在高速太陽風的觀測中得知, 阿爾法粒子和質子間存在著一定的相對速度, 此一現象啟發我們去探討阿爾法粒子如何在電漿中引發其不穩定性, 為了尋找此一不穩定性, 我們藉由電腦程式Waves in Homogenous Anisotropic Multicomponent Plasma (WHAMP)的幫助來求解色散方程式, 並且使用不同種類的粒子:質子、阿爾法粒子、和電子, 和改變質子和阿爾法粒子間的相對速度及阿爾法粒子的濃度來研究電漿中的不穩定性有何變化, 結果顯示, 當阿爾法粒子濃度增加或是阿爾法粒子和質子間的相對速度增加時, 不穩定性皆有增強的趨勢存在, 在此篇研究中我們發現此一類型的不穩定性是由質子和電子所引發的一種雙流不穩定性(two-stream instabilities), 並且阿爾法粒子會因為電中性和零電流的條件下影響電子的分布, 這些研究結果都和潘羅斯準則(Penrose criterion)一致

Observations of the relative velocity between alpha particles and protons in the fast solar wind motivate our study of how the alpha particle properties may cause instabilities in the plasma. In order to find out the instabilities, we solve for the dispersion relation through a computer program, Waves in Homogenous Anisotropic Multicomponent Plasma (WHAMP). The computer code allows us to include different species of particles: alpha particles, protons and electrons. Using WHAMP, we study the change of instabilities with varying relative velocity and the alpha particle density. The instabilities are stronger with increasing relative velocity at fixed alpha density, and change with increasing alpha density at fixed relative velocity. The unstable wave mode is recognized as two-stream instabilities associated with the relative velocity between the electron and the main proton population. The electrons are affected by the alpha particle density and velocity because of quasineutrality and currentless condition in the solar wind. The conditions for the instabilities are consistent with the Penrose criterion.

Jeffrey, A. and D. Zwillinger, Table of Integrals, Series, and Products Seventh Edition, Academic Press, 2007.
Marsch, E., et al., Solar wind protons: Three dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU, Journal of Geophysical Research, 87, 52-72, 1982.
Marsch, E., et al., Solar wind helium ions: Observations of the Helios solar probes between 0.3 and 1 AU, Journal of Geophysical Research, 87, 35-51, 1982.
Murphree, J.S., Frequency Analysis of the 4-6 KeV Electron Flux Associated with a Weak Auroral Arc, Ph.D. thesis, Rice University, 1974.
Penrose, O., Electrostatic instabilities of a uniform non-Maxwellian Plasma, Physics of Fluids, 3, 2, 1960.
Rönnmark, K., WHAMP-waves in homogenous, anisotropic multicomponent plasmas, KGI report, 179, 1982.
Steinberg, J. T., and A. J. Lazarus, Differential flow between solar wind protons and alpha particles: First WIND observations, Geophysical Research Letters, 23, 1183-1186, 1996.