1. 1 Importance of two-fluid in helicity injection current drive

2. Jarboe 8-13-07 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. Jarboe 8-13-07 3 Current follows open field lines in CHI experiments 1 m

4. Jarboe 8-13-07 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 E x. (v = E x /B ). In two fluid, with large , a small cross field current balances E x with no flow (Small j x drives j z which produces E x ) Initially, with Hall j y   j z  (  ) 2 j x. Without Hall j x  j y

5. Jarboe 8-13-07 Single-fluid dynamo appears harder to drive than two-fluid dynamo, Substitute etc. 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. Jarboe 8-13-07 Nonlinear GEM Benchmark 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 m i /m e = 25? For benchmarking only NIMROD may need a dj/dt term in Ohm’s 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.

7. Jarboe 8-13-07 Hall Physics affects low frequency physics through the whistler wave Dispersion diagram for right handed parallel electromagnetic wave

8. Jarboe 8-13-07 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 Ohm’s law with a calibration factor might be useful, since it will be difficult to model very high frequency Hall physics.

9. Generalized Ohm’s law including Hall terms is needed to analyze the dynamo. The essence of the pressureless, perfectly conducting generalized Ohm’s 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 Maxwell’s equations, the generalized Ohm’s law is only valid in an inertial (non-accelerating) frame. WARNING: Maxwell’s equations and the generalized Ohm’s law are not valid in fluctuating flux coordinates.

10. Jarboe 8-13-07 Dynamo mechanism may come from fluctuation modes coupling the driven and confinement regions Time averaging the generalized Ohm’s 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.

11. Jarboe 8-13-07 confinement region anti-current drive driven region current drive Mode crossection (black) in plane of equilibrium field (red, blue) 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.) Intuitive shape of relaxation dynamo mode emerges

12. Jarboe 8-13-07 A magnetic probe array was inserted into a rotating CHI driven discharge on HIT-II. Discharge has a well repeating n=1 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] Experimental data also shows a current driving n=1 mode structure in an ST. Toroidal angle [radians] Poloidal flux at innermost probe (10cm) Time [ms] Shot # 26070 Fluctuation flux at 3ms, (10μWb spacing)