Importance of two-fluid in helicity injection current drive

1
Importance of two-fluid in helicity injection
current drive
2
Outline of points

• Current can follow field lines without ion-fluid
  flow
• Current is a two fluid phenomenon
• Single-fluid dynamo looks harder to drive than
  two-fluid dynamo
• GEM challenge shows that two-fluid MHD gives
  faster reconnection than just resistive MHD
• Hall Physics affects low frequency physics
  through the whistler wave

3
Current follows open field lines in CHI
experiments
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Current can follow field lines without ion-fluid
flow

• In Figure, the electrodes are blue. Assume no
  pressure. In steady state, current approximately
  follows B-field.
• In single fluid cross-field current is required
  to maintain the necessary flows to balance Ex. (v
  Ex/B ).
• In two fluid, with large ??, a small cross field
  current balances Ex with no flow
• (Small jx drives jz which produces Ex)
• Initially, with Hall jy ? ??jz  ?  (??)2jx.
  Without Hall jx ? jy

5
Single-fluid dynamo appears harder to drive than
two-fluid dynamo
,
Without Hall, in steady state, (
) for parallel current drive
Where v is of the massive fluid With Hall

• It is the electron motion in both cases that
  does the current drive.
• In two-fluid, ion motion is not necessary.
  Hence, it should be easier.
• (Dynamo across closed flux is possible.)

6
GEM challenge shows that two-fluid MHD gives
faster reconnection than just resistive MHD

• Cannot expect resistive MHD to predict
  relaxation rates in HIT-SI and HIT-II
• NIMROD may be most accurate. Others use mi/me
  25?
• For benchmarking only NIMROD may need a dj/dt
  term in Ohms law because the others have massive
  electrons.
• Since the saturation of Hall effects is often
  ions carrying their own current, such a dj/dt
  term with a calibration coefficient, determined
  by experiments, might be useful.

Nonlinear GEM Benchmark
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Hall Physics affects low frequency physics
through the whistler wave
Dispersion diagram for right handed parallel
electromagnetic wave
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Summary

• Discrepancy seen between HIT-SI and resistive MHD
  is expected.
• Similar discrepancy may be found in the
  flux-amplification cases of HIT-II.
• Two-fluid effects should be in the correct
  direction for better agreement with HIT-SI (?? ?
  100). (HIT-SI appears to have much higher
  relaxation rates than resistive MHD.)
• A dj/dt term in the Ohms law with a calibration
  factor might be useful, since it will be
  difficult to model very high frequency Hall
  physics.

9
Generalized Ohms law including Hall terms is
needed to analyze the dynamo.

• The essence of the pressureless, perfectly
  conducting generalized Ohms law with Hall
  physics is that the electron fluid is tied to the
  magnetic field.
•  
• Resistivity allows the slippage between magnetic
  field and the electron fluid.
•  
• The pressureless generalized Ohms law is found by
  a Lorentz transformation from the inertial
  electron fluid frame (where E ?j) to the Lab
  frame yielding
• Thus, like Maxwells equations, the generalized
  Ohms law is only valid in an inertial
  (non-accelerating) frame.
• WARNING Maxwells equations and the generalized
  Ohms law are not valid in fluctuating flux
  coordinates.

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Dynamo mechanism may come from fluctuation modes
coupling the driven and confinement regions

• Time averaging the generalized Ohms law
  including the Hall terms yields Ji 99
•  For simplicity, assume ion fluctuation currents
  are small
•  
• Fluctuation magnetic structure alone provides the
  coupling between driven and confinement regions
  and our intuitive pictures of field line tension
  and pressure are valid.

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Intuitive shape of relaxation dynamo mode emerges

• Assumes electron flow is in the direction of
  field
• ? External drive must overcome anti-current drive
• Current drive can maintain closed flux current
• Sheared electron flow due to lamada gradient
  distorts mode resulting in cross-field current
  drive stress.
• Practically any mode will cause relaxation CD.
• First mode will stabilize rest. (Get the physics
  right and mode should be right one.)

Mode crossection (black) in plane of
equilibrium field (red, blue)
 

anti-current drive
driven region
confinement region
current drive
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Experimental data also shows a current driving
n1 mode structure in an ST.
Fluctuation flux at 3ms, (10µWb spacing)

• A magnetic probe array was inserted into a
  rotating CHI driven discharge on HIT-II.
• Discharge has a well repeating n1 mode so that a
  rigid rotation analysis reveals the toroidal mode
  structure.
• Current drive and anti-current driving
  fluctuations have also been measured on RFP Den
  Hartog 99, Fontana 00 and spheromks al-Karkhy
  93

Toroidal angle radians Poloidal flux at
innermost probe (10cm)
Time ms Shot 26070