MHD simulations of astrophysical and laboratory jets under different magnetic field configurations

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Abstract

This paper presents the results of MHD simulations of astrophysical and laboratory supersonic jets under a superposition of poloidal (Br, Bz) and toroidal (Bϕ) magnetic fields. It is shown that the escaping matter is quickly collimated by the magnetic field. A shock wave of an elongated shape is formed, which moves from the target to the boundary of the chamber, leaving behind a stable flow. A periodic shock wave structure is observed inside the main conical expanding shock wave. It is shown that the toroidal component of the magnetic field remains in the region throughout the entire calculation and plays a role in the collimation of the flow. The poloidal magnetic field decreases in the region of the jet cone, but remains in the simulation region throughout the calculation and also participates in flow collimation. Thus, both components Bz and Bϕ take part in the collimation of the flow by the magnetic field. The width of the jet and the opening angle of the cone Ɵ depend on the magnitude of the magnetic field induction. As the field increases, the jet becomes narrower and the cone angle decreases. Initially, we do not specify the rotation of the jet Ω. However, due to the presence of the Bϕ field, the substance acquires angular velocity and twists along the z axis. The simulation results are in agreement with laboratory jets arising in the experiment at the Neodymium laser installation, and with the previously obtained results of MHD modeling of jet formation separately, in poloidal or toroidal magnetic field.

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About the authors

О. D. Toropina

Space Research Institute, Russian Academy of Sciences

Author for correspondence.
Email: toropina@cosmos.ru
Russian Federation, Moscow

G. S. Bisnovatyi-Kogan

Space Research Institute, Russian Academy of Sciences

Email: toropina@cosmos.ru
Russian Federation, Moscow

S. G. Moiseenko

Space Research Institute, Russian Academy of Sciences

Email: toropina@cosmos.ru
Russian Federation, Moscow

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Supplementary files

Supplementary Files
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2. Fig. 1. Laser experiment setup. Laser radiation is directed onto target M (Cu 30 μm, 50 μm, or Ta 50 μm). Heating of the target generates two directed proton beams, which are detected by CR-39 track detectors A and B.

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3. Fig. 2. Diagram of the simulation region: an inertial cylindrical coordinate system centered at the target, with the axis perpendicular to the target, is used. A poloidal B and toroidal magnetic field Bϕ are specified. The central target area is a homogeneous cylinder of radius RdRmax, Zmax and thickness ZdRmax, Zmax.

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4. Fig. 3. Flow pattern during jet formation in a magnetic field at times (top to bottom, left to right): T1 = 0.1, T2 = 0.8, T3 = 1.6, T4 = 2.5 for the case with parameters b0 = 1, β = 10⁻², and M = 3. Colored shading indicates the logarithm of density; thin solid lines correspond to poloidal field lines.

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5. Fig. 4. Jet structure in a magnetic field at time T4 = 2.5. Top: case with b0 = 1, β = 10⁻², and M = 3. Bottom: case with b0 = 1, β = 10⁻², and M = 6. Colored shading indicates the logarithm of density; thin solid lines correspond to poloidal field lines. For detail visualization, the contrast is reduced.

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6. Fig. 5. Distribution of the logarithm of material density along the z-axis at r = 0.01 (solid line) and r = 0.16 (dashed line) at time T = 2.5 for the case with β = 10⁻² and M = 3.

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7. Fig. 6. Mach number M = ν/cs along the z-axis at r = 0.01 (solid line) and r = 0.16 (dashed line) at time T = 2.5 for the case with β = 10⁻² and M = 3.

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8. Fig. 7. Distribution of magnetic field induction along the r-axis at the same distance z = 0.2 at times T = 0.0, T = 1.2, T = 2.5 for the case with β = 10⁻² and M = 3.

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9. Fig. 8. Distribution of magnetic field induction Bz along the r-axis at z = 0.01, z = 1.128, z = 2.56 at time T = 2.5 for the case with β = 10⁻² and M = 3.

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10. Fig. 9. Distribution of angular velocity ω along the r-axis at z = 1.128 at times T = 0.0 (solid line), T = 1.2 (dotted line), and T = 2.5 (dashed line) for the base case with b0 = 1.0, β = 10⁻², and M = 3.

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11. Fig. 10. Flow pattern during jet formation in a magnetic field at times (top to bottom, left to right): T1 = 0.1, T2 = 0.8, T3 = 1.6, T4 = 2.5 for the case with b0 = 0.5, β = 10⁻², and M = 3. Colored shading indicates the logarithm of density; thin solid lines correspond to poloidal field lines.

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12. Fig. 11. Flow pattern at the same moment T4 = 2.5 for three cases differing in magnetic field induction magnitude. From left to right, field amplification factors are b0 = 0.5, b0 = 1.0, and b0 = 2.0. The Mach number is the same and equal to M = 3.

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