Beyond the 90° Problem: A Physical Resonance Gap in Cosmic Ray Transport at Large Pitch Angles

Cosmic ray (CR) transport is governed by gyroresonant interactions that drive streaming instabilities, which regulate pitch angle scattering and energy transfer. Traditionally, quasilinear theory (QLT) is used to model CR streaming, and it predicts that CRs at 90° pitch angles cannot gyroresonantly scatter with Alfvén waves — the so-called "90° problem". While this implies a scattering barrier that prevents CR isotropization, the 90° problem has been attributed to invalid approximations inherent in the theoretical framework of QLT.

However, less consideration has been given to the fact that the magnetohydrodynamic (MHD) approximation breaks down for waves gyroresonant with CRs at pitch angles well below 90°.

Here I employ a two-fluid plasma model that includes electron dynamics to analytically examine gyroresonant interactions at small scales, where MHD fails. This reveals a physical resonance gap that affects CRs across a finite range of large pitch angles, not just at the singular 90° value.

These findings elevate the scattering barrier predicted by the 90° problem from a theoretical curiosity to a physical reality. I examine potential mechanisms that can bridge this resonance gap, including magnetic mirroring effects and resonance broadening processes.

Beyond the existence of the resonance gap, the non-MHD treatment also reveals fast-growing whistler modes and additional wave excitations, challenging CR scattering models based on single-wave-frame approximations.