Strike point control for the National Spherical Torus Experiment

This paper presents the first control algorithm for the innerand outer-strike point position for a Spherical Torus (ST) fusion experiment and the performance analysis of the controller. A liquid lithium divertor (LLD) will be installed on NSTX which is believed to provide better pumping than lithium coatings on carbon PFCs. The shape of the plasma dictates the pumping rate of the lithium by channelling the plasma to LLD, where the strike point location is the most important shape parameter. Simulations show that the density reduction depends on the proximity of the strike point to LLD. Experiments were performed to study the dynamics of the strike point, design a new controller to change the location of the strike point to the desired location and stabilize it. The most effective poloidal field (PF) coils in changing innerand outer-strike points were identified using equilibrium code. The PF coil inputs were changed in a step fashion between various set points and the step response of the strike point position was obtained. From the analysis of the step responses, proportional–integral–derivative controllers for the strike points were obtained and the controller was tuned experimentally for better performance. The strike controller was extended to include the outer-strike point on the inner plate to accommodate the desired low outer-strike points for the experiment with the aim of achieving ‘snowflake’ divertor configuration in NSTX. (Some figures in this article are in colour only in the electronic version) 1. NSTX strike point control for LLD 1.1. LLD installation at NSTX In order to improve the performance of the confined plasma and to better control the core plasma density, the National Spherical Torus Experiment (NSTX,R = 0.85 m, a < 0.67 m, R/a > 1.27) [1] has been investigating the use of lithium as a surface coating material. To reach this aim, NSTX has been installed with an evaporative lithium system (LiThium EvaporatoR or LiTER) to coat the graphite tiles that cover the inner walls [2]. This led to 50% reductions in L-mode density and 15% reductions in H-mode [3]. The introduction of a second evaporator in 2008 improved energy confinement times (τE > 100 ms) and pulse lengths (1.8 s), and reduced edge localized mode activity [4]. Currently, the liquid lithium divertor (LLD) is being installed at NSTX in order to overcome the continuous increase in the core density during the shots. LLD is a thick, toroidally continuous liquid lithium surface, which will absorb a significant particle flux (see figure 1). The LLD is a joint collaboration between Sandia National Laboratory, University of California at San Diego and the NSTX project. 1.2. Importance of strike point control for NSTX operation with LLD The particles that hit the NSTX wall dominantly follow the last closed flux surface and thus land near the outer-strike point, the location on the wall that has the same magnetic flux as the last closed flux surface. Employing the multi-fluid code UEDGE edge numerical plasma transport simulation code, Stotler et al [5] studied the effect of the reduced recycling that is provided by the LLD module. Their results show that density reduction depends on the proximity of the outer-strike point to LLD. In addition, the strike point must avoid hitting the coaxial helicity injection (CHI) gap [6], since this may induce a disruption of the plasma. Finally, it is important to control the gap between the strike point and LLD since the heat flux is very highly concentrated near the strike point, and this heat may be damaging to the LLD structure. Thus, in order to obtain better and more consistent density reduction and to avoid contact with the LLD and the CHI gap, the strike point position is of critical importance. With this motivation, we started the development and implementation of the strike point control algorithm. 0029-5515/10/105010+08$30.00 1 © 2010 IAEA, Vienna Printed in the UK & the USA Nucl. Fusion 50 (2010) 105010 E. Kolemen et al Figure 1. Illustration of the LLD in the NSTX. 2. Preliminary studies of strike point dynamics 2.1. Analysis of the strike point motion via ISOLVER To gain insight into strike point control, we carried out preliminary studies using ISOLVER. ISOLVER is a predictive free-boundary auto-convergent axisymmetric equilibrium solver developed by Huang and Menard [7]. This software takes the normalized pressure, current profiles and boundary shape as input, after which it matches a specified plasma current and β and computes coil currents as its output. Alternatively, the coil currents can be specified as the input and the boundary shape as output. First, we tried to determine which poloidal field (PF) coil(s) should be used for outer-strike point control. Currently at NSTX, PF3L is used for vertical stability control. This leaves PF1AL, PF1BL and PF2L as the available control inputs. ISOLVER simulations showed that, due to its proximity to the desired radial outer-strike point location, rst-o, PF2L is two to three times more effective than the alternative coils. Thus, PF2L was chosen as the sole controller for the outerstrike point. We then started to analyse the single input single output model (SISO) from PF2L current to the outer-strike point position. 2.2. First-order-plus-dead-time (FOPDT) model for SISO Analysing the effect of PF2L on the outer-strike point location, we gained two important insights. First, ISOLVER analysis showed that the input/output system is linear in the region of interest as shown in figure 2 and roughly a 1 kA change in PF2L current leads to a change of 5 cm in radial outer-strike point location. Thus, it is reasonable to model its dynamics as a linear ordinary differential equation of which the first-order form is the simplest one to adopt. Second, there are delays from the request of control input to action in the system. Most importantly, the real time EFIT (EFITRT) [8] calculations take a few milliseconds. In order to control the strike point, we must first calculate its location, 2 2.5 3 3.5 4 4.5 5 5.5 64 66 68 70 72 74 76 78 80 82 84 PF2L Current [kA] R sp [c m ] ISOLVER Simulation Linear Fit: R sp =5.4*I+54 Figure 2. Relationship between the radial strike point position and the PF2L current. which means that we must wait until the data from EFITRT are available. We concluded that, for the purpose of control design, the simplest model for the SISO dynamics (PF2L current to Strike Point change) is a FOPDT model, which would be representative of the real system dynamics. In the time domain, the FOPDT is written as ẏ(t) = − + Ku(t − L) T (1) or, in the more commonly used form in the Laplace domain, the transfer function, G, from the control, u, to output, y, is G(s) = y(s) u(s) = K 1 + sT e−sL. (2) FOPDT is defined in terms of three parameters: the static gain K , the time constant T and the dead time L. This is the most commonly used process model in proportional–integral– derivative (PID) controller tuning. 3. System identification experiment In order to control a system of interest, we must first identify the internal dynamics of that system. This process is called system identification. In our case this entailed estimating the parameters K , T and L of the FOPDT model. We designed an experiment to find these parameters from the process reaction curve (PRC), which is the open-loop output response of a process to a step change in the input (see [9] and references therein). This commonly used system identification method is based on the time domain response of the system. The step response of the FOPDT model given in equation (2) is y(t) = K (1 − e−(t−L)/T )) u; t > L = 0; t L. (3) In the system identification experiment, we introduced perturbations in the PF2L requests and measured the strike point response. From the experimentally obtained PRC, the three parameters are found by curve fitting.