  Cosmic ray (CR)-driven instabilities play a decisive role during particle
acceleration at shocks and CR propagation in galaxies and galaxy clusters.
These instabilities amplify magnetic fields and modulate CR transport so that
the intrinsically collisionless CR population is tightly coupled to the thermal
plasma and provides dynamical feedback. Here, we show that CRs with a finite
pitch angle drive electromagnetic waves (along the background magnetic field)
unstable on intermediate scales between the gyro-radii of CR ions and electrons
as long as CRs are drifting with a velocity less than half of the Alfv\'en
speed of electrons. By solving the linear dispersion relation, we show that
this new instability typically grows faster by more than an order of magnitude
in comparison to the commonly discussed resonant instability at the ion
gyroscale. We find the growth rate for this intermediate-scale instability and
identify the growing modes as background ion-cyclotron modes in the frame that
is comoving with the CRs. We confirm the theoretical growth rate with a
particle-in-cell (PIC) simulation and study the non-linear saturation of this
instability. We identify three important astro-physical applications of this
intermediate-scale instability, which is expected to 1. modulate CR transport
and strengthen CR feedback in galaxies and galaxy clusters, 2. enable electron
injection into the diffusive shock acceleration process, and 3. decelerate CR
escape from the sites of particle acceleration which would generate gamma-ray
halos surrounding CR sources such as supernova remnants.
