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Gyrokinetic simulations: Difference between revisions
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<ref>[http://rmp.aps.org/abstract/RMP/v79/i2/p421_1 A.J. Brizard and T.S. Hahm, ''Foundations of nonlinear gyrokinetic theory'', Rev. Mod. Phys. '''2''', 421 (2007)]</ref> | <ref>[http://rmp.aps.org/abstract/RMP/v79/i2/p421_1 A.J. Brizard and T.S. Hahm, ''Foundations of nonlinear gyrokinetic theory'', Rev. Mod. Phys. '''2''', 421 (2007)]</ref> | ||
<ref>[http://iopscience.iop.org/0741-3335/53/4/045001 Felix I. Parra and Iván Calvo, ''Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry'', 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. | <ref>[http://iopscience.iop.org/0741-3335/53/4/045001 Felix I. Parra and Iván Calvo, ''Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry'', 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. | ||
Kinetic theory describes the evolution of the distribution function <math>f(\vec r, \vec v)</math> on the basis of the Vlasov equation: | |||
:<math> | |||
\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 | |||
</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 less 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 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. | ||