Gerhardt_Characteristics Poster_APS 2003
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Transcript Gerhardt_Characteristics Poster_APS 2003
Characteristics of Biased Electrode Discharges in HSX
S.P. Gerhardt, D.T. Anderson, J. Canik, W.A. Guttenfelder, and J.N. Talmadge
HSX Plasma Laboratory, U. of Wisconsin, Madison
1. Structure of the
Experiments
3. Two Time Scales
Observed in Flow
Damping
General Structure of Experiments
•
•
Mach Probes in HSX
•
•
•
6 tip mach probes measure plasma flow speed and
direction on a magnetic surface.
2 similar probes are used to simultaneously measure
the flow at high and low field locations, both on the
outboard side of the torus.
Data is analyzed using the unmagnetized model by
Hutchinson.
•
Looking To The
Magnetic Surface
•
Convert flow magnitude and angle into flow in two
directions:
U t X t cos X t
2
•
•
3
•
•
•
B / Bo 1 H cos4 M cos4
Mirror :
U
Model Fits Flow Rise Well
Mirror
Tokamak Basis Vectors Can Differ from
those in Net Current Free Stellarator.
3
•
This allows the calculation of the radial electric field evolution:
U 1 e t /1 S1e S3e 1 e t / 2 S2e S 4e
•
2. The Biased Plasma as a Capacitor
Impedance in Smaller in the Mirror
Configuration
Bias Waveforms Indicate a
“Capacitance” and an Impedance
Decay Time:
=33x10-6 seconds
Impedance: R=V/I=36
C= /R=8.9x10-7F
Acumulated Charge from
“Charging Current”:
Q=2.33 Coulombs
Voltage: V=310 Volts
C=Q/V=7.5x10-7F
•
•
Impedance1/n consistent with
radial conductivity scaling like n.
Consistent with both
neoclassical modeling by
Coronado and Talmadge or
anomalous modeling by,for
instance, Rozhansky and
Tendler.
Current peaks at the calculated separatrix.
Electrode Current Profile does not follow the density
profileElectrode is not simply drawing electron saturation
current.
•
•
Linear I-V relationship
Consistent with linear viscosity
assumption.
Very little current drawn when
collection ions collect
electrons in all experiments in
this poster.
•
Mirror, F
Mirror, slow rate
QHS, F
QHS, slow rate
Two time scales/two direction flow evolution.
6. Observations of and Reductions in
Turbulence With Electrode Bias.
Vf Fluctuation Reduction with Bias
•
•
“Forced Er” Plasma Response Rate is
Between the Slow and Fast Rates.
t0
t 0
t /
U t U E 1 e
e BQ1 E 1 1 Q2 e F t Q2 e t /
•
Total Conductivity
Combination of neutral
friction and viscosity
determines radial
conductivity.
Mirror agreement is
somewhat better.
Viscosity Only
Neutrals Only
The Coronado and Talmadge Model
Overestimates the Rise Times By 2
Distinct Spectral Peaks in the Electrode Current
r/a.7
r/a.9
QHS
Configuration
• 50 kHz mode remains unsuppressed by bias. See Poster by C. Deng
• Electrostatic transport measurements soon. See Poster by W. Guttenfelder
1/in
QHS
Mirror
Mirror
Fast Rates, QHS and Mirror
ExB flows and compensating Pfirsch-Schlueter flow will grow
on the same time scale as the electric field.
Parallel flow grows with a time constant F determined by
viscosity and ion-neutral friction.
d d
QHS
Assume that the electric field, d/d,is turned on quickly
Er 0
Er 0 E 1 e t /
•
J
1/in
Formulation #2: The Electric Field is Quickly
Turned On.
The “Forced Er” model Underestimates
the QHS time
•
Measurements
4
d
t d t 0 F1 1 e t /1 F2 1 et / 2
d
d
•
Define the radial conductivity
as
t / 2
•
<B>=0 in net current
free stellarator, but not
a tokamak.
2*1e-7*48*14*5361
=.7205
2
t / 1
•
Mirror
2
1
•
QHS
S1…S4, 1 (slow rate), and 2 (fast rate) are flux surface quantities related to the
geometry.
Break the flow into parts damped on each time scale:
•
Similar model 2 time scale / 2 direction fit is used to fit
the flow decay.
1
QHS Modeled Radial Conductivity agrees to a
Factor of 3-4
QHS
Original calculation by Coronado and Talmadge
After solving the coupled ODEs, the contravariant components of the flow are
given by:
<B>= Boozer g=
t /
t /
S 1 e S
S 1 e S
1 e
QHS Flow Damps Slower, Goes Faster For
Less Drive.
R
Use Hamada coordinates, using linear neoclassical viscosities.
No perpendicular viscosity included.
Predicted form off flow rise from
modeling:
U (t ) C 1 exp t / f fˆ C s 1 exp t / s sˆ
U1, fit t C f 1 exp t / f cos f Cs 1 exp t / s cos s U1SS
Symmetry Can be Intentionally Broken
with Trim Coils
U 1 e
Fit flows to models
U 2, fit t C f 1 exp t / f sin f Cs 1 exp t / s sin s U 2 SS
Need quantities like <e·e >, <e·e >, <e·e >,<||>, <| ·
|>.
Previous calculation used large aspect ratio tokamak
approximations.
Method involves calculating the lab frame components of the
contravariant basis vectors along a field line, similar to Nemov.
Solve these with Ampere’s Law
t
4 J plasma J ext
Formulation #1: The External Radial
Current is Quickly Turned On.
U 2,exp t X 2 t sin X 3 t
Probe measures Vf with a proud pin.
QHS :
B / Bo 1 H cos4
•
•
•
t
B U B mi N iin B U
As the damping is reduced, the flow rises more slowly, but to a
higher value.
Full problem involves two momentum equations on a flux surface2
time scales & 2 directions.
1,exp
X
I sat X 1 exp 2 .641 cos X 3 .71 cos X 3
2
•
•
0
t0
U jB 1 exp t / nm t 0
•
t
c
BP U
J BP mi N iin BP U
g B B
mi N i
Take a simple 1D damping problem:
0 t0
dU
mn
F U , F
dt
Has solution
jB t 0
•
Two time scales/directions come from the coupled momentum
equations on a surface.
mi N i
Flow Analysis Method
•
We Have Developed a Method to Calculate
the Hamada Basis Vectors
Solve the Momentum Equations on a Flux
Surface
Simple Flow Damping Example
•
5. Comparisons Between QHS and
Mirror Configurations of HSX
4. Neoclassical Modeling of Plasma Flows
r/a
r/a
r/a
• 50 kHz peak becomes dominant as the probe moves in.
• Do these simply reflect density fluctuations?
7. Computational Study: Viscous Damping in
Different Configurations of HSX