Page 21 - Fundamentals of Magnetic Thermonuclear Reactor Design

Engineering and Physical Principles of the Magnetic Fusion Chapter | 1 3

The shape of the plasma flux cross-section and the plasma position in the
vacuum chamber are controlled by the vertical magnetic field generated by po-
loidal field coils.
Plasma loses energy steadily due to its heat conductivity across the magnetic
field, electromagnetic radiation and other physical phenomena. This determines
its energy confinement time τ , in which a system’s energy decreases е times
E
provided that no heating is applied. With this parameter, one can express the
condition for fusion reactor stationary operation mode (for reaction 3 type and
plasma temperature T = 10 keV using the Lawson criterion):
20
τ ⋅ n E ≥10 m 3 – ⋅s (1.2) n⋅τE≥1020m-3⋅s
−3
20
With plasma concentration taken conservatively as close to 10 m , it fol-
lows from (1.2) that the required energy confinement time is several seconds.
1.3 BASIC CORRELATIONS
After many years of tokamak research, quite a few scalings (empirical results of
using the similarity laws to relate the energy confinement time τ to the plasma,
E
electrophysical and structural features of a fusion device) have been obtained.
Without going into details, let us confine the discussion to a scaling adopted for
the International Thermonuclear Experimental Reactor (ITER) design purposes:

0.69
τ = 0.0562 ⋅ I P 0.93 ⋅ B 0.93 ⋅ n 0.41 ⋅ A i 0.19 ⋅ R 1.97 ε ⋅ 0.58 ⋅ k 0.78 P / aux (1.3) τE=0.0562⋅IP0.93⋅Bt00.93⋅n0.4
t0
E
1⋅Ai0.19⋅R1.97⋅ε0.58⋅k0.78/Pa
where A is the mass of ions, in atomic units (A = 2; A = 3; A = 2.5); ε = a/R; ux0.69
i
T
D
DT
I is the plasma current, MA; B is the toroidal field at plasma axis, T; n is the
t0
P
−3
19
plasma concentration, 10 m ; R, a are plasma major and minor radii, m; P aux
is the additional heating power, MW; k is the elongation of a plasma column
cross-section; and τ is the energy confinement time in seconds [2, 3].
E
Joule heating of the discharge current is used for the initial plasma heating-
up process in tokamaks. However, plasma electrical resistance, and thus Joule
heating, tends to decrease with increasing temperature, while losses due to radi-
ation tend to grow. For this reason, additional heating methods are used to raise
the plasma temperature further. These methods include the introduction of fast
atoms and electromagnetic radiation at different frequencies, plasma adiabatic
compression by an increasing magnetic field and so on.
The stability of a plasma column in a magnetic fusion device is described by
the Kruskal–Shafranov criterion:
aB
q = t0 >1 (1.4) q=aBt0RBP>1
RB P
where B is the poloidal magnetic field of the plasma current. For a plasma
p
column to be stable, condition q > 1 must be fulfilled. Generally, q is set to be
∼3 for a reactor.