Beam model of Doppler backscattering

We use beam tracing -- implemented with a newly-written code, Scotty -- and the reciprocity theorem to derive a model for the linear backscattered power of the Doppler Backscattering (DBS) diagnostic. Our model works for both the O-mode and X-mode in tokamak geometry (and certain regimes of stellarators). We present the analytical derivation of our model and its implications on the DBS signal localisation and the wavenumber resolution. To determine these two quantities, we find that it is the curvature of the field lines and the magnetic shear that are important, rather than the curvature of the cut-off surface. We also provide an explicit formula for the hitherto poorly-understood quantitative effect of the mismatch angle. Consequently, one can use this model to correct for the attenuation due to mismatch, avoiding the need for empirical optimisation. This is especially important in spherical tokamaks, since the magnetic pitch angle is large and varies both spatially and temporally.Comment: This is the version that passed peer review. No major changes, but many improvements to writing styl

Validating and optimising mismatch tolerance of Doppler backscattering measurements with the beam model

We use the beam model of Doppler backscattering (DBS), which was previously derived from beam tracing and the reciprocity theorem, to shed light on mismatch attenuation. This attenuation of the backscattered signal occurs when the wavevector of the probe beam's electric field is not in the plane perpendicular to the magnetic field. Correcting for this effect is important for determining the amplitude of the actual density fluctuations. Previous preliminary comparisons between the model and Mega-Ampere Spherical Tokamak (MAST) plasmas were promising. In this work, we quantitatively account for this effect on DIII-D, a conventional tokamak. We compare the predicted and measured mismatch attenuation in various DIII-D, MAST, and MAST-U plasmas, showing that the beam model is applicable in a wide variety of situations. Finally, we performed a preliminary parameter sweep and found that the mismatch tolerance can be improved by optimising the probe beam's width and curvature at launch. This is potentially a design consideration for new DBS systems

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for ky rho i greater than or similar to 0.1<i in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, k(y) is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and rho(i) is the ion gyroradius. At k(y)rho(i) greater than or similar to 1<i, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as ky rho i similar to(rho i/rho e)LTe/R0 similar to 1<i and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, Kx rho e similar to 1<i, where K-x is the effective radial wavenumber. Here, rho(e) is the electron gyroradius, R-0 is the major radius of the last closed flux surface, and 1/L-Te is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by ExBExB shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for kyρi ≳ 0.1 in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, ky is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and ρi is the ion gyroradius. At kyρi ≳ 1, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as kyρi ∼ (ρi/ρe)LTe/R0 ∼ 1 and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, Kxρe ∼ 1, where Kx is the effective radial wavenumber. Here, ρe is the electron gyroradius, R0 is the major radius of the last closed flux surface, and 1/LTe is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by E × B shear. ETG modes are very resilient to E × B shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for $k_y \rho_i \gtrsim 0.1$ in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, $k_y$ is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and $\rho_i$ is the ion gyroradius. At $k_y \rho_i \gtrsim 1$, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as $k_y \rho_i \sim (\rho_i/\rho_e) L_{Te} / R_0 \sim 1$ and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, $K_x \rho_e \sim 1$, where $K_x$ is the effective radial wavenumber. Here, $\rho_e$ is the electron gyroradius, $R_0$ is the major radius of the last closed flux surface, and $1/L_{Te}$ is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by $\mathbf{ E} \times \mathbf{ B}$ shear. ETG modes are very resilient to $\mathbf{ E} \times \mathbf{ B}$ shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport

Recent progress in L-H transition studies at JET: Tritium, Helium, Hydrogen and Deuterium

We present an overview of results from a series of L-II transition experiments undertaken at JET since the installation of the ITER-like-wall (JET-ILW), with beryllium wall tiles and a tungsten divertor. Tritium, helium and deuterium plasmas have been investigated. Initial results in tritium show ohmic L-H transitions at low density and the power threshold for the L-H transition (P-LH) is lower in tritium plasmas than in deuterium ones at low densities, while we still lack contrasted data to provide a scaling at high densities. In helium plasmas there is a notable shift of the density at which the power threshold is minimum ((n) over bar (e,min)) to higher values relative to deuterium and hydrogen references. Above (n) over bar (e,min) (He) the L-H power threshold at high densities is similar for D and He plasmas. Transport modelling in slab geometry shows that in helium neoclassical transport competes with interchange-driven transport, unlike in hydrogen isotopes. Measurements of the radial electric field in deuterium plasmas show that E-r shear is not a good indicator of proximity to the L-H transition. Transport analysis of ion heat flux in deuterium plasmas show a non-linearity as density is decreased below (n) over bar (e,min). Lastly, a regression of the JET-ILW deuterium data is compared to the 2008 ITPA scaling law