A small spherical 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 = 0.85\,\mathrm{m}

, minor radius

a = 0.65\,\mathrm{m}

, toroidal field

B_0 = 0.55\,\mathrm{T}

, deuterium ions (

m_i = 2m_p

) and electrons with

T_e = T_i = 1.0\,\mathrm{keV}

, density

n_i = n_e = 5.0\times10^{19}\,\mathrm{m^{-3}}

, and outboard pressure scale length

L_p = 0.20\,\mathrm{m}

. Treat the outboard midplane as having curvature radius

R_c = R_0

and treat it as unshielded (no good-curvature averaging, no shear). ((a)) Using the curvature-drift mechanism (an outward effective gravity for particles on curved field lines, as in the drift picture of gravitational and curvature drifts), estimate the interchange growth rate

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

at this outboard midplane and its e-folding time. ((b)) At the

q = 2

surface the resistivity is

\eta = 2.0\times10^{-8}\,\Omega\,\mathrm{m}

. Using

B_0

a

and

n_i,m_i

above to form the Alfven speed and Alfven time, and taking 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}

, taking

\Delta'a

of order unity.

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