Temperature dependence of pinches in tokamaks (original) (raw)

Self-consistent electron transport in tokamaks

Physics of Plasmas, 2007

Electron particle, momentum, and energy fluxes in axisymmetric toroidal devices are derived from a version of the action-angle collision operator that includes both diffusion and drag in action-space ͓D. A. Hitchcock, R. D. Hazeltine, and S. M. Mahajan, Phys. Fluids 26, 2603 ͑1983͒; H. E. Mynick, J. Plasma Phys. 39, 303 ͑1988͔͒. A general result of the theory is that any contribution to transport originating directly from the toroidal frequency of the particle motion is constrained to be zero when the electron temperature is equal to the ion temperature. In particular, this constraint applies to those components of the particle and energy fluxes that are proportional to the magnetic shear, independent of the underlying turbulence and of whether the particles are trapped or untrapped. All the total fluxes describing collisionless transport of passing electrons in steady-state magnetic turbulence contain contributions proportional to the conventional thermodynamic drives, which are always outward, and contributions proportional to the magnetic shear, which have both magnitude and sign dependent on the ion-electron temperature ratio. The turbulent generalization of Ohm's law includes a hyper-resistive term, which flattens the current density profile on a fast time scale, and a turbulent electric field, which can have both signs depending on the electron-ion temperature ratio.

Heat Pinches in Electron-Heated Tokamak Plasmas: Theoretical Turbulence Models versus Experiments

Physical Review Letters, 2005

Two fluid turbulence models, the drift wave based quasilinear 1.5D Weiland model and the electromagnetic global 3D nonlinear model CUTIE, have been used to account for heat pinch evidence in off-axis modulated electron cyclotron heating experiments in the Rijnhuizen Tokamak Project. Both models reproduce the main features indicating inward heat convection in mildly off-axis cases. In far-off-axis cases with hollow electron temperature profiles, the existence of outward convection was reproduced only by CUTIE. Turbulence mechanisms driving heat convection in the two models are discussed.

Invariant Measure and Turbulent Pinch in Tokamaks

Physical Review Letters, 1995

It is shown that electron transport due to a generic low-frequency electrostatic turbulence in tokamak geometry results in the relaxation to a peaked, self-sustained plasma density profile no(r), rather than to a diffusion-induced Oat distribution. The relaxed density profile depends on the magnetic geometry and the distribution of turbulence. The associated inward pinch velocity V, = DV lnno results from the competition of the turbulent diffusion of trapped electrons over the poloidal magnetic flux coordinate P and the collisional relaxation toward a Maxwellian distribution function.

Turbulent Particle Transport in Magnetized Plasmas

Physical Review Letters, 2003

Particle transport in magnetized plasmas is investigated with a fluid model of drift wave turbulence. An analytical calculation shows that magnetic field curvature and thermodiffusion drive an anomalous pinch. The curvature driven pinch velocity is consistent with the prediction of turbulence equipartition theory. The thermodiffusion flux is found to be directed inward for a small ratio of electron to ion pressure gradient, and reverses its sign when increasing this ratio. Numerical simulations confirm that a turbulent particle pinch exists. It is mainly driven by curvature for equal ion and electron heat sources. The sign and relative weights of the curvature and thermodiffusion pinches are consistent with the analytical calculation.

The impact of energetic particles and rotation on tokamak plasmas

Journal of Physics: Conference Series, 2010

We discuss two contributions that elucidate the impact of energetic particles and rotation on tokamak plasmas: FLOW-M (M. J. Hole and G. Dennis, Plasma Phys. Control. Fusion 51, 035014, 2009), a generalisation of the ideal MHD flow code FLOW to multiple quasi-neutral fluids, and recent work on steady poloidal and toroidal bulk flows in tokamak plasmas [K. G. McClements and M.J. Hole, Phys. Plasmas 17, 082509 ]. Hole and Dennis have generalized ideal MHD to consider multiple quasi-neutral fluids, each in thermal equilibrium and each thermally insulated from each other such that no population mixing occurs. Kinetically, such a model may be able to approximate the ion or electron distribution function in regions of velocity phase space with a large number of particles, at the expense of more weakly populated phase space, which may have uncharacteristically high temperature and hence pressure. As magnetic equilibrium effects increase with the increase in pressure, this work constitutes an upper limit to the effect of energetic particles. McClements and Hole have examined the effects of poloidal and toroidal flows on tokamak plasma equilibria in the MHD limit. Transonic poloidal flows, of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B θ /B, can cause the (normally elliptic) Grad-Shafranov (G-S) equation to become hyperbolic in part of the solution domain. The discontinuity in variables produced by this transition indicates a breakdown in the validity of the MHD model in tokamak plasmas. It is pointed out that the range of poloidal flows for which the G-S equation is hyperbolic increases with plasma beta and B θ /B, thereby complicating the problem of determining spherical tokamak plasma equilibria with transonic poloidal flows. When the assumption of isentropic flux surfaces is replaced with the more tokamak-relevant one of isothermal flux surfaces, a simple expression can be obtained for the variation of density on a flux surface when poloidal and toroidal flows are simultaneously present. Combined with Thomson scattering measurements of density and temperature, this expression could be used to infer information on poloidal and toroidal flows on the high field side of a tokamak plasma, where direct measurements of flows are not generally possible.

Transport and Turbulence with Innovative Plasma Shapes in the TCV Tokamak

2010

We present recent results on turbulence measurements in TCV L-mode plasmas. It has been shown that the heat transport is reduced by a factor of two for a plasma at negative triangularity compared with a plasma at positive triangularity. This transport reduction is reflected in the reduction of the temperature fluctuation level, in the low frequency part of the spectrum (20-150 kHz), measured by correlation ECE in the outer equatorial plane. Moreover, the radial correlation length of the turbulence is typically reduced by a factor of two at negative triangularity compared with positive triangularity. Nonlinear gyrokinetic simulations predict that the TEM turbulence might be dominant for these TCV plasmas. The TEM induced transport is shown to decrease with decreasing triangularity and increasing collisionality. Both dependences are in fairly good agreement with experimental observations. We also report on an innovative divertor magnetic configuration: the snowflake (SF) divertor whose properties are expected to affect the local heat load to the divertor plates in particular during ELMs when compared with the classical single-null (SN) divertor. In L-mode plasmas, the intermittent particle and heat transport in the SOL is associated with the presence of "blobs" propagating in the radial direction. Intermittency is compared between SN and SF configurations by looking at the statistical properties of the ion saturation current J sat measured with Langmuir probes (LPs) in the LFS scrape-off layer. For ELMy H-mode SF plasmas, the time evolution of J sat during ELMs is estimated with LPs covering the strikepoints target zones.

Electron thermal transport in tokamak: ETG or TEM turbulences?

This paper reports progress on numerical and theoretical studies of electron transport in tokamak including: (1) electron temperature gradient turbulence; (2) trapped electron mode turbulence; and (3) a new finite element solver for global electromagnetic simulation. In particular, global gyrokinetic particle simulation and nonlinear gyrokinetic theory find that electron temperature gradient (ETG) instability saturates via nonlinear toroidal couplings, which transfer energy successively from unstable modes to damped modes preferably with longer poloidal wavelengths. The electrostatic ETG turbulence is dominated by nonlinearly generated radial streamers. The length of streamers scales with the device size and is much longer than the distance between mode rational surfaces or electron radial excursions. Both fluctuation intensity and transport level are independent of the streamer size. These simulations with realistic plasma parameters find that the electron heat conductivity is much smaller than the experimental value and in contrast with recent findings of flux-tube simulations that ETG turbulence is responsible for the anomalous electron thermal transport in fusion plasmas. The nonlinear toroidal couplings represent a new paradigm for the spectral cascade in plasma turbulence.

Toroidal flow and radial particle flux in tokamak plasmas

Physics of Plasmas, 2009

Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by non-axisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas and non-resonant components induce "global" toroidal flow damping torque throughout the plasma. Also, poloidal magnetic field transients on the magnetic field diffusion time scale can influence plasma transport. Many of these processes can also produce momentum pinch and intrinsic flow effects. This paper presents a comprehensive and self-consistent description of all these effects within a fluid moment context. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfvén waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along a field line, incompressible flows within a flux surface); and ion collisions (damping of poloidal flow). Finally, plasma transport across magnetic flux surfaces is induced by the many second order (in the small gyroradius expansion) toroidal torque effects indicated above. Non-ambipolar components of the induced particle transport fluxes produce radial plasma currents. Setting the flux-surface-average of the net radial current induced by all these effects to zero yields the transport-timescale equation for evolution of the plasma toroidal flow. It includes a combination of global toroidal flow damping and resonant torques induced by nonaxisymmetric magnetic field components, poloidal magnetic field transients and momentum source effects, as well as the usual collision-and microturbulence-induced transport. On the transport time scale the plasma toroidal rotation determines the radial electric field for net ambipolar particle transport. The ultimate radial particle transport is composed of intrinsically ambipolar fluxes plus non-ambipolar fluxes evaluated at this toroidal-rotation-determined radial electric field.

Turbulent momentum pinch of diamagnetic flows in a tokamak

2013

Abstract: The ion toroidal rotation in a tokamak consists of an $ E\ times B $ flow due to the radial electric field and a diamagnetic flow due to the radial pressure gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis force studied in previous work is only applicable to the $ E\ times B $ flow. In this Letter, the momentum pinch for the rotation generated by the radial pressure gradient is calculated and is compared with the Coriolis pinch.

On the `magnetic' nature of electron transport barriers in tokamaks

Plasma Physics and Controlled Fusion, 2002

The formation of internal transport barriers in the vicinity of rational magnetic surfaces in tokamaks with braided magnetic fields is studied for a simplified model of the perturbed magnetic field with a broad spatial spectrum and a monotonous shear profile. The island overlap criterion is used to derive a condition for barrier formation. This condition links the amplitude and the spectral width of the perturbation with the shear parameter. Numerical experiments with the MHD Monte-Carlo code E3D, where the problem of plasma heat conductivity is solved in 3D, confirm this formation of transport barriers in the case of a monotonous shear profile. Assuming that experimentally observed electron internal transport barriers are the result of local reduction of electron heat transport due to the magnetic field braiding, the amplitude and spectral width of magnetic perturbations are estimated for the tokamak RTP.