### Theory Weekly Highlights for December 2019

##### December 20, 2019

A transparent analytic expression was derived for the pitch-angle deflection (diffusion) frequency ν for fast electrons elastically scattering off partially ionized impurity atoms. Injection of impurity atoms into a hot plasma results in rapid cooling leaving impurity ions in various charge states Z, which alters the scattering rate and dissipation of supra-thermal and runaway electrons. This problem was recently considered by Hesslow et al (2017), but it is still shrouded in misconceptions. In two extreme limits - fully stripped ions and neutral impurities - the expression for ν is of the same form, ν~Z^2 ln(Λ), but with different expressions for the Coulomb log function ln(Λ). An effective Coulomb log for intermediate charge states was derived by constructing an atomic form factor and using the Born approximation for the differential elastic scattering cross-section. For a given electron energy the effective Coulomb log increases smoothly with Z from Z=0 to fully stripped. This formula will be used in the bounce-averaged Fokker Planck code CQL3D to study runaway electrons following impurity injection.

##### December 13, 2019

A paper “ Reduced model of high-Z impurity redeposition and erosion in tokamak divertor and its application to DIII-D experiments” by J. Guterl et al has been published in the journal Plasma Physics and Controlled Fusion. The paper presents a reduced model of high-Z impurities erosion and re-deposition in divertor plasma conditions. It is shown that the spatial distribution of redeposited high-Z impurities is well approximated by an analytical distribution characterized by a few parameters. The ratio of net erosion rates of tungsten measured experimentally from tungsten samples of different sizes exposed to the same attached plasma conditions are well reproduced with this reduced model.

##### December 06, 2019

To explore the effect of magnetic field on the pellet ablation rate, a simple analytical formula was derived for the cross-field cloud radius r_{x} of the ablation tube extended along the magnetic field lines. It takes advantage of the fact that in a strong magnetic field the crosswise flow is subsonic and therefore the outward ablation pressure gradient force balances the Lorentz jxB pinching force. A simple scaling law for the mass continuity equation was used reminiscent of Sweet-Parker’s resistive reconnection model. It was found that r_{x} decreases inversely with B-field while increasing with the square root of (electrical resistivity times pressure). These trends are being verified using the 2-D MHD code FronTier. The cloud radius r_{x} is an important parameter since it regulates the field-aligned column density of the ablation tube, and in turn pellet shielding: a narrower ablation tube results in more shielding and reduced ablation rate. The r_{x} scaling is therefore a critical step in the formulation of a 2-D analytical model with the aim of understanding the effect of the B field on the ablation rate.

**Disclaimer**

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

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