Gyrokinetic simulations: Difference between revisions

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-The gyrokinetic formalism <ref>[http://pof.aip.org/pfldas/v31/i9/p2670_s1?isAuthorized=no T. S. Hahm. Nonlinear gyrokinetic equations for tokamak microturbulence. Physics of Fluids 31, 2670, 1988.]</ref><ref>[http://rmp.aps.org/abstract/RMP/v79/i2/p421_1 A. J. Brizard and T. S. Hahm. Foundations of nonlinear gyrokinetic theory. Reviews of Modern Physics 2, 421, 2007.]</ref> is based on first principles and provides a valuable tool for investigating low frequency turbulence in fusion plasmas.
+The gyrokinetic formalism <ref>T.S. Hahm, ''Nonlinear gyrokinetic equations for tokamak microturbulence'', [[doi:10.1063/1.866544|Phys. Fluids '''31''', 2670 (1988)]]</ref>
-The Theory Group at the [[Laboratorio Nacional de Fusión]] collaborates with the [http://www.bsc.es/ Barcelona Supercomputing Center] and the [http://www.ipp.mpg.de/ippcms/eng/index.html Max Planck IPP at Greifswald] for the development and exploitation of the [[EUTERPE]]  global gyrokinetic code.
+<ref>A.J. Brizard and T.S. Hahm, ''Foundations of nonlinear gyrokinetic theory'', [[doi:10.1103/RevModPhys.79.421|Rev. Mod. Phys. '''2''', 421 (2007)]]</ref>
+<ref>Felix I. Parra and Iván Calvo, ''Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry'', [[doi:10.1088/0741-3335/53/4/045001|Plasma Phys. Control. Fusion '''53''' (2011) 045001]]</ref> is based on first principles and provides a valuable tool for investigating low frequency turbulence in fusion plasmas.
-The code [[EUTERPE]] has been benchmarked against the TORB code <ref>[http://pop.aip.org/phpaen/v9/i3/p898_s1 Hatzky, R Tran, TM Konies, A Kleiber, R Allfrey, SJ .Energy conservation in a nonlinear gyrokinetic particle-in-cell code for ion-temperature-gradient-driven modes in theta-pinch geometry. PHYSICS OF PLASMAS, 9- 3,p. 912,2002.]</ref><ref>C. N¨uhrenberg, R. Hatzky, S. Sorge, et al. Global ITG Turbulence in
+Kinetic theory describes the evolution of the distribution function <math>f(\vec r, \vec v)</math> on the basis of the [[:Wikipedia:Vlasov equation|Vlasov equation]]:
-Screw-Pinch Geometry. IAEA TM on Innovative Concepts and Theory
+:<math>
-of Stellarators, Madrid 2005</ref> in both linear and non-linear simulations <ref>Edilberto Sánchez , Ralf Kleiber, Roman Hatzky, Alejandro Soba, Xavier Sáez, Francisco Castejón and Jose M. Cela. Linear and non-linear simulations using the
+\frac{\rm d f}{\rm d t} = \frac{\partial f}{\partial t} + \vec v \cdot \nabla_r f + \frac{q}{M}(\vec E + \vec v \times \vec B)\cdot \nabla_v f = 0
-EUTERPE gyrokinetic code. To appear in IEEE Transaction on Plasma Science (2010)</ref>.
+</math>
+The gyro-kinetic approach introduces a simplification by decomposing the full particle orbits into a rapid gyration about the magnetic field lines and a slow drift of the gyro centre <math>\vec R</math>:
+:<math>\vec r = \vec R + \vec \rho(\alpha)</math>
+where <math>\alpha</math> is the gyro-angle. By averaging over this gyro-angle one arrives at the  gyro-kinetic equation, which describes the evolution of the gyro centre in a phase space with one less dimension than the full Vlasov equation due to the averaging over the gyro-phase angle:
+:<math>f(\vec R, v_{||},v_\perp)</math>
+The gyro-kinetic equation is only valid for studying phenomena on timescales longer than the inverse of the gyro-frequency, and spatial scales larger than the gyro-radius. This is appropriate for, e.g., ITG (ion temperature gradient) turbulence.
+== Research activities ==
+The Theory Group at the [[Laboratorio Nacional de Fusión]] collaborates with the [http://www.bsc.es/ Barcelona Supercomputing Center] and the [http://www.ipp.mpg.de/ippcms/eng/index.html Max Planck IPP at Greifswald] for the development and exploitation of the [[EUTERPE]] global gyrokinetic code.
+The code [[EUTERPE]] has recently been benchmarked against the TORB code <ref>R. Hatzky, T.M. Tran, A. Konies, R. Kleiber, S.J. Allfrey, ''Energy conservation in a nonlinear gyrokinetic particle-in-cell code for ion-temperature-gradient-driven modes in theta-pinch geometry'', [[doi:10.1063/1.1449889|Phys. Plasmas, '''9'''-3, 912 (2002)]]</ref><ref>C. Nührenberg, R. Hatzky, S. Sorge, et al., ''Global ITG Turbulence in Screw-Pinch Geometry'', [ftp://ftp.iaea.org/pub/Physics%20Section/Stellarator/presentations/c_nuehrenberg_tm5.pdf IAEA TM on Innovative Concepts and Theory of Stellarators, Madrid (2005)]</ref> in both linear and non-linear simulations.<ref>Edilberto Sánchez, Ralf Kleiber, Roman Hatzky, Alejandro Soba, Xavier Sáez, Francisco Castejón and Jose M. Cela, ''Linear and non-linear simulations using the EUTERPE gyrokinetic code'', [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5491114 IEEE Transactions on Plasma Science 38-1, 2119 (2010)]</ref>
 ==References==
 <references />