  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.
