Arnold H. Kritz

Physics basis of Multi-Mode anomalous transport module

The derivation of Multi-Mode anomalous transport module version 8.1 (MMM8.1) is presented. The MMM8.1 module is advanced, relative to MMM7.1, by the inclusion of peeling modes, dependence of turbulence correlation length on flow shear, electromagnetic effects in the toroidal momentum diffusivity, and the option to compute poloidal momentum diffusivity. The MMM8.1 model includes a model for ion temperature gradient, trapped electron, kinetic ballooning, peeling, collisionless and collision dominated magnetohydrodynamics modes as well as model for electron temperature gradient modes, and a model for drift resistive inertial ballooning modes. In the derivation of the MMM8.1 module, effects of collisions, fast ion and impurity dilution, non-circular flux surfaces, finite beta, and Shafranov shift are included. The MMM8.1 is used to compute thermal, particle, toroidal, and poloidal angular momentum transports. The fluid approach which underlies the derivation of MMM8.1 is expected to reliably predict, on an energy transport time scale, the evolution of temperature, density, and momentum profiles in plasma discharges for a wide range of plasma conditions.

Microtearing modes in tokamak discharges

Microtearing modes (MTMs) have been identified as a source of significant electron thermalntransport in tokamak discharges. In order to describe the evolution of these discharges, it isnnecessary to improve the prediction of electron thermal transport. This can be accomplished bynutilizing a model for transport driven by MTMs in whole device predictive modeling codes. Thenobjective of this paper is to develop the dispersion relation that governs the MTM driven transport.nA unified fluid/kinetic approach is used in the development of a nonlinear dispersion relation fornMTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, arbitrarynelectron-ion collisionality, electron temperature and density gradients, magnetic curvature, and theneffects associated with the parallel propagation vector. An iterative nonlinear approach is used toncalculate the distribution function employed in obtaining the nonlinear parallel current and the nonlinearndispersion relation. The third order nonlinear effects in magnetic fluctuations are included,nand the influence of third order effects on a multi-wave system is considered. An envelope equationnfor the nonlinear microtearing modes in the collision dominant limit is introduced in order to obtainnthe saturation level. In the limit that the mode amplitude does not vary along the field line, slab geometry,nand strong collisionality, the fluid dispersion relation for nonlinear microtearing modes isnfound to agree with the kinetic dispersion relation. Published by AIP Publishing.n[http://dx.doi.org/10.1063/1.4953609]nI. INTRODUCTIONnMicro-instabilities can result in turbulence that influencesnenergy confinement in tokamak discharges. One suchnmicro-instability is the microtearing mode (MTM), antearing-parity mode centered on high-order rational surfaces.nMicrotearing instability can provide a significant contributionnto the electron thermal transport in low-aspect rationtokamaks.1–5 The MTMs lead to a tearing and subsequentnreconnection of the magnetic field. MTMs are shortwavelengthnion scale (low kh) electromagnetic instabilitiesnthat are driven by electron temperature gradients.6–8 It wasnproposed that when the magnetic field has a component innthe same direction as the electron temperature gradient, ancurrent is driven in the direction of the magnetic field line,nwhich can destabilize MTMs. These modes propagate in thenelectron diamagnetic drift direction and depend on the electronnion collisionality.9,10 Consequently, transport driven bynMTM instabilities depends on both the electron ion collisionnfrequency and the electron temperature gradient. Thenresearch carried out in this paper indicates that when thenelectrostatic effects are included, MTMs also depend on thendensity gradient.

Effect of pedestal height and internal transport barriers on International Thermonuclear Experimental Reactor target steady state simulations

The Tokamak simulation code (TSC) is used to provide initial conditions for predictive TRANSPort and integrated modeling code (PTRANSP) simulations of ITER target steady state scenarios. The PTRANSP simulations are carried out using the new multi-mode (MMM7.1) and the gyro-Landau-fluid (GLF23) transport models. It is found that there are circumstances under which the total fusion power decreases with increasing pedestal temperature height. When the total current (from magnetic axis to plasma edge) is fixed, an increased fraction of the current is concentrated in the pedestal region as the pedestal height is increased. As a consequence of the fixed total current, this results a smaller fraction of the current in the core plasma and, consequently, lower energy confinement. In previous simulations of ITER, in which the fusion power increased with increasing pedestal temperature height, the plasma current from the top of the pedestal to the magnetic axis was held fixed independent of the pedestal temperature....

Validation of transport models using additive flux minimization technique

A new additive flux minimization technique is proposed for carrying out the verification and validation (V&V) of anomalous transport models. In this approach, the plasma profiles are computed in time dependent predictive simulations in which an additional effective diffusivity is varied. The goal is to obtain an optimal match between the computed and experimental profile. This new technique has several advantages over traditional V&V methods for transport models in tokamaks and takes advantage of uncertainty quantification methods developed by the applied math community. As a demonstration of its efficiency, the technique is applied to the hypothesis that the paleoclassical density transport dominates in the plasma edge region in DIII-D tokamak discharges. A simplified version of the paleoclassical model that utilizes the Spitzer resistivity for the parallel neoclassical resistivity and neglects the trapped particle effects is tested in this paper. It is shown that a contribution to density transport, in ...

Effect of resonance broadening on the evolution of the edge of a turbulent spectrum

The extent to which nonlinear wave‐particle resonance broadening results in a narrowing of an incident lower‐hybrid wave spectrum is investigated. This narrowing is of concern because it could make control of lower‐hybrid heating difficult. It is shown numerically, however, that relatively uniform spatial power deposition occurs if resonance broadening effects are treated consistently on both the wave spectrum and the particle distribution.

Final Technical Report for Center for Plasma Edge Simulation Research

The CPES research carried out by the Lehigh fusion group has sought to satisfy the evolving requirements of the CPES project. Overall, the Lehigh group has focused on verification and validation of the codes developed and/or integrated in the CPES project. Consequently, contacts and interaction with experimentalists have been maintained during the course of the project. Prof. Arnold Kritz, the leader of the Lehigh Fusion Group, has participated in the executive management of the CPES project. The code development and simulation studies carried out by the Lehigh fusion group are described in more detail in the sections below.

Investigation of ELM [edge localized mode] Dynamics with the Resonant Magnetic Perturbation Effects

Topics covered are: anomalous transport and E x B flow shear effects in the H-mode pedestal; RMP (resonant magnetic perturbation) effects in NSTX discharges; development of a scaling of H-mode pedestal in tokamak plasmas with type I ELMs (edge localized modes); and divertor heat load studies.

Power deposition and current drive by intense microwave beams in tokamaks

Electron trapping by intense wave electric fields can alter the power deposition of electron‐cyclotron waves in a tokamak when high‐power sources are employed. The effect of wave trapping is examined in a ray‐tracing study that utilizes plasma and wave parameters appropriate for the Microwave Tokamak Experiment (MTX) [National Technical Information Service Document No. DE‐88016919 (1986)]. It is found that while wave trapping does result in some degradation in the rate of power deposition, single‐pass power deposition is expected to remain significant in MTX. In examining current drive for MTX, the influence of electron trapping in the magnetic wells of the tokamak equilibrium field is included. Relativistic and magnetic trapping effects reduce the driven current by 25% to 50%. This initial study does not include the effects of gradients in the magnetic field and wave vector and therefore provides lower bounds for the power deposition and driven current.