# 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}ρ_{i} >~ 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 ρ_{i} is the ion gyroradius. At k_{y}ρ_{i} >~ 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}ρ_{i} ∼ (ρ_{i} /ρ_{e})L_{T e}/R_{0}∼ 1 and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, K_{x} ρ_{e} ∼ 1, where K_{x} is the effective radial wavenumber. Here, ρ_{e} is the electron gyroradius, R_{0} is the major radius of the last closed flux surface, and 1/L_{T e} is the logarithmic electron temperature gradient. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. 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 demonstrate that the novel toroidal ETG instability could be important for transport.