MODELING AND ENGINEERING APPLICATIONS FOR WEAKLY TURBULENT PLASMA

35th EPS Conference on Plasma Phys. Hersonissos, 9 - 13 June 2008 ECA Vol.32D, P-1.114 (2008) MODELING AND ENGINEERING APPLICATIONS FOR WEAKLY TURBULENT PLASMA S.V. Ryzhkov Bauman Moscow State Technical University, Moscow, Russian Federation Magnetic systems like the Field Reversed Configuration (FRC) and Spheromak (S), where a plasma is immersed in a linear external magnetic field geometry, called compact tori (CT) [1]. There are four all known FRC equilibria – spherical Hill’s vortex [2], elongated Hill’s vortex/ Solov’ev model [3], Steinhauer analytical equilibrium (SAE) [4] and quasy equilibrium (racetrack). The first one is described by \psi_{HV} = - \frac{3 B_e r^2}{4} \left(1 - \frac{r^2}{r_s^2} - \frac{z^2}{l_s^2}\right), where B_e is the field at ∞, k = l_s/r_s, r_s is the separatrix radius at z=0 plane, l_s is the half length. Magnetic field flux inside the separatrix for the FRC SAE \psi_{SAE} = - \frac{B r^2}{2} \left[ 1 - \frac{r^2}{a^2} - \frac{z^2}{b^2} + \frac{1 - N}{1 + (6 + N)(\varepsilon^2 / 4) + (1 + N)(\varepsilon^4 / 4) + N(\varepsilon^6 / 32)} \right. \times \left. \left[ \frac{\varepsilon^2}{4} \left(1 + \frac{\varepsilon^2}{2}\right) - \left(1 - \frac{\varepsilon^4}{8}\right)\left(\frac{\varepsilon^2 r^2}{4 a^2} - \frac{z^2}{b^2}\right) - \left(1 + \frac{\varepsilon^2}{4}\right)\left(\frac{\varepsilon^4 r^4}{8 a^4} - \frac{3\varepsilon^2 r^2 z^2}{2 a^2 b^2} + \frac{z^4}{b^4}\right) \right] \right], where B is the nominal magnetic field, ε = r_s/l_s, N is the shape index (1 - HV and 0 - racetrack). First term is the elongated Hill's vortex, second – the correction for the equilibrium flexibility. FRCs have the prolate shape while spheromaks more often use the oblate configuration. Even for recent compact tori experiments [5 and see Table I] with modest (for controlled fusion level) parameters: length, l_s ~ 1m; radius (or separatrix), r_s ~ 0.4 m; average beta, <β> ~ 20 – 90 %; energy confinement time, τ_E ~ 1 ms; ion temperature T_i ~ 3 keV; electron temperature, T_e ~ 0.5 keV; external magnetic field B_e ~ 3T and electron density n_e ~ 10^21 m^-3, the prolate form prevail over oblate. Last experiments have shown the weak turbulence in both plasma core and edge. CTs have charged particle transport losses which flow out the ends of the device. It is very crucial question because of plasma sustainment and getting power from high energy particles – the thermonuclear reaction products.