In magnetized plasmas, temperature anisotropy manifests as distinct temperatures (T
⊥j
, T
∥j
). Numerous prior studies have demonstrated that as plasma beta (β
∥j
) increases, the range of temperature anisotropy (R
j
= T
⊥j
/T
∥j
) narrows. This limiting effect is conventionally taken as evidence that kinetic microinstabilities are active in the plasma, and has been previously observed for protons in the magnetosheath. This study is the first to use data from the Magnetic Multiscale Mission to investigate these instability-driven limits on alpha particle (ionized helium) anisotropy in Earth’s magnetosheath. The distribution of data over the (β
∥j
, R
j
) plane was plotted and shows the characteristic narrowing in the range of R
j
-values as β
∥j
increases. The contours of the data distribution align well with the contours of the constant growth rate for the ion cyclotron, mirror, parallel firehose, and oblique firehose instabilities, which were calculated using linear Vlasov theory.