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
Introduction to Heavy Ion Beam Probe (HIBP)
Proca-Green parallel plate energy analyzer
• Electron density measurement
)(0 svesvionspp
ss rnlFFI
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
Introduction to Heavy Ion Beam Probe (HIBP)
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
Introduction to Heavy Ion Beam Probe (HIBP)
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)
Instrumental error analysis
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
entrance slit length (cm)
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
Yellow: Effective region
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
detector length (cm)
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
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
)
Primary and secondary beam in MST-HIBP system Sample volume
About half of secondary beam scraped-off
Instrumental error analysisSimulation at 3.7 ms after sawtooth crash
-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
About half of secondary beam scraped-off
Instrumental error analysisSimulation at 3.7 ms after sawtooth crash
-15 -10 -5 0 5 10 15-0.5
0
0.5Secondary impact at entrance aperture
Yellow: Effective region
entrance slit length (cm)
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
About half of secondary beam scraped-off
Instrumental error analysisSimulation at 3.7 ms after sawtooth crash
-15 -10 -5 0 5 10 15-1.5
-1
-0.5
0
0.5
1
1.5Secondary impact at detector & current density profile
Yellow: Effective region
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
detector length (cm)
dete
ctor
wid
th (c
m)
Primary and secondary beam in MST-HIBP system Detector plane
About half of secondary beam scraped-off
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
Instrumental error analysis
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.