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Exact conservation laws for gyrokinetic Vlasov-Poisson equations
Post-edited
Authors : Tronko, Natalia (Author of the conference)
CIRM (Publisher )
35L65 - Conservation laws
70S10 - Symmetries and conservation laws
82C40 - Kinetic theory of gases
82D10 - Plasmas
35Q83 - Vlasov-like equations
CIRM (Publisher )
Abstract :
The momentum transport in a fusion device such as a tokamak has been in a scope of the interest during last decade. Indeed, it is tightly related to the plasma rotation and therefore its stabilization, which in its turn is essential for the confinement improvement. The intrinsic rotation, i.e. the part of the rotation occurring without any external torque is one of the possible sources of plasma stabilization.
The modern gyrokinetic theory [3] is an ubiquitous theoretical framework for lowfrequency fusion plasma description. In this work we are using the field theory formulation of the modern gyrokinetics [1]. The main attention is focussed on derivation of the momentum conservation law via the Noether method, which allows to connect symmetries of the system with conserved quantities by means of the infinitesimal space-time translations and rotations.
Such an approach allows to consistently keep the gyrokinetic dynamical reduction effects into account and therefore leads towards a complete momentum transport equation.
Elucidating the role of the gyrokinetic polarization is one of the main results of this work. We show that the terms resulting from each step of the dynamical reduction (guiding-center and gyrocenter) should be consistently taken into account in order to establish physical meaning of the transported quantity. The present work [2] generalizes previous result obtained in [4] by taking into the account purely geometrical contributions into the radial polarization.
MSC Codes : The modern gyrokinetic theory [3] is an ubiquitous theoretical framework for lowfrequency fusion plasma description. In this work we are using the field theory formulation of the modern gyrokinetics [1]. The main attention is focussed on derivation of the momentum conservation law via the Noether method, which allows to connect symmetries of the system with conserved quantities by means of the infinitesimal space-time translations and rotations.
Such an approach allows to consistently keep the gyrokinetic dynamical reduction effects into account and therefore leads towards a complete momentum transport equation.
Elucidating the role of the gyrokinetic polarization is one of the main results of this work. We show that the terms resulting from each step of the dynamical reduction (guiding-center and gyrocenter) should be consistently taken into account in order to establish physical meaning of the transported quantity. The present work [2] generalizes previous result obtained in [4] by taking into the account purely geometrical contributions into the radial polarization.
35L65 - Conservation laws
70S10 - Symmetries and conservation laws
82C40 - Kinetic theory of gases
82D10 - Plasmas
35Q83 - Vlasov-like equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 17/08/14 Conference Date : 04/08/14 Subseries : Research talks arXiv category : Mathematical Physics Mathematical Area(s) : Mathematical Physics ; PDE Format : QuickTime (.mov) Video Time : 00:55:54 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-08-04_Tronko.mp4 
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Information on the Event
Event Title : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmasEvent Organizers : Campos Pinto, Martin ; Charles, Frédérique ; Guillard, Hervé ; Nkonga, Boniface Dates : 21/07/2014 - 29/08/2014 Event Year : 2014 Event URL : http://smai.emath.fr/cemracs/cemracs14/
Citation Data
DOI : 10.24350/CIRM.V.18555703Cite this video as: Tronko, Natalia (2014). Exact conservation laws for gyrokinetic Vlasov-Poisson equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18555703 URI : http://dx.doi.org/10.24350/CIRM.V.18555703 |
Bibliography
- [1] Brizard, A.J. New variational principle for the Vlasov-Maxwell equations. Physical Review Letters 84 (2000), no. 25, 5768-5771 - http://dx.doi.org/10.1103/physrevlett.84.5768
- [2] Brizard, A.J. and Tronko, N. Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations. Physics of Plasmas 18, 082307 (2011), no. 8 - http://dx.doi.org/10.1063/1.3625554
- [3] Brizard, A.J. and Hahm, T.S. Foundations of Nonlinear Gyrokinetic Theory. Reviews of Modern Physics 79 (2007), no. 2, 421-468 - http://dx.doi.org/10.1103/revmodphys.79.421
- [4] Scott, B. and Smirnov, J. Energetic consistency and momentum conservation in the gyrokinetic description of tokamak plasmas. Physics of Plasmas 17, 112302 (2010), no. 11 - http://dx.doi.org/10.1063/1.3507920
