Plasma Dynamics Lab HIBP Abstract Measurements of the radial equilibrium potential profiles have...
2
Plasma Dynamics Lab HIBP Abstract Measurements of the radial equilibrium potential profiles have been successfully obtained with a Heavy Ion Beam Probe (HIBP) in the core () of the Madison Symmetric Torus (MST) Reversed Field Pinch. Typically, has a magnitude of up to 1.0-2.0 kV in a standard 380 kA discharge. The core profile of the electrostatic potential fluctuations and electron density fluctuations have also been measured in MST. The measured ranges from 30-50 V rms and ranges from 10-20% for this same standard 380 kA discharge. While most of the data obtained thus far have been for standard discharges at a variety of plasma currents, preliminary measurements have also been obtained for other discharge conditions, including biased discharges and pulsed poloidal current drive (PPCD) discharges. Confinement is significantly improved in PPCD discharges and HIBP measurements obtained thus far show very distinct changes in , and . The general status of HIBP measurements on MST will be presented including representative data from all types of discharges and measurement development issues. I. Principle of Heavy Ion Beam Probing ) ( 0 sv e sv ion s p p s s r n l F F I q q k I I 0 = initial primary current injected into the plasma ion = ion cross-section for primary to secondary ions l sv = sample volume length n e (r sv ) =electron density at the sample volume k = a multiplying factor between 1~10 due to electrons emitted by the detector plates F p = primary beam attenuation F s = secondary beam attenuation q s = charge of the secondary beam q p = charge of the primary beam e e s s n n i i ~ ~ High Current Standard Plasmas RESULTS: • ~ 1700 - 2000V • E r ~ 1.7 - 2 kV/m • PLASMAS: • I p ~ 380 kA, ~ ±1% • n e ~ .95 x 10 13 cm -3, ~ ±5% • V n=6 ~ 30km/s, ~±10% • F ~ -0.22 • T e ~ 300 eV Multiple Shot Analysis • Three intervals, 1.5ms duration each • ~1.5 ms after crash • mid way between crashes • ~2.5 ms before crash Potential is Positive Between Sawtooth Crashes • After Crash – Phi ~ 1735 V – ±125V scatter about trend-line • Mid-cycle – Peak phi ~ 2kV – ±125V scatter about trend • Before Crash – Peak phi ~ 2kV – ±150V scatter about trend Scatter may be due to • Variations in density • Variations in mode velocity • Variations in magnetic profiles and thus sample volumes 1.25 1.5 1.75 2 2.25 0 2 4 6 8 R adialSw eep (kV ) Phi(kV) 1.25 1.5 1.75 2 2.25 0 2 4 6 8 R adialSw eep (kV ) Phi(kV ) 1.25 1.5 1.75 2 2.25 0 2 4 6 8 R adialS w eep (kV ) Phi (kV Potential Tracks the Mode Velocity • Measured instantaneous potential tracks evolution of the mode velocity • m=1, n=6 mode velocity • Potential at which v n=6 = 40 km/s does not overlap at v n=6 = 20 km/s • Sample volume ~ r=22cm • Data from over 50 shots • Differences between and v n=6 profiles may be due to evolution in B and motion of the sample location 1 1.25 1.5 1.75 2 2.25 0 10 20 30 40 50 V elocity (km /s) Potential ( Potential and Electric Field Profiles in High I p Discharges • Measurement locations determined for data in potential scatter plots • Average sample position and potential computed from a 1-1.6cm range • Scatter in the potential and radial location are depicted by the vertical and horizontal ranges • Electric field profiles computed from the average potentials and average sample volume spacing 1400 1500 1600 1700 1800 1900 2000 0 5 10 15 20 25 30 35 M inorradius (cm ) Potential 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 0 5 10 15 20 25 30 35 M inorradius (cm ) Electric field After Crash Mid-cycle Before Crash 1400 1500 1600 1700 1800 1900 2000 0 5 10 15 20 25 30 35 M inorradius (cm ) Potential ( 1400 1500 1600 1700 1800 1900 2000 0 5 10 15 20 25 30 35 M inor radius (cm ) Potential 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 M inorradius (cm ) Electric field 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 M inor radius (cm ) Electric field ( Potential Profile Measurements in Low Current Discharges • Peak ~ 1400 V • Peak ~ 500 V lower than in High I p discharges • Measurements ~ 2 ms after crash 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -5 -4 -3 -2 -1 0 RadialSw eep (kV ) Potential ( 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 10 20 30 40 50 M inor R adius (cm ) Potential ( Electric Field Profiles in Low Current Rotating Plasmas • Average E r ~ 1.5kV/m • The electric field is outwardly directed • Recall, E ~ 2 kV/m in high I p discharges • Large error bars on E r (neg. E r ) due to shot to shot scatter in potential and artifacts of data processing -0.5 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 m inorradius (cm ) E (v/m ) • Singly charge heavy ions (primaries) are injected into the plasma • Some primary ions are further ionized by collisions with plasma electrons • The magnetic field separates the secondary ion trajectories from the primary ions. The combined primary and secondary ion trajectories appear as shown in the system figure above • The secondary ions are detected by ion collection plates split vertically and horizontally so that four separate currents are monitored • This permit measurements of the electric potential, fluctuations of potential and electron density, and magnetic vector potential, localized to the ionization position • The secondary beam current I s ( the sum of the four split plate signals) is given by • Assuming ion is a weak function of plasma temperature T e , which is about a few hundred eV in the core of the MST plasma, I s is proportional to the density n e (r sv ) • The relative density fluctuation level at the sample volume is then obtained from • The currents on the top two plates are summed to produce i upper while the bottom two plates sum to i lower . • The energy of the secondary ion leaving the plasma differs from that of the primary ion by the change in potential energy . Thus, to determine potential, we use a Proca and Green type energy analyzer and the following relationship P s AN s p HIBP p AC s p qV q q G F i i qV q q • G and F are geometric functions of the analyzer angle • V AN is the analyzer voltage and V AC is the accelerator voltage
Plasma Dynamics Lab HIBP Abstract Measurements of the radial equilibrium potential profiles have been successfully obtained with a Heavy Ion Beam Probe
Plasma Dynamics Lab HIBP Abstract Measurements of the radial
equilibrium potential profiles have been successfully obtained with
a Heavy Ion Beam Probe (HIBP) in the core () of the Madison
Symmetric Torus (MST) Reversed Field Pinch. Typically, has a
magnitude of up to 1.0-2.0 kV in a standard 380 kA discharge. The
core profile of the electrostatic potential fluctuations and
electron density fluctuations have also been measured in MST. The
measured ranges from 30-50 V rms and ranges from 10-20% for this
same standard 380 kA discharge. While most of the data obtained
thus far have been for standard discharges at a variety of plasma
currents, preliminary measurements have also been obtained for
other discharge conditions, including biased discharges and pulsed
poloidal current drive (PPCD) discharges. Confinement is
significantly improved in PPCD discharges and HIBP measurements
obtained thus far show very distinct changes in, and. The general
status of HIBP measurements on MST will be presented including
representative data from all types of discharges and measurement
development issues. I. Principle of Heavy Ion Beam Probing I 0 =
initial primary current injected into the plasma ion = ion
cross-section for primary to secondary ions l sv = sample volume
length n e (r sv ) =electron density at the sample volume k = a
multiplying factor between 1~10 due to electrons emitted by the
detector plates F p = primary beam attenuation F s = secondary beam
attenuation q s = charge of the secondary beam q p = charge of the
primary beam High Current Standard Plasmas RESULTS: ~ 1700 - 2000V
E r ~ 1.7 - 2 kV/m PLASMAS: I p ~ 380 kA, ~ 1% n e ~.95 x 10 13 cm
-3, ~ 5% V n=6 ~ 30km/s, ~10% F ~ -0.22 T e ~ 300 eV Multiple Shot
Analysis Three intervals, 1.5ms duration each ~1.5 ms after crash
mid way between crashes ~2.5 ms before crash Potential is Positive
Between Sawtooth Crashes After Crash Phi ~ 1735 V 125V scatter
about trend- line Mid-cycle Peak phi ~ 2kV 125V scatter about trend
Before Crash Peak phi ~ 2kV 150V scatter about trend Scatter may be
due to Variations in density Variations in mode velocity Variations
in magnetic profiles and thus sample volumes Potential Tracks the
Mode Velocity Measured instantaneous potential tracks evolution of
the mode velocity m=1, n=6 mode velocity Potential at which v n=6 =
40 km/s does not overlap at v n=6 = 20 km/s Sample volume ~ r=22cm
Data from over 50 shots Differences between and v n=6 profiles may
be due to evolution in B and motion of the sample location
Potential and Electric Field Profiles in High I p Discharges
Measurement locations determined for data in potential scatter
plots Average sample position and potential computed from a 1-
1.6cm range Scatter in the potential and radial location are
depicted by the vertical and horizontal ranges Electric field
profiles computed from the average potentials and average sample
volume spacing After Crash Mid-cycle Before Crash Potential Profile
Measurements in Low Current Discharges Peak ~ 1400 V Peak ~ 500 V
lower than in High I p discharges Measurements ~ 2 ms after crash
Electric Field Profiles in Low Current Rotating Plasmas Average E r
~ 1.5kV/m The electric field is outwardly directed Recall, E ~ 2
kV/m in high I p discharges Large error bars on E r (neg. E r ) due
to shot to shot scatter in potential and artifacts of data
processing Singly charge heavy ions (primaries) are injected into
the plasma Some primary ions are further ionized by collisions with
plasma electrons The magnetic field separates the secondary ion
trajectories from the primary ions. The combined primary and
secondary ion trajectories appear as shown in the system figure
above The secondary ions are detected by ion collection plates
split vertically and horizontally so that four separate currents
are monitored This permit measurements of the electric potential,
fluctuations of potential and electron density, and magnetic vector
potential, localized to the ionization position The secondary beam
current I s ( the sum of the four split plate signals) is given by
Assuming ion is a weak function of plasma temperature T e, which is
about a few hundred eV in the core of the MST plasma, I s is
proportional to the density n e (r sv ) The relative density
fluctuation level at the sample volume is then obtained from The
currents on the top two plates are summed to produce i upper while
the bottom two plates sum to i lower. The energy of the secondary
ion leaving the plasma differs from that of the primary ion by the
change in potential energy. Thus, to determine potential, we use a
Proca and Green type energy analyzer and the following relationship
G and F are geometric functions of the analyzer angle V AN is the
analyzer voltage and V AC is the accelerator voltage
Slide 2
Plasma Dynamics Lab HIBP E ~ 0 V/m in Locked Discharges Average
potential ~ 580 V ~ 500-600V less than in standard rotating plasmas
Drop in potential possibly due to degradation of ion confinement,
reduction in mode velocity or changes in bulk fluid rotation
Scatter ~ 100 V; reduced scatter likely due to uniformity of mode
velocity ~ 0 km/s, variations in density remain Potential profile
relatively flat, E r small/zero Biasing experiment 2 electrodes,
inserted 8-10cm Negative biasing for 10ms with respect to MST wall
Discharges lock then reaccelerate when biasing is turned off
Density rises dramatically Unlike a standard locked discharge,
sawteeth do not cease E ~ 0 V in Biased Discharges The potential is
positive, but ~ 200-250V lower than in a standard locked discharge
The potential profile is flat over the region sampled The lower
possibly due to: higher n e (~20-40%) better confinement of e -
HIBP Measurements Facilitate Experimental Investigation of Ion
Radial Force Balance Simplified equilibrium radial force balance
for the ion species is given by: Quantities: E r HIBP radial
electric field n e FIR electron density profile v IDS ion toroidal
and poloidal flow velocities (and m=1,n=6 mode velocity) P
Rutherford, Thomson scattering pressure gradient inferred from ion,
electron temp. B MSTFit reconstructed equilibrium field profile Z
Assumed = 2 Assumptions -in equilibrium -incompressible plasma
flows -isotropic pressure gradient Radial Force Balance in Low
Current Standard Discharges HIBP measured E r is compared to the
total computed, and individual RHS terms Agreement between measured
and computed E r in the range of r = 16-27cm Contribution from v x
B term 3- 6x greater than pressure gradient term in core, 2x
greater toward edge The Computed Electric Field Incorporates
Mid-Sawtooth Cycle Measured Quantities Measured ion and electron
temperature profiles are similar in low current discharges For r
< 23 cm, n ~ 0 The ratio of toroidal to poloidal flow velocities
is ~ 5-7. All quantities are from low current discharges, mid-cycle
Limited Measurements Contribute to Uncertainty in E r Ion flow
velocities Chord localized (15 cm) rather than profile measurements
Past experimental measurements indicate that the flow velocity
decreases toward the plasma edge (v x B in edge likely smaller than
computed) A 20% change in the flow velocity is enough to est.
agreement between measured and computed E r Pressure Gradient The
uncertainty in the pressure gradient is < 3% The uncertainty in
the ion-temperature measurements is ~ 20-30% Due to lack of spatial
resolution Uncertainty in T i translates to an uncertainty of ~ 500
V/m at r~25-33cm Measured E r Uncertainty in the measurement ~ 700
V/m Radial Force Balance in Low Current Locked Discharges Pressure
profiles from standard discharges Ion temperature is assumed to be
close to the impurity temperature measured mid-cycle; this is based
on the similarity of measurements in a standard discharge near a
sawtooth crash Calculated E r is negative The ratio of toroidal to
poloidal flow velocities now ~ 1; decrease of the toroidal flow
velocity from standard to locked discharges dramatically reduces
computed E r The use of T impurity results in a pressure term that
is 30% lower than in the standard discharge Radial Force Balance in
Low Current Biased Discharges Suppression of electrostatic
fluctuation induced transport has been observed with negative
biasing The HIBP measurement of E r, while not shown, is close to
zero over the range illustrated The electron temperature and
density profiles were measured in the biased discharges. The n e
profile is hollow and the gradient positive in the region
investigated. The toroidal flow decreases and the ratio of toroidal
to poloidal flow ~ 2 Low Current Force Balance Summary The computed
electric field tends to agree with the measured electric field
toward the core of the plasma, with greater deviation toward edge
The v x B term increases with radius and is the dominant term in
both standard and biased discharges The v x B term is reduced in
both locked and biased discharges due to reduction in flow
velocities The profile of the biased discharge pressure term is
partly due to the hollow density profile and positive density
gradient (transport barrier) Computation of the radial electric
field would improve with Profile measurements of flow velocities
Profile measurements of the ion temperature, mid-cycle in locked
and biased discharges Experimental investigation of radial force
balance in high current discharges Experimental Investigation of
Radial Force Balance in High Current Discharges The radial electric
field is computed during two intervals (after (a) and before (b))
The HIBP measured E r is shown for the same two time intervals Both
calculated and measured show and increase in E r over the sawtooth
cycle The n=6 phase velocity tends to be lower in the time window
after the crash than the window before. The result, is a smaller
contribution from v x B. Particle Drifts in MST Due to Radial
Electric Field and Pressure Gradients Two drifts are considered:
ExB and diamagnetic drift; E r and P are both measured: Comparisons
to IDS measurements are made (near r=20 cm) : v ExB + v P ~ 8.6
km/s; v IDS = -4.5 km/s (sign error may exist) : v ExB + v P ~ 8.6
km/s; v IDS = 22.5 km/s The ExB drift dominates in the core, the
diamagnetic toward the edge Radial Electric Field Predicted by
Stochastic Field Theory Does Not Match Measurements Prediction from
stochastic field theory (Harvey) is compared with measured E r and
ion radial force balance This theory examines the relation between
particle and heat flux, and the ambipolar electric field Ambipolar
field is 1-2 orders smaller than either of the others Plasma
rotation is not taken into account in the theory/eqn. Agree only
when one considers that measured and predicted fields are both
positive. Toroidal and Poloidal Flow Velocity Measurements Due to
higher temperatures C-V emission moves outward to 30 < r < 40
cm. Thus, the measurement region is no longer coincident with the
HIBP measurement of E r The global m=1,n=6 mode phase velocity is
used instead Discharge Differences HIBP E r measurements are
carried out in 383kA discharges, ion pressure gradients and phase
velocities from 373 kA discharges Time Windows 1.5 - 2.5 ms after a
sawtooth crash and 2-3 ms before a crash An m=0 perturbation
applied by horizontal and vertical field error correction coils at
the gap cause the n=6 mode to lock Sawteeth cease and local large
amplitude density fluctuations decrease Confinement is poorer than
in rotating plasmas The data are from two discharges, one
realizationeach discharge (I p ~ 275 kA) The upper trace: n e ~ 0.5
x 10 13 cm -3 v n=6 ~ 32.5 km/s The lower trace: n e ~ 1.0 x 10 13
cm -3 v n=6 ~ 28 km/s Effect of Plasma Density and Rotation on
Potential Measurements Locked Discharges