magnetopause forms at a characteristic length (m) from the field source. The ionized plasma wind particles create a current sheet, known as the Chapman–Ferraro current along the magnetopause, which compresses the magnetic field lines facing the oncoming plasma wind by a factor of 2 at magnetopause as shown in Figure 2a. The magnetopause deflects charged particles, which affects their streamlines and increases the density at magnetopause. A magnetospheric bubble or cavity forms that has very low density downstream from the magnetopause. Upstream from the magnetopause a bow shock develops. Simulation results often show the particle density through use of color with an example shown in the figure according to the legend in the lower left. This figure uses aspects of the general structure from Figure 3 Figure 1 and Figure 2a, and aspects of the plasma density from Figure 1, and Figure 2. Magnetohydrodynamic model Magnetic sail designs operating in a plasma wind share a theoretical foundation based upon a magnetohydrodynamic (MHD) model, sometimes called a fluid model, from plasma physics for an artificially generated magnetosphere. Under certain conditions, the plasma wind and the magnetic sail are separated by a magnetopause that blocks the charged particles, which creates a drag force that transfers (at least some) momentum to the magnetic sail, which then applies thrust to the attached spacecraft. The figure depicts the MHD model. Starting from the left a plasma wind in a plasma environment (e.g., stellar, ISM or an ionosphere) of effective velocity with density (kg/m3) encounters a spacecraft with time-varying velocity (m/s) that is positive if accelerating and negative if decelerating. The apparent plasma wind velocity from the spacecraft's viewpoint is . The spacecraft and field source generate a magnetic field that creates a magnetospheric bubble extending out to a magnetopause preceded by a bow shock that deflects electrons and ions from the plasma wind At magnetopause the field source magnetic pressure equals the kinetic pressure of the plasma wind at a standoff shown at the bottom of the figure. The characteristic length (m) is that of a circular sail of effective blocking area where is the effective magnetopause radius. Under certain conditions the plasma wind pushing on the artificial magnetosphere bow shock and magnetopause creates a force (N) on the magnetic field source that is physically attached to the spacecraft so that at least part of the force causes a force on the spacecraft, accelerating it