Gyrokinetic secondary instability theory for electron and ion temperature gradient driven turbulence

Plunk, Gabriel
November 2007
Physics of Plasmas;Nov2007, Vol. 14 Issue 11, p112308
Academic Journal
The instabilities that drive turbulence and transport in tokamaks themselves become unstable at finite amplitude to secondary instabilities. These “secondaries” are a key part of the nonlinear physics. This work presents a fully gyrokinetic secondary instability theory for electron temperature gradient (ETG) and ion temperature gradient (ITG) driven turbulence. The electrostatic gyrokinetic equation is solved in the local approximation to find “fast” secondary modes that satisfy γs>γp and can therefore lead to mode saturation. Finite Larmor radius and other kinetic effects are treated exactly capturing kρ>1 as well as kρ<1 quasisingular behavior. This theory is therefore well suited to describe the intermediate regime of ITG/ETG coupling. The secondary instability of toroidal (k|=0) and slab (LT/R=0) primary modes is computed along with spectral characteristics and parametric dependence. The results of this paper include a robust secondary growth rate at high kρ and, in the case of ETG, a strong sensitivity to the kinetic form of the primary mode. The convergence properties of the computation of the secondary instability of ETG toroidal modes underscores the need for proper k-space resolution in simulations. The parametric dependence of the secondary mode growth rate reveals a mechanism for the transport suppression near marginal stability that is associated with the Dimits shift. A strengthening of secondary instability at small LT/R suggests that secondary instabilities may play a role in the formation of electron internal transport barriers.


Related Articles

  • A family of analytic equilibrium solutions for the Grad–Shafranov equation. Guazzotto, L.; Freidberg, J. P. // Physics of Plasmas;Nov2007, Vol. 14 Issue 11, p112508 

    A family of exact solutions to the Grad–Shafranov equation, similar to those described by Atanasiu et al. [C. V. Atanasiu, S. Günter, K. Lackner, and I. G. Miron, Phys. Plasmas 11, 3510 (2004)], is presented. The solution allows for finite plasma aspect ratio, elongation and...

  • Stability analysis of internal ideal modes in low-shear tokamaks. Wahlberg, C.; Graves, J. P. // Physics of Plasmas;Nov2007, Vol. 14 Issue 11, p110703 

    The stability of internal, ideal modes in tokamaks with low magnetic shear in the plasma core is analyzed. For equilibria with large aspect ratio, a parabolic pressure profile and a flat q profile in the core, an exact solution of the ideal magnetohydrodynamic (MHD) stability equations is found....

  • Development of drift-resistive-inertial ballooning transport model for tokamak edge plasmas. Rafiq, T.; Bateman, G.; Kritz, A. H.; Pankin, A. Y. // Physics of Plasmas;Aug2010, Vol. 17 Issue 8, p082511 

    A new model is developed for transport driven by drift-resistive-inertial ballooning modes (DRIBMs) in axisymmetric tokamak plasmas. The model is derived using two-fluid reduced Braginskii equations in a generalized s⁁-α geometry. The unified theory includes diamagnetic effects, parallel...

  • Role of trapped electron mode turbulence in internal transport barrier control in the Alcator C-Mod Tokamak. Ernst, D. R.; Bonoli, P. T.; Catto, P. J.; Doriand, W.; Fiore, C. L.; Granetz, R. S.; Greenwald, M.; Hubbard, A. E.; Porkolab, M.; Redi, M. H.; Rice, J. E.; Zhurovich, K. // Physics of Plasmas;May2004, Vol. 11 Issue 5, p2637 

    Nonlinear gyrokinetic simulations of trapped electron mode (TEM) turbulence, within an internal particle transport barrier, are performed and compared with experimental data. The results provide a mechanism for transport barrier control with on-axis radio frequency heating, as demonstrated in...

  • Structure of Global Tokamak Scalings. Dnestrovskij, Yu. N. // Plasma Physics Reports;Feb2002, Vol. 28 Issue 2, p166 

    In empirical tokamak scalings, not all of the standard engineering parameters are independent. Thus, the larger the tokamak, the higher the required plasma current and input power. Also, by using higher magnetic fields, it is possible to raise the plasma density. Instead of the plasma density,...

  • High-Q plasmas in the TFTR tokamak. Jassby, D. L.; Barnes, C. W.; Bell, M. G.; Bitter, M.; Boivin, R.; Bretz, N. L.; Budny, R. V.; Bush, C. E.; Dylla, H. F.; Efthimion, P. C.; Fredrickson, E. D.; Hawryluk, R. J.; Hill, K. W.; Hosea, J.; Hsuan, H.; Janos, A. C.; Jobes, F. C.; Johnson, D. W.; Johnson, L. C. // Physics of Fluids B: Plasma Physics;Aug91, Vol. 3 Issue 8, p2308 

    In the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 26, 11 (1984) ], the highest neutron source strength S[sub n] and D-D fusion power gain Q[sub DD] are realized in the neutral-beam-fueled and heated "supershot" regime that occurs after extensive wall conditioning to...

  • Sawtooth studies with q-profile measurement on TFTR(abstract)[sup a]. Levinton, F.M.; Batha, S.H.; Yamada, M.; Zakharov, L.; Zarntorff, M.C. // Review of Scientific Instruments;Jan1995, Vol. 66 Issue 1, p372 

    Measures the q profile for plasma equilibrium and theories of MHD instabilities in a Tokamak Fusion Test Reactor (TFTR). Measurement of diagnostic and accurate profiles.

  • Performance of the Tokamak Fusion Test Reactor bolometers. Schivell, J. // Review of Scientific Instruments;May85, Vol. 56 Issue 5, p972 

    For the past year we have been making use of a horizontally viewing 19-channel array and a bolometer which views a narrow cross-sectional slice of the plasma. More recently, we have also obtained results from a second, vertically viewing array. Software has been developed to translate the data...

  • Modelling of radiative divertor operation towards detachment in experimental advanced superconducting tokamak. Chen, YiPing; Wang, F. Q.; Zha, X. J.; Hu, L. Q.; Guo, H. Y.; Wu, Z. W.; Zhang, X. D.; Wan, B. N.; Li, J. G. // Physics of Plasmas;Feb2013, Vol. 20 Issue 2, p022311 

    In order to actively control power load on the divertor target plates and study the effect of radiative divertor on plasma parameters in divertor plasmas and heat fluxes to the targets, dedicated experiments with Ar impurity seeding have been performed on experimental advanced superconducting...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics