Proton temperature anisotropy upper bound

The electromagnetic proton cyclotron instability and the mirror instability are driven by the proton temperature anisotropy T ⊥ p / T ‖ p > 1, where ⊥ and ‖ denote directions relative to the background magnetic field. Linear theory and one‐dimensional hybrid simulations imply that the former mode grows more rapidly over 0.05 ≤ β ‖ p ≤ 5 and that wave‐particle scattering by its enhanced fluctuations imposes an upper bound on the temperature anisotropy of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0001 where and B 0 is the background magnetic field. Here S p and α p are fitting parameters, and . This paper describes results from more general two‐dimensional hybrid simulations, which permit both instabilities to grow simultaneously. These simulations confirm the one‐dimensional results on the initial domain ; enhanced fluctuations display the properties of the proton cyclotron instability and α p ≃ 0.4. On this domain the two‐dimensional simulations also yield an upper bound for the fluctuating field energy density of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0005 with fitting parameter . The simulations on the initial domain 10 ≤ β ‖ p ≤100 show spectral characteristics of both instabilities and exhibit a more stringent bound on the proton anisotropy, in agreement with observations in the terrestrial magnetosheath.