Three Regimes and Four Modes for the Resonant Saturation of Parallel Ion-beam Instabilities

Motivated by recent advances in laboratory experiments on parallel ion-beam instabilities, we present a theoretical framework for-and simulations of-their evolution toward shock formation and Fermi acceleration. After reviewing the linear theory of beam instabilities, with an emphasis on how magnetic helicity and polarization depend on properties of the beam, we compare the evolution and saturation of three distinct parameter regimes: (I) the left-handed non-resonant regime; (II) the right-handed beam-gyroresonant regime; (III) the balanced, mixedturbulence regime.