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The pQCD interactions are Debye screened. The screening mass is given by [13] 

<img src='content_image/340661.jpg'>

where n$_{f}$ is the number of quark flavor, and f$_{g}$ and f$_{q}$ are the distribution function of gluons and quarks at a certain quantum state. For a pure gluon matter f$_{q}$ = 0. 

The initial parton distribution for BAMPS calculations is the same as that chosen in Refs. [9, 11]: an ensemble of gluon minijets with transverse momenta greater than p$_{0}$ = 1 . 4 GeV, produced via semihard nucleon-nucleon collisions within a Glauber picture. The value of p$_{0}$ was chosen by matching the parton cascade result of the final transverse energy per rapidity to the experimental data [9, 11]. Quark minijets, which take about 20% of the total parton number, are neglected for present studies, in order to easily make comparisons with the previous results obtained in [11]. 

To take into account the quark-gluon changing process gg ↔ q ¯ q and the elastic as well as the bremsstrahlung process involving light quarks, we effectively enlarge the gluon degener- acy factor d$_{G}$ . With a larger d$_{G}$ than 16, the ggg → gg process is suppressed [see Eq. (3)] and thus more particles (i.e. quarks) will be produced. This numerical prescription indicates two assumptions: (1) Quarks are massless. (2) The elastic and the bremsstrahlung process involving quarks are identical with those of gluons according to Eqs. (1)-(3). These assump- tions lead to the same kinetic equilibration of quarks and gluons, i.e., f$_{q}$ ∼ f$_{g}$ . The second assumption overestimates the interaction rate of a quark approximately by the color-charge factor 9 / 4 due to the dominance of gg → gg , qg → qg , gg ↔ ggg and qg ↔ qgg in kinetic equilibration. The real equilibration of quarks is expected to be slower than that of gluons. Moreover, the present prescription used to include quarks cannot separate quarks from glu- ons. The relative fraction of the quark (or gluon) number to the total parton number is not known. Quark thermalization by real quark dynamics will be investigated in the future [25]. The simplified version used here serves as a tool to study the effect on the elliptic flow when varying the number of parton degrees of freedom. 

The enlarged d$_{G}$ value can be obtained when considering a fully thermalized system of quarks and gluons. In this case f$_{q}$ = f$_{g}$ and the parton distribution function is given by f = d$_{G}$f$_{g}$ + d$_{Q}$f$_{q}$ = ( d$_{G}$ + d$_{Q}$ ) f$_{g}$ , where d$_{Q}$ = 24 is the quark degeneracy factor for n$_{f}$ = 2. To include effective quark degrees of freedom in BAMPS we enlarge d$_{G}$ from 16 for a pure gluon system to 40 for a quark gluon system with two flavors. 

