Free Access
Issue
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
Page(s) 929 - 947
DOI https://doi.org/10.1051/m2an/2011068
Published online 03 February 2012
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. XXIII (1992) 1482–1518. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.A. Arsenev, Existence in the large of a weak solution of Vlasov’s system of equations. Z. Vychisl. Mat. Mat. Fiz. 15 (1975) 136–147. [Google Scholar]
  3. M. Bostan, The Vlasov-Poisson system with strong external magnetic field. Finite Larmor radius regime. Asymptot. Anal. 61 (2009) 91–123. [MathSciNet] [Google Scholar]
  4. P. Degond, Global existence of smooth solutions for the Vlasov-Fokker-Planck equations in 1 and 2 space dimensions. Ann. Sci. École Norm. Sup. 19 (1986) 519–542. [Google Scholar]
  5. E. Frénod and A. Mouton, Two-dimensional finite Larmor radius approximation in canonical gyrokinetic coordinates. J. Pure Appl. Math. : Adv. Appl. 4 (2010) 135–166. [MathSciNet] [Google Scholar]
  6. E. Frénod and E. Sonnendrücker, The finite Larmor radius approximation. SIAM J. Math. Anal. 32 (2001) 1227–1247. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Frénod, A. Mouton and E. Sonnendrücker, Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations. Numer. Math. 108 (2007) 263–293. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method. Math. Models Methods Appl. Sci. 19 (2009) 175–197. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. P. Ghendrih, M. Hauray and A. Nouri, Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions. KRM 2 (2009) 707–725. [CrossRef] [Google Scholar]
  10. F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with strong magnetic field. J. Math. Pures Appl. 78 (1999) 791–817. [CrossRef] [Google Scholar]
  11. V. Grandgirard et al., Global full-f gyrokinetic simulations of plasma turbulence. Plasma Phys. Control. Fusion 49 (2007) 173–182. [CrossRef] [Google Scholar]
  12. D. Han-Kwan, The three-dimensional finite Larmor radius approximation. Asymptot. Anal. 66 (2010) 9–33. [MathSciNet] [Google Scholar]
  13. D. Han-Kwan, On the three-dimensional finite Larmor radius approximation : the case of electrons in a fixed background of ions. Submitted (2010). [Google Scholar]
  14. Z. Lin, S. Ethier, T.S. Hahm and W.M. Tang, Size scaling of turbulent transport in magnetically confined plasmas. Phys. Rev. Lett. 88 (2002) 195004-1–195004-4. [CrossRef] [PubMed] [Google Scholar]
  15. P.L. Lions and B. Perthame, Propagation of moments and regularity for the three-dimensional Vlasov-Poisson system. Invent. Math. 105 (1991) 415–430. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Mouton, Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel. KRM 2 (2009) 251–274. [CrossRef] [Google Scholar]
  17. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Ukai and T. Okabe, On classical solutions in the large in time of two-dimensional Vlasov’s equation. Osaka J. Math. 15 (1978) 245–261. [MathSciNet] [Google Scholar]
  19. J. Wesson, Tokamaks.Clarendon Press-Oxford (2004). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you