Page 42 - Fundamentals of Magnetic Thermonuclear Reactor Design

24 Fundamentals of Magnetic Thermonuclear Reactor Design

2
2
2
∆Ψcs≍2πRcs ⋅Bcs. ∆Ψ cs ≈π R ⋅ B . (2.4)
cs
cs
For instance, in ITER, a solenoid average radius of 1.7 m and an external
radius of 2.05 m are required to ensure a magnetic flux of ∼240 Wb.
With the magnetic fields being so strong, the requirements on their quality
−4
are high; the error fields (B ) must be very small (B /B < 10 ). In addition,
tc
err
err
magnetic field variations associated with the TF non-uniformity caused by the
discrete nature of the electromagnetic coil system (a corrugation) must be within
∼1%. These issues may be resolved by the removal of the TF coil outside from
the plasma external boundary or (and) using ferromagnetic inserts. The neces-
sary major radius of external TF leg, R TFe , may be estimated using the Eq. (2.3)
 R TFe   N TF ≈ Nq A, (2.5)

a
RTFeR+aNTF≍NTFq95A,  R +  TF 95
where N is the number of TF coils. The corresponding level of magnetic rip-
TF
−1
ples at the plasma boundary is (N q A) .
TF
The superconducting TF coil thickness ∆ can be estimated as
TF
∆TF≍0.002BtcBt0R[m,T]. ∆ TF ≈ 0.002 BB Rm[, T].
tc
0 t
The torus loop voltage amplitude should be 10–15 V for a plasma break-
down, inductive current rise and maintenance.
2.5.2 In-Chamber Conditions: Breakdown
High-vacuum conditions in the chamber must be provided prior to a discharge.
Then, a working gas is fed into the chamber until the pressure (p) is 1–10 mPa.
In ITER it is around 1 mPa. An electrical breakdown is driven by a vortex elec-
tric field, generally combined with gas heating using electron cyclotron reso-
nance in the UHF range. For a breakdown to occur, the following condition
must be met:

αLeff>1, α L eff >1, (2.6)
where α ≈ A p exp(−Bp/E) is the first Townsend coefficient (for hydrogen iso-
−1
−1
−1
−1
topes A ≈ 3.83 m ·Pa ; B ≈ 93.8 V·m ·Pa ); L is the effective length
eff
of magnetic field lines inside vacuum chamber (connection length) (Fig. 2.12).
The ITER design uses the following approximation [10]:
B
L eff ≈ 0.25 ⋅ ⋅ t , (2.7)
a
Leff≍0.25⋅a⋅BtBstr, B str
where a is the minor radius of the breakdown area, B is the toroidal magnetic
t
field, and B is the amplitude of poloidal stray fields in the breakdown area.
str
Recent 2D and 3D simulations of connection length for the ITER breakdown
case [20] demonstrated that L can be about 2–3 times larger than Eq. (2.7).
eff