A large 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 = 2.9\,\mathrm{m}

, minor radius

a = 0.90\,\mathrm{m}

, toroidal field

B_0 = 3.4\,\mathrm{T}

, deuterium ions (

m_i = 2m_p

) with

T_i = T_e = 3.0\,\mathrm{keV}

, density

n_i = n_e = 3.0\times10^{19}\,\mathrm{m^{-3}}

, and outboard pressure scale length

L_p = 0.50\,\mathrm{m}

. ((a)) Take the outboard midplane as unshielded, with curvature radius

R_c = R_0

. Using the curvature-drift picture (curvature acting as an effective outward gravity), estimate the interchange growth rate

\gamma \approx \left(T_i/m_iR_cL_p\right)^{1/2}

and its e-folding time. ((b)) The resistivity at the

q = 2

surface is

\eta = 5.0\times10^{-9}\,\Omega\,\mathrm{m}

. Form the Alfven speed and Alfven time from

B_0

a

and

n_i,m_i

, take the resistive diffusion time over the minor radius

a

, compute the Lundquist number

S

, and estimate the tearing growth time from

\gamma\tau_A \sim S^{-3/5}

with

\Delta'a

of order unity.