### Theory Weekly Highlights for July 2013

##### July 26, 2013

As part of a collaboration with D. Brennan (PPPL) and J.M. Finn (LANL), a new effort was initiated to explore the stable discrete MHD spectrum using GATO. The immediate aim is to find how unstable ideal kink modes transition through marginal stability as they are stabilized and move through the continuum. The longer term goal is to evaluate the possibility of destabilization of the ideally stable modes from fast particles. For this, the option in GATO of removing the continuum by modifying the kinetic energy normalization was systematically tested. This option removes complications from numerical coupling of the stable kink modes with the continua. In the first set of calculations a complete stable Sturmian series of m/n = 1/1 modes was found with increasing number of radial nodes (see also Highlight from July 13 2007 at Theory Weekly Highlights for July 2007.) A sequence of 50 such modes was found, including one on the unstable side. The relationship of these modes to the magnetosonic branch is being explored. Future work will follow the modes as they are destabilized by increasing beta and will also analyze the effect of fast ions on the ideally stable kink modes. This code capability also has utility in determining the plasma response from non-axisymmetric field perturbations in the same manner as employed in the IPEC code.

##### July 19, 2013

Significant progress was made in the development and validation of the reduced cyclokinetics code rCYCLO. rCYCLO was developed to test for the breakdown of 5D gyrokinetics (GK) at high turbulence levels against 6D cyclokinetics (CK) which dynamically follows the gyrophase. The motivation is to account for the apparent shortfall in GYRO gyrokinetic transport in near edge L-mode plasmas. The rCYCLO code currently has an adiabatic electron model. The ion model focuses on the non-linear ExB motion, which can break the gyro-averaging approximation. Since the less important parallel field perturbations and motion are ignored, rCYCLO actually tests 4D-CK against 3D-GK for ITG turbulence. The added dimension refers to an expansion in Fourier harmonics of the gyro-phase. Preliminary results at low turbulence level suggest (contrary to our hopes) that cyclokinetic transport tends to be less (not more) than gyrokinetic transport. We are hopeful that adding a strongly collisional electron model more appropriate to the L-mode edge will reverse this trend. However, final validation of rCYCLO must prove that CK always recovers GK at sufficiently high relative ion cyclotron frequency (inverse ρ*). This becomes more difficult at higher turbulence levels.

##### July 12, 2013

The viscosity coefficient of the electron perpendicular stress tensor in Braginskii’s theory was corrected by the addition of a term of the same order of magnitude. The additional term arises through a more careful treatment of the mass-ratio expansion of the Coulomb collision operator. The work is reported in a paper that has been accepted for publication in Physics of Plasmas.

##### July 05, 2013

Calculations have confirmed a novel explanation for why a massive neutral gas jet penetrates to the q = 2 surface despite being retarded below the ballistic penetration rate. The model proposes that this result is due to the friction force generated when the gas atoms deposited in the vacuum region interpenetrate, via diffusion, the essentially “stationary” plasma ions pinned to the magnetic field. The mutual ion-neutral diffusion coefficient D was calculated using the Chapman-Enskog solution of the Boltzmann collision operator. A neutral atom and a deuteron ion attract each other with the inverse-fifth polarization force, and the resulting momentum exchange elastic collision cross section leads to a mutual diffusion coefficient, D. Surprisingly large values of D for helium, neon and argon gases were calculated with typical values of D = 61, 38, and 18 m2/s, respectively, leading to inward propagation speeds of 100 m/s, in good agreement with AXUV measurements of the neutral–plasma ionization front moving towards the q = 2 surface in Tore Supra and DIII-D. Helium yields 3 times more free electrons to the plasma than argon, consistent with its larger D and faster penetration speed. The mobility coefficient for deuterons in neon gas can be determined from D and was within 1% of published experimental values.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification

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