Page 22 - Fundamentals of Magnetic Thermonuclear Reactor Design

4 Fundamentals of Magnetic Thermonuclear Reactor Design

A discharge current and a toroidal magnetic field relate as

a
2 π B t0   2
2
Ip≤2πBt0q⋅µ ⋅aR ⋅R I p ≤ µ ⋅ q 0 ⋅  ⋅ R (1.5)
 
0
R
µ 0 where µ is magnetic permeability.
0
One of the tokamak’s important characteristics is the ratio between plasma
gas-kinetic pressure and the pressure of a confining magnetic field.
k ⋅⋅ (T + T ) i
n
β = B 2 e (1.6)
t
βt=kB⋅n⋅Te+TiBt02/2µ 0 B /2 µ 0
t0
where k is the Boltzmann constant. In a magnetohydrodynamic approximation,
B
a
βt≤aR⋅q2. β ≤ ⋅ (1.7)
t
Rq ⋅ 2
For a tokamak with an aspect ratio (R/а) of around 3.3, β is close to 3% if
t
the stability criterion q is set at around 3. Apparently, the magnetic field pressure
must be essentially greater than the plasma gas-kinetic pressure. In other words,
it is the magnetic field’s ‘brutal force’ that confines plasma within a tokamak.
One may increase the β parameter a little extending the plasma column’s
t
cross-section along the vertical axis and let it obtain a D shape. This will allow
2
an approximately (1+ k )/2 times increase in the stability margin and maximum
allowable plasma current.
Spherical tokamaks, notable for their aspect ratio close to 1, can increase the
β . For example, a β of around 40% was achieved in some experiments on the
t
t
NSTX spheromak (having an aspect ratio of 1.3).
From these estimates and the expression (1.1), we derive the power of a
fusion device based on the tokamak concept:
< σv >
2
⋅
2 p = k β B 4 ⋅ ⋅EV (1.8)
pfus=kβt2Bt04⋅〈σv〉kBT ⋅Ef⋅Vp⋅ fus t t 0 ) 2 f p
(kT
B
Modern electromagnetic systems, including superconducting ones, can gen-
erate fields up to (5–6) T at the plasma column axis (12–13 T ‘on the winding’).
Considering this limitation and using the expression (1.8), one can derive an
approximate volume density of heat generated by a tokamak; it is close to
3
1 MW/m .
In conclusion, we note that the tokamak, unlike its fission counterpart, can-
not be small and low-power in principle. As follows explicitly from (1.3) and
(1.8), it must be a large device with a heating power of around 1 GW. A range of
problems in areas, such as magnetic, vacuum and cryogenic technologies; radia-
tion materials science; thermal engineering; radiochemistry; electronics; pulse
electrical engineering and automated control systems, must be solved on the