Studies of Non-Abelain Plasma Instabilities

In the theoretical study of quark-gluon plasma (QGP), understanding how such plasma equilibrate in heavy-ion collisions is important and challenging. Baier et al. [12] have investigated the effects of individual particle collisions on subsequently equilibrating the plasma. However, Arnold, Lenaghan and Moore showed that the process of thermalization is not controlled only by such individual particle collisions in the weak-coupling limit [5]; one must also take into consideration the collective process in the plasma in the form of plasma instabilities [33, 37, 38, 15, 34, 30, 31, 32]. To analyze correctly the effects of plasma instabilities, it is important to understand whether the chromo-magnetic fields grow as large in non-abelian gauge theories as in abelian ones. Arnold and Lenaghan conjectured that the fields associated with non-abelian plasma instabilities will line up in color space when their self-interactions become important, and that they then grow as approximately abelian configurations [8]. Rebhan, Romatschke, and Strickland indeed found unabated exponential growth beyond the non-abelian scale in 1 dimensional plasma [3]. Arnold, Moore and Yaffe then investigated the full 3 dimensional theory [10]. They found significant differences. Though the magnetic energy continues to grow with time, it eventually becomes linear with time, rather than exponential. To elucidate the origin of this difference, I studied the intermediate case of two spatial dimensions [7]. Depending on how the "two-dimensional" theory is formulated, either behavior can be obtained. It was found that non-abelian effects will prevent late-time exponential growth if and only if no gauge-field polarizations are included outside of the subset of spatial dimensions simulated. After understanding the case of moderate anisotropic hard particle distribution, the next natural step is to investigate the more extreme anisotropic initial conditions. To understand how the magnetic fields generated by plasma instabilities scale with anisotropy, Arnold and Moore measured the dependence of the soft magStudies of Non-Abelian Plasma Instabilities ii netic fields B caused by non-abelian Weibel instabilities on the anisotropy of the hard particle distribution in 3 spatial dimensions and found B ∼ θ µ where µ is consistent with 1 [9]. To confirm the result, I repeated the analysis in 2 spatial dimensions and found the same result.

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