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•  Describes collisional motion of particles due to Coulomb forces in non-uniform electric and magnetic fields [6]

•  Begins with an application of Boltzmann’s Equation, Eq. (1)

•  Describes time evolution of distribution function (f) in 6-D position/velocity phase space (x,v)

•  Influenced by Coulomb force F = q(E + v x B) •  Collision operator in form of Fokker-Planck [7]

•  Able to write down equations for particle density, mean velocity, and higher velocity moments to combine with conservation equations

•  Describe linear relationships between flux and force quantities, such as heat flux (q) and the temperature (T) gradient force, Eq. (2)

•  Neoclassical curvature and grad-B drifts, combined with the magnetic mirror effect, lead particles into trapped orbits

•  Radial force balance requires that temperature and pressure gradients lead to a parallel flow of particles

•  This is the so-called “bootstrap current” •  Many models for bootstrap current based on a few plasma

parameters •  E.g. Model by Sauter et al. [4, 5], Eq. (3)

NEOCLASSICAL  TRANSPORT  

OBJECTIVES  •  Original program plotted radial electric fields •  Added features:

•  Plot in same/new window •  Overlay plots of the same type •  Make colormaps over entire time/radial domain •  Read in unformatted ion and electron flux data

•  Updated GUI

PLOTTING  TOOLS  •  Implemented a RESTART function into the electron code

•  Outputs data at regular intervals •  Able to restart simulation at last checkpoint with

zero loss of significance in the calculation •  Verified implementation of Sauter’s formulae into the post-

processing script, along with checks for model parameters

GTC-­‐NEO  CODE  DEVELOPMENT   FUTURE  WORK  •  Implementation of new particle loading routine into the

GTC-NEO electron code for better scaling (e.g. at NERSC) •  Bootstrap current model verification using GTC-NEO •  Quantification of anomalous ion thermal transport in NSTX

based on comparison between measurement and GTC-NEO •  Study of neoclassical transport in NSTX-U given predicted

plasma profiles as inputs for GTC-NEO

REFERENCES  [1] Masayuki Ono, S. M. Kaye, Y-K. M. Peng, G. Barnes, W. Blanchard, M. D. Carter, J. Chrzanowski, L. Dudek, R. Ewig, D. Gates, et al. Nuclear Fusion, 40(3Y):557, 2000. [2] W. X. Wang, W. M. Tang, F. L. Hinton, L. E. Zakharov, R. B. White, and J. Manickam. Computer physics communications, 164(1):178–182, 2004. [3] W. X. Wang, G. Rewoldt, W. M. Tang, F. L. Hinton, J. Manickam, L. E. Zakharov, R. B. White, and S. Kaye. Physics of Plasmas (1994-present), 13 (8):082501, 2006. [4] Olivier Sauter, Clemente Angioni, and Y.R. Lin-Liu. Physics of Plasmas, 6(7):2834–2839, 1999. [5] Olivier Sauter, Clemente Angioni, and Y.R. Lin-Liu. Physics of Plasmas, 9(12):5140, 2002. [6] F. L. Hinton and R. D. Hazeltine. Reviews of Modern Physics, 48(2):239, 1976. [7] Marshall N Rosenbluth, William M MacDonald, and David L Judd. Physical Review, 107(1):1, 1957.

ACKNOWLEDGEMENTS  This project was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI).

Establish a foundation for studying neoclassical transport in NSTX [1] using the GTC-NEO code [2, 3]: •  Explore literature to learn the basics of neoclassical

transport •  Develop tools for plotting outputs from the GTC-NEO code •  Become familiar with bootstrap current model by Sauter et

al. [4, 5] •  Implement new features into the GTC-NEO code, such as a

RESTART function and models for calculating the bootstrap current in the post-processing script

* Contact: msp73@drexel.edu

Obligatory comic courtesy of Randall and xkcd.com

1Undergraduate  Physics,  Drexel  University,  Philadelphia,  PA,  2Princeton  Plasma  Physics  Laboratory,  Princeton,  NJ  M.  S.  Parsons1*,  S.  Ethier2  and  E.  Feibush2  

Prepara.on  for  a  Computa.onal  Study  of  Plasma  Transport  in  NSTX  

SAUTER’S  FORMULAE  •  Plotted model of bootstrap current by Sauter et al. [4, 5]

over a wide range of temperatures and densities with NSTX-like parameters [1]

•  All coefficients have a low temperature dependence at low densities, and low density dependence at low temperatures

•  For the pressure gradient term, the contribution becomes more significant at lower collisionalities (low n, high T) with a high trapped particle fraction

NUMERICAL  STUDY  USING  GTC-­‐NEO  •  Implemented a collision multiplier term (collmult) •  Used circular plasma profiles while varying collisionality •  Examined cases for collmult = 1.0, 2.0, 4.0, 10.0 •  Found incredible variation between collmult = 1.0 / 10.0.

•  Working backwards, it was found that the electric field profile produced by the ion code and used as an input to the electron code varied greatly in each case

•  Tracing back further, differences in the particle collision weighting function are seen as early as t = 20 of 40,000

•  Collisionality determines the time step used by the code •  Conclusion: unsurprisingly, the timescale of collisions

chosen plays a crucial role in the computational stability of the simulation

Radial profiles over time of electron energy flux for collmult = 1.0

Radial profiles over time of electron energy flux for collmult = 10.0

Colored lines correspond to constant values of the L31 bootstrap current coefficient as a function of density and temperature.

The height of the surface represents collisionality as a function of density and temperature, with blue/red for low/high L31.

(a) ft = 0.01 (b) ft = 0.40 (c) ft = 1.00

nT