10

Fast Method for Radial Electric Field Correction of Motional Stark Effect Data in DIII-D

Database results

Conclusions Overall, it seems as though the partial Er method creates some real

improvement over shots with no Er analysis and ought to be used routinely in EFIT reconstructions. However, the addition of an estimated diamagnetic term seems to hinder results. Certain positions and times may also yield less positive

results, so more analysis is necessary to look at what occurs at the plasma edges and at boundary times.

Acknowledgements

Case studies Motivation This project develops a new equilibrium reconstruction

procedure that is automatic and easy to use, in which only the toroidal rotation component of radial force balance is used to correct the motional stark effect data. This data is used in equilibrium reconstruction on the DIII-D tokamak by including the radial electric field effect in the determination

of the magnetic pitch angles. This is expected to give a more accurate result than ignoring the radial electric field

effect for discharges with co-neutral beam injection.

MSE and Er background

This project would not have been possible without support from the National Undergraduate Fellowship Program, funding from the DOE, and constant assistance from the DIII-D experiment at General Atomics. In addition, many processes used codes created by

John Ferron, Craig Petty, Tim Luce, Chris Holcomb, and Will Fox.

L. Bergsten, Dartmouth College; C.C. Petty, GA

Example shot 136848, at time 3005 s

Er against radius, for the full Er correction method, for no method, Er is zero

Low VΦ case (balanced NBI): shot 145455, time 1905 s

High VΦ case (all co-NBI): shot 145940, time 1905 s

Er against radius, full Er correction (black) overlay with partial Er method (red)

Er against radius, full Er correction (black) overlay with partial Er method (red)

Safety factor against radius, full Er correction (black) overlay with partial Er method (pink) and no Er method

(blue)

Safety factor against radius, full Er correction (black) overlay with partial Er method (pink)

and no Er method (blue)

Χ2 values for the partial Er method without the addition of the diamagnetic

term (black) and with the term (red).

MSE chi2

Χ2 values for the full Er option (black), the partial Er option (red) and the no Er option

(blue).

MSE chi2

Safety Factor against radius, overlay no Er correction (black) and full Er correction (pink)

Radial electric field correction to MSE

diam

For the diaterm, we substitute the emission amplitude of the

carbon line for the carbon density because the former is

easily available between shots. However, it seems this approximation does more

harm than good, as MSE Χ2 values become much higher

(moving past the range on the plot) when the diamagnetic

term is added.

The MSE diagnostic on DIII-D uses Stark splitting of spectral lines to determine the magnetic field inside the tokamak. MSE gives the pitch angle of the magnetic field (tan Υ) as

well as other measures to reconstruct the plasma equilibrium, but the radial electric field in the tokamak

disturbs and alters this angle measurement.

The following histograms show an attempt to survey results for

a variety of shots and times. The plot to the right shows

overlain histograms of MSE Χ2 values for three different Er

correction methods. The data seem rather similar, which

means this particular test of the methods is inconclusive.

Nu

mb

er o

f Ca

ses

Nu

mb

er o

f Ca

ses

When VΦ is high, the partial Er method approximation is most accurate. The above plots demonstrate this clearly, as the partial Er method remains close

to the full Er method (and much more so than the no Er method).

The partial Er method approximation is least accurate when VΦ is low, as the factors it ignores become significant. The above plots show that in this case,

the partial Er method overestimates Er and is much less accurate than the case above.