1 EXS/P6-37

Plasma Control Studies Using DIII-D Design Tools in Support of ITER

D.A. Humphreys1, N.W. Eidietis1, J.R. Ferron1, G.L. Jackson1, M.J. Lanctot1, M.L. Walker1, A.S. Welander1; G. Raupp2, W. Treutterer2; P. de Vries3, J. Snipes3, A. Winter3

1General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA 2Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching, Germany 3ITER Organization, Route de Vinon sur Verdon, 13067 St Paul lez Durance, France Abstract Control analysis and design tools developed at DIII-D [1] have been applied to ITER in studies supporting design of the ITER Plasma Control System (PCS) [2] to prepare for the upcoming PCS Preliminary Design Review (PDR). These studies include assessment of an extremum-seeking approach to real-time error field correction, advances in vertical controllability metrics, simulation of plasma initiation, and development of an integrated algorithmic approach to exception handling toward disruption-free operation of ITER. Integrated simulations have demonstrated the robustness and mutual compatibility of key control algorithms, as well as the potential of critical exception handling algorithms for limiting the disruption frequency in ITER. The present studies follow the ITER PCS Preliminary Design focus on control requirements for the First Plasma and Pre-Fusion Plasma Operations (H/He species) operating phases of ITER. Selected control scenarios are studied in several phases of the plasma discharge, including plasma startup, rampup, rampdown, and asynchronous response to off-normal or fault conditions. These studies confirm the existence and consistency of control solutions with both device resources and PCS architecture. 1. Introduction The ITER Plasma Control System (PCS) is presently under design in preparation for ITER operations. The present Preliminary Design [3] phase in this process focuses on analysis of control scenarios it must produce, along with the algorithms and supporting functions that must be executed in real time to accomplish the scenarios. Algorithms can be applied to either continuous control functions (which are executed during normal operation), or exception handling functions (which are executed when an off-normal event, or “exception,” occurs). Extensive analyses of these aspects of the ITER PCS have been performed by an international team consisting of members of the ITER Organization, the Culham Centre for Fusion Energy (CCFE), the Consortio di Ricerca per l'Energia e le Applicazioni Tecnologiche dell'Elettromagnetismo (CREATE), the Commisariat à l’Energie Atomique (CEA), General Atomics (GA), and the Max-Planck-Institut für Plasmaphysik (IPP, which leads the team). The present work focuses on the application of GA design and analysis tools [1] in use at the DIII-D National Fusion Facility to selected ITER control scenarios in this project.

2. ITER Plasma Control System Preliminary Design Context The Preliminary Design of the ITER PCS focuses on the requirements of First Plasma (FP) and Pre-Fusion Plasma Operations (PFPO). Goals for control scenario analysis in the PCS Preliminary Design include demonstration of consistency of resources and control requirements, existence proofs for key control needs, identification of implications for the PCS architecture design, quantification of control performance and dynamics, and identification of gaps between design needs and resources provided by the balance of the ITER plant. Application of DIII-D design tools primarily focused on developing candidate control schemes and algorithms for key discharge phases including plasma initiation, current rampup, rampdown, and rapid plasma termination. Responses to MHD were studied using vertical instability as a model for a variety of potentially disruptive modes (e.g. resistive wall modes, tearing modes, radiative instabilities, as well as the axisymmetric mode itself). In addition to such specific control algorithms, the ITER PCS will supply a set of “support

2 EXS/P6-37

functions” known to be critical to enable various control loops to operate effectively, and identified as useful to many stakeholders elsewhere in the ITER operational plant. DIII-D design tools have also been applied to the study and design of some of these support functions, including real-time equilibrium reconstruction and real-time error field correction (EFC).

3. DIII-D and ITER Control Design Tools The GA Tokamak System Design Toolbox (TokSys) [1] is a machine and control design environment implemented in Matlab/Simulink® [4], developed for use at DIII-D and now applied to many devices worldwide, including those that share the DIII-D Plasma Control System [5]. The environment includes specialized infrastructure for defining device geometry and electromagnetic characteristics, including magnetic diagnostics common to most tokamaks. Models of important conductors are represented, including axisymmetric poloidal field (PF) coils and nonaxisymmetric coils for error field correction or edge localized mode (ELM) suppression, vacuum vessel elements, and other conducting structure. A variety of plasma models are available in standardized forms, including the axisymmetric nonrigid ideal or resistive plasma response, resistive current profile evolution, and 0D particle and energy confinement for density and stored energy control. Nonaxisymmetric plasma response models provided include tearing modes (Modified Rutherford Equation) and resistive wall modes (RWM). Actuator models are provided corresponding to all of these plasma responses, including coil power supplies, fueling gas valve sources, impurity injection sources, neutral beams and ECH/ECCD sources for heating and current drive, and launcher control models for ECH beam direction. TokSys also includes an array of control design tools, specialized for regulation or stabilization algorithms in tokamaks. One important class of such tools are the simulations that make use of the fundamental TokSys models and modules, including nonlinear, resistive axisymmetric evolution codes (gsevolve) and axisymmetric plasma response models based on the linearly-perturbed plasma equilibrium response (gspert). The TokSys simulation environment has made significant contributions to the ITER Plasma Control System Simulation Platform (PCSSP), a highly flexible simulation framework under development by an international team including the ITER Organization, CREATE, IPP, and GA [6]. PCSSP is intended to support ongoing development of the ITER PCS by testing candidate architectural and algorithmic solutions.

4. Control Scenario Studies 4.1. Plasma Startup

A TokSys kinetic initiation module has been developed, adapted for ITER application, and integrated with plasma evolution modules to enable simulation and study of plasma breakdown/burnthrough control. The physics model implemented in the module represents the initial breakdown/avalanche process as well as burnthrough of fuel and specified impurities in the presence of applied ECH, with self-consistent evolution of electron and ion densities and temperatures, as well as Zeff [7, 8]. Fuel gas and impurity densities are accounted for and require initial specification for reliable simulation. Although in the presence of sufficient EC power the breakdown success itself is not particularly sensitive to these gas properties, the result of the burnthrough process is quite sensitive. Final temperature and plasma density following burnthrough in particular are very sensitive to initial gas conditions (and thus wall conditions and recycling). Simulations of control during ITER breakdown and burnthrough show successful initiation with sufficient electric field and reasonable ranges of neutral prefill densities, ECH assist powers, and varying rates of change of the plasma volume.

3 EXS/P6-37

Fig. 1. illustrates two such initiation simulations, in which burnthrough fails or succeeds (in deuterium in these studies) even with applied ECH assist power of 2 MW, depending on the applied electric field. The maximum available field of 0.3 V/m is successful, while 0.1 V/m fails to burn through under these conditions. Initial neutral prefill densities in the range of 1-10 µtorr (10-3 – 10-2 Pa) and 2-4 MW of ECH power are expected to provide an efficient starting point for initiation in ITER First Plasma. 4.2 Rampup An important challenge for the rampup phase in ITER is to monitor and maintain distance from ideal MHD stability boundaries as the profile evolves to reduce the probability and frequency of disruptions. In actual operation ITER will use a detailed algorithm such as DCON [9] configured to run in realtime. For the PCS Preliminary Design, a candidate approach and an analytic proxy for full realtime ideal stability calculation has been identified. Analytic expressions are useful for control-level demonstration and study of functional stability regulation loops. We follow the approach of Turnbull [10], who represented the ideal MHD stable space in terms of q(a) and q0 and applies the analysis to DIII-D experiments for validation. The stability boundaries correspond well to the onset of disruption (both minor and major) ascribed to resistive or ideal kinks, or resistive interchange modes in DIII-D discharges.

An analytic representation approximating the kink stability boundary described in [10] is given by the function:

€

qa ≈1q020 − 0.5 + 2q0 + 0.2sin 4π q0 − 0.5[ ]( ), (Eq. 4.2-1)

the function describes a contour in qa vs q0 space (solid line in Fig. 2), representing two quantities that are reasonably reconstructable if sufficient internal current profile measurements are made, particularly near the magnetic axis. The key plasma parameters envisioned to be regulated to manage proximity to MHD boundaries are the internal inductance and plasma current. Together, control of these parameters allows regulation of the edge safety factor (qa) itself, and the ratio of the edge safety factor to axis safety factor (q0),

m3

m3

200

400

600

Failed burnthru: 2 MW, 0.1 V/m Successful burnthru: 2 MW, 0.3 V/mPlasmaVolume

PlasmaVolume

Te, Ti Te, Ti

Ip Ip

(Varies, not fixed)

(Rolls over, not sustained) (Sustained, rising...)

eV

0

40

80

MA

eV

MA

0.0

0.2

0.4

200

400

600

0

100

200

Time (s)

00 1 2 3 4 5 6

Time (s)0 1 2 3 4 5 6

2

4

FIG. 1. Illustration of breakdown and burnthrough variability for two scenarios

4 EXS/P6-37

which can be related to the internal inductance [11]. Although the central q is difficult to control, the internal inductance can be regulated by varying the loop voltage, and thus the dIp/dt. During rampup, dIp/dt control can be constrained to minimize a weighted sum of squared plasma current and internal inductance errors to achieve an acceptable balance of both goals [12], or to minimize a single metric quantifying the target distance from the stability boundary. Fig. 2a. shows the trajectory in (qa, q0) space during rampup from a DIII-D discharge (#167062), which began stable (although the initial point falls to the right in the “unstable” region, it rapidly enters the stable space), but transitioned into the low-q0 unstable space and experienced a major disruption due to a large internal kink. By contrast, following sufficient cleaning of the machine in normal startup operations, Fig. 2b. shows a rampup (shot #167134) which remains stable throughout the rampup process (and indeed the entire discharge). Good distance is maintained from the stability boundary throughout.

4.3 Rampdown Simulations have been done to analyze survivability of ITER rampdown scenarios due to VDE onset as a function of current rampdown rate, starting at 15 MA with an electron temperature of 10 keV and dropping to 5 keV at half current (see [13] for similar DINA scenarios). An initially challenging internal inductance of 1.0 is used for maximum challenge to the vertical control system, and consistent with an initial 10 keV temperature. In each case, the elongation is reduced from full aperture of 1.85 to 1.55 as the current is dropped, keeping q95 above 3.5. Below kappa of 1.55 at low current the X-point configuration can be compromised. If the requirement of maintaining the divertor during rampdown is relaxed, the plasma can be limited at much lower elongation with much higher controllability robustness.

FIG. 2. Illustration of DIII-D discharge rampup trajectories and ideal MHD stability space. Solid line shows stability boundary from [Turnbull 2005], with stable region above the line. a) (#167062 ) Rampup is terminated by major disruption approximately half way up the ramp. b) (#167134) Discharge remains stable throughout the rampup. Green circle indicates first time point of trajectory, and red X indicates last time point (major disruption in #167062, end of ramp in #167134). Each point corresponds to a realtime equilibrium reconstruction slice, whose data are used for the calculation.

0 1 2 3 4 5 60

1

2

3

4

5

6

167134 q95 vs q0

q95

q00 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

7

8

167062 q95 vs q0

q95

q0

Unstable

Stable Stable

Unstable

(a) (b)

qa qa

q0 q0

5 EXS/P6-37

A nominal rampdown in ITER requires > 80 sec for these conditions, which has been demonstrated experimentally to be robust to VDE below a final current level of 1.4 MA [13, 14, 15]. The results of a study of survivable rampdown rates over many cases are shown in Figure 3. These cases represent thermal plasmas that experience a sudden drop in current, modeling conversion to runaway current (Ire) with varying amplitude (y-axis). The runaway beam is modeled as a thermal plasma whose resistivity is varied to produce different decay rates (x-axis). The results therefore reflect the maximum controllable rampdown of a thermal current or runaway beam (if its profile were to evolve like a decaying thermal current). The elongation is dropped as fast as possible to 1.55 during the current decay to help increase controllability. In Figure 3, blue circles indicate controllable cases, while red X’s indicate VDE’s. The dashed line provides a notional indication of the controllability boundary. The figure shows that starting at 15 MA, a maximum (average) rampdown rate of ~ 1 MA/s is survivable, although with unreliable margins. Note that this result neglects constraints on deliverable grid power, identified in recent studies as potentially reducing the achievable ramp rate to somewhat below this value [16].

5. Algorithms and Exception Handling 5.1 Realtime Error Field Correction A real-time extremum seeking error field correction scheme tested on DIII-D [17] has been applied to ITER simulations to automatically determine the optimal correction field phase and amplitude. Even though the early non-neutronic, low current operating phase is expected to tolerate higher disruptivity than the high performance (D-D, D-T) phases, error field correction is still expected to be important in essentially all phases of operation, both to avoid locked modes and to prepare for the later phases of ITER operation. By oscillating fields from in-vessel RMP coils and maximizing plasma toroidal rotation (Fig. 4.), the end point of the search (green dot) occurs close to the actual optimal correction (red square).

5.2 Vertical Stability Controllability and Exception Handling Loss of vertical control resulting in an unrecoverable VDE is a critical event that must be largely prevented in ITER (most critically at higher current levels, and particularly in higher internal inductance regimes). Continuous control, robust to expected noise and disturbances, as well as an effective prediction, detection, and response system in the Exception Handler, must be implemented to accomplish this.

FIG. 3. Scoping study of controllable rampdown rates for thermal plasmas (Ire=0), or runaway electron plasmas (following a drop in initial current resulting in conversion to RE).

6 EXS/P6-37

Vertical control provides a general example of the set of functions and general exceptions that are common to many kinds of instabilities that will be actively stabilized in ITER. Reference commands and measurement signals are provided to the control loop. A continuous controller provides stabilizing commands to power supplies, while, in parallel, a separate controller regulates the proximity to the controllability boundary through equilibrium modification (elongation, betap, internal inductance, profile characteristics, proximity to conducting walls, etc…). This process maintains sufficient distance from such boundaries to provide robustness to disturbances, uncertainties, and faults (see also [18]). A Faster than Real Time Simulation functions in parallel to provide projection ahead and enable responses to predicted exceptions. The control supervisor that manages continuous control and exception handling can be implemented as multiple connected finite state machines (FSM; Fig. 5). In Figure 5, the state transitions of the form “DZ>C” correspond to rules related to ΔZMAX of the form

where ΔZMAX(γZ, VPS, …) denotes the controllable displacement capability of the system, while ΔZMAX|Req’d represents the controllable displacement required at a given time. represents the RMS amplitude of perturbations (noise, disturbances) to the vertical position. Note that studies suggest initially CNOM may correspond to ΔZMAX/a~9%, CWARN to ΔZMAX/a~5-7%, and CALARM to ΔZMAX/a~4% [19].

ΔZMAX γZ ,VPS,...( )Z

PERT

>ΔZMAXZ

Req 'd

≡CNOM

Re Current (kA−t)

Im C

urre

nt (k

A−t

)

−2 0 2 4 6−2

−1

0

1

2

3

4

5

6

7

95

100

105

110

115

120

125

0

50

100

0

5

Re Current (kA)

0 50 100 150 200 250 300

0

5

10

Simulation Time (s)

Im Current (kA)

LToroidal angularmomentum L (kg m2/s)

max

L Lmax

optimal setpoint

start

end

Toro

idal

ang

ular

mom

entu

m (k

g m

2 /s)

FIG. 4. Simulation of real-time error field correction in ITER. The algorithm converges to optimum real and imaginary components of RMP coil currents in less than 200 sec, assuming momentum confinement time of 3.7 sec and NBI torque of 35 N-m

7 EXS/P6-37

As a rapidly calculable proxy for the controllability ΔZMAX, an analytic approximation to the stability margin in ITER has been derived for use in control simulations, and is given by

This approximation makes use of an analytic scaling with internal inductance li, elongation κ, and poloidal beta βP [20], with coefficients resulting from a best fit to behavior perturbed around the 15 MA ITER baseline shape and gaps. A stability margin of ~0.14 has been estimated in previous studies to correspond to loss of vertical control, and ~0.16 to an estimate of an effective CALARM value in ITER [19]. Simulations of exception handling during rampdown have been done to study integrated effects in preventing or mitigating a loss of vertical control (vertical displacement event, VDE), and preparing for mitigating a major disruption (MD) using the Disruption Mitigation System (DMS). Fig. 6 shows the rampdown scenario, producing a rapidly rising internal inductance, li, and rapidly falling stability margin with increasing risk of VDE onset. The stability margin mS calculated in simulated realtime from the measured equilibrium values (blue curve in Fig. 6d) is filtered (black dashed curve), and this smoother value is used to determine the trigger condition. Crossing the CALARM value of mS = 0.16 in this filtered signal sends the trigger to the DMS to inject a large quantity of Ar (the primary DMS actuator is presently considered to be Shattered Pellet Injection, or SPI). After a delay of 40 ms accounting for communication from PCS to Central Interlock System (which triggers the DMS), valve response, ballistic delay times, and thermal quench onset, this produces a current quench with a specified quench time of 80 ms (not self-consistently determined). In the absence of runaway electron generation, the current quench would produce the dashed red curve in Fig. 6a. However, a runaway beam conversion of 70% (of the current at the start of the current quench) is specified in the scenario. The dashed green curve shows an undamped RE current at this amplitude. However, in the simulated DMS scenario (dashed cyan curve) a second signal is sent to the DMS to trigger additional impurity injection. After a delay of 15 ms accounting for firing response and ballistic delay time, the RE beam damps with a (specified, not self-consistently determined) time constant of 20 s. Starting at

mS ≈1.47

κ −1.13( )1+ e−2ℓi+1( )

2−1

⎡

⎣⎢⎢

⎤

⎦⎥⎥1+ 0.60 βP − 0.1( ){ }

TerminationState(s)...

VSCNominal

RegulationVS Controllability Control

VSCPredicted Warning

State

VSCWarning

State

VSCAlarmState

VSCAlternate Operating Scenario

DZpred < Cwarn

DZ < Cwarn

DZ > Cnom

DZ > Cnom

DZ > Cnom

DZ < Cwarn

DZ < Calarm

Calarm < DZ < Cwarn

VDE: Zout_of_range

dZdt_out_of_range

DZ < Cwarn

VSC Nominal Regulation- Regulate dZmax- Balance w/ shape goals

VSC Predicted Warning- Pred > 4 sec warning- Project filtered d(dZmax)/dt- Change weighting of shape goals- Incr. weight dropping kappa, li, ...

Informationto other FSM's

VSC Warning- Warn > 2 sec before alarm- Override shape/profile goals- Drop kappa, drop li, ...- Move plasma to incr. coupling

VSC Alarm- Warn > 2 sec before VDE- Override most(?) system goals- Prep for possible VDE...- Repurpose VS1,2,3; RMP; gyrotrons, beams, ...

FIG. 5. Vertical stability control finite state machine, with descriptions of responses in each state.

8 EXS/P6-37

this current level, the final runaway beam is vertically controllable for this slow damping rate.

6. Conclusions

Control scenario studies are an integral part of the ITER PCS Preliminary Design effort. Such studies demonstrate candidate solutions for ITER control algorithms, inform the architectural design, and confirm consistency between resources provided by the ITER plant and requirements for adequate control performance. Control design and simulation tools in the GA TokSys Toolbox have been extensively applied to the PCS Preliminary Design. Simulations of plasma startup scenarios have quantified sensitivities in successful initiation. An analytic expression has been derived to quantify a representation of the ideal MHD stability boundary and enable regulation of stability in rampup control scenarios. Plasma current rampdown rates that enable stable vertical control have been quantified, and a general approach to exception handling has been designed and applied to simulation of a DMS triggering scenario.

This work was supported by the Max-Planck-Institut für Plasmaphysik under contract IPP-PCS-20140627, and under ITER Framework Contract ITER CT 14/6000000148. Disclaimer: The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

References[1] Humphreys, D.A., et al, Nucl. Fusion 47 (2007) 943 [2] Snipes, J.A., et al, Fus. Eng. and Design 89 (2014) 507 [3] Snipes, J.A., et al, this conference, EXS/P6-36 [4] http://www.mathworks.com [5] Penaflor, B.G., et al, Fus. Eng. and Design 83 (2008) 176 [6] Walker, M.L., et al, Fus. Eng. and Design 89 (2014) 518 [7] Lloyd, B., et al, Nucl. Fus. 31 (1991) 2031 [8] Kim, H.T., et al, Plasma&Phys.&&&Control.&Fus.,&55&(2013)&124032 [9] Glasser, A., et al, Bull. Am. Phys. Soc. 42 (1997) 1848 [10] Turnbull, A., et al, Fus. Sci. and Tech., 48 (2005) 875 [11] Wesson, J.A., “Tokamaks”, Oxford Univ. Press, Oxford, UK (1987)

[12] Jackson, G.L., et al, Nucl. Fusion 49 (2009) 115027 [13] Casper, T., et al, Nucl. Fus. 54 (2014) 013005 [14] Politzer, P.A., et al, Nucl. Fus. 50 (2010) 035011 [15] de Vries, P., et al, this conference, EXS/P6-41 [16] Gribov, Y., 43rd EPS Conf. on Pl. Phys., Leuven, Belgium, 2016, P4.066 [17] Lanctot, M.J., et al, Nucl. Fus. 56 (2016) 076003 [18] Humphreys, D.A., et al, Phys. Plasmas 22 (2015) 021806 [19] Humphreys, D.A., et al, Nucl. Fusion 49 (2009) 115003 [20] Ferrara, M., et al, Nucl. Fus. 48 (2008) 065002

FIG. 6. Plasma current rampdown without drop in elongation, resulting in a falling stability margin (less stable plasma). Bold Red dashed line = DMS trigger limit corresponding to CALARM=0.16. Solid red line = DMS trigger time.

(a)

(b)

(c)

(d)