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Heat-Flux Measurements from Collective Thomson-Scattering ... · PDF file 526.2 P s (normalized) 526.6 Thomson scattering from IAW’s (calculated) 527.0 440 0.0 0.5 1.0 460 A(q) P

Feb 05, 2021

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  • R. J. Henchen University of Rochester Laboratory for Laser Energetics

    46th Annual Anomalous Absorption Conference

    Old Saybrook, CT 1–6 May 2016

    Heat-Flux Measurements from Collective Thomson-Scattering Spectra

    1

    qTS qSH = –l Te

    1100 0.00

    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

    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 Rochester Laboratory for Laser Energetics

    W. Rozmus

    University of Alberta

    3

  • Space ~3 vte

    ve

    Te

    fe

    fe = f0 + f1 M

    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 m T4

    /

    /

    e

    e 4 1 2

    5 2 l

    K =

  • 525.8 0.0

    0.5

    1.0

    526.2

    P s (n

    o rm

    al iz

    ed )

    526.6

    Thomson scattering from IAW’s (calculated)

    527.0

    440 0.0

    0.5

    1.0

    460

    A(q) P

    s (n

    o rm

    al iz

    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 k Z f k

    2 1 2e e e

    i

    2 2 ~ r f

    | ~ r f | ~= +^ b bh l l

    – –dv v v

    m k e n

    k i

    k f

    4 –e e

    e e

    2

    2

    :

    : 2 2

    | 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 (

    ar b

    it ra

    ry u

    n it

    s)

    P s

    (n o

    rm al

    iz ed

    )

    10–5

    10–4

    10–3

    10–2

    10–1

    100

    Effect of heat flux on electron distribution function

    Effect of heat flux on EPW scattering feature (q/qfs = 0.035)

    vz vte

    2 4 –4 –2 0 0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    vz vte

    2 4

    f0 M

    fSHe

    –vz EPW +vz

    EPW

    f0 f SHe = f0 + f

    SH 1

    M

    M

  • Thomson scattering was used to measure the heat flux, electron temperature, and electron density in 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

    D k

    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

    1 700

    650

    600

    550

    500

    450

    400

    2 3 Time (ns)

    Raw EPW data

    1 2 3 Time (ns)

    Background shot

    1 2 3 0.0

    0.5

    1.0

    Time (ns)

    Subtracted spectra

    W av

    el en

    g th

    ( n

    m )

    P s (n

    o rm

    al iz

    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

    W av

    el en

    g th

    ( 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)

    W av

    el en

    g th

    ( n

    m )

    E P

    W f

    ea tu

    re IA

    W f

    ea tu

    re

    P s (n

    o rm

    al iz

    ed )

    P s (n

    o rm

    al iz

    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 3 Time (ns)

    W av

    el en

    g th

    ( n

    m )

    Wavelength (nm)

    A m

    p lit

    u d

    e (n

    o rm

    al iz

    ed )

    EPW lineout, 1500 nm from target, t = 2.5 ns

    450 550500 600

    P s (n

    o rm

    al iz

    ed )

    Data lineout q = 0.043 qfs

    Te = 1.0 keV ne = 5.3 × 1019 cm–3

    Ion feature, 1500 nm from target

    Wavelength (nm)

    A m

    p lit

    u d

    e (n

    o rm

    al iz

    ed )

    IAW lineout, 1500 nm from target, t = 2.5 ns

    1

    524.5 0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    525.0 525.5

    526

    525

    524

    2 3 Time (ns)

    W av

    el en

    g th

    ( n

    m )

    Data lineout Fit

    Te = 1.0 keV

  • The electron temperature and density measurements are used to infer the heat flux

    E24100a

    11

    1100 0.9

    0.2 0.4 0.6 0.8 1.0 1.2

    1.2

    1.4

    1.6

    1.8

    1.0

    1.1

    1.2

    1.3

    1.4

    1300

    Distance from target (nm)

    n e

    (x 10

    20 c

    m –3

    )

    Distance from target (nm)

    Thermal conductivity at t = 2.5 ns

    T e (

    ke V

    )

    l (

    W /c

    m ·

    K )

    (× 10

    4 )

    Electron temperature and density profiles at t = 2.5 ns

    1500 1100 1300 1500 1100 0.00

    0.02

    0.04

    0.06

    1300

    Distance from target (nm)

    q S

    H /q

    fs

    SH heat flux at 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)

    A m

    p lit

    u d

    e (n

    o rm

    al iz

    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

    650600 0.0

    0.2

    0.4

    0.6

    0.8

    1.2

    1.0

    Wavelength (nm)

    A m

    p lit

    u d

    e (n

    o rm

    al iz

    ed )

    EPW lineout, 1500 nm from target, t = 2.5 ns

    600 625575

    Te = 1.1 keV ne = 1.19 × 1020 cm–3

    Data lineout q = 0 q = 0.015 qfs

    Data lineout q = 0 q = 0.043 qfs

    Te = 1.0 keV ne = 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

    1100 0.00

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    1200

    q /q

    fs

    1300

    Distance from target (nm)

    H

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