Magnetic field in expanding quark-gluon plasma

Intense electromagnetic fields are created in the quark-gluon plasma by the external ultrarelativistic valence charges. The time evolution and the strength of this field are strongly affected by the electrical conductivity of the plasma. Yet, it has recently been observed that the effect of the magnetic field on the plasma flow is small. We compute the effect of plasma flow on magnetic field and demonstrate that it is less than 10%. These observations indicate that the plasma hydrodynamics and the dynamics of electromagnetic field decouple. Thus, it is a very good approximation, on the one hand, to study QGP in the background electromagnetic field generated by external sources and, on the other hand, to investigate the dynamics of magnetic field in the background plasma. We also argue that the wake induced by the magnetic field in plasma is negligible.

Figure 1

The geometry of the heavy-ion collisions. Ion remnants move with velocity $\pm \mathit{v}$. The plasma's velocity is $\mathit{u}$. We emphasize that the valence electric charges $dq$ are external to the plasma. The geometry in the $xy$ plane is shown in Fig. 2.

Figure 2

The geometry of the heavy-ion collisions in the transverse plane. The two heavy-ion remnants (big circles) move in opposite directions along the $z$ axis, see Fig. 1. The element of charge $dq$ is located at the same $z$ as an ion remnant (i.e., it is not inside the plasma). Its projection on the transverse plane is depicted by the square. The small circle indicates the element of plasma moving with velocity $\mathit{u}$. The observation point is denoted by the $+$ symbol. The impact parameter $\mathit{s}$ points from one nuclear center to another one.

Figure 3

The vector potential $\mathit{A}={\mathit{A}}^{\left(0\right)}+{\mathit{A}}^{\left(1\right)}$ created at a representative point $z=0, b=1$ fm, $\varphi =\pi /6$ (see Fig. 2) in QGP by a remnant of the gold ion moving with the boost factor $\gamma =100$ ($\sqrt{s}=0.2$ TeV) and impact parameter $\left|\mathit{s}\right|=3$ fm. Left: vector potential ${\mathit{A}}^{\left(0\right)}$ in the nonexpanding plasma. Right: the relative contribution of the plasma expansion. The plasma emerges at $\tau =0.2$ fm/$c$.

Figure 4

Dotted line, $A_z^{\left(1\right)}$; dashed line, $A_{\varphi }^{\left(1\right)}$; solid line, $-A_b^{\left(1\right)}$ components of the correction ${\mathit{A}}^{\left(1\right)}$ to the vector potential (in units of $m_{\pi }/e$) due to the plasma expansion. The geometric and kinematic parameters are the same as in Fig. 3. The cylindrical coordinates are defined with respect to the $z$ axis of Fig. 2, which is the laboratory frame for heavy-ion collisions.