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First Plasma Scenario Development forHL-2M

X. M. Song1, J. X. Li1, J. A. Leuer2, J. H. Zhang1 and X. Song1

1Southwestern Institute of Physics, P.O. Box 432 Chengdu 610041, China2General Atomics P.O.Box85608, San Diego, CA 92186-5608 (Retired)

Corresponding Author: songxm@swip.ac.cn

Abstract:

The main parameters of HL-2M are presented. A Matlab-based tool for tokamak modelingand plasma scenario development is developed. With this tool, two scenarios for first plasmaare designed for HL-2M commissioning campaign. The two scenarios including one limiterconfiguration and one divertor configuration are compatible with the magnetic diagnosticsystem and power supply system, which are not fully equipped and well tested. The keyparameters for the two scenarios are as follows: toroidal field 1.4T , plasma current 200kAwith 1000ms flattop. For the sake of simplicity and safety, only small parts of PF coilsare used in the plasma discharge, no initial magnetization is exploited, no PF current zero-crossing is allowed, no VDE is expected. To facilitate obtaining the plasma, two gyrotronsof 68GHz with 500kW each are exploited for preionization and assisted startup.

1 INTRODUCTION

HL-2M tokamak is now under construction in China as a modification to the HL-2Afacility. It is a real challenge to build a new machine in fusion community. HL-2M suffersfrom a long delay for the first plasma. Successfully obtaining the first plasma is veryimportant because it is related to not only engineering but government qualification ofthe machine, so simple and practical first plasma scenarios using a minimum of powersupplies and coils are recommended. Our two scenarios for first plasma are designed withideas from the available tokamak modeling and plasma scenario method[1]. This paperpresents the main parameters of HL-2M, and introduces the two first plasma scenarios.In Section 2, the parameters of PF and CS are presented. In section 3, the Matlab-basedtool for plasma discharge scenario development is introduced. Two plasma scenarios withthe waveforms of PF coils are described in Section 4.

2 Main Parameters of HL-2M

HL-2M Tokamak with conventional conductor has nominal parameters as follows: Ip =1.5 − 3MA, B = 2.2T , major radius= 1.78m, minor radius= 0.65m. Fig. 1 shows thegeometry of HL-2M device. The PF system has CS together with 8 pairs PF coils (innerPF1-PF4, top-bottom PF5-6, outer PF7-8). Coil PF4, PF5 and PF6, which usually areused to form the divertor configuration, are called divertor coils. Vacuum Vessel (VV)is made of Inconel 625 with a double-wall structure; each wall is 5mm thick with 20mm

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FIG. 1: Geometry of HL-2M.

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FIG. 2: The limited plasma.

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FIG. 3: The diverted plasma.

apart. TF coils consist of 20 sets of coils with 7 turns each. The geometric parameters ofPF and CS coils are shown in Table I. The X, Z, W , H are the radial position, verticalposition, width and height of each coil, respectively. Angle is the tilted angle in degreeof each coil with horizontal line. Nr, Nz are the layer number in radial and verticaldirection respectively, due to the space occupied by jump connection, the total turns maybe less than Nr × Nz. In Table II, The electromagnetic parameters of PF and CS coils

TABLE I: Geometric Parameters of PF and CS

X(mm) Z(mm) W (mm) H(mm) Angle Nr ×Nz

CS 748 0 116.75 3442.3 0 96(2 × 48)PF1 912 185 50.4 352.4 0 28(2 × 14)PF2 912 586 50.4 352.4 0 28(2 × 14)PF3 912 987 50.4 352.4 0 28(2 × 14)PF4 912 1388 50.4 352.4 0 28(2 × 14)PF5 1092 1753 183 220 0 28(5 × 6)PF6 1501 1790 257 146 0 27(7 × 4)PF7 2500 1200 183 220 64 28(5 × 6)PF8 2760 480 183 220 0 28(5 × 6)

are presented. R and Imax are resistance and maximum permitted current for each coil,respectively. Bv and Br are calculated vertical and radial magnetic field coefficient inplasma area (R : 1.2 − 2.2m, Z : ±0.6m). From Table II, the maximum Bv is 155.9(Gauss/kA), which belong to PF8, that means PF8 is the best coil to take charge ofradial position control; and the maximum Br is 56.3 (Gauss/kA), which belong to PF7,that means PF7 is the best coil to take charge of vertical position control.

In Table III, the inductances for plasma and PF coils are presented. The inductanceinvolved with plasma has a weak dependence with plasma parameters, here taken thefollowing plasma parameters: major radius = 1.78m, minor radius = 0.65m, elongation

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= 1.8, triangularity = 0.With parameters in these table, we have designed two first plasma discharge scenarios

with our Code. One is limited scenario, whose flat top plasma shape is shown in Fig. 2,and the other is diverted scenario, whose flat top plasma shape is shown in Fig. 3.

3 The Tool for Scenario Design

The tool for Scenario design is known as Shape Editor (SE), because it was developedto design plasma shape at first. With more functions integrated into SE, it become apowerful tool with a friendly Graphic User Interface (GUI). In this paper, only functionsinvolved with discharge scenario design will be introduced.

In our discharge scenario modeling, the plasma discharge consists of five distinctphases: Initial Magnetization (IM), Break Down (BD), Ramp Up (RU), Flat Top (FT),and Ramp Down (RD) phases. For plasma scenario development, the PF current forplasma scenario is decomposed into two components: flux and equilibrium. The flux com-ponent provides flux for plasma resistive consumption and inductively drives the plasmacurrent during RU; it is heavily dependent on plasma evolution history. The equilibriumcomponent, although affected by plasma position and shape, slightly changed by βp andcurrent distribution profile, is approximately proportional to plasma current. The equi-librium component provides plasma position and shape control, while the flux componentcontrols plasma current. The key functions for SE code is introduced as follows:1) To edit and get the target plasma shape There are three list boxes, basisShape,targetShape and cacheShape. The plasma shapes available are stored in three folders anddisplayed in three list boxes. You can start a shape editing by selecting a shape from theselist boxes. After every step of editing, the temporary shape will be stored in cacheShapelist box; If you find a editing action is wrong, you can return to the temporary shape byjust clicking the temporary shape name in cacheShape list box. You can edit the plasmaboundary or one divertor leg. The divertor leg can be moved or rotated. For plasmaboundary, you can move the whole plasma shape, horizontally or vertically, or zoom inor zoom out. You can also select one of the 16 red control points in the boundary andmove it to change the boundary around this point. If you are not skillful in the drag-dropaction with mouse when editing, you can obtain your target shape by using the EDIT andSLIDER CONTROL UI in the two panels in the middle bottom in the UI of SE code. 2)To calculate flux component

There are two ways to calculate the flux component, both use the points on the

TABLE II: Electromagnetic Parameters of PF and CS

R(mΩ) Imax(kA) Bv(Gauss/kA) Br(Gauss/kA)

CS 0.85 220 −12.4 25.7PF1 7.774 14.5 −34.5 11.6PF2 7.774 14.5 −20.3 31.7PF3 7.774 14.5 −1.4 31.1PF4 7.774 14.5 5.9 21.8PF5 3.557 38 11.4 20.5PF6 4.89 38 23.1 30.1PF7 7.563 39 94.1 56.3PF8 7.563 38 155.9 34.9

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boundary of a target shape to build an overdetermined equation. one way is to set fieldon the boundary to zero, that is IPF · GF = 0. The other way is to set the flux on theboundary (sometimes together with divertor legs) to a constant, that is IPF · Gψ = C.Here the IPF is the PF current configuration for flux component, GF and Gψ are Greenfunction for field and flux. Generally, we take the point number to be 3000 to 5000, andbuild a cost function

F = norm(IPF ·GF ) + w · norm(IPF ) or F = norm(IPF ·Gψ − C) + w · norm(IPF )

Here, norm is the 2-norm of a vector, w is the weighting factor and should take a valueto let the two term to be the same order of magnitude. The weighting term is veryimportant, which can make sure that the solution is stable and feasible in engineering.To minimize the cost function we can find the flux component. It is easy to solve thisequation by Matlab function mldivide which solves the over-determined problem in theleast squares sense. PF current configuration for flux component is the IM state we startto breakdown the plasma.3)To get the plasma target shape for a PF current configuration

With an initial try plasma current distribution, we can solve the Grad-Shafranovequilibrium equation by iteration to find the convergence solution. But if the shape isa Single Null, simple iteration may lead to failure because of the vertical instability.With a vertical feedback control function in our code, we can do the iteration until theregulating vertical position is very small, then we will find the convergence solution forSN configuration.4) To get the equilibrium component for the target plasma shape

First step: We estimate a PF current configuration and try an initial plasma currentdistribution which satisfy the Grad-Shafranov equilibrium equation, and find the fluxerror of the points on the target plasma boundary (sometimes together with divertor

TABLE III: Inductance of plasma and PF Coils

mH Ip CS PF1U PF2U PF3U PF4U PF5U PF6U PF7U PF8U

Ip 0.003CS 0.022 1.17

PF1U 0.027 0.77 2.17PF1L 0.027 0.77 1.04PF2U 0.023 0.75 0.97 2.17PF2L 0.023 0.75 0.46 0.24PF3U 0.018 0.70 0.44 0.97 2.17PF3L 0.018 0.70 0.24 0.14 0.09PF4U 0.012 0.60 0.23 0.44 1.00 2.17PF4L 0.012 0.60 0.14 0.09 0.06 0.04PF5U 0.012 0.40 0.18 0.30 0.54 1.06 2.78PF5L 0.012 0.40 0.12 0.08 0.05 0.04 0.03PF6U 0.019 0.36 0.24 0.36 0.55 0.81 1.56 3.98PF6L 0.019 0.36 0.16 0.11 0.08 0.06 0.06 0.10PF7U 0.047 0.42 0.41 0.49 0.53 0.54 0.73 1.37 8.30PF7L 0.047 0.42 0.34 0.27 0.21 0.17 0.19 0.32 1.03PF8U 0.064 0.45 0.47 0.48 0.46 0.41 0.52 0.89 3.53 9.53PF8L 0.064 0.45 0.44 0.38 0.32 0.26 0.30 0.52 1.77 3.26

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legs) with respect to a reference point, then get the regulating PF current by iso-fluxfeedback control policy, that is dIPF ·Gψ = dψ. Here dIPF is the regulating PF current,Gψ is Green function for flux, dψ is flux error of the points on the target plasma boundary.Like the way above to calculate the flux component, we take the point number to be 3000to 5000, and build a cost function

F = norm(dIPF ·Gψ − dψ) + w · norm(dIPF )

Again, we will emphasize that the weighting term is very important. The regulating PFcurrent is the solution to minimize the cost function.

Second step: After getting the regulating PF current, we solve the Grad-Shafranovequilibrium equation and get a new plasma current distribution, then again, we get a newregulating PF current by iso-flux feedback control policy.

We repeat the second step again and again until the regulating PF current is verysmall and the new plasma current distribution does not change too much, that means weget the convergence solution. This solution is the equilibrium component.5) To model the vacuum vessel, and calculate the eddy current for everyplasma scenario

Generally, we use 80 filaments to model the vacuum vessel, then calculate the resistanceof these filaments and the involved inductance together with mutual inductance amongPF coil, plasma and vacuum vessel. The eddy current can be calculated for every plasmadischarge scenario, the stray field from eddy current can be compensated by additionalcurrent in PF8 to keep the field null good enough during breakdown phase.6) To model the plasma resistance

We use H.Preis plasma resistance model[2] to calculate the resistive flux consuminginstead of the Ejima model[1, 3, 4]for simplicity without losing authenticity. The keyconcept of this model is plasma resistance change dramatically in breakdown and rampup phases. The resistance curve of plasma can be calculated by this model throughthe following law. After the Townsend avalanche of the primary electron, the electrondensity and the degree of ionization grow linearly, and plasma resistance accordingly dropslinearly. After the complete ionization the electron temperature increases linearly, andthe resistance drops as 1

T3/2e

. The resistance of plasma in the runaway tail is smaller than

that of flat top phase. With this model, the resistive flux consumption can be estimatedfor every scenario.7) To edit and get the target plasma current waveform

We have a dedicated UI to set the plasma waveform, there are ten nodes in thewaveform, we can not add or delete a node in the waveform. From the node 4 to node5, the plasma shape transfer from the RU phase limiter shape to the flat top shape, andfrom the node 8 to node 9, the plasma shape return to the RD phase limiter shape.8) To design the plasma discharge scenario

With all the functions above ready, the steps to design a discharge scenario are asfollows. Set the IM state according to the working coils; Select a limiter shape for RUand RD states; Select a flat top shape for FT state; Select a waveform for Ip curve; Selectthe H.Preis parameters for plasma resistance model and build the Rp waveform; Solvethe involved ODE for the given Ip waveform to calculate the PF current evolution curves;Calculate the PF voltage evolution curves with circuit parameters.

Other functions, such as data visualization and data management functions are notdescribed here, introducing all functions of SE code is not the purpose of this paper.

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4 Two First Plasma Scenarios

With the tool above, we design two scenarios for first plasma campaign, their plasmashapes are shown in Fig.2 and Fig.3. In first plasma campaign, for the sake of simplicityand safety, our design principles are as follows.

1) Minimum number of PF coils: For limiter configuration, only CS+PF6+PF8are used. For divertor configuration, CS+PF3+PF4+PF6+PF8 are used.

2) No zero-crossing PF current: we do not start from IM state but from a zerostate with current in all PF coil equal to zero to avoid current in PF coil to cross zero.For divertor configuration, coil PF3 and PF4 do not contribute for flux component, thisis also to avoid the current in coil PF3 and PF4 to cross zero.

3) No vertical instability: For limiter configuration, the elongation k = 1, and fordivertor configuration, the elongation k = 1.2.

4) Best flux component: We optimize the flux component algorithm, for the sameCS current, we get larger field null area with more driving flux.

5) More simple resistive flux consuming estimate: We use H. Preis plasmaresistance model[2] instead of Ejima model[1, 3, 4] to estimate the resistive flux consumingfor simplicity without losing authenticity.Specific reasons for selecting working PF coils on HL-2M:

6) CS: CS power supply is ready, and CS will provide more flux swing to drive plasma.7) PF8: PF8 is the best coil to control plasma radial position which is inevitable.

The Ohmic power supply at HL-2A can be used as the PF8 power supply in first plasmacampaign.

8) PF6: With PF6, we can build a limited plasma with elongation k=1 and divertedplamsa with elongation k=1, no VDEs are expected. The VF power supply at HL-2A canbe used as the PF6 power supply in first plasma campaign.

9) PF3 and PF4: For the above diverted plasma, both coil PF3 and PF4 will beused to halve the coil currents otherwise the coil currents will close to the engineering limiteven if the target plasma current is as small as 200kA. Coil PF5 is not chosen because itwill cause a larger elongation we don’t want to have in first plasma campaign. New powersupply for PF3 and PF4 will be ready in the first plasma campaign.

With coil CS+PF8+PF6, good enough field nulls can be obtained. In Table IV, twofield null configuration with their driving flux swing are presented, the corresponding fieldnull are shown in Fig. 4 and in Fig. 5.

TABLE IV: First plasma field null configuration

kA CS PF6 PF8 ψ(VS)

I 100 36.83 2.53 6.10II 100 35 2.7 6.05

With PF3 and PF4, a divertor configuration in high field side with elongation k = 1.2can be obtained, this configuration will cause instability not in vertical direction but inradial direction, this instability will be controlled by coil FP8.

The involved curves for limited scenarios with k = 1, is shown in Fig. 6, the workingcoils are CS+PF6+PF8. The involved curves for diverted scenarios with k = 1.2, is shownin Fig. 7, the working coils are CS+PF3+PF4 +PF6+PF8. For both scenarios, only coilCS+PF6+PF8 contribute for flux component and are used to control plasma current.The current curves of PF coils for the two scenarios have been calculated with a plasma

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resistive model which can estimate the resistive flux consumption. In both Fig. 6 andFig. 7, Ip is plasma current. Rp is the plasma resistance in microohm, plotted in commonlogarithm (base 10), In the ramp down phase, the resistance of plasma in the runawaytail is smaller than that of flat top phase. ICS, IPF3, IPF4, IPF6 and IPF8 are currentcurves for coil CS, PF3, PF4, PF6 and PF8, respectively. UCS, UPF3, UPF4, UPF6 andUPF8 are voltage curves for coil CS, PF3, PF4, PF6 and PF8, respectively.

In Fig. 7, from t = 200ms to t = 360ms, plasma shape transfers from limiter todivertor configuration, and from t = 1720ms to t = 1920ms, plasma shape transfers fromdivertor to limiter configuration. This divertor is in high field side with a little radialinstability but no vertical instability.

Because our Ip waveform is piecewise, the voltage curves are not so smooth. Theseunsmoothed curves are transferred to piecewise waveforms and use as the feedforwardwaveforms in our plasma control system.

5 Summary

The simple and safe scenarios in this paper will lead to successful commissioning in firstplasma campaign. The ideas and principles to design a simple and safe scenario when theinvolved subsystems are not fully equipped and well tested will generate a wealth of newknowledge with regard to the successful commissioning of new tokamaks. The weightingconstraint for the overdetermined equation we described in section III can make sure thesolution of PF current configuration is stable and feasible in engineering. SE, the Matlab-based tool for plasma discharge scenario development we introduced here is useful andpowerful for Tokamaks in general and for small tokamaks in particular. Through this tool,we have studied and validated the plasma divertor configuration for ITER and CFETR,and we are designing and validating the plasma discharge scenarios for the new small

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FIG. 6: Curves of limited scenario.

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FIG. 7: Curves of diverted scenario.

tokamaks, such as these in Tsinghua University and Nanchang University in China.

This work is supported by the Chinese National Fusion Project for ITER under grantNo. 2015GB105004.

References

[1] J. A. Leuer, B. J. Xiao, D.A Humphreys, et al. Fusion Science and Technology: VOL.57, JAN 2010.

[2] H. Preis, H. Wedler, Proceedings of the 9th Symposium on Fusion Technology, 1976,Pages 753-758. Garmisch–Partenkirchen (FRG), June 14–18, 1976.

[3] J. A. Leuer, N. W. Eidietis, J. R. Ferron, D. A. Humphreys, et al. IEEE TRANS-ACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 3, MARCH 2010.

[4] S. Ejima, R. W. Callis, J. L. Luxon, R. D. Stambaugh, T. S. Taylor, and J. C. Wesley,Nucl. Fusion, vol. 22, no. 10, pp. 1313–1319, Oct. 1982.