The interaction between a moving object and a stationary plasma leads to a disturbance in the local plasma, resulting in rarefaction on the downstream or wake side and, in the case where plasma is back-scattered, plasma compression on the upstream or ram side. These changes have consequences on the currents to surfaces and thus on the charging characteristics of the spacecraft. On the ram side, ion collection is enhanced and at the limit the ion current is approximately the ion density swept up by the spacecraft motion.
Figure C-3 (see [10]) shows that wakes have a complicated structure with ion streams that converge to form an axial peak, cross over and diverge in the far wake.
In the wake immediately adjacent to the spacecraft, ions are excluded because they have insufficient thermal velocity to enter this region from the downstream side. Usually, electrons have sufficient thermal velocity but because of the space charge that is created when they enter the wake without the ions, they too are largely excluded. As a result a region of less and higher space charge appears in the wake. The extent of the void region depends on the speed of the spacecraft relative to the speed at which the plasma can respond to fill it. Because the plasma acts collectively, it responds as fast as the ion acoustic velocity (vs).
where:
• vs is acoustic velocity in m s-1,
• k is the Boltzmann constant,
• Te and Tiare electron and ion temperatures respectively in K,
• Mi is ion mass in kg, and
•
is a constant, usually
3 for the case of plane waves.
In laboratory plasmas, the ion temperature is often negligible compared to that of the electrons and it is not uncommon to see the acoustic velocity written as:
(Ti=0)
Figure C-3: Schematic diagram of wake structure around an object at relative motion with respect to a plasma
The Mach number (M) is the ratio of the spacecraft velocity (vu) to the acoustic velocity
The rarefaction wave at the
edge of the wake region has a characteristic angle to the velocity vector, the
Mach angle (
).
Where the object is uncharged, ion trajectories fill the wake void at the same angle. The length of the void is then given by the Mach angle and the width of the object (see Figure C-4).
An object in the wake, charged to a high negative potential, can cause the trajectories to converge at a higher angle and so the void can be shorter.
The wake void region is larger for large spacecraft and those with high Mach numbers. From Table C-2, it can be seen that wakes are most important at low altitudes.
The regime for which the spacecraft speed is higher than the ionic thermal speed but lower than the electron thermal speed is called meso-sonic. This is always the case on low altitude spacecraft.
Assuming a neutral wake with a Boltzmann electron distribution, Cooke 1996 [14] has shown that the potential in the wake V as a function of the radius r of the body in the limit of infinite Mach number can be fitted by
for r/lD ranging from 1 to 1000.
