Ergodic magnetic limiter for the TCABR

Closed Analytical Formulae for Multi-Pole Magnetic Rings

“…The same result is obtained from (19) by use of ∂B z /∂ψ = r∂B ψ /∂z (vanishing curl). For finite thickness (32) may be integrated…”

“…(21) is also obtained from (12) in the limit t → 0 by the relation ∂B r /∂z = ∂B z /∂r (vanishing curl). Thus B r -and B z -fields are related by (19) and (21).…”

“…The magnetic fields of these structures were expressed as rapidly converging Fourier series [17,18], series with Bessel functions [19] and in closed form [20,21]. Twodimensional confinement systems for ion sources were calculated in [22].…”

Mapping the intrinsic stochasticity of tokamak divertor configuration

“…On the assumption of an MHD ideal plasma-magnetic field equilibrium satisfying the Grad Shafranov equation [12,21], namely, where non resistive Maxwell equations apply [22], one has that, in particular, ∇ · B = 0 and therefore the usual vector potential A exists such that B = ∇ × A Then, given the metric condition B ·R/dR = B ·φ/Rdϕ = B ·Ẑ/dZ where the unitary vector ϕ = R∇ϕ, then a magnetic field line evolves along the toroidal direction as…”

“…Therefore, the inherent use of area preserving maps to model the system has turned out to be an often revealing as well as processing-time saving practice since as early as the 1950's [7,8]. Built upon them, the so called test-particle theories began exploring transference phenomena in stochastic field equilibria [9] by exploiting the vast possibilities of these discrete maps [10,11] and even modelling actual tokamak facilities [12].…”