# Final Technical Report

## Abstract

Final Technical Report for U.S. Department of Energy Grant No. DE-FG02-09ER55005 Nonlinear FLR Effects in Reduced Fluid Models Alain J. Brizard, Saint Michael's College The above-mentioned DoE grant was used to support research activities by the PI during a sabbatical leave from Saint Michael's College in 2009. The major focus of the work was the role played by guiding-center and gyrocenter (linear and nonlinear) polarization and magnetization effects in understanding transport processes in turbulent magnetized plasmas. The theoretical tools used for this work include Lie-transform perturbation methods and Lagrangian (variational) methods developed by the PI in previous work. The present final technical report lists (I) the peer-reviewed publications that were written based on work funded by the Grant; (II) invited and contributed conference presentations during the period funded by the Grant; and (III) seminars presented during the period funded by the Grant. I. Peer-reviewed Publications A.J. Brizard and N. Tronko, 2011, Exact momentum conservation for the gyrokinetic Vlasov- Poisson equations, Physics of Plasmas 18 , 082307:1-14 [http://dx.doi.org/10.1063/1.3625554 ]. J. Decker, Y. Peysson, A.J. Brizard, and F.-X. Duthoit, 2010, Orbit-averaged guiding-center Fokker-Planck operator for numerical applications, Physics of Plasmas 17, 112513:1-12 [http://dx.doi.org/10.1063/1.3519514]. A.J. Brizard, 2010, Noether derivation of exact conservation lawsmore »

- Authors:

- Publication Date:

- Research Org.:
- Saint Michael's College

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE SC Office of Fusion Energy Sciences (SC-24)

- OSTI Identifier:
- 1060716

- Report Number(s):
- Final Report

- DOE Contract Number:
- FG02-09ER55005

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Brizard, Alain J.
```*Final Technical Report*. United States: N. p., 2009.
Web. doi:10.2172/1060716.

```
Brizard, Alain J.
```*Final Technical Report*. United States. doi:10.2172/1060716.

```
Brizard, Alain J. Thu .
"Final Technical Report". United States. doi:10.2172/1060716. https://www.osti.gov/servlets/purl/1060716.
```

```
@article{osti_1060716,
```

title = {Final Technical Report},

author = {Brizard, Alain J},

abstractNote = {Final Technical Report for U.S. Department of Energy Grant No. DE-FG02-09ER55005 Nonlinear FLR Effects in Reduced Fluid Models Alain J. Brizard, Saint Michael's College The above-mentioned DoE grant was used to support research activities by the PI during a sabbatical leave from Saint Michael's College in 2009. The major focus of the work was the role played by guiding-center and gyrocenter (linear and nonlinear) polarization and magnetization effects in understanding transport processes in turbulent magnetized plasmas. The theoretical tools used for this work include Lie-transform perturbation methods and Lagrangian (variational) methods developed by the PI in previous work. The present final technical report lists (I) the peer-reviewed publications that were written based on work funded by the Grant; (II) invited and contributed conference presentations during the period funded by the Grant; and (III) seminars presented during the period funded by the Grant. I. Peer-reviewed Publications A.J. Brizard and N. Tronko, 2011, Exact momentum conservation for the gyrokinetic Vlasov- Poisson equations, Physics of Plasmas 18 , 082307:1-14 [http://dx.doi.org/10.1063/1.3625554 ]. J. Decker, Y. Peysson, A.J. Brizard, and F.-X. Duthoit, 2010, Orbit-averaged guiding-center Fokker-Planck operator for numerical applications, Physics of Plasmas 17, 112513:1-12 [http://dx.doi.org/10.1063/1.3519514]. A.J. Brizard, 2010, Noether derivation of exact conservation laws for dissipationless reduced fluid models, Physics of Plasmas 17, 112503:1-8 [http://dx.doi.org/10.1063/1.3515303]. F.-X. Duthoit, A.J. Brizard, Y. Peysson, and J. Decker, 2010, Perturbation analysis of trapped particle dynamics in axisymmetric dipole geometry, Physics of Plasmas 17, 102903:1-9 [http://dx.doi.org/10.1063/1.3486554]. A.J. Brizard, 2010, Exact energy conservation laws for full and truncated nonlinear gyrokinetic equations, Physics of Plasmas 17, 042303:1-11 [http://dx.doi.org/10.1063/1.3374428]. A.J. Brizard, J. Decker, Y. Peysson, and F.-X. Duthoit, 2009, Orbit-averaged guiding-center Fokker-Planck operator, Physics of Plasmas 16, 102304:1-9[http://dx.doi.org/10.1063/1.3249627]. A.J. Brizard, 2009, Variational Principles for Reduced Plasma Physics, Journal of Physics: Conference Series 169, 012003 [http://dx.doi.org/10.1088/1742-6596/169/1/012003]. II. Invited and Contributed Conference Presentations A.J. Brizard and N. Tronko, Momentum conservation law for the gyrokinetic Vlasov-Poisson equations, 53rd Annual Meeting of the APS Division of Plasma Physics, Salt Lake City (Utah), November 14-18, 2011. A.J. Brizard, P.J. Morrison, C. Chandre, and E. Tassi, On the road to the Hamiltonian formulation of gyrokinetic theory, 52nd Annual Meeting of the APS Division of Plasma Physics, Chicago (Illinois), November 8-12, 2010. F.-X. Duthoit, A.J. Brizard, Y. Peysson, and J. Decker, Lie-transform perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry, 2010 International Sherwood Fusion Theory Conference, Seattle (Washington), April 19-21, 2010. N. Tronko and A.J. Brizard, Gyrokinetic momentum conservation law, 2010 International Sherwood Fusion Theory Conference, Seattle (Washington), April 19-21, 2010. C. Chandre and A.J. Brizard, Hamiltonian formulation of reduced Vlasov-Maxwell equations, 50th Annual Meeting of the APS Division of Plasma Physics, Dallas (Texas), November 17-21, 2008. A.J. Brizard, Nonlinear FLR effects in reduced fluid models, Invited Presentation at 11th Easter Plasma Meeting, Torino (Italy), April 15-17, 2009. III. Seminars Reduced Fokker-Planck operators for advanced plasma simulations, seminar given at CEA Cadarache (France), May 25, 2009. Ray phase-space methods in linear mode conversion, seminar given at CPT Luminy (France), April 1, 2009. Old and new methods in gyrokinetic theory, seminar given at CEA Cadarache (France), March 20, 2009. Hamiltonian theory of adiabatic motion of relativistic charged particles, seminar given at CPT Luminy (France), March 11, 2009. Noether method for fluids and plasmas, seminar given at CEA Cadarache (France), February 5, 2009. Nonlinear FLR effects in reduced fluid models, invited speaker at the Journee de la Dynamique Non Lineaire, Centre de Physique Theorique, CNRS Luminy (Marseille, France), June 3, 2008.},

doi = {10.2172/1060716},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2009},

month = {12}

}