Schematic diagram of simulation domain. Antiparallel current density is supplied at the center of the domain. Solar wind is assumed to be a uniform plasma flow in the direction.
Time evolutions of Lorentz force acting on coil current density. (a) Dependence on domain size, standoff time, and solar wind flow velocity. Domain size for case B (dashed line) is enlarged compared with that in case A (solid line). The standoff time for case C (dotted line) is twice that for case A. Solar wind flow velocity is set equal to zero for the “stationary” case (dashed-dotted line). (b) Relationship between Lorentz force (solid line) and the momentum loss rate of the solar wind plasma (dashed line).
(Color) Color-coded contour plots of (a) mass density Ro, (b) out-of-plane current density and (c) out-of-plane magnetic field in a quasi-steady state. Green lines represent magnetic field lines. Note: the displayed region is larger in (c) than in (a) and (b).
Time evolution of drag coefficient. Interval marked by “()” is used for time averaging the results shown in Fig. 5.
(a) Profiles of magnetic field, , at steady state (dashed line) and for original magnetosphere, , (dotted line) along the equatorial line (). Profile of induced current density, , is also shown as the solid line. (b) Relationship between the induced current, , (solid line) and variations of the magnetic field gradient terms, and (dotted and dashed lines, respectively).
(a) Profiles of magnetic field gradient, , at steady state for runs A1–A7. For comparison, the magnetic field gradient corresponding to the gradient scale is represented by the dashed line. (b) Profiles of induced current density at steady state for runs A1–A7. The current density values corresponding to the gradient scale and are also shown.
Dependence of half-width of current layer on the scale of original magnetosphere. Half-widths normalized by the local electron gyration radius and by the scale of magnetosphere are denoted by and , respectively.
(Color) Profiles of force terms in the two-fluid equation. Electron force terms in (a) x-direction and (b) z-direction. (c) Ion force terms in the x-direction. Cyan, green, and red lines stand for inertia, electric, and magnetic force terms along equatorial line, respectively. The pressure term is separated into scalar (blue lines) and off-diagonal (purple lines) components for panels (a) and (c).
(a) Profiles of electron force terms from Eq. (5) at steady state for runs A3–A7. Solid and dashed lines denote electric force term and kinetic term including inertia and pressure terms, respectively. (b) Electron number density profiles along equatorial line for runs A3–A7.
Profiles of induced current density resulting from series B and C. (a) Solid, dashed, and dotted lines represent profiles for runs B1, B2, and B3, respectively. (b) Solid, dashed, and dotted lines represent profiles for runs C1, C2, and C3, respectively. Profiles of original magnetic field, , are given as solid lines marked “original field.”
Scale dependence of drag coefficients. (a) Solid line marked with represents drag coefficient obtained from series B. Dotted () and dashed () lines represent electron and ion drag coefficients, respectively. (b) Dotted lines marked with and represent estimated electron and ion drag coefficients obtained from series A, respectively. Electron and ion drag coefficients obtained from series C are denoted by large dots and squares, respectively.
(a) Schematic diagram for the evaluation of drag coefficient. (b) Drag coefficient as a function of magnetosphere scale obtained from simulation runs A1-A6 (asterisk). Solid line stands for the theoretical relationship (Eq. (15)). Upper and lower horizontal lines represent the limit value of drag coefficient (Eq. (17)) and the typical value in the small magnetosphere regime (Eq. (16)), respectively.
(Color) (a) Color contours of mass density and (b) out-of-plane magnetic field resulting from finite IMF. Green lines represent magnetic field lines.
(a) Time evolution of drag coefficient. Solid and dashed lines denote the drag coefficient resulting from finite and zero IMF cases, respectively. The interval marked by “()” is used for time averaging the data in panel (b). (b) Spatial profiles for induced current density resulting from finite (solid line) and zero (dashed line) IMF cases.
(Color online) Color-coded contour plots of number density for electrons with (a) A flag of “1,” which have not passed through and (b) A flag of “0,” which have passed through . Curved lines in both panels represent magnetic field lines.
(Color online) Velocity distribution of electrons and ions with flag “1” along the equatorial line. Vertical and horizontal axes are velocity in the x-direction and distance from coil center, respectively. (a) and (b) Electron velocity distributions obtained under finite and zero IMF, respectively. (c) and (d) Ion distributions obtained under finite and zero IMF, respectively.
Dimensionless parameters for simulation series A (A1–A7) and the additional example A0.
Typical dimensionless parameters for simulation series B and C.
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