A circular tokamak has major radius

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Fusion plasmas

Plasma Physics, Ch Whether it stays held: the energy principle, interchange, kink and tearing

Problem

R_0 = 1.65\,\mathrm m

, minor radius

a = 0.65\,\mathrm m

and toroidal field

B_\varphi = 2.5\,\mathrm T

at the plasma edge. Using

2\pi/\mu_0 = 5.0\times10^6

in SI units, the plasma current relates to the edge safety factor

q_a

I_p[\mathrm{MA}] = \frac{5a^2B_\varphi}{R_0q_a}.

((a)) Find the Kruskal-Shafranov current ceiling, at

q_a = 1

. ((b)) Find the current allowed by the practical operating limit

q_a = 2

. ((c)) Operating at

q_a = 2

with the current found in (b), use Troyon's empirical limit

\beta_t[\%] \le \beta_NI_p[\mathrm{MA}]/(a[\mathrm m]B_0[\mathrm T])

with

\beta_N = 2.8

and

B_0 = B_\varphi

to find the maximum toroidal beta.