Response of internal transport barriers to central electron heating and current drive on ASDEX Upgrade

Wolf, R. C.; Günter, S.; Leuterer, F.; Peeters, A. G.; Pereverzev, G.; Gruber, O.; Kaufmann, Michael; Lackner, K.; Maraschek, M.; McCarthy, Patrick J.; Meister, H.; Salzmann, H.; Schade, S.; Schweinzer, J.; Suttrop, W.

doi:10.1063/1.874006

Cited by 37 publications

(40 citation statements)

References 12 publications

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“…It is noted here that since in tokamaks M θ < 0.1 the flow term in (2) is perturbative around the "static" equilibrium M θ = 0. Also, the choice q min = 2 was made because according to experimental evidence for q min < 2 strong MHD activity destroys confinement possibly due to a double tearing mode [18]. A similar result was found numerically for one-dimensional cylindrical equilibria with hollow currents in Ref.…”

Section: Resultssupporting

confidence: 56%

Tokamak MHD equilibria with reversed magnetic shear and sheared flow

Poulipoulis

Throumoulopoulos

Tasso

2004

Plasma Phys. Control. Fusion

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Analytic solutions of the magnetohydrodynamic equilibrium equations for a cylindrically symmetric magnetically confined plasma with reversed magnetic shear, s < 0, and sheared flow are constructed by prescribing the safety factor-, poloidal velocity-and axial velocity-profiles consistently with experimental ones. On the basis of the solutions obtained in most of the cases considered it turns out that an increase of |s| and of the velocity components result in larger absolute values for the radial electric field, E r , its shear, |dE r /dr| ≡ |E ′ r |, and the E × B velocity shear, ω E×B = |d/dr(E × B/B2 )|, which may play a role in the formation of Internal Transport Barriers (ITBs) in tokamaks. In particular for a constant axial magnetic field, ω E×B at the point where E ′ r = 0 is proportional to 1 − s. Also, |E ′ r | and ω E×B increase as the velocity shear takes larger values. The results clearly indicate that s < 0 and sheared flow act synergetically in the formation of ITBs with the impact of the flow, in particular the poloidal one, being stronger than that of s < 0.

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Section: Resultssupporting

confidence: 56%

Tokamak MHD equilibria with reversed magnetic shear and sheared flow

Poulipoulis

Throumoulopoulos

Tasso

2004

Plasma Phys. Control. Fusion

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“…The choice q min ≥ 2 was made because according to experimental evidence for q min < 2 strong MHD activity destroys confinement possibly due to a double tearing mode [19]. A similar result was found numerically for one-dimensional cylindrical equilibria with hollow currents in [20].…”

Section: Resultssupporting

confidence: 51%

“…Neglecting in the Hall-MHD momentum equation the convective flow term (which for the case under consideration corresponds to M θ = 0), the term j × B in (19) can be expressed in terms of the total pressure gradient:…”

Section: Two-fluid Cylindrical Equilibria With Reversed Magnetic Shearmentioning

confidence: 99%

Two-fluid tokamak equilibria with reversed magnetic shear and sheared flow

Poulipoulis

Throumoulopoulos

Tasso³

2007

J. Plasma Phys.

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The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of two-fluid model. The study is based on exact self-consistent solutions in cylindrical geometry by means of which the impact of the magnetic shear, s, and the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components, v iz and v iθ , on the radial electric field, E r , its shear, |dE r /dr|, and the shear of the E × B velocity, ω E×B ≡ |d/dr(E × B/B 2 )|, is examined. For a wide parametric regime of experimental concern it turns out that the contributions of the v iz , v iθ and pressure gradient (∇P i ) terms to E r , |E ′ r | and ω E×B are of the same order of magnitude. The contribution of the ∇P i term is missing in the framework of magnetohydrodynamics (MHD) [G. Poulipoulis et al. Plasma Phys. Control. Fusion 46 (2004) 639]. The impact of s on ω E×B through the ∇P i term is stronger than that through the velocity terms; in particular for B z = constant, the contributions of the ∇P i and velocity terms to ω E×B at the point where dE r /dr = 0 are proportional to (1 − s)(2 − s) and (1 − s), respectively. The results indicate that, alike MHD, the magnetic shear and the sheared toroidal and poloidal velocities act synergetically in producing electric fields and therefore ω E×B profiles compatible with ones observed in discharges with ITBs; owing to the ∇P i term, however, the impact of s on E r , |E ′ r | and ω E×B is stronger than that in MHD.

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“…the magnetic shearŝ. The effects of the latter on plasma microturbulence has been the subject of numerous experimental [19][20][21][22][23] , theoretical 24 , as well as numerical [25][26][27][28] studies. In this context, it was also found that negative magnetic shear can help improve the plasma confinement in a tokamak by decreasing the level of turbulence.…”

Section: B Robustness While Varying the Temperature Gradientmentioning

confidence: 99%

Dynamic procedure for filtered gyrokinetic simulations

Morel¹,

Navarro²,

Albrecht-Marc³

et al. 2012

Physics of Plasmas

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Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers. I. MOTIVATION AND CONTEXTIn the area of fluid turbulence, theories are usually based on the notion of an inertial range in which the energy cascades from larger scales to (somewhat) smaller scales mediated by the quadratic nonlinearity. The role of the smallest scales is then to dissipate energy in the so-called dissipative range. In numerical simulations, this picture has led to the development of Large Eddy Simulation (LES) techniques that are based on the idea that neglecting the small scales can be compensated by introducing a dissipative model for the eddy viscosity 1 .A Direct Numerical Simulation (DNS) is supposed to retain all the scales from the injection range down to the dissipative range. This requires an enormous numerical effort in the case of high Reynolds number flows. On the contrary, a LES coarsens the simulation grid and only retains the largest scales (which are problem-dependent), while the small scales (which are assumed to be universal) are replaced by a model. In Fourier space, such a coarsening can be seen as the action of a low-pass filter. Since the scale range is truncated, the dissipation scales can not be reached, and the modeling basically consists of the introduction of artificial dissipation mechanisms. From a more mathematical viewpoint, one notes that the filtering operation does not commute with the nonlinear term that transfers energy from largest to smallest scales, and the major problem of LES consists in finding a satisfying closure for representing the influence of the unresolved scales.Recent gyrokinetic studies have shown that Ion Temperature Gradient (ITG) driven turbulence exhibits a direct and local cascade of a nonlinear invariant, namely the free energy. 2 Such a cascade is analogous to the kinetic energy cascade in three dimensional NavierStokes turbulence. The important difference is that the a) pmorel@ulb.ac.be quadratic conserved quantity in fluid dynamics is the kinetic energy, while it is the free energy in gyrokinetics. The latter quantity is the sum of both the perturbed entropy and the electrostatic energy. Transfers between entropy and electrostatic energy ar...

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Response of internal transport barriers to central electron heating and current drive on ASDEX Upgrade

Cited by 37 publications

References 12 publications

Tokamak MHD equilibria with reversed magnetic shear and sheared flow

Tokamak MHD equilibria with reversed magnetic shear and sheared flow

Two-fluid tokamak equilibria with reversed magnetic shear and sheared flow

Dynamic procedure for filtered gyrokinetic simulations

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