analysis of instrumental effects in hibp equilibrium potential profile measurements on the mst-rfp

Analysis of instrumental effects in HIBP equilibrium potential profile measurements on the MST-RFP

Xiaolin Zhang Plasma Dynamics Lab, Rensselaer Polytechnic Institute

MST Group, University of Wisconsin-Madison

Outline

• Introduction to Heavy Ion Beam Probe (HIBP) diagnostics

• Equilibrium potential measurements• Intrumental error analysis• Conclusion• Future work

Introduction to Heavy Ion Beam Probe (HIBP)

HIBP can measure• electrostatic potential (r)

• electron density ne(r)

• electron temperature Te(r)

• magnetic vector potential A(r)& their fluctuations

HIBP applied in TEXT, MST, helicon plasma, etc


Proca-Green parallel plate energy analyzer

• Electron density measurement

)(0 svesvionspp

ss rnlFFI

qq

kI

Is: secondary beam current

Ip: primary beam current

Fp, Fs: beam attenuation factors

ion: ionization cross-section for primary to secondary ions

lsv: sample volume length

ne: local electron density


C1

C3

C2

C4

Beam image on the split plates of energy analyzer

• Plasma potential measurement

}),(),({2LU

LUIIad ii

iiFGeVW

gain factor

22 cossin4

tan),(I

DIDI d

YXG

off-line processing factor

22 cossin8

)tancos(sin),(I

IaaI d

wF

q = Wd - Wp

Wd: secondary beam energy

Wp: sprimary beam energy

ion beam Na+ or K+

Na+ enters plasma

magetic field separates Na++ from Na+

Na++ detected in the energy analyzer

Na++ in the split plate detector


Equilibrium potential measurements

5 10 15 20 25 30 35 400

20

40

c 1(nA

)

24-Jun-2001

5 10 15 20 25 30 35 400

20

40

c 2 (nA

)

Shot No. =31

5 10 15 20 25 30 35 400

20

40

c 3 (nA

)

5 10 15 20 25 30 35 400

20

40

c 4 (nA

)5 10 15 20 25 30 35 40

0

50

sum

(nA

)

5 10 15 20 25 30 35 40

1

2

c(KV

)

5 10 15 20 25 30 35 40250

300

350

400

I p (KA

)

5 10 15 20 25 30 35 405

10

15n 0(x

1012

/cm

3 )

5 10 15 20 25 30 35 40-0.4

-0.3

-0.2

-0.1

F

t(ms)5 10 15 20 25 30 35 40

0

20

40

Mod

e sp

eed

(km

/s)

t(ms)

Raw data ( 380 kA standard discharge)

• sawtooth crash indicated by the abrupt drop of signals

• strong trend of potential with m/n = 1/6 mode velocity

• the dominant tearing mode fluctuations eliminated by 10 kHz LP filter

Equilibrium potential measurements Calibration of the energy analyzer

-6 -4 -2 0 2 4 6 82.93

2.94

2.95

2.96

2.97

2.98

2.99

Entrance angle -30( )

Gai

n

calculated (XD=654.03 mm, YD=124.96 mm)center detector (calibrated)bottom detector (calibrated)

-8 -6 -4 -2 0 2 4 6 80.01

0.015

0.02

0.025

0.03

0.035

Entrance angle -30 ( )(slit width = 2 mm)

F

center detector (calibrated)bottom detector (calibrated)calculated (fitted slit width = 2.7 mm)

}{LU

LUa ii

iiFGeVW

Beam energy

analyzer voltage detector

signals

good agreement between the calibration and theory

Beam entrance angle is centered at 30.

Equilibrium potential measurements Equilibrium potential profile measurements

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.5

0

0.5

1

1.5

2

2.5

= r/a

pote

ntia

l (k

V)

380kA SD380kA SD(locked)290kA SD390kA PPCD500kA PPCD(locked)

Equilibrium potential is obtained by averaging within 0.2ms time window ensembles in 20~50 shots

0.2 ~ 0.35 kV potential scattering (not shown)

potential profiles are obtained by changing the steering voltage from shot to shot

relatively flat profiles at r/a ~ 0.3 to 0.8, indicating weak Er

potential in PPCD discharges is smaller than in standard discharges, indicating improved electron confinement

Instrumental error analysis

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

r/a

Sca

led

pote

ntia

l (kV

)

Potential profile during 25 standard discharge shots

(ensembles are obtained during flattop period of discharge, away from sawtooth crashes)

HIBP measurements in MST-RFP exhibit

variations of currents on the detector during a sawtooth cycle

unexplained shot to shot potential variations

Possible reasons:

evolution and fluctuation of fields

variation of location, size and orientation of sample volume

variation of other plasma parameters: electron density, plasma current, etc

signal scrape-off effects (blocked by ports, apertures, structures in beamline)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

r/a

Sca

led

pote

ntia

l (kV

)

Potential profile during 25 standard discharge shots

(ensembles are obtained during flattop period of discharge, away from sawtooth crashes)


to centerline of the entrance apertureto bottom edge of the entrance aperture

to top edge of the entrance aperture

dsample volume

Finite-sized beam model

Schematic of primary beam and sample volume

A beam trajectory code is used to compute the sample volumes within the plasma and their trajectories in HIBP beamlines.

Beam is emulated by several trajectories at the boundary traced to centerline and edges of the entrance aperture, respectively

The beam is assumed to have a circular-shaped cross-section and uniform or Gaussian current density profile

Including secondary beam scrape-off effects

Simulation parameters

1.5 cm beam diameter& Gaussian profile

Constant electron density and temperature profile

380 kA standard discharge

to centerline of the entrance aperture

to bottom edge of the entrance aperture

to top edge of the entrance aperture

dsample volume

Schematic of primary beam and sample volume

Instrumental error analysisSimulation at 3.7 ms after sawtooth crash

148150

152154 8

10

1214

15

16

17

18

19

20

21

MST Y axis (cm)MST major radius X(cm)

3D sample volume view

MS

T Z

axis

(cm

)

-6 -4 -2 0 2 4 6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Outer Exit Port

Y (cm) (toroidal)

Z (c

m)

(radi

al) magnetic strcture

-15 -10 -5 0 5 10 15-0.5

0

0.5Secondary impact at entrance aperture

Yellow: Effective region

entrance slit length (cm)

entr

ance

slit

wid

th (c

m)

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8-0.4

-0.2

0

0.2

0.4


entr

ance

slit

wid

th (c

m)

current density profile

-15 -10 -5 0 5 10 15-1.5

-1

-0.5

0

0.5

1

1.5Secondary impact at detector & current density profile


detector length (cm)

dete

ctor

wid

th (c

m)

0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8-0.5

0

0.5


dete

ctor

wid

th (c

m)

Primary and secondary beam in MST-HIBP system

Sample volume Magnetic structure

Entrance aperture Detector plane

About half of secondary beam scraped-off


148150

152154 8

10

1214

15

16

17

18

19

20

21

MST Y axis (cm)

MST major radius X(cm)

3D sample volume view

MS

T Z

axis

(cm

)

Primary and secondary beam in MST-HIBP system Sample volume



-6 -4 -2 0 2 4 6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Outer Exit Port

Y (cm) (toroidal)

Z (c

m) (

radi

al) magnetic strcture

Primary and secondary beam in MST-HIBP system Magnetic structure



-15 -10 -5 0 5 10 15-0.5

0

0.5Secondary impact at entrance aperture



entra

nce

slit

wid

th (c

m)

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8-0.4

-0.2

0

0.2

0.4

entrance slit length (cm)en

tranc

e sl

it w

idth

(cm

)

current density profile

Primary and secondary beam in MST-HIBP system Entrance aperture



-15 -10 -5 0 5 10 15-1.5

-1

-0.5

0

0.5

1

1.5Secondary impact at detector & current density profile



dete

ctor

wid

th (c

m)

0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8-0.5

0

0.5


dete

ctor

wid

th (c

m)

Primary and secondary beam in MST-HIBP system Detector plane


Instrumental error analysisSimulation throughout a sawtooth cycle

18 20 22 240

10

20

30

c 1

HIBPsimu-insimu-out

18 20 22 240

10

20

30

c 2

18 20 22 240

10

20

30

c 3

t (ms)18 20 22 24

0

10

20

30

c 4

t (ms)

18 19 20 21 22 23 24

16

17

18

19

20

21

22

t (ms)

r (c

m)

sample volume position

Secondary current signals on detector

Sample volume position variation

Good agreement of general trend of the signals between measurements and simulation

• significant signal scrape-off during a sawtooth cycle ( mostly by steering plates and grids on ground plate of the analyzer)

• sample volume position varies up to 3.5 cm over a sawtooth cycle

Instrumental error analysisPotential estimation with iteration algorithm

18 19 20 21 22 23 240

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

t (ms)

Pot

c (kV

)

HIBPsimu

Potential variation

• signal scrape-off has insignificant contribution to potential measurements due to the negligible slant angle of the beam images on the detectoroutput pot

calculated currents consistentwith measured HIBP signals?

secondary beam energy = primary beam energy+ potential measured

run finite-sized beam simulation

calculate secondary currents on four slit plates of detector

N

adjust potential

Y

Simu_in

Simu_out

18 19 20 21 22 23 240

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

t (ms)

Pot

c (kV

)

HIBPsimu

signal scrape-off has insignificant contribution to potential measurements due to the negligible slant angle of the beam images on the detector


source Uncertainties of the source Potential uncertainty (KV)

UV loading 0.9 nA (rms) < 0.017

Power supply ripples ~3.4 Vpp (Vg), ~ 0.2 Vpp (Va) < 0.010

Density gradient Density variation along the sample volume length

-0.06 ~ 0.01 ( r ~ 0.18m)0.05 ~ 0.11 ( r ~ 0.4 m)

Beam attenuation Beam intensity attenuated along sample volume by ionization

-0.43 V ( r ~ 0.18 m)–24.6 V ( r ~ 0.4 m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.5

1

1.5

r (m)

n e (1013

cm-3

)

-1.75 ms before-0.25 ms before+0.75 ms after

Other factors including non-uniform electric field inside the analyzer, mechanical misalignment will contribute insignificantly to potential error.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.5

1

1.5

r (m)

n e (1013

cm-3

)

-1.75 ms before-0.25 ms before+0.75 ms after

Electron density profile obtained from MSTFit over the sawtooth cycle during a typical 380 kA standard discharge. The fat lines along the density profiles show the simulated HIBP sample volume length.

Conclusion

• equilibrium potential profiles measured by HIBP are relatively flat, indicating weak radial electric field

• finite-sized beam simulation shows good agreement with measurements. Signal scrape-off has insignificant effects on potential variations.

• Other factors including UV loading, power supply ripples, density gradient and beam attenuation will contribute insignificantly to potential error in the interior region of the plasma.

Future work

•improve beam focusing

•real time feedback control of the secondary beam system to improve the beam alignment and reduce the beam scrape-off

•numerical experiment by using finite-sized beam model to investigate the effects of magnetic fluctuations and other variations of plasma parameters on HIBP potential measurements.

analysis of instrumental effects in hibp equilibrium potential profile measurements on the mst-rfp

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