The atoms sputtered from the first-wall into the plasma can lead to considerable degradation of the energy viability of the fusion reaction chain. The reason for this can be summarized as follows. As the sputtered impurity atoms enter the
high temperature plasma, they collide with the plasma fuel ions and electrons and thereby become ionized. Only if these impurities feature a low proton number will they be completely ionized upon entering the plasma. For heavier impurity atoms (e. g. Fe, Ni, …), full ionization will not be possible in the plasma, hence leaving them in states of incomplete ionization, notwithstanding the exhibition of high charge numbers depending on the plasma temperature. Evidently, the overall Z of the plasma is increased, and consequently also the bremsstrahlung radiation which was seen to vary with Z2. Since several types of impurity ions may be present in a plasma at specific concentrations and different charge number, our previous formula for the bremsstrahlung power, Eq. (3.44), should, more correctly, be rewritten as

Ры= Abr^N N efiTe = AbrZeffN2eJkTe (13.14a)

has been introduced.

Additionally, a further important radiation process occurs which is due to the incomplete ionization of impurity atoms. Partly ionized atoms can be collisionally excited to a higher atomic energy level, and subsequently emit electromagnetic radiation by spontaneous transition to a lower energy level. The radiation frequency associated herewith is characteristic for each possible specific transition, and hence this radiation is called line radiation. In the case of a non-negligible impurity concentration in the plasma, the associated line radiation is seen to significantly contribute to the plasma radiation losses.

Since the line radiation PUne is proportional to both N-, and Ne, we introduce an ion-specific radiation parameter |/rad, i by

(Pbr), + (P tme)l

N, N.

which is displayed in Fig.13.7 as a function of plasma temperature. If this parameter is multiplied by the product of the electron density and the density of the i-th impurity, the respective radiation power due to both bremsstrahlung and line transitions is immediately found. Figure 13.7 now makes evident the substantial increase in radiation losses when high Z impurities enter the plasma. Only a very small concentration of such impurities can therefore be permitted in a fusion plasma if it is to be ignited. The straight dotted lines in Fig.13.7 indicate the normalized bremsstrahlung radiation for the case that the atoms of the considered element were fully stripped of electrons. As the plasma temperature increases, such states of complete ionization become more probable and the radiation parameters |/radii are seen to asymptotically approach the respective corresponding straight dotted lines characterizing the bremsstrahlung from fully

Electron Temperature, Te (keV)

Fig. 13.7: Normalized radiation power, |/rad = (Pbr + Pime)/ (N, Ne), as it depends on the
plasma electron temperature. The dotted lines denote the normalized bremsstrahlung
radiation of the completely ionized respective atoms.

ionized atoms.

While a detailed analysis of the adverse effect of the impurity atoms may involve complex transport calculations, an appreciation of some of the implications can be formulated as follows. Consider an initially pure hydrogen — state unit volume of plasma containing deuterons and tritons of equal density and their associated electrons all at temperature Tj. That is, we have Nd = Nt, Nj=Nd+Nt, Nj = Ne and a total thermal energy density in the fusion domain of

£rt, i=i(^ + ^)fc7i — (13.16a)

The contaminated state subsequently contains an additional number of Nz impurity ions and NzZ impurity electrons per unit volume; here Z is the ionization number for the atoms sputtered from the first wall. At thermal equilibrium with a temperature T2 we therefore have

E, h,i = + Xz + Ne + NzZ)kT2 . (13.16b)

In the absence of energy injection and the imposition of sharing of thermal energy among all ions and electrons, we may take Eth, i = Eth,2 and obtain

N+ N

:TX (13.17)

for which, evidently, T2 < T b This plasma cooling effect may be more compactly represented by the introduction of an impurity ratio gz defined by

The associated increased bremsstrahlung radiation power losses can be assessed by taking the ratio

Рыл _r{Ne + NzZ)2Zeff

Рыл AbrNeNiJH

with Zeff according to Eq.(13.14b), however noting that the electron density here is Ne + NzZ. Using the definition for the impurity ratio gz of Eq.(13.18) then gives

^ = (l+giZfz*M d3.20b)

ґЬгЛ V

and introducing the temperature ratio of Eq.(13.19) then yields

Pbr,2_ d+gzZf

which shows that bremsstrahlung power losses have indeed increased, even though the temperature was somewhat reduced (T2 < Ti). Hence, this radiation emission, as well as the line radiation previously discussed and which may substantially contribute to plasma power losses, will further cool down the plasma.

Note that those fusion products having Z > 1 (helium) will result in greater bremsstrahlung radiation as well. Therefore, these so-called ash ions should be controlled in a fusion plasma so as not to accumulate to concentrations that are too high. The adverse impurity effect can be controlled by several methods. Two
of the most important are the following: i) the use of divertors which involves magnetic field lines leading out of the plasma chamber to ion collectors so that ions following these lines do not hit the wall and hence do not produce impurities, and ii) the use of low-Z first-wall materials which do not cause such a large increase in the radiation loss even if their concentration in the plasma remains high.