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Plasma radiation Bolometry X-Ray

Introduction to the Diagnosis of Magnetically Confined Thermonuclear Plasma

Core diagnostics II: Bolometry and Soft X-rays

• J. Arturo Alonso

Laboratorio Nacional de Fusión EURATOM-CIEMAT E6 P2.10 arturo.alonso@ciemat.es

version 0.1 (March 7, 2011)

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 1 / 22

Plasma radiation Bolometry X-Ray

Outline

1

Plasma radiation Continuum spectrum

2

Bolometry: total radiated power The metal-resistor bolometer Sample experimental bolometric data

3

Soft X-ray diagnostic: core MHD phenomena X-Ray Imaging Systems Sample experimental SXR data

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 2 / 22

Plasma radiation Bolometry X-Ray

Outline

1

Plasma radiation Continuum spectrum

2

Bolometry: total radiated power The metal-resistor bolometer Sample experimental bolometric data

3

Soft X-ray diagnostic: core MHD phenomena X-Ray Imaging Systems Sample experimental SXR data

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 3 / 22

Plasma radiation Bolometry X-Ray

A loss of power and a source of information

There are at least two reasons why one could be interested in the radiation emitted by the plasma:

1 It is a power loss mechanism. Remember the power

balance Sα + Sh = Srad + Sκ . (thought to take part in the physics of the density limit [2]).

2 It carries information about the plama it was emitted from.

Different processes emit electromagnetic radiation in a plasma: Cyclotron –acceleration by the Lorentz force in the B-field Bremsstrahlung –collisions between unlike particles Recombination –collisions with e− capture Atomic transitions – of excited e− in the atom’s quantum levels

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 4 / 22

Plasma radiation Bolometry X-Ray

Plasma radiation mechanisms

Radiation type e− state Physical mechanism Cyclotron free-free acceleration by the Lorentz force Bremsstrahlung free-free e−–ion inelastic collisions Recombination free-bound e−–ion collision and e− capture Line bound-bound e− transition between atom’s quantum levels Cyclotron radiation is absorbed and reemitted (plasma is

• ptically thick in that wavelength –ECE diagnostic)

Brems + Recombination produce the continuum spectrum Line radiation produces the ions’ characterisctic spectra Total spectrum is a rather complicated mixture of lines and continuum

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 5 / 22

Plasma radiation Bolometry X-Ray

Spectral regions

Spectral Region Wavelength / Energy Region Near Infrared 700-1200 nm / 1-2 eV Visible 400-700 nm / 2-3 eV Ultraviolet (UV) 200-400 nm / 3-6 eV Vacuum Ultraviolet (VUV) 30-200 nm / 6-40 eV Extreme Ultraviolet (EUV) 10-30 nm / 40-120 eV Soft X-Ray 0.1-10 nm / 120-12000 eV Only relatively high-Z impurities have lines above the keV (E0 ≈ 13.6Z2 eV). Different detectors used for different spectral regions (i.e. semiconductors for IR and visible cameras or AXUV photodiodes, dispersive elements in spectrometers) Bolometers are sensitive to photon energies from 1eV to 10 keV (used as power loss monitors)

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 6 / 22

Plasma radiation Bolometry X-Ray

Bremsstrahlung spectra

The Bremmstrahlung radiation (W/m3eV) emitted by a Maxwellian electron distribution colliding with an i-species ion population is [3] dPBrem

i

dE = CneniZ2

i gff

e−E/Te √Te . Summed over the ion species, the total power density is dPBrem dE = Cn2

eZeffgff

e−E/Te √Te , with Zeff = 1 ne

• i

niZ2

i

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 7 / 22

Plasma radiation Bolometry X-Ray

Recombination radiation

Recombination radiation power density can be written in compact form as dPRec

i

dE = (γ(Te, Zi) − 1) dPBrem

i

dE . The pre-factor is a complicated sum over the possible final electron quamtum level [1]. It includes low energy cutoffs corresponding to the different bound energies of these final states For a fixed Te the recombination radiation preserves the e−E/Te dependence on the photon’s energy. Total contiuumm radiation (Brem. + Rec.) is then dPContinuum

i

dE = γ(Te, Zi)dPBrem

i

dE , and γ is consequently termed the enhancement factor.

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 8 / 22

Plasma radiation Bolometry X-Ray

Relative importance of radiation processes

Total spectrum is complicated by emission lines on top of a

• continuum. Impurty types and concentrations vary from

machine to machine. Not much can be said in general. Nonetheless, Line radiation can be strong in the relativelly cold (Te ∼ 1 − 10 eV), neutral and impurity rich plasma in the Edge/SOL and divertor region. For Te of the order of the quamtum potentials of the impurites, recombination dominates the continuum (γ ∼ 2 − 100) In fusion reactor conditions (Te 10 keV, Zeff ≈ 1) total radiated power is mainly due to Bremsstrahlung radiation.

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 9 / 22

Plasma radiation Bolometry X-Ray

Relative importance of radiation processes

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 10 / 22

Plasma radiation Bolometry X-Ray

Outline

1

Plasma radiation Continuum spectrum

2

Bolometry: total radiated power The metal-resistor bolometer Sample experimental bolometric data

3

Soft X-ray diagnostic: core MHD phenomena X-Ray Imaging Systems Sample experimental SXR data

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 11 / 22

Plasma radiation Bolometry X-Ray

To monitor radiated power

Plasma emits most of its energy in a spectral range from 1 eV to 10 keV Bolometric detectors need to have high efficiency across this range The general scheme is an absorber and a thermometer absorber heats up due to the absorbed radiation thermometer measures changes in the absorber’s temperature form which the instantaneous radiated power can be derived

Heat sink absorber

thermometer weak thermal link

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 12 / 22

Plasma radiation Bolometry X-Ray

Viewing geometries chord camera aperture detector

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 13 / 22

Plasma radiation Bolometry X-Ray

The metal-resistor bolometer

Thin layers of metals have the required efficiency, and their resistance depends linearly on their temperature The radiated power can be computed directly form changes in the absorber temperature Prad = C d∆T dt + ∆T τ

• .

C is the absorber heat capacity and τ a time constant characteristic of the thermal coupling to a heat sink.

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 14 / 22

Plasma radiation Bolometry X-Ray

The metal-resistor bolometer

Bolometers are mounted in sets of 4 in a Wheatstone bridge configuration, 2 exposed (measuring), 2 shielded (reference). The voltage drop across the bridge is ∆V = VB Rmeas − Rref Rmeas + Rref ≈ VB Rmeas − Rref 2R0 where R = R0(1 + α∆T). Then ∆T = k∆V .

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 15 / 22

Plasma radiation Bolometry X-Ray

Sample Bolometry data: Density limit disruption in JET

• G. Arnoux et al., Nucl. Fusion 49 (2009) 085038

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 16 / 22

Plasma radiation Bolometry X-Ray

Outline

1

Plasma radiation Continuum spectrum

2

Bolometry: total radiated power The metal-resistor bolometer Sample experimental bolometric data

3

Soft X-ray diagnostic: core MHD phenomena X-Ray Imaging Systems Sample experimental SXR data

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 17 / 22

Plasma radiation Bolometry X-Ray

SXR diagnostics

For keV plasmas continuum radiation is particularly sensitive to Te variations in the SXR part or the spectrum. SXR diagnotics: X-ray Crystal spectroscopy - High spectral resolution - information from emission lines of medium-Z impurities Pulse Height Analyser - Medim spectral resolution - Photon counting detector to estimate Te AXUV cameras - Coarse spectral resolution (with filters) - arrays of diodes for tomographic inversion

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 18 / 22

Plasma radiation Bolometry X-Ray

AXUV photodiodes and fitlers

High QE for SXR photons (built-in High-Pass filter) Insensitivity to Neutrals and ECRH Strong E-dependence of foil transmitance T ∼ e−µ(E)d , µ(E) ≈ E−3 + Absortion edges

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 19 / 22

Plasma radiation Bolometry X-Ray

Filter arrangements for imputiry or Te monitoring

Te: High-Pass filter from mass abosortion exponential transmission profile log T(E) ∼ −E−3 Impurity lines: Band pass filter from the signal difference of two detectors with different filters (select elements and thicknesses for appropriate absortion edges)

Filter 1 Filter 2

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 20 / 22

Plasma radiation Bolometry X-Ray

Sample SXR data: Shafranov shift in W7-AS

When SXR signal is filtered for Te sensitivity, the emissivity is expected to be constant in flux surfaces.

Anton, Plasma Phys. Contol. Fus. 38 (1996) 1849

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 21 / 22

Plasma radiation Bolometry X-Ray

Sample SXR data: tomographic reconstruction of an Alfven mode in W7-AS

• A. Weller, et al., Rev. Sci. Instrum. 70, 484 (1999)

SVD and Tomography will be treated in another lecture.

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 22 / 22

Plasma radiation Bolometry X-Ray

• S. Von Goeler, W. Stodiek, H. Eubank, H. Fishman,
• S. Grebenshchikov, and E. Hinnov.

Thermal x-ray spectra and impurities in the st tokamak. Nuclear Fusion, 15(2):301, 1975. Martin Greenwald. Density limits in toroidal plasmas. Plasma Physics and Controlled Fusion, 44(8):R27, 2002. BC Stratton, M Bitter, KW Hill, DL Hillis, and JT Hogan. Passive Spectroscopic Diagnostics for Magnetically-confined Fusion Plasmas. Technical report, Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States), 2007.

Core diagnostics II: Bolometry and Soft X-rays, A. Alonso, copyleft 2010 22 / 22