On the timescales of controlled termination of tokamak plasmas

Abstract

The RAPTOR code is used to model how the time required for controlled termination of Ohmic plasmas scales from present tokamaks like TCV and JET, to reactor-grade tokamaks like ITER and DEMO. We show that ramping the plasma current $I_p$ down to 20% of the flat-top value over a time $Δt_{ramp-down}=τ_{LR}=L_i/R$, with internal inductance $L_i$ and resistance $R$ evaluated at flat-top conditions, results in an approximately self-similar peaking of the current density for these four tokamaks, indicating the adequacy of $τ_{LR}$ as a relevant timescale for cross-machine comparison, yielding $τ_{LR} =$ 0.033s (TCV), 2.87s (JET), 63.2s (ITER) and 166.9s (DEMO). Note that $τ_{LR}$ is easy to evaluate, both in systems codes and on a real-time control system. For the simulated ramp-downs with $Δt_{ramp-down}=τ_{LR}$, the end-of-ramp-down normalized internal inductance $\ell_{i3}$ is limited below 2. An $I_p$ ramp-down faster than $τ_{LR}=L_i/R$ requires a reversal of the boundary loop voltage and leads to the formation of a broad plasma layer carrying current in the direction opposite to the total plasma current, concomitant with $\ell_{i3}>2$, a central region with low magnetic shear and strongly peaked pressure profiles. Significant reduction of plasma volume and elongation, as foreseen for ITER and DEMO, is shown to counteract the reversal of current density and the $\ell_{i3}$ increase, while easing vertical stability control, potentially enabling faster $I_p$ ramp-down scenarios. Experimental and theoretical studies should be performed to test the feasibility of such fast termination scenarios, notably with respect to vertical position control, shape control and (resistive) beta limits. A simple analytical model is proposed and applied to estimate $τ_{LR}$ based on 0D engineering parameters for different tokamaks and for different operating points.

Figures (11)

• Figure 1: LCFS evolution TCV, JET, ITER, DEMO
• Figure 2: TCV (top) and JET (bottom) RAPTOR ramp-down simulations over $\Delta t_{ramp-down}=\tau_{LR}$ and $\Delta t_{ramp-down}=0.6\tau_{LR}$, for constant and varying $\kappa$. (a) $I_p$ [MA]; (b) $\kappa$; (c) $\ell_{i3}$; (d) $q_{95}$; (e) $I_{p,rev}/I_p$, with integrated reverse current $I_{p,rev}$; (f) $\min(j_{par})$ [MA/m$^2$]; (g) H-factor $H_{98y,2}$, Greenwald fraction $f_{Gw}$; (h) pressure peaking factor $p_0/\langle p\rangle$; (i) on-axis to boundary loop voltage difference $U_{l,0}-U_{l,b}$ [V]; (j) boundary loop voltage $U_{l,b}$; volume-averaged $\langle T_e \rangle$; (k) $\beta_N$.
• Figure 3: ITER (top) and DEMO (bottom) RAPTOR ramp-down simulations over $\Delta t_{ramp-down}=\tau_{LR}$ and $\Delta t_{ramp-down}=0.6\tau_{LR}$, for constant and varying $\kappa$. (a) $I_p$ [MA]; (b) $\kappa$; (c) $\ell_{i3}$; (d) $q_{95}$; (e) $I_{p,rev}/I_p$, with integrated reverse current $I_{p,rev}$; (f) $\min(j_{par})$ [MA/m$^2$]; (g) H-factor $H_{98y,2}$, Greenwald fraction $f_{Gw}$; (h) pressure peaking factor $p_0/\langle p\rangle$; (i) on-axis to boundary loop voltage difference $U_{l,0}-U_{l,b}$ [V]; (j) boundary loop voltage $U_{l,b}$; volume-averaged $\langle T_e \rangle$; (k) $\beta_N$.
• Figure 4: Normalized enclosed plasma current $I_{p,int}/I_p$ [MA] at the end of the RAPTOR simulation for TCV (top left), JET (top right), ITER (bottom left) and DEMO (bottom right), for ramp-down times $\Delta t_{ramp-down}=\tau_{LR}$ and $\Delta t_{ramp-down}=0.6\tau_{LR}$, for constant and varying $\kappa$.
• Figure 5: JET RAPTOR ramp-down simulations over $\Delta t_{ramp-down}=\tau_{LR}$ with varying $\kappa$, for constant and reducing on-axis toroidal magnetic field $B_0$. (a) $I_p$ [MA]; (b) $B_0$ [T]; (c) $q_{95}$; (d) $\ell_{i3}$.