Soft x-ray tomography on HT-7 tokamak

K.Y. Chen, L.Q. Hu, Y.M. Duan

HT-7

Outline

• Experimental set-up

• Theoretical background

• Performance of the tomography system

• A case study

• Summary

HT-7

Experimental set-up

Major radius: 1.22 mMinor radius: 0.27 mFive cameras46 channels for each cameraThickness of beryllium filter 12.5 μm. Distance for plasma center to slit: 400 Maximum sampling rate: 250 kHzSpatial resolution : 0.6 ~ 1.5 cm

Data acquisition: Photon Be filter Photon diode Preamplifier Amplifier AD Control room

HT-7

Theoretical background

),( pf

dLrgd

AAdP incincap

,4

coscos2

'det

),(2

'det ,4

coscos

pL

incincap dLrgd

AAP

),(

,),(

pL

dLrgpf

The quantity in brackets can be divided into the left side to define the Chord ‘brightness’ , with units of W·m-2.

The tomography problem

HT-7

Assuming soft x-ray (SXR) emissivity is constant on magnetic surfaces, the contours of SXR emissivity represent the magnetic surface structure.Our task is to invert the line-integrated soft x-ray (SXR) data to reconstruct the SXR emissivity distribution, i.e. magnetic surface structure.

Theoretical background

Solution of the tomography problem

The Fourier–Bessel inversion method is used to generate tomographic reconstructions from the soft X-ray data. The local emissivity can be expanded in terms of Fourier harmonics to yield:

max max1

, ,0 0 ( , )

( , ) [ cos( ) sin( )] ( )m l

c s lm l m l m m

m l L p

f p a m a m J r dL

max

0

sin)(cos)(),(m

m

sm

cm mrgmrgrg

If gm(r) is expanded in terms of Bessel series, the chord brightness f(p,φ) can be written as

Where 1lm is the l th zero of the Bessel function. After numerical

Integration along the chords L(p,φ), Eq. (1) can be put in a matrix form and inverted to obtain the am,l coefficients and consequently the local emissivities. Usually, the radial expansion limit lmax is adequate, whereas the angular expansion limit mmax is restricted by the number of soft x-ray cameras. For a soft x-ray imaging system with N cameras, mmax can be N-1/2 at most, where 1/2 represents the component of cos (Nθ) or sin (Nθ).

HT-7

(1)

Performance of the tomography system

Simulation of emissivity distributions

Assuming a pure hydrogen or deuterium plasma, the emissivity is simulated as

where equilibrium temperature and density profiles are derived from PHA temperature diagnostic and HCN density diagnostic in a typical discharge. The perturbed temperature and density distributions are simulated with Kadomtsev’s model.

ee Tnrg 2),(

HT-7

ξ= 0.3

ξ= 0.2

mmax=11/2 mmax=2 mmax=3

A case study HT-7

A typical sawtoothing discharge with LHCD and IBW

Temporal evolution of main plasma parameters

Expanded view of SXR intensities

Mid-oscillation Pre-cursor oscillation

Mid-oscillation HT-7

Results of singular value decomposition

Eigenvalue Chrono Topo

Tomographic reconstructions

A B C

Sawtooth crash HT-7

Results of singular value decomposition

Eigenvalue Chrono Topo

Tomographic reconstructions

D E F

Discussion

• Mid-oscillations are primarily due to hot core displacement and the rotation of m=1 magnetic island. The appearance of mid-oscillations indicate that m=1 during the sawtooth does not necessarily mean sawtooth crash.

• Mid-oscillations are frequently observed in LHCD plasmas, while seldom observed in ohmic-heating plasmas. This suggests that LHCD may play an important role in resulting in the oscillations. The modified current density profile may be responsible for the growth, saturation and decay of the oscillations.

• Sawtooth crash is due to the growth of m=1 mode. Sometimes m=2 mode may play a role in the crash, but this is seldom observed.

• After the crash, the soft x-ray emissivity in the plasma center is relatively cold. This may be due to the large pressure gradient outside the inversion surface. Besides, low SXR intensity does not necessarily mean low temperature.

HT-7

Summary HT-7

•The soft x-ray imaging system on HT-7 tokamak contains five soft x-ray cameras. The temporal and spatial resolution are 4 μs and 0.6-1.5 cm respectively.

•Fourier-Bessel inversion method was used to reconstruct the distribution of soft x-ray emissivity.

•The inversion accuracy is associated with the number of angular harmonic and the displacement of plasma hot core.

•The tomographic results show that mid-oscillation and sawtooth crash are primarily due to the behavior of m=1 mode.

Thank you for attention!

HT-7