the heavy ion beam diagnostic - application for a small ... · the heavy ion beam diagnostic -...

The Heavy Ion Beam Diagnostic - Application for a Small Fusion Device

Artur Malaquias Camberra , 26th of August 2013

A. Malaquias, I.S. Nedzelskiy, R.B. Henriques, C. Silva, H. Fernandes

Diagnostics in fusion plasma devices shall provide for

Machine protection and safe operation

Plasma Control

Performance optimization

Plasma control and performance are critical for economic viability of fusion

- stability, confinement, heating efficiency, fuelling, power exhaust –

Calling for measurements and physics studies on present devices:

Control of MHD modes (magnetic measurements)

Disruptive modes

NTMs leading to instabilities and increased transport

Alfvén Eigenmodes

Turbulence and transport (density, temperature, potential, lost particles)

Gradients, fluctuation levels, instabilities induced losses (e.g. Alfvén)

Large amount of diagnostic techniques is available today

Magnetic and Electric Probes

Spectroscopic and Optical

Beam and Laser aided

Particle (ions and neutrals)

Fusion (gamma, neutron)

Most required for physics studies are diagnostics that can measure the different plasma parameters and their interplay at different radial locations

Heavy Ion Beam Diagnostic can in principle measure simultaneously the radial profiles and fluctuation spectra for:

Electron density and temperature

Plasma internal magnetic field

Plasma potential

The operation of the HIBD in a small fusion device – tokamak ISTTOK

Outline

• HIBD principles and layouts

• Application to a small tokamak

– Retrieval of plasma parameters

Density, temperature, poloidal field, potential

– The fluctuation measurements

• Summary and future plans

HIBD principles and layouts


PlasmaBT

I+

I++

secçãodo feixe

detectorde intensidadee posição

fenda

plac

as co

nduc

tora

s

I+++

HIBProbe concept

HIBDiagnostic concept

Multiple cell detector (Secondary ions)

Toroidal direction

Primary beam detector

Measurable plasma parameters

Plasma density – Secondary beam current is strongly determined by local electron density (and ion density for Ti>2keV)

Electron temperature – Secondary beam current depends on effective cross section as determined by electron temperature (and ion for Ti>2keV)

Plasma potencial – Secondary beam energy is a unique function of plasma potential at the ionization point (electrostatic approach)

Poloidal field – Plasma current generates a plasma magnetic poloidal field that governs the beam trajectories in the toroidal direction giving rise to a charateristic spatial distribution at the detector

Application to a small tokamak - ISTTOK


Beam trajectories

i x,y,z

B and E are updated on each iteration step

Electric field (input) = inverted parabola with peak eV ~ 3/2 KTe

Electro-magneto static approach

Magnetic field (calculated) = toroidal field + poloidal field (external +) plasma current

Beam divergence (input)

Beam

dia

met

er

assimetric current density profile

(at the detector)

Plasma Poloidal Magnetic Field - Plasma current model

Asymmetric current profiles are generated

by a combination of symmetric profiles

Radial symetric profiles

Beam attenuation – effective cross-sections

Tp (eV) Tp (eV)

Integration of cross-section over Maxwellian distribution of electron velocities

MOST IMPORTANT IONIZATION REACTIONS:

Beam attenuation – path integral

Primary beam (I+)

tertiary beams (I3+)

secondary beam (I2+) density and temperature profiles

Secondary beam attenuation

Primary beam attenuation

Secondary beam generation

Beam attenuation – path integral

(dl - detector cell height projected into the primary beam path)

Detectorsecundário

Câmara

Plantaformasuperior do ISTTOK

Isolador

Válvula

Medidorde pressão

Pulsador

Fonte iónica

Isolador

Filtro demassa

Detector primário

Sistema dedeflecçãodo feixe

Isoladorcerâmico

Bomba Turbomolecular

FichasBNC

Célula deFaraday

Bomba turbomolecular

HIBD Layout

Toroidal field – determines y coordinate

Poloidal field – determines z coordinate

Retrieval of plasma parameters


1122(det) )(ˆ)( 2 dsrrnABII jjeoj σ++ =

ˆ)(exp.)(ˆ)(.

.ˆ)(ˆ)(expI2I

223212

113112102

(det)

1

B

A

Rpr ejje

rR

Aeej

j

j

i

dssndlrrn

dssnsn

−

+−=

∫

∫++

σσ

σσ

Primary beam attenuation (integral form)

Primary beam attenuation Secondary beam attenuation

Tertiary beam generation

Simplified version

A1=0 (week primary beam attenuation due to tertiary ion production)

B=1 (weak secondary beam attenuation)

dlII

rnj

jje +

+

=2

)(ˆ2(det)

12σ

The generation factor (n.σ) can be related to the secondary currents by:

∑−=−

=

+++1

0

2(det)2

10

j

LLj III

Step 1: Simplified model

0

10

20

30

40

50

60

70

80

0 5 10 15 20# cel

corre

ntes

(nA

)

Step 1: Simplified model retrieves (n.σ) normalized profile

Detected secondary beam currents

ne(0) = 1×1019

Te(0) = 200 eV

Eb=22 keV

I0=1 uA

0

1

2

3

4

5

6

-10 -5 0 5 10

raio (cm)

n x

(m

-1)

assumidorecuperado

0

0.2

0.4

0.6

0.8

1

1.2

-10 -5 0 5 10

raio (cm)

n x

(n

orm

aliz

ado)

assumidorecuperado

# row

Radius (cm) Radius (cm)

retrieved inputed

retrieved inputed

Simplified version

A1=0 (week primary beam attenuation due to tertiary ion production)

B ≠ 1 (moderate secondary beam attenuation)

Step 2: Intermediate model

Primary beam (I0+)

secondary beam att.

(I2+I3+) ≠ 0

(I+I3+) = 0

Total secondary current generated along primary beam path

Total secondary current lost for tertiary ions

Simplified version

Attenuation of each secondary beam I2+I3+

Step 2: Intermediate model

1ˆ 23 <<

∫ p

j

R

r e dsn σ

For ISTTOK the exp() argument is small

Linearized attenuation of each secondary beam I2+I3+

=

∫−−≅ +++→+ p

jRr ejjj dsnIII 23

2232 ˆ1 σ

Similar normalized shape for the primary and secondary beams’ attenuation profiles:

Step 2: Intermediate model (secondary beam attenuation factor)

Beam path (m)

A suitable loss factor can be obtained from the ratio:

Step 2: Intermediate model (secondary beam attenuation factor)

Loss current by each secondary beam

Loss current by all secondary beams

TAKING RELATIVE IDENTICAL QUANTITIES AND REPLACING INTEGRALS BY DISCRETE

EXPERIMENTAL VALUES

N – TOTAL NUMBER OF DETECTOR ROWS

L – CORRESPONDING DETECTOR ROW FOR IONIZATION POINT j

0

1

2

3

4

5

6

-10 -5 0 5 10

raio (cm)

nex

12 (

m-1

)

recuperado

assumido

The integral attenuation of each secondary beam can be estimated from:

Step 2: Intermediate model (secondary beam attenuation)

Total current of tertiary ions due to: I2+I3+

Plasma radius (cm)

Retrieved nσ

A1 ≠ 0 (moderate primary beam attenuation due to tertiary ion production)

B ≠ 1 (moderate secondary beam attenuation)

Step 3: Accounting for the reaction I+I3+

Tertiary beams generation factor

For a given temperature the ratio between production of secondaries and tertiaries is constant



Plasma temperature varies along the radius, but ratio remains fairly constant for a range of profiles at a given max. temperature

0.200.230.250.280.300.330.35

osc5

osc3 oc

o

picad

o

parab

olico

quad

rado

Frac

ção

de te

rciá

rios

R

100200300

Te(0) (eV)

(Cur

rent

rat

io o

f te

rcia

ries

to

seco

ndar

ies)

0

2

4

6

8

-10 -5 0 5 10

'assumido'

'recuperado'

a)

b)

c)

Osc5

0123456

-10 -5 0 5 10

'assumido'

'recuperado'T e = 200 eVn e = 1x1019 m-3

0

2

4

6

8

-10 -5 0 5 10

'assumido'

'recuperado'

a)

b)

c)

Oco

a) Te = 100 eV e ne = 5×1018 m-3

b) Te = 200 eV e ne = 1×1019 m-3

c) Te = 300 eV e ne = 1.5×1019 m-

3.

Model recovers very well the profile of

Plasma radius (cm) Plasma radius (cm)

inputed retrieved

inputed retrieved

Plasma radius (cm)

retrieved inputed

4.5

1.4

-1.6

-4.4

3.55.

57.59.

511.513

.515.517

.519.521

.523.525

.527.529

.5

0

1

2

3

4

5

neσ 1

2 (m-1

)

raio

(cm)tempo (ms)

4.5

2.4

0.4

-1.6

-3.5

3.5

5.5

7.5

9.5

11.5

13.5

15.5

17.5

19.5

21.5

23.5

25.5

27.5

29.5

raio (cm)

tem

po (m

s)

Plasma current

Experimental results

4.7

-2.4

1622

2834

4046

5258

32.8

0

0.01

0.02

0.03

0.04

0.05

nex

σ12

(u.a

.)

raio (

cm)

tempo (ms)

4.7

1.1

-2.4

1316192225283134374043464952555861

raio (cm)

tem

po (m

s)

Experimental results Alternated discharge (2 cycles)

-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3

-0.2

0.2

0.4

0.6

Hg +→Hg 3+ and Xe +→Xe 2+ (E = 22 keV, αHg = 32.0º, αXe = 33.3º).

0

4

8

12

50 100 150 200 250 300 350

temperatura (eV)

Rac

ios

(abs

.)

Hg

Xe

12

12

ˆˆ

σσ

(a)

Hg

Xe

13

12

ˆˆ

σσ

(b)

Retrieval of electron density and temperature

Two species method

(quasi-constant function of temperature)

(high sensivity as a function of temperature)

The Hg2+ currents (not detected) are estimated from the Xe2+ currents via:

22

1212

ˆˆℜ

= XeHg

XeHg nn σσ

Hg+ primary beam current at each ionization point is retrieved iteratively by:


The primary beam current at ionization point has to be determined for Xe and Hg

using the nσ retrieval method

j = ionization P (1,2,..N)

L = cell number (0,…,N)

50

100

150

200

250

300

350

-6 -4 -2 0 2 4 6

Raio (cm)

Tem

pera

tura

(eV

)

0

5

10

15

20

Den

sida

de (x

1018

m-3)densidade

temperatura

50

100

150

200

250

300

350

-6 -4 -2 0 2 4 6

Raio (cm)

Tem

pera

tura

(eV)

0

5

10

15

20

Den

sida

de (x

1018

m-3)

densidade

temperatura


Plasma radius (cm)

Plasma radius (cm)

Electron density and temperature are very well retrieved

density

density

temperature

temperature

Plasma current for 2 discharges Radial average density for two discharges

-20

213

19

25

31

0

70

140

210

T e (e

V)

R (cm)

t (ms)

-20

213

19

25

31

4

6

8

10

12

n e (1

018 m

-3)

R (cm)

t (ms)

interferometer

Te ne




Plasma potential measurements

MCAD

Cs+

Stop Start

Modulator

Cs2+

Primary detector

Sample volumes Plasma

Average plasma potential

measurements

Absolute plasma potential measurements

1e

Plasma potential measurements - method

K1S + eVS = K1P + eVP K2P + 2eVP = K2D + 2eVD VP = (K2D - K1F) + (2VD - VF)

Energy conservation

K1P ≈ K2P

S - source

D - detector

P

x

y

z Ch1

Ch2

Ch3

Ch4

MCAD “Start” “Stop”

Control module

Cylindrical plates

XY-alignment plates

Z-plates

620 mm

TOF-path module

Plasma potential measurements - setup

-8 -6 -4 -2 0 2 4 6 8-800

-700

-600

-500

-400

-300

-200

-100

0

100

Φpl, V

r, cm

Plasma potential measurements – experimental results

Langmuir probes

Negative biasing by emissive electrode

Discharge 1 – no biasing

Discharge 2 – biasing

(<ne> = 4.5×1018)



Plasma magnetic poloidal field determination

In ISTTOK all ion trajectories are very close to radial

Plasma poloidal field determination – cylindrical approximation

Secondary detector matrix

Primary detector matrix

1st ionization dl (dt)

1

2)1(

2)1()1(21

211

2)1( 2

1

s

TaTvzzz pd+++++ +++=

Primary beam initial position

secondary beam increment from

plasma bondary to detector position

Velocity of primary beam at ionization point ; secondary

time of flight

Secondary ions average

acceleration from ionization point to plasma perifery Secondary beam

position at cell (1)

Poloidal magnetic field outside the plasma:

Motion in magnetic field inside the plasma:

y

z x

Provides for calculation of initial conditions

( )dtT

TvdtTvzzzdv

j

jpjjjjjjdjj

21

)1(2

)(2

)(21

)1(2)()(2

)1(2

)1()1,( −

−+−−−=

+

++

++++

+++

+

dtdvdtvzz jjjjj+

++++

+ −+= )1,()()()1( 21

++

+++ −= )1,()()1( jjjj dvvv

dtdvTvTv jjjpjjpj+

++

+++ −= )1,()(

2)()1(

2)1( 2

21

21

21

taking the z displacement between two consecutive cells:

poloidal field module can be obtained from force equation

Plasma poloidal field determination – recursive method

+++ − 2

)(2

)1( jdjd zz

mean time of flight

local increments on: z, v, a

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-10 -5 0 5 10

raio (cm)

j (

MA

/m2 )

j plano

j parabolóico

j picado

-31

-28

-25

-22

-5.5 -5.1 -4.7 -4.3 -3.9 -3.5 -3.1 -2.7

z (mm)

y (c

m)

plano

parabolóico picado

Plasma poloidal field determination – profile retrieval

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-10 -5 0 5 10

raio (cm)

j (M

A/m

2 )

assimétrico

-31

-28

-25

-22

-5.5 -5.1 -4.7 -4.3 -3.9 -3.5 -3.1 -2.7

z (mm)

y (c

m)

picado

assimétrico

0

5

10

15

20

25

30

-10 -5 0 5 10

Raio (cm)

Bp (

mT)

o B p+ recuperado B p+ assumido - B p total

Plasma poloidal field determination – profile retrieval

0

1000

2000

3000

4000

5000

6000

7000

8000

0.00 10.00 20.00 30.00

TIME (ms)

P L A

S M

A C

U R

R E N

T ( A

)

#2939

#2940

T1 T2 T3 T4

Bp

1.2

1.6

2.0

2.4

2.8

3 4 5 6 7

Row Number

ζ ( y

) ( m

m )

T 1

T 2

T 3

T 4

-1

0

1

2

3 4 5 6 7

Row Number

P o l o

i d a l

F i e

l d N

o r m

a l i s

e d t o

P l a

s m a

C u r

r e n t

( a . u

. )

T

T T T

A1 A2

A3 A4

1

2 3 4


Two similar discharges were used

(due to limited number of ADCs)

Profile flattening (T1T4) Magnetic axis

displacement to outside



Fluctuations Measurements

Fluctuation measurements – hardware improvements )(~~eTnσ

new detection system (low noise)

Frequency bandwidth

Phase shift

new home made amplifiers (250 kHz)

Fluctuation measurements – experimental results )(~~eTnσ

Excellent improvement on S/N

HIBD - spectra Mirnov Coil - spectra


MHD fluctuations

Noise FFT Clear cross-correlation patterns between HIBD and Mirnov


cross correlation between different detector cells radial structure of the mode

Fluctuation amplitude profile

Signals are coherent with rational flux surface located near the

plasma edge (m=1?)

Fluctuation simulations – frequency domain limits )(~~eTnσ

Test profile 200 kHz Φ = 0

Φ = 180

Sampling rate at 2 MHz

The fluctuation structure is well recovered and with negligible phase

distortion

Fluctuation simulations – frequency domain limits )(~~eTnσ

Test profile 500 kHz Φ = 0

Φ = 180

Sampling rate at 5 MHz

The fluctuation structure is well recovered but phase distortion is

around 15%

phase information can be regained by accounting for the time of flight of primary and secondary beams and off-setting the cell signals

to the same time reference


Summary

At ISTTOK the HIBD allows for the determination of the: plasma density, electron temperature, plasma potential and plasma poloidal magnetic field

The absolute profiles can be obtained for frequencies up to 250 kHz (ISTTOK) utilizing well tested retrieval methods

The fluctuations’ measurements by HIBD show no path integral effect in the range of frequencies of the amplifiers

The HIBD can provide unique possibilities for studying MHD modes and in particular Toroidal Alfvén Eigenmodes by providing the simultaneous measurements of plasma potential, plasma density and poloidal field fluctuations.

The HIBD can provide also gradients and absolute fluctuation measurements for turbulence studies.


Future plans

Measurements and characterization of turbulence response under limiter biasing, GAM studies, validation with Langmuir probes (edge)

Characterization of MHD fluctuation activity and mode location in alternating plasma discharges, validation with Mirnov coils

Develop electrostatic combined detector for simultaneous measurements of fluctuations and profiles of plasma poloidal field, plasma potential and nσ (PhD student)

Develop studies under international collaboration activities - MAST, TJ-II, (PhD Student)

References

”Time–of-flight energy analyser for the plasma potential measurements by a heavy ion beam diagnostic” S. Nedzelskiy, A. Malaquias, B. Gonçalves, C. Silva, C. A. F. Varandas, and J. A. C. Cabral, REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 75, NUMBER 10 OCTOBER 2004, pp. 3514-3516 in Proceedings of 15th Topical Conference High-Temperature Plasma Diagnostics, San Diego, California, April 19-22,2004

"The Heavy Ion Beam Diagnostic for the Tokamak ISTTOK" J.A.C. Cabral, A. Malaquias, A. Praxedes, W. van Toledo, and C.A.F. Varandas. IEEE Transations on Plasma Science, vol 22 nº4, August 1994.

"Analysis of the ISTTOK plasma density profile evolution in sawtooth discharges by heavy-ion beam probing" J.A.C. Cabral, C.A.F. Varandas, A. Malaquias , A. Praxedes, M. P. Alonso, P. Belo, R. Canário, H. Fernandes, J. Ferreira, C. J. Freitas, R. Gomes, J. Pires, C. Silva, A. Soares, J. Sousa and P.H.M. Vassen Plasma Phys. Control. Fusion 38 (1996) 51-70 "Evolution of the poloidal magnetic field profile of the ISTTOK plasma by heavy ion beam probing" A. Malaquias, J. A. C. Cabral, C.A.F. Varandas and R. Canário Fusion Engineering and Design, 34-35 (1997) 671-674 “Evolution of the tokamak ISTTOK plasma density and electron temperature radial profiles determined by heavy ion beam probing” A. Malaquias, I.S. Nedzelskii, C.A.F. Varandas, and J.A.C. Cabral Review of Scientific Instruments, V70, N1, Jan 1999, Part II. Pp. 947-950

“Engineering Aspects of an Advanced Heavy Ion Beam Diagnostic for the TJ-II Stellarator” A. Malaquias, C. Varandas, J.A.C. Cabral, L.I. Krupnik, S.M. Khrebtov, I.S. Nedzelskij, Yu. V. Trofimenko, A. Melnikov, C. Hidalgo, I. Garcia-Cortes Fusion Technology V.1 pp. 869, 1996

Multichannel time-of-flight technique for plasma potential profile measurements by heavy ion beam diagnostic on the tokamak ISTTOK , I. S. Nedzelskiy, A. J. Malaquias, Yu. I. Tashchev, C. Silva, H. Figueiredo, H. Fernandes, and C. A. F. Varandas, Rev. Sci. Instrum., 77, 033505 (2006) “New detection system and signal processing for the tokamak ISTTOK heavy ion beam diagnostic”, R. B. Henriques, I. S. Nedzelskiy, A. Malaquias, and H. Fernandes, Rev. Sci. Instrum. 83, 10D705 (2012); http://dx.doi.org/10.1063/1.4729496 (3 pages)

“Internal measurements of Alfvén eigenmodes with heavy ion beam probing in toroidal plasmas”, A.V. Melnikov et al., Nucl. Fusion 50 (2010) 084023 (11pp) doi:10.1088/0029-5515/50/8/084023

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