Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
B 2 2
φe
− B φ
≈ 2B φe
B φe
− B φ
= 2B φeδΦ
πa p
2
14.9
where
δΦ = πa p 2 B φe
− B φ
14.10
is the diamagnetic flux of the longitudinal (toroidal) field. We will discus its measurement later;
it is the difference in toroidal flux in the plasma column when the plasma is initiated. Defining
β I
= 8π
µ 0
I p
2
pdS φ
S φ
∫
i.e. β I
= 2µ 0
p
2
for a circular cross section 14.11
B
θa
with B θa
= µ 0 I p
2πa p
the poloidal field at the plasma edge, we can write
β I
= 1+ 8πB φeδΦ
µ 0 2 I p
2
14.12
From this equation we write the net flux difference δΦ = (µ 0 I p ) 2 /(8πB φe ).(β I - 1) as the sum of
the paramagnetic flux δΦ p :
δΦ p
= − µ 2 2
0
I p
14.13
8πB φe
due to the poloidal component of the force free plasma current, and the diamagnetic flux δΦ d :
δΦ d
= −δΦ p
β I
14.14
due to the poloidal currents providing pressure balance for the finite pressure.
Toroidal, non circular geometry
In a torus curvature must be accounted for: Corrections with coefficients (a/R) appear in the RHS
of the equation for β I . For β I