The first wall surrounding a fusion plasma is bombarded by both electromagnetic radiation and escaping plasma particles. Numerous effects such as temperature changes, thermal stresses, and erosion must be considered in wall design. One important effect we will discuss here is that of material erosion by sputtering. In this process, the incident ions or neutrals from the plasma possess sufficient energy to cause "billiard ball"-type collisions in the wall material, possibly leading to the ejection of wall atoms into the plasma, as suggested in Fig. 13.4.

To gain some insight into this important plasma-wall interaction, consider the process suggested in Fig. 13.5. A plasma ion of mass mi and velocity Vj enters the
first-wall and collides elastically with a stationary atom of mass m2. Using the notation of Fig. 13.5, we write the momentum and energy balances for such elastic events as

/ /

mxvx=mxvx cos 6x+m2v2 cos 62 (component 11 to vt) (13.4a)

/ /

mxvx sin01=m2v2 sin62 (component _Lto v,) (13.4b)

and

where Ei„c is the kinetic energy of the incident ion.

The other important parameter is the average distance a plasma ion moves into the first wall before it collides with an atom. Since all two-body collisions can be characterized by a microscopic cross-section, we use

<Jcoi = nR I2 (13.8)

where Ri>2 is the distance of closest approach of an ion of mass m, and energy Einc to characterize the interaction with the wall atom of mass m2 in the elastic collision process. Taking these latter atoms to be of density N2 then gives the relevant macroscopic cross-section £coi as

1ы = о col N2 • (13.9)

Further, the mean-free-path of material penetration is

Ai,2

Hence, it follows that

(13.13)

F i>u oc EincGcol N2

where К is a proportionality constant and the latter expression emphasizes the particularly important dependencies.

Experimentally measured sputtering ratios are presented in Fig. 13.6 for various first wall materials bombarded by monoenergetic deuterons. The sputtering ratios generally increase with energy of the incident ion-as suggested in Eq.(13.13)-until a point is reached where most collisions occur at such a depth that the probability of escape of the knock-ons is substantially reduced; thereafter, the yield decreases with incident energy. Hence, Eq.(13.13) is only applicable to the lower energy region of these curves since it neglects the effect of subsequent collisions or knock-ons.

In addition to physically weakening the wall as material is sputtered away, sputtered material that enters the plasma can have serious effects on plasma energetics. This will be considered next.