Page 201 - Fundamentals of Magnetic Thermonuclear Reactor Design

Vacuum and Tritium System Chapter | 6 183

Effective impurities concentration is measured by plasma effective charge.
Plasma effective charge is a metric used to measure the impurities. An equation
for it is as follows:
1 + ∑ n( Zj n /) ⋅ Z j 2
Z eff = j ,
1 + ∑ n( Zj n /) ⋅ Z j
j Zeff=1+∑j(nZj/n)⋅Zj21+∑j(nZj/n
where n is the concentration of impurity ions with atomic number Z . For a )⋅Zj,
j
Zj
pure hydrogen plasma, Z = 1.
eff
The length of an MFR operating cycle is many orders of magnitude greater
than the lifetime of atoms in plasma. For this reason, impurities appear in an
ionised state, with the Z going up and approaching a maximum value of Z with
eff
increasing temperature.
In addition, the influx of impurities triggers changes in the plasma current
distribution. Low-Z impurities constrict the current channel and cause a local
flux of plasma onto the wall, while heavy impurities cause a drop of the central
plasma temperature.
There is another group of phenomena in the vacuum chamber, associated
with the charge exchange of ions. A ‘cold’ particle flowing into the plasma from
the boundary area gets recharged, transferring its electron to a fast hydrogen ion.
The latter, becoming an atom, brings its kinetic energy to the wall cooling down
the plasma. The energy flow of the plasma is proportional to the concentration of
neutral gas in the wall boundary area. For a pure protium plasma surrounded by
protium, energy losses due to ion charge exchange are of the same order as those
−5
caused by bremsstrahlung radiation, if its pressure is higher than ∼10 Pa.
The charge exchange with atoms is particularly important for such appli-
cations as plasma ‘traps’ with a high power fast particles injection. In these
‘traps’, high-temperature plasma is prevented from accumulating by a charge
exchange between injected particles and residual gas atoms. For a plasma to
achieve concentration n, the neutral gas concentration, n , and the injected ion
0
beam density, j, must satisfy
1
n 0 ≤ n ,
τσ n ≤n1τ j σ,
j
0
where τ is the ion’s total lifetime, and σ is the neutral beam charge exchange
cross section. Because neutral beam injectors deliver cold neutral gas to a trap
in addition to a beam of fast atoms and an injected beam inevitably gets ther-
malised, linear plasma traps need evacuating pumps with a high flow rate capac-
3
3
ity of an order of 10 m /s.
An opposite situation is possible when charged particles are captured and
entrapped following charge exchange. This happens when a beam of fast atoms
is injected into a low-temperature dense plasma. In this case, the injected par-
ticle’s charge exchange on cold ions causes an increase in ion temperature due
to the substitution of slow ions with fast ones.