Dynamics of Whistler Spheromaks in Magnetized Plasmas

Recent laboratory experiments [Stenzel et al., Phys. Rev. Lett. 96, 095004 (2006)] have demonstrated interesting phenomena of propagating nonlinear whistler structures (spheromaks) and stationary field-reversed configurations, whose magnetic fields exceed the ambient magnetic field strength. Our objective here is to present simulation studies for these nonlinear whistler structures based on the three-dimensional nonlinear electron magnetohydrodynamic equations. The robustness and longevity of the propagating whistler spheromaks found in the experiments are confirmed numerically. Varying the toroidal field of the spheromak in the initial conditions, we find that the polarity and the amplitude of the toroidal field determine the propagation direction and speed of the spheromak. Our simulation results are in excellent agreement with those observed in the laboratory experiments.

Figure 1

The initial magnetic field at time $t=0\mu \mathrm{s}$. (a) The $z$ component of the magnetic field, with a cut at $x=0$ through the $yz$ plane. Reversed field maxima $B_z\approx -7\mathrm{G}$ are located at $z\simeq 7.5\mathrm{cm}$. (b) The vector field ($B_y$, $B_z$), with a solid line indicating where $B_z=0$. (c) The toroidal magnetic field component $B_x$.

Figure 2

The magnetic field at time $t=1.14\mu \mathrm{s}$. (a) The $z$ component of the magnetic field, with a cut at $x=0$ through the $yz$ plane. Reversed field maxima $B_z\approx -7\mathrm{G}$ are located at $z\simeq 17.5\mathrm{cm}$. (b) The vector field ($B_y$, $B_z$), with a solid line indicating where $B_z=0$. (c) The toroidal magnetic field component $B_x$.

Figure 3

The magnetic field at time $t=2.3\mu \mathrm{s}$. (a) The $z$ component of the magnetic field, with a cut at $x=0$ through the $yz$ plane. A reversed field maximum $B_z\approx -7.5\mathrm{G}$ is located at $z\simeq 25\mathrm{cm}$. (b) The vector field ($B_y$, $B_z$), with a solid line indicating where $B_z=0$. (c) The toroidal magnetic field component $B_x$.

Figure 4

(a) The $z$ component of the magnetic field, with a cut at $x=0$ through the $yz$ plane, at time $t=1.14\mu \mathrm{s}$, for the case of an initially zero toroidal field. Reversed field maxima $B_z\approx -12\mathrm{G}$ are located at $z\simeq 15\mathrm{cm}$. (b) The vector field ($B_y$, $B_z$), with a solid line indicating where $B_z=0$. (c) The toroidal magnetic field component $B_x$.

Figure 5

(a) The $z$ component of the magnetic field, with a cut at $x=0$ through the $yz$ plane, at time $t=2.3\mu \mathrm{s}$, for the case of an initially zero toroidal field. Reversed field maxima $B_z\approx -7\mathrm{G}$ are located at $z\simeq 20\mathrm{cm}$. (b) The vector field ($B_y$, $B_z$), with a solid line indicating where $B_z=0$. (c) The toroidal magnetic field component $B_x$.