Fig. 1. ADX Cutaway View

POWER SYSTEMS ANALYSIS AND DESIGN FOR ADX*

D.R. Terry, S. Wolfe, J. Doody, J. Irby, W. Cochran, B. LaBombard, W. Burke, R. Vieira Plasma Science and Fusion Center

Massachusetts Institute of Technology Cambridge, MA, USA dterry@psfc.mit.edu

Abstract— The Advanced Divertor eXperiment (ADX) [1] is a compact, high field (6.5 T with possible upgrade to 8 T), high power density tokamak being proposed to test new advanced divertor concepts at reactor-level conditions. Development and testing of advanced Lower Hybrid Current Drive (LHCD) and Ion Cyclotron Range of Frequency (ICRF) concepts including high-field-side launch capability is also an important goal for ADX [2], [3].

Where possible the design of the ADX experiment will make extensive use of existing power systems at MIT that presently support Alcator C-Mod, which includes a 225 MVA alternator/flywheel (2 GJ stored energy) and 32 MVA (peak) substation. Analysis of existing alternator/flywheel, substation, and power system supply capabilities and their application to support ADX operation up to 6.5 T will be discussed. Power system supplies, magnet voltages and currents and operating requirements based on the current point design will be presented. Potential power system upgrades that would support ADX operation at 8 T and 2 MA plasma current will also be described.

Keywords—ADX; Alcator C-Mod; power systems; tokamak

I. INTRODUCTION A proposal is being made by the MIT Plasma Science and Fusion Center (PSFC) and collaborators for a high-performance Advanced Divertor eXperiment (ADX). This tokamak will be designed to address critical gaps in the world fusion program on the path to next-step devices, including fusion nuclear science facility (FNSF), fusion pilot plant (FPP) and demonstration power plant (DEMO). ADX is a compact high field (6.5 T with possible upgrade to 8 T), high power density tokamak that will allow tests of new advanced divertor concepts at reactor-level conditions. See Fig. 1. Development and testing of advanced LHCD and ICRF concepts including high-field-side launch capability is also an important goal for ADX. The ADX experiment would, where possible, make extensive use of the existing C-Mod power systems at the MIT PSFC, including a 225MVA alternator with 75 Ton flywheel, substation with 13.8kV, 3 phase 32MVA capability, and many power supplies. Preliminary analysis of the existing alternator/flywheel, substation and power supply capabilities

on ADX at up to 6.5 T is underway and will be discussed below. Section II provides a description of the substation and alternator/flywheel system. Section III gives details on the existing C-Mod supplies being considered for use on ADX. Section IV will describe ADX TF supply requirements. Section V will present the ADX power supply and poloidal field coils analysis and Section VI will give results and comments and provide a brief discussion of ADX requirements for 8 T, 2 MA plasma current operation.

II. SUBSTATION AND ALTERNATOR/FLYWHEEL SYSTEM

A. Substation The existing 13.8 kV three phase line to the Alcator C-Mod substation is capable of providing 32MVA pulsed power for 1s and to 42MVA peak power for 100ms. Recent power system tests during upgrade of the utility company protective relays has confirmed the peak power capabilities. For the C-Mod system the line is used to directly provide power for ICRF and LHCD systems, long-pulse diagnostic neutral beam and the EF2 and EFC magnet supplies. The line also powers the 2MVA drive motor for the alternator/flywheel system.

* Work is supported by U.S. Department of Energy, Cooperative Grant No. DE-FC02-99ER54512-CMOD.

Fig. 2. 225 MVA Alternator and 75 Ton Flywheel

Fig. 3. C-Mod Supplies and Coils

Fig. 4. C-Mod Power Room

B. Alternator/Flywheel System A 225MVA, 14.4kV alternator with a 68,000 kg flywheel is

available. See Fig. 2. Together the alternator and flywheel store 2 GJ of energy to power the C-Mod OH1 coil, OH2 upper and lower coils (OH2-U, OH2-L), EF1 upper and lower coils (EF1-U, EF1-L), EF3 upper and lower coils (EF3-U, EF3-L), EF4 upper and lower coils (EF4-U, EF4-L) and TF magnet, with most of it going to the TF magnet [4][5][6][7]. The maximum energy available from the alternator/flywheel system for the pulse is limited by the maximum alternator/flywheel speed at the start of the current ramp up in the TF magnet and minimum speed at the end of the TF magnet flattop current. For a typical 8 T pulse, 370MJ is available with a start speed of 1731 RPM and end speed of 1568 RPM. For the first iteration of ADX requirements estimates of the TF magnet current flattop pulse length at 6.5 T, 370MJ was used as the limit. An upgrade of the system peak power and stored energy will likely be required for future upgrades being considered (8T, 2MA plasma current).

The pulsed power limit of the alternator/flywheel system is determined by many factors, including available stored energy, alternator impedance parameters, power conversion system parameters, load profile alternator field power system performance, voltage regulator performance and system performance under fault conditions [8]. With the present power converter design, exceeding the limit will probably result in converter commutation failures. The limit is unlikely to be overheating of the alternator winding unless the alternator regulator allows significant overfluxing of the field with associated localized stator iron overheating. Overvoltage of the stator winding under some fault conditions (eg. loss of load) could occur depending on alternator voltage regulator parameters. It may be possible to achieve higher MVA capability with the existing system, but a complete system analysis and study must be done before considering an upgrade in alternator/flywheel performance. For the first iteration of power system capability estimates, the experience gained from many years of successful operation on C-Mod will be used in determining ADX operational limits.

III. C-MOD POWER SUPPLIES AVAILABLE The Alcator C-Mod power supplies available for use on the proposed ADX tokamak are described in the following paragraphs and shown in Fig. 3 and Fig. 4. Several iterations of analysis and the ADX coil design will be required to determine the optimal power supply requirements and recommended use of the existing supplies [4]. This work is based on the first of them.

A. Connections There are 14 primary magnets (coils) on Alcator C-Mod with eleven power converters providing current to them. All except the EF3, EF4 and EFC magnets are driven by their own supply. EF3-U and EF3-L coils are driven in series by one supply while EF4-U and EF4-L are driven in parallel by a single supply with resistive compensation to equalize currents. The EFC supply drives the EFC-U and EFC-L coils in an anti-series connection. A fast chopper supply is used for the low

inductance EFC coils, allowing the magnet to provide rapid control of the plasma vertical position.

B. Implementation

EF1, OH1 and OH2 supply currents are commutated using gated silicon-controlled rectifiers (SCR) with pulse-forming

Fig. 5. ADX TF Pulse Length Determination

networks to interrupt switch current flow. Plasma discharge is initiated by the 8 to 10 V loop voltages generated. The complex interaction of EF and OH produced fields is carefully tuned to provide the poloidal field null needed for breakdown. Liquid nitrogen is used to cool the coils and give coil resistances lower than those at room temperature by a factor of 6.

IV. EXISTING ALCATOR C-MOD AND ADX TF MAGNET REQUIREMENTS AND ANALYSIS

Initially, ADX will be designed for 6.5 T, 1.0 MA plasma operation and it is important to know in the initial design stages the maximum TF flattop current pulse length achievable with the existing C-Mod system. Since detailed data is available for a wide range of C-Mod operating scenarios, a simple model was developed in PSIM using data from experiments at different TF fields, including 8 T [9]. 8 T field data used requires the most stored energy, 371MJ, or the maximum total energy available from the existing alternator/flywheel system. Data from coil measurements and 8 T C-Mod shot # 1110216010 were used to create the model. Similar C-Mod shot data from the same run day for 5.4T, 6.32T, 6.97T, 7.3T, 7.65T was used to confirm that the model worked for different field requirements. The TF energy requirements for each of these was compared and in all cases the TF energy requirements were ~81% of the available alternator energy to end of TF flattop (EOF) current. The remaining energy is available for the other C-Mod supplies. The ADX TF magnet will be of similar design to that of C-Mod but coils will be taller by ~0.5 meters and have a total coil resistance increase of ~7.5%. An increase in current requirement of 0.72/0.67 *(C-Mod TF flattop current) will accompany the coil changes. On C-Mod, 185kA TF current at flattop is required for 6.5 T operation. The estimated ADX TF current at flattop is 199kA and is used in the simulation.

A. Model The PSIM model gives a good estimate of the maximum TF magnet flattop current at EOF using the following method: The model used 0.0092 H and 0.00215 Ohms for the TF magnet and bus, based on the MA-turn requirements and new ADX magnet and bus resistance. Using the maximum start RPM and minimum EOF RPM for the alternator/flywheel, the available energy for the pulse to EOF current was found to be 371 MJ. The estimated time required to reach an ADX TF Magnet flattop current of 199kA was determined to be 1.94 s using the available average ramp up voltage of the TF supply, or 1174 V. Voltage required at flattop current to maintain the required current is 408 V, and the peak ADX TF output power was calculated as shown in Fig. 5 at TF supply current flattop. Alternator/flywheel peak output power was determined to be 272 MW based on the C-Mod shot data. The ADX TF Energy required to EOF was calculated in the model to be 302 MJ. Using the 1.23 conversion factor determined by the C-Mod data for 81.3% of available alternator energy required for ADX TF Energy Required, the Alternator Energy required was found, as expected, to be 371MJ. Subtracting the Total

Pulse Energy to EOF from the maximum available Alternator/Flywheel Energy to EOF gives the maximum ADX TF pulse length of 0.72 s (no more energy available). The TF power supply is a two-quadrant supply and puts some energy back into the alternator/flywheel system when it is in inversion. The available -521 volts during power supply inversion gives a reasonable inversion time of 2.55 s.

V. ADX POWER SUPPLIES ANDPOLOIDAL FIELD COILS ADX coils will be somewhat different than the C-Mod coils, but designs may be possible that would allow continued use of the C-Mod power supplies, with or without upgrades. See Fig. 6 for the proposed ADX coil arrangement for the point design being considered for this analysis. The values at time t=1.0 s in the Fig. 7 worksheet are taken to be the Xpoint target equilibrium for the initial point design at 1.0MA plasma current using the coil radial and Z location and number of turns indicated. Mutual inductances and Green’s functions for the ADX coil set were obtained using SOLDESIGN code [10].

A. Worksheet Description The Fig. 7 worksheet contains a time sequence of states during a “typical” 1 MA shot getting up to and coming down from the reference equilibrium and was used to investigate the power supply requirements for the ADX coil set specified.

Fig. 6. ADX Coil Cross Section for Xpoint

Fig. 7. Work Sheet for Determining ADX Power Supply Requirements

Except for the reference case, for which the currents are fully specified, the current evolution is fabricated according to a set of requirements based partly on experience on Alcator C-Mod and partly on some general considerations described below.

Real C-Mod shot data with similar time history are used as a basis for some of the ADX features. The proposed ADX plasma current waveform with calculated current and voltage waveforms are shown in Fig. 8. Times and time intervals for the worksheet represent:

1.) t = 0 to 0.04 s – Initiation, initial current formation - At t=0^- a field null is produced, defined in terms of Bz, Br, and curvature index on axis (where the curvature index Nc = -(R/Bz)*dBz/dR). Only coils which initially carry current in the same direction as the plasma are energized. Ramp up of the energized coils before t=0 was not considered here. At t=0 a voltage blip is produced to break down the plasma and begin the initial current rise, assisted by opening "commutation switches", i.e. solid-state thyristor interrupters on several of the co-current supplies, while energizing negative voltages on some reverse current coils (notably EF3).

2.) t=0.04 to 0.20 s - Early current rise and shaping - At the beginning of this phase the commutation switches are re-closed and the coil voltages must be provided by the power supplies alone. During this interval the plasma current is raised to a little over half the final value, and the cross-section is elongated and a divertor configuration may be established at the primary Xpoint. Connection to the secondary Xpoint is not envisioned here, but all coils begin to ramp toward their flattop current levels.

3.) t=0.20 to 0.60 s - Final current ramp-up - During this interval the plasma is brought to the target current and shaping is fully established. t=0.60 s is the Beginning of Flattop (BOF). Plasma heating and current drive

Fig. 8. ADX Plasma Current with Calculated Coil Currents and Voltages

may start during this interval, or may wait until BOF. The flux consumption for the case shown is considered typical for an ohmic all-inductive ramp-up, with the plasma resistive voltage in the 1 to 2 V range.

4.) t=0.60 to 1.5 s – Flattop - Three time points are shown to illustrate coil current evolution during plasma flattop, assuming a near constant shape and plasma conditions are maintained. The flux swing is required to inductively maintain the plasma current against resistive losses with an effective resistive voltage of about 1.4 V, corresponding to a relatively cold ohmic discharge and therefore demanding the largest projected flux swing. The currents at 1.0 s are those of the calculated Xpoint target equilibrium, while the BOF and EOF are extrapolated.

5.) t=1.5 to 1.93 s – Rampdown - The plasma current is ramped down to near zero under control, maintaining a stable equilibrium, though probably not maintaining the advanced divertor configuration in the typical case. Many of the PF and DX coils do not reach zero by the end of this phase, but are assumed to ramp down to zero under maximum inversion voltage after plasma termination.

B. Methodology Used No additional ADX equilibria have been generated for this initial exercise. The t=0 currents were defined based on a standard C-Mod startup, with currents adjusted to produce a near-null at the ADX nominal axis location, i.e. Bz~Br < .005T, with positive field curvature 0 < Nc < +1.5. The initial flux linkage, ~1.7 volt-seconds, is consistent with the typical C-Mod startup, as are the OH1 and OH2 currents. The initial plasma point at 0.04 s is also designed to satisfy equilibrium and stability contraints on Bz0, Br0, and dBz/dR (where the curvature index Nc = -(R/Bz)*dBz/dR). Flux consumption is roughly modeled on the comparable C-Mod shot. The intermediate current rise case again is designed to satisfy global equilibrium and stability constraints, with a prescribed negative curvature index corresponding to a controllably elongated plasma, -1 < Nc < 0 with Ip=650kA, roughly corresponding to the C-Mod example. The OH, EF1-4, and DX1 coil currents were adjusted to produce satisfactory values of the on-axis fields and gradients, while remaining DX coils were set to be on a trajectory leading to their final values. The BOF time slice at 0.6sec is scaled from the reference ADX equilibrium at 1.0 s using the following rules: The Bz0 and Nc are equal to those at 1.0 s. The flux near the four nominal Xpoint locations (0.65,+/-0.35) and (0.95,+/-0.75) is set to be 0.7 volt-seconds greater than in the reference case, corresponding to a 1.75V resistive loop voltage over the 0.4 s interval. The Bz and Br at the Xpoint locations are set to be equal to the reference (presumed to be zero, since they are supposed to be Xpoints). The assumption is that the plasma contribution to the flux is unchanged since the plasma parameters are unchanged in flattop. The currents of all 25 coils are solved by pseudo-inversion of the resulting (16x25) coefficient matrix, weighted according to the nominal current capacity of each coil. The EOF time slice at 1.5 s is determined in the same manner as for the BOF, with flux change of 0.6 volt-seconds in 0.5 s corresponding to a reduced resistive loop voltage of 1.2 V. The end-of-rampdown snapshot at 1.93 s satisfies the global equilibrium and stability constraints on Bz0, Br0, and dBz/dR, but Xpoint geometry wasn’t considered. The reverse voltages required are large but less than the forward voltages in the main discharge.

C. Assumptions Made For this iteration, a number of assumptions were made. ADX EFC requirements are assumed to equal C-Mod EFC requirements. DX1-U,L will each have a single power supply and use an existing upgrade design for C-Mod EF2 four quadrant supply. ADX OH1 and OH2 coils will be considered equal to the C-Mod coils and use the same supplies. The new OH3 coil is considered to be the same as the ADX OH2 coil, and commutation circuits are required for all OH supplies as in C-Mod. The ADX EF4 coils are to be run in parallel as in C-Mod and use an upgraded C-Mod EF4 supply. ADX EF3

coils are assumed to be in series, as in C-Mod and designed to use the existing EF3 supply if possible. The 8 new DX2-DX5 power supplies will use modular H-bridge converters with shared DC supply if possible.

VI. RESULTS AND COMMENTS As expected, the largest voltages occur at initiation (t=0 s) and for forward biased coils the supplies can be assisted by commutation resistors. The EF2 and EF3 coils require large voltages at this stage, over 1 kV. For EF2, no current is required before 0.04 seconds, so the voltage (up to 1.3kV in this case) could appear across an open switch. The EF3 coils begin to swing negative at this time in order to provide equilibrium vertical field for the nascent plasma, so this supply must provide substantial voltage at this time, as on C-Mod. The total voltage in EF3U and EF3L is 3150V, which is uncomfortably close to the rating of the existing EF3 supply if the EF3 coils are to be connected in series. This requirement can be relaxed by reducing the number of turns to 75 turns per coil, as in the C-Mod coil set, providing similar headroom on the voltage rating. Individual EF2 coils could also be reduced back to 80 turns as on C-Mod. The current requirements in these coils in this scenario are quite modest compared to the C-Mod coils of the same name, less than 2 kA (or 0.250 MA-t), so decreasing the turns should keep the current and voltage within the specifications of the proposed "new EF2" four quadrant supply designed for use on C-Mod. The new DX1 coils, as well as the new EF1 coils, carry substantial currents, near 5kA/turn, in this scenario. Voltage requirements on the supplies are modest, with maximum values near 100 volts in the 0.04 to 0.20 s interval. For this scenario neither the EF1 or DX1 coils need four quadrant capability, and maintain almost constant current throughout the scenario. However, these coils will need to provide a large variety of fields corresponding to the different classes of ADX divertor configurations, so at this point it seems prudent to retain four-quadrant capability. The currents and voltages for the EF1 supply are within the rating of the existing C-Mod EF1 supply. The voltage and current requirements for EF4 coils in this scenario challenge the capability of the existing C-Mod supply as configured. The voltage after switch closure (0.04 to 0.2 s) is over 1.1 kV per coil, while the present supply can provide only ~900V and the maximum current of 6.3kA per coil (~13kA if the coils are connected in parallel) exceeds the present rating of 10kA. However, the ultimate current capability of the supply is 50kA (or 25kA each in forward and reverse bridge, if symmetric four quadrant operation is maintained), so the current may not be a power supply limitation. The specified currents also exceed slightly the administrative limits on C-Mod, which were derived from stress considerations. These need to be re-defined for the ADX configuration, considering the other coil current requirements and locations. The voltage requirement is also preliminary, since the ADX cylinder was not modeled in this exercise. However, the main effect of the cylinder will be to slow the response of the fields at the plasma to changes in the EF4 coil

currents, so to the extent that the large swing in the EF4 currents is required to match the flux swing, the voltage demand may be under-estimated by this scenario. Some reduction in the number of turns in the ADX EF4 coils may be beneficial in limiting the voltage requirement on the supply, but a more complete study is required. Reduction of coil number of turns as much as possible should be considered for the next iteration. This reduces the voltage requirements for the supplies in normal operation and reduces the voltage appearing at the terminals and on the internal bus work during commutation and especially during disruption events. Going forward we will consider reducing EF2 to 80 turns, EF3 to 75 turns, EF4 to 84 turns, as in C-Mod. Considerations include current density and resistances, but the present scenario would not tax any of these more than in C-Mod. Consideration of ADX operation at 8T and 2MA plasma currents is just beginning, but it is likely that an upgrade to the alternator/flywheel system and possibly the substation will be required. Initial study of the ADX TF magnet requirements indicates that the existing system will not reach ADX 8T flattop current with the available energy. Upgrade to the existing systems will require a more detailed analysis.

ACKNOWLEDGMENT The authors wish to thank those on the Alcator C-Mod

team for their many contributions to this work.

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