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Collisional and Electromagnetic Physics in Gyrokinetic Models

  • Author(s): Crandall, Paul
  • Advisor(s): Carter, Troy;
  • Jenko, Frank
  • et al.

One of the most challenging problems facing plasma physicists today involves the

modeling of plasma turbulence and transport in magnetic confinement experiments.

The most successful model to this end so far is the reduced gyrokinetic model. Such a

model cannot be solved analytically, but can be used to simulate the plasma behavior

and transport with the help of present-day supercomputers. This has lead to the development

of many different codes which simulate the plasma using the gyrokinetic model

in various ways. These models have achieved a large amount of success in describing

the core of the plasma for conventional tokamak devices. However, numerous difficulties

have been encountered when applying these models to more extreme parameter

regimes, such as the edge and scrape-off layer of the tokamak, and high plasma devices,

such as spherical tokamaks. The development and application of the gyrokinetic

model (specifically with the gyrokinetic code, GENE) to these more extreme parameter

ranges shall be the focus of this thesis.

One of the main accomplishments during this thesis project is the development of

a more advanced collision operator suitable for studying the low temperature plasma

edge. The previous collision operator implemented in the code was found to artificially

create free energy at high collisionality, leading to numerical instabilities when one

attempted to model the plasma edge. This made such an analysis infeasible. The

newly implemented collision operator conserves particles, momentum, and energy to

machine precision, and is guaranteed to dissipate free energy, even in a nonisothermal

scenario. Additional finite Larmor radius correction terms have also been implemented

in the local code, and the global code version of the collision operator has been adapted

for use with an advanced block-structured grid scheme, allowing for more affordable

collisional simulations.

The GENE code, along with the newly implemented collision operator developed

in this thesis, has been applied to study plasma turbulence and transport in the edge

(tor = 0:9) of an L-mode magnetic confinement discharge of ASDEX Upgrade. It

has been found that the primary microinstabilities at that radial position are electron

drift waves destabilized by collisions and electromagnetic effects. At low toroidal mode

numbers, ion temperature gradient driven modes and microtearing modes also seem to

exist. In nonlinear simulations with the nominal experimental parameters, the simulated

electron heat flux was four times higher than the experimental reconstruction,

and the simulated ion heat flux was twice as high. However, both the ion and electron

simulated heat flux could be brought into agreement with experimental values by lowering

the input logarithmic electron temperature gradient by 40%. It was also found

that the cross-phases between the electrostatic potential and the moments agreed well

for the part of the binormal spectrum where the dominant transport occurred, and was

fairly poor at larger scales where minimal transport occurred.

Finally, a new scheme for evaluating the electromagnetic fields has been developed

to address the instabilities occurring in nonlinear local and global gyrokinetic simulations

at high plasma . This new scheme is based on evaluating the electromagnetic

induction explicitly, and constructing the gyrokinetic equation based on the original distribution,

rather than the modified distribution which implicitly takes into account the

induction. This new scheme removes the artificial instability occurring in global simulations,

enabling the study of high scenarios with GENE. The new electromagnetic

scheme can also be generalized to a full-f implementation, however, it would require

updating the field matrix every time-step to avoid the cancellation problem. The new

scheme (including the parallel nonlinearity) does not remove the local instability, suggesting

that that instability (caused by magnetic field perturbations shorting out zonal

flows) is part of the physics of the local model.

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