spatially along the slit direction, yielding a final spectral and
b
e
c
a
u
s
e
spatial sampling of 4.4 pm and 0. 51, respectively.
The observed prominence can be seen in Fig. 1, were the
gne
with a map of the photospheric magnetic flux. They show that in
X-axis represents the position along the slit and the Y-axis is 80
the prominence on both sides of the observed FOV (hereafter,
prominence feet), which are connected to each other with a
.
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-
20
cos (90◦ − θ)
In Fig. 3 we sketch the geometry of the prominence. In particu-
10
5
0
B=0 Case, No Hanle effect. contour lines (right side). The filament has a length of about
140
β ∼ 17◦ is the angle that the prominence forms with the merid-
n Polarization is zero on axis,
130
120
lar, we show a top view of the prominence using STEREO-B
Laser
R
LOS and the long axis of the prominence is α = 90◦ + β, where
top
in the sky-plane. Finally, SDO/HMI ma
the right hand side (solar west) of the prominence, positive po-
the magnetic field vector in the promine
60
nce
bod
y
a
n
s
otropy.
tog
ram
sp
rovi
n The polarization is non-monotonic motions that are mainly parallel to the solar limb, similar to
cal of interactive hedgerow prominences (Pettit 1943; Hirayama 1985). The long-term evolution of the prominence can be seen
􏰂 􏰃
ield
regionrepresentsthesolardisk.TherestofthedarkareascorrespondtopixelswhoseStokesQ/IandU/Isignalsdidnotexceed5timestheir rotatedduetotheHanleecfofse#ct.=0
str
corresponding noise levels. the 304 Å filter the prominence appearance is rather different. motions in the feet of this prominence on 19 May 2011 using B
en
gth, i
ncli
na
tion,
and
az
imu
th m
aps
res
ultin
as a function of field strength,
showing a small puptic=k in the
3E
p = 1 cos α
p= Rigid Rotor B field Case
2
side 1 2
Stokes vector Q, B, polarization and alpha_2vsnormalized radius of plasma.
Different lines show
plots at different B 0
fields.
r0=0.5 and Dr = 0.1
B=0
8+E(13cos' ) 1B
side
B=0
will yield JB from the plot.
s
side
8 + E (1 − 3 co2 s2 α ) 1 2
top
1
cos ↵ 2
p =
Vector Magnetic Field Orientations B(Bz, B , B )
n Analysis is done in saturation limit. Measurables cannot cos#=0
p=+17%max
and-40%minat
cos(JB)=0 and
2 2 Bz(r)=Bz0tanh((r r0)/(r0r))
p =
Axial;
2 8+E1(13cos 'B)
jB/2pi=0.25,0.75
Bz(r)=Bz0tanh((r r0)/(r0r))
theta phi
2