High Current Standard Plasmas

1
High Current Standard Plasmas
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 Vrms 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.

• The currents on the top two plates are summed to
  produce iupper while the bottom two plates sum to
  ilower.
• 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

Potential and Electric Field Profiles in High Ip
Discharges
After Crash

• 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

• G and F are geometric functions of the analyzer
  angle
• VAN is the analyzer voltage and VAC is the
  accelerator voltage

I. Principle of Heavy Ion Beam Probing

• Multiple Shot Analysis
• Three intervals, 1.5ms duration each
• 1.5 ms after crash
• mid way between crashes
• 2.5 ms before crash

• RESULTS
• ? 1700 - 2000V
• Er 1.7 - 2 kV/m
• PLASMAS
• Ip 380 kA, ? 1
• ne .95 x 1013 cm-3, ? 5
• Vn6 30km/s, ?10
• F -0.22
• Te 300 eV

Mid-cycle
Before Crash
Potential is Positive BetweenSawtooth Crashes
Potential Profile Measurements inLow Current
Discharges

• 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 Is ( the sum of the
  four split plate signals) is given by

• 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

• Peak ? 1400 V
• Peak ? 500 V lower than in High Ip discharges
• Measurements 2 ms after crash

I0 initial primary current injected into the
plasma ?ion ion cross-section for primary to
secondary ions lsv sample volume length ne(rsv)
electron density at the sample volume k a
multiplying factor between 110 due to electrons
emitted by the detector plates Fp primary beam
attenuation Fs secondary beam attenuation qs
charge of the secondary beam qp charge of the
primary beam
Potential Tracks the Mode Velocity
Electric Field Profiles in Low Current Rotating
Plasmas

• Measured instantaneous potential tracks evolution
  of the mode velocity
• m1, n6 mode velocity
• Potential at which vn6 40 km/s does not
  overlap ? at vn6 20 km/s
• Sample volume r22cm
• Data from over 50 shots
• Differences between ? and vn6 profiles may be
  due to evolution in B and motion of the sample
  location

• Average Er 1.5kV/m
• The electric field is outwardly directed
• Recall, E 2 kV/m in high Ip discharges
• Large error bars on Er (neg. Er) due to shot to
  shot scatter in potential and artifacts of data
  processing

• Assuming ?ion is a weak function of plasma
  temperature Te, which is about a few hundred eV
  in the core of the MST plasma, Is is proportional
  to the density ne(rsv)
• The relative density fluctuation level at the
  sample volume is then obtained from

2
Limited Measurements Contribute to Uncertainty in
Er
E 0 V in Biased Discharges
Experimental investigation of radial force
balance in high current discharges
Effect of Plasma Density and Rotation on
Potential Measurements

• 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 Er
• Pressure Gradient
• The uncertainty in the pressure gradient is lt 3
• The uncertainty in the ion-temperature
  measurements is 20-30
• Due to lack of spatial resolution
• Uncertainty in ?Ti translates to an uncertainty
  of 500 V/m at r25-33cm
• Measured Er
• Uncertainty in the measurement 700 V/m

• 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 ne (20-40)
• better confinement of e-

• Toroidal and Poloidal Flow Velocity Measurements
• Due to higher temperatures C-V emission moves
  outward to 30 lt r lt 40 cm. Thus, the measurement
  region is no longer coincident with the HIBP
  measurement of Er
• The global m1,n6 mode phase velocity is used
  instead
• Discharge Differences
• HIBP Er 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

• The data are from two discharges, one
  realizationeach discharge (Ip 275 kA)
• The upper trace
• ne 0.5 x 1013 cm-3
• vn6 32.5 km/s
• The lower trace
• ne 1.0 x 1013 cm-3
• vn6 28 km/s

Locked Discharges
Radial Force Balance in Low Current Locked
Discharges
Experimental Investigation of Radial Force
Balance in High Current Discharges

• An m0 perturbation applied by horizontal and
  vertical field error correction coils at the gap
  cause the n6 mode to lock
• Sawteeth cease and local large amplitude density
  fluctuations decrease
• Confinement is poorer than in rotating plasmas

• 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 Er 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 Er
• The use of Timpurity results in a pressure term
  that is 30 lower than in the standard discharge

HIBP Measurements Facilitate Experimental
Investigation of Ion Radial Force Balance

• The radial electric field is computed during two
  intervals (after (a) and before (b))
• The HIBP measured Er is shown for the same two
  time intervals
• Both calculated and measured show and increase in
  Er over the sawtooth cycle
• The n6 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.

• Simplified equilibrium radial force balance for
  the ion species is given by
• Quantities
• Er HIBP radial electric field
• ne FIR electron density profile
• v IDS ion toroidal and poloidal flow
  velocities (and m1,n6 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 Biased
Discharges
E 0 V/m in Locked Discharges
Particle Drifts in MST Due to Radial Electric
Field and Pressure Gradients
Radial Force Balance inLow Current Standard
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, Er small/zero

• Suppression of electrostatic fluctuation induced
  transport has been observed with negative biasing
• The HIBP measurement of Er, while not shown, is
  close to zero over the range illustrated
• The electron temperature and density profiles
  were measured in the biased discharges. The ne
  profile is hollow and the gradient positive in
  the region investigated.
• The toroidal flow decreases and the ratio of
  toroidal to poloidal flow 2

• Two drifts are considered ExB and diamagnetic
  drift Er and ?P are both measured
• Comparisons to IDS measurements are made (near
  r20 cm)
• ? vExB v?P 8.6 km/s vIDS -4.5 km/s (sign
  error may exist)
• ? vExB v?P 8.6 km/s vIDS 22.5 km/s
• The ExB drift dominates in the core, the
  diamagnetic toward the edge

• HIBP measured Er is compared to the total
  computed, and individual RHS terms
• Agreement between measured and computed Er 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

Biasing experiment
The Computed Electric Field Incorporates
Mid-Sawtooth Cycle Measured Quantities
Radial Electric Field Predicted by Stochastic
Field Theory Does Not Match Measurements
Low Current Force Balance Summary

• Prediction from stochastic field theory (Harvey)
  is compared with measured Er 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.

• 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

• Measured ion and electron temperature profiles
  are similar in low current discharges
• For r lt 23 cm, ?n 0
• The ratio of toroidal to poloidal flow velocities
  is 5-7.
• All quantities are from low current discharges,
  mid-cycle

• 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