Skip to main content
    • Aa
    • Aa

Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas

  • J. R. Myra (a1), D. A. D’Ippolito (a1), D. A. Russell (a1), M. V. Umansky (a2) and D. A. Baver (a1)...

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\boldsymbol{E}\times \boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas
      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas
      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas
      Available formats
Corresponding author
Email address for correspondence:
Hide All
BaverD. A., MyraJ. R. & UmanskyM. V. 2011 Linear eigenvalue code for edge plasma in full tokamak X-point geometry. Comput. Phys. Commun. 182, 16101620.
BurrellK. H. 1997 Effects of inline-graphic $\boldsymbol{E}\times \boldsymbol{B}$ velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices. Phys. Plasmas 4, 14991518.
CattoP. J., RosenbluthM. N. & LiuC. S. 1973 Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field. Phys. Fluids 16, 17191729.
ConnorJ. W. & TaylorJ. B. 1984 Resistive fluid turbulence and energy confinement. Phys. Fluids 27, 26762681.
D’AngeloN. 1965 Kelvin–Helmholtz instability in a fully ionized plasma in a magnetic field. Phys. Fluids 8, 17481750.
D’IppolitoD. A., MyraJ. R. & ZwebenS. J. 2011 Convective transport by intermittent blob-filaments: comparison of theory and experiment. Phys. Plasmas 18, 060501,1–48.
FisherD. M., RogersB. N., RossiG. D. & GuiceD. S. 2015 Three-dimensional two-fluid Braginskii simulations of the large plasma device. Phys. Plasmas 22, 092121,1–11.
GarbetX., FenziC., CapesH., DevynckP. & AntarG. 1999 Kelvin–Helmholtz instabilities in tokamak edge plasmas. Phys. Plasmas 6, 39553965.
GotoR., MiuraH., ItoA., SatoM. & HatoriT. 2015 Formation of large-scale structures with sharp density gradient through Rayleigh–Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects. Phys. Plasmas 22, 032115,1–10.
GuzdarP. N., DrakeJ. F., McCarthyD., HassamA. B. & LiuC. S. 1993 Three-dimensional fluid simulations of the nonlinear drift-resistive ballooning modes in tokamak edge plasmas. Phys. Fluids B 5, 37123727; and references therein.
HortonW., TajimaT. & KamimuraT. 1987 Kelvin–Helmholtz instability and vortices in magnetized plasma. Phys. Fluids 30, 34853495.
ItohK., ItohS.-I., DiamondP. H., HahmT. S., FujisawaA., TynanG. R., YagiM. & NagashimaY. 2006 Physics of zonal flows. Phys. Plasmas 13, 055502,1–11.
KrasheninnikovS. I., D’IppolitoD. A. & MyraJ. R. 2008 Recent theoretical progress in understanding coherent structures in edge and SOL turbulence. J. Plasma Phys. 74, 679717.
KrasheninnikovS. I., RyutovD. D. & YuG. 2004 Large plasma pressure perturbations and radial convective transport in a tokamak. J. Plasma Fusion Res. 6, 139143.
LeeX. S., CattoP. J. & AamodtR. E. 1982 Instabilities driven by the parallel variation of the electrostatic potential in tandem mirrors. Phys. Fluids 25, 14911492.
MiuraA. & PritchettP. L. 1982 Nonlocal stability analysis of the MHD Kelvin–Helmholtz instability in a compressible plasma. J. Geophys. Res. 87, 74317444.
MyraJ. R. & D’IppolitoD. A. 2005 Edge instability regimes with applications to blob transport and the quasicoherent mode. Phys. Plasmas 12, 092511,1–10.
MyraJ. R., D’IppolitoD. A. & RussellD. A. 2015 Turbulent transport regimes and the scrape-off layer heat flux width. Phys. Plasmas 22, 042516,1–11.
MyraJ. R., D’IppolitoD. A., XuX. Q. & CohenR. H. 2000 Resistive X-point modes in tokamak boundary plasmas. Phys. Plasmas 7, 22902293.
OnoM., KayeS. M., PengY.-K. M., BarnesG., BlanchardW., CarterM. D., ChrzanowskiJ., DudekL., EwigR., GatesD. et al. 2000 Exploration of spherical torus physics in the NSTX device. Nucl. Fusion 40, 557562.
PerkinsF. W. & JassbyD. L. 1971 Velocity shear and low-frequency plasma instabilities. Phys. Fluids 14, 102115.
PopovichP., UmanskyM. V., CarterT. A. & FriedmanB. 2010 Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device. Phys. Plasmas 17, 102107,1–11.
PritchettP. L. 1987 Electrostatic Kelvin–Helmholtz instability produced by a localized electric field perpendicular to an external magnetic field. Phys. Fluids 30, 272275.
RicciP. & RogersB. N. 2013 Plasma turbulence in the scrape-off layer of tokamak devices. Phys. Plasmas 20, 010702,1–4.
RogersB. N. & DorlandW. 2005 Noncurvature-driven modes in a transport barrier. Phys. Plasmas 12, 062511,1–12.
RussellD. A., D’IppolitoD. A., MyraJ. R., CanikJ. M., GrayT. K. & ZwebenS. J. 2015 Modeling the effect of lithium-induced pedestal profiles on scrape-off-layer turbulence and the heat flux width. Phys. Plasmas 22, 092311,1–11.
SimakovA. N. & CattoP. J. 2003 Drift-ordered fluid equations for field-aligned modes in low- inline-graphic ${\it\beta}$ collisional plasma with equilibrium pressure pedestals. Phys. Plasmas 10, 47444757; and erratum in 2004 Phys. Plasmas 11, 2326–2326.
SugiyamaL. E. & StraussH. R. 2010 Magnetic X-points, edge localized modes, and stochasticity. Phys. Plasmas 17, 062505,1–16.
TerryP. W. 2000 Suppression of turbulence and transport by sheared flow. Rev. Mod. Phys. 72, 109165.
TsidulkoYu. A., BerkH. L. & CohenR. H. 1994 Instability due to axial shear and surface impedance. Phys. Plasmas 1, 11991213.
UmanskyM. V., XuX. Q., DudsonB., LoDestroL. L. & MyraJ. R. 2009 Status and verification of edge plasma turbulence code BOUT. Comput. Phys. Commun. 180, 887903.
VranješJ. & TanakaM. Y. 2002 On the magnetohydrodynamic Kelvin–Helmholtz instability driven by a nonuniform ion drift. Phys. Plasmas 9, 43794382.
WangL. F., XueC., YeW. H. & LiY. J. 2009 Destabilizing effect of density gradient on the Kelvin–Helmholtz instability. Phys. Plasmas 16, 112104,1–6.
WangW. X., EthierS., RenY., KayeS., ChenJ., StartsevE., LuZ. & LiZ. Q. 2015 Identification of new turbulence contributions to plasma transport and confinement in spherical tokamak regime. Phys. Plasmas 22, 102509,1–16.
XiP. W., XuX. Q., WangX. G. & XiaT. Y. 2012 Influence of equilibrium shear flow on peeling-ballooning instability and edge localized mode crash. Phys. Plasmas 19, 092503,1–9.
XuX. Q., DudsonB. D., SnyderP. B., UmanskyM. V., WilsonH. R. & CasperT. 2011 Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT inline-graphic $++$ code. Nucl. Fusion 51, 103040,1–10.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 7
Total number of PDF views: 62 *
Loading metrics...

Abstract views

Total abstract views: 146 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.