R. J. HenchenUniversity of RochesterLaboratory for Laser Energetics
46th Annual Anomalous Absorption Conference
Old Saybrook, CT1–6 May 2016
Heat-Flux Measurements from Collective Thomson-Scattering Spectra
1
qTSqSH = –l Te
11000.00
0.01
0.02
0.03
0.04
0.05
0.06
1200q/q
fs1300
Distance from target (nm)
Heat flux at t = 2.5 ns
1400 1500
D
k2~(m2~ = 526 nm)
Te
D
k
ks
TS collection
3~ drive beams(2 ns, 1.3 × 1014 W/cm2)
qSH = –l Te
D
Al
Thomson scattering from ion-acoustic waves (IAW’s)and electron plasma waves (EPW’s) was used to measure heat flux in coronal plasmas
Summary
• Changes in Landau damping caused by heat flux were seen in the relative amplitudes of Thomson-scattering spectra from IAW’s and EPW’s
• Local plasma conditions obtained from Thomson scattering provide an independent measurement of the heat flux using the Spitzer–Härm (SH) thermal-transport model
• The two methods of measuring the heat flux are in good agreement over the locations probed
TC12765
2
Collaborators
S. X. Hu, R. K. Follet, J. Katz, V. N. Goncharov, and D. H. Froula
University of RochesterLaboratory for Laser Energetics
W. Rozmus
University of Alberta
3
Space ~3 vte
ve
Te
fe
fe = f0 + f1M
An experiment was designed to test Spitzer–Härm thermal transport in laser-produced coronal plasmas
E24257a
4
These experiments measured the heat flux, electron temperature, and density as functions of space in a coronal plasma.
–q Tedl=
lnZ e mT4
/
/
e
e4 1 2
5 2l
K=
525.80.0
0.5
1.0
526.2
Ps (n
orm
aliz
ed)
526.6
Thomson scattering from IAW’s (calculated)
527.0
4400.0
0.5
1.0
460
A(q)P
s (n
orm
aliz
ed)
615
Thomson scattering from EPW’s (calculated)
Wavelength (nm)625 635
Collective Thomson scattering can measure the heat flux and local plasma conditions
E24096a
5
, –S k k f k kZ f k
2 1 2e ee
i
2 2~ r f
| ~ rf| ~= +^ b bh l l
– –dv vv
m ke n
k i
kf
4–e e
ee
2
2
:
:22
|r
~ c=
3
3#
f f fe M SH0 1= +
,P S k1 2s i? ~
~ ~+b ^l h Te?mD
ne?mD
Changes in the electron distribution function caused by heat flux affect the Thomson scattering from EPW’s
E24230a
6
–4 –2 0
f e (
arb
itra
ry u
nit
s)
Ps
(no
rmal
ized
)
10–5
10–4
10–3
10–2
10–1
100
Effect of heat flux on electrondistribution function
Effect of heat flux on EPWscattering feature (q/qfs = 0.035)
vz vte
2 4 –4 –2 00.0
0.2
0.4
0.6
0.8
1.0
vz vte
2 4
f0M
fSHe
–vzEPW +vz
EPW
f0f SHe = f0 + f
SH1
M
M
Thomson scattering was used to measure the heat flux, electron temperature, and electron densityin coronal plasmas
E24097a
7
• Thomson scattering (TS) provides local measurements of Te, ne, and q
in an .50 × 50 × 50-nm3 volume
• Probing five different locations provides values for Te
• An independent measure of q is obtained from Te, ne, and Te
D
D
Thomson scattering provides two separate measurements of heat flux by probing plasma waves along the direction of the temperature gradient.
k2~(m2~ = 526 nm)
Te
Dk
ks
TS collection
3~ drive beams(2 ns, 1.3 × 1014 W/cm2)
qSH = –l Te
D
Al
The up- and downshifted EPW features were measured with a large signal-to-background ratio
E24271a
8
1700
650
600
550
500
450
400
2 3Time (ns)
Raw EPW data
1 2 3Time (ns)
Background shot
1 2 30.0
0.5
1.0
Time (ns)
Subtracted spectra
Wav
elen
gth
(n
m)
Ps (n
orm
aliz
ed)
Thomson-scattering spectra obtained at five locations in the corona were used to measure the heat flux
E24098a
9
700
600
500
400
0.0
0.5
1.0
0.0
0.5
1.0
z = 1500 nmz = 1400 nmz = 1300 nmz = 1200 nmz = 1100 nm
Wav
elen
gth
(n
m)
1
526
525
524
2 3
Time (ns)
1 2 3
Time (ns)
1 2 3
Time (ns)
1 2 3
Time (ns)
1 2 3
Time (ns)
Wav
elen
gth
(n
m)
EP
W f
eatu
reIA
W f
eatu
re
Ps (n
orm
aliz
ed)
Ps (n
orm
aliz
ed)
The scattering spectra are fit to determine the electron temperature and density
E24099a
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
700
600
500
400
0.0
1.0
0.5
Electron feature, 1500 nm from target
1 2 3Time (ns)
Wav
elen
gth
(n
m)
Wavelength (nm)
Am
plit
ud
e (n
orm
aliz
ed)
EPW lineout, 1500 nm from target, t = 2.5 ns
450 550500 600
Ps (n
orm
aliz
ed)
Data lineoutq = 0.043 qfs
Te = 1.0 keVne = 5.3 × 1019 cm–3
Ion feature, 1500 nm from target
Wavelength (nm)
Am
plit
ud
e (n
orm
aliz
ed)
IAW lineout, 1500 nm from target, t = 2.5 ns
1
524.50.0
0.2
0.4
0.6
0.8
1.0
1.2
525.0 525.5
526
525
524
2 3Time (ns)
Wav
elen
gth
(n
m)
Data lineoutFit
Te = 1.0 keV
The electron temperature and density measurements are used to infer the heat flux
E24100a
11
11000.9
0.20.40.60.81.01.2
1.2
1.4
1.6
1.8
1.0
1.1
1.2
1.3
1.4
1300
Distance from target (nm)
ne
(x10
20 c
m–3
)
Distance from target (nm)
Thermal conductivityat t = 2.5 ns
T e (
keV
)
l (
W/c
m ·
K)
(×10
4 )
Electron temperature and densityprofiles at t = 2.5 ns
1500 1100 1300 1500 11000.00
0.02
0.04
0.06
1300
Distance from target (nm)
qS
H/q
fs
SH heat fluxat t = 2.5 ns
1500
Te fit
The relative amplitudes of the EPW scattering features were used to measure heat flux
E24101a
12
Wavelength (nm)
Am
plit
ud
e (n
orm
aliz
ed)
EPW lineout, 1100 nm from target,t = 2.5 ns
0.0
0.2
0.4
0.6
0.8
1.2
1.0
6506000.0
0.2
0.4
0.6
0.8
1.2
1.0
Wavelength (nm)
Am
plit
ud
e (n
orm
aliz
ed)
EPW lineout, 1500 nm from target,t = 2.5 ns
600 625575
Te = 1.1 keVne = 1.19 × 1020 cm–3
Data lineoutq = 0q = 0.015 qfs
Data lineoutq = 0q = 0.043 qfs
Te = 1.0 keVne = 5.2 × 1019 cm–3
Two experimental configurations measured heat flux parallel and perpendicular to the target normal
E24729a
13
AI target AI target
k2~ ks"
k" "
k2~ ks"
k" "
k 9 q
q"q
" "
"
k < q" "
Differences in the relative amplitudes of the EPW scattering features between the two configurations show the effect of heat flux
TC12766
14
0.0
0.2
0.4
0.6
0.8
1.0
500450 550 600
Wavelength (nm)
EPW feature 1400 nm from target, 1.75 ns k
The heat-flux values obtained by matching electron feature amplitudes are in good agreement with the temperature-gradient measurements
E24103a
15
11000.00
0.01
0.02
0.03
0.04
0.05
0.06
1200
q/q
fs
1300
Distance from target (nm)
Heat flux at t = 2.5 ns
1400 1500
qTSqSH = –l Te
D
Summary/Conclusions
16
Thomson scattering from ion-acoustic waves (IAW’s)and electron plasma waves (EPW’s) was used to measure heat flux in coronal plasmas
TC12765
• Changes in Landau damping caused by heat flux were seen in the relative amplitudes of Thomson-scattering spectra from IAW’s and EPW’s
• Local plasma conditions obtained from Thomson scattering provide an independent measurement of the heat flux using the Spitzer–Härm (SH) thermal-transport model
• The two methods of measuring the heat flux are in good agreement over the locations probed