Spontaneous generation of temperature anisotropy in a strongly coupled magnetized plasma

A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components, thus leading to the emergence of strong and long-lived temperature anisotropies when the plasma is locally perturbed. An extended heat equation is shown to describe this process accurately.

Figure 1

Relative temperature differences $\mathrm{\Delta }T/T$ and $\mathrm{\Delta }{T}_{\perp }/T$ ($T$ is the equilibrium temperature) as a function of heat bath coupling frequency ${\nu }^b$. When both temperature differences coincide, the heat bath coupling frequency equals the isotropization rate [Eq. (6)].

Figure 2

Isotropization time scale as a function of $\beta$ for $\mathrm{\Gamma }=100$. The straight lines shows an exponential extrapolation and the Dubin estimate.

Figure 3

Temperature profile along the $x$ axis at the start of the relaxation ($t{\omega }_p=0$) and at two later times. A sinusoidal fit (solid lines) through the simulation data (dashed lines) is shown at each time instant.

Figure 4

Time evolution of the normalized temperature perturbation amplitude (cf. Fig. 3) at two different coupling strengths. The solid lines indicate an exponentially decaying fit to the simulation data.

Figure 5

Time scale of temperature relaxation ${\tau }^{\mathrm{th}}$ as a function of coupling strength $\mathrm{\Gamma }$.

Figure 6

Thermal conductivity calculated from temperature relaxation time scale. For comparison, results from Refs. [42] (SC) and [14] (OBD) based on the Green-Kubo relations and from Ref. [43] (DH) based on a nonequilibrium method are shown.

Figure 7

Profiles of the field-parallel and field-perpendicular temperatures in a magnetized system at two different times. The temperature gradient is oriented along the magnetic field. A sinusoidal fit through the data is shown at each time instant.

Figure 8

Solutions (normalized) of Eqs. (25) and (26) for different ratios of the thermal diffusivities and isotropization rate.

Figure 9

Temporal dependence of sinusoidal amplitude (normalized) for different magnetic fields and $\mathrm{\Gamma }=100$. Compare with Figs. 8–8. The dashed lines in panels (a) and (d) show data for $\mathrm{\Gamma }=1$.

Figure 10

Anisotropy $K_D\left(t\right)=K_{\perp }\left(t\right)-K_{\parallel }\left(t\right)$ (simulation results, thin lines) and best fit to theoretical curves (strong lines) for different values of $\beta$. The broken line segment follows an exponential decay $exp(-\delta t)$ as a guide for the eye for $\beta =1.4$.

Figure 11

Maximum value of $K_D\left(t\right)=K_{\perp }\left(t\right)-K_{\parallel }\left(t\right)$ relative to $K_0$ as a function of $\beta$ (simulation data).

Figure 12

Time constant of the exponential decay of $K_D\left(t\right)\sim exp(-\delta t)$ at long times (simulation data).

Figure 13

Isotropization rate $\nu$ and effective anisotropization rate $k^2({\alpha }_{\parallel }-{\alpha }_{\perp })$ as a function of beta [data from fit to $K_D\left(t\right)$].

Figure 14

Estimation of critical magnetic field strengths as a function of the perturbation length for various plasma densities.