INSTITUTE OF PHYSICS PUBLISHING and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION

Nucl. Fusion 45 (2005) 1463–1473 doi:10.1088/0029-5515/45/12/001

Solenoid-free toroidal plasma start-upconcepts utilizing only the outer poloidalfield coils and a conducting centre-postWonho Choe1, Jayhyun Kim1 and Masayuki Ono2

1 Department of Physics, Korea Advanced Institute of Science and Technology,373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea2 Princeton Plasma Physics Laboratory, Princeton University, NJ 08540, USA

Received 10 December 2004, accepted for publication 1 September 2005Published 22 November 2005Online at stacks.iop.org/NF/45/1463

AbstractEventual elimination of the in-board Ohmic heating solenoid is required for the spherical torus (ST) to function asa compact component test facility and as an attractive fusion power plant. An in-board Ohmic solenoid, along withthe shielding needed for its insulation, can dramatically increase the size and, hence, the cost of the plant. Advancedtokamak reactor designs also assume no or a small in-board solenoid to reduce the size and cost of the plant. Inaddition, elimination of the in-board solenoid greatly reduces the coil stresses and simplifies the coil design. Here,we investigate using static as well as dynamic codes in ST geometries with two complementary solenoid-free plasmastart-up approaches: one utilizes only the outer poloidal field coils to create a relatively high quality field null regionwhile retaining significant poloidal flux, and the other takes advantage of the poloidal flux stored in the conductingcentre-post to create a start-up condition similar to that of the conventional Ohmic solenoid method. We find that itis therefore possible to come up with a promising configuration, which produces a quality multi-pole field-null andsufficient loop-voltage needed for plasma initiation and significant poloidal flux for subsequent current ramp-up.The present solenoid-free start-up concept, if proved feasible, can be readily extended to higher field devices due torelatively simple physics principles and favourable scaling with the device size and toroidal field.

PACS numbers: 52.55.Dy; 52.55.Fa; 52.55.Wq

(Some figures in this article are in colour only in the electronic version)

1. Introduction

In the fusion research conducted worldwide, the Ohmicheating solenoid has been commonly used to start-up tokamak,spherical torus (ST) [1] and other toroidal plasmas aiming todevelop an attractive fusion power source. A conventionalOhmic solenoid is placed in the in-board side of the toroidalplasma such as the one shown in figure 1, and it produces avery large vertical field (i.e. poloidal magnetic flux) inside theOhmic coil and essentially zero field outside the solenoid orinside the plasma region. This property makes it well suited toinitiate a toroidal plasma current by magnetic induction sincethe plasma initiation usually requires a very small transversestray field.

However, looking towards attractive/economical fusionpower plants, the in-board Ohmic solenoid places a highpremium on the cost of the plant. An in-board Ohmic solenoid,along with the shielding needed for its insulation, increasesthe size and, hence, the cost of the plant. This problemtends to become increasingly severe as the plasma aspect

ratio R/a is reduced toward unity, where ‘R’ and ‘a’ denotemajor radius and minor radius, respectively. As can be seenfrom figure 1, the in-board region shrinks in size as R/a isdecreased. The problem is particularly challenging for the STreactors where the aspect ratio is typically of the order of 1.5which means that the available in-board radial space is onlyhalf that of the plasma minor radius. This tight space wouldmake the placement of the Ohmic solenoid and the relatedneutron shielding and blanket impractical. Indeed, ST-basedfusion systems including the component test facility (CTF)[2, 3] and power plant designs (e.g. ARIES-ST [4]) assumecomplete elimination of the Ohmic solenoid. It is worthwhileto note that the designs for much higher aspect-ratio advancedtokamak reactors such as ARIES-AT [5] also assume no orsmall in-board solenoid. However, at the present time, thereis no proven method available for a solenoid-free start-up oftokamak/ST reactors.

The non-inductive start-up and current ramp-up methodsutilizing radio frequency (rf) and neutral beam injection (NBI)current drive have been successfully demonstrated on various

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Plasma Plasma

Conventional Ohmic Heating Coil

Ra

In-board Region

Out-boardRegion

Out-boardRegion

Mid-plane

Figure 1. A schematic depiction of the in-board and out-boardregions. The location of a conventional solenoidal Ohmic inductioncoil is also shown.

devices, but at sub-mega-ampere (MA) level [6–8]. The boot-strap current over-drive based ramp-up is also identified as apromising current ramp-up technique in reactor designs wherethe very long ramp-up time (∼ days) requirement is not an in-herent issue for a steady-state reactor system. However, it ishighly desirable to have a method to ramp-up the current inshorter time compared with the reactor core component ther-mal time constant (∼ hours) as the plasma operations may beinterrupted for a variety of reasons in the course of the fusionpower plant operations. A method based on coaxial helicityinjection (CHI) [9,10] has been successfully demonstrated onspheromaks and smaller ST devices. It is now being testedon NSTX at about 0.5 MA level. However, these methods aregenerally plasma physics intensive so that considerable physicsR&D effort will be required to extend these techniques towardmulti-MA regimes needed for the next generation devices.

The inductive variances of plasma start-up without Ohmicsolenoid are also being pursued at sub-MA level with somesuccess. The MAST experiment routinely uses in-vesselpoloidal field (PF) coils at larger major radii than plasmafor solenoid-free plasma initiation and current ramp-up bymeans of merging and compression [11]. This approach couldhowever limit the horizontal mid-plane access needed, forexample, for the removable blanket module for the CTF. Thereis an idea of creating a hot ST plasma by merging two STs asdemonstrated in the TS-3 device [12]. Recently, this conceptwas tested on MAST producing significant plasma current of∼150 kA. Although this implementation used internal coils toinitiate the plasma, the concept in principle should be realizableusing more reactor compatible external coils provided thatthe effects of the induced wall eddy currents can be properlycompensated.

It has been also suggested that plasma heating andassociated vertical field ramp-up can provide an efficient means

of plasma current ramp-up. Inductive plasma current start-upcan be induced by outer vertical field coils with the help ofthe strong heating power and with the small central solenoidflux for flux waveform adjustment [13] or without the OHtransformer [14]. However, the TSC simulation suggests thatit may not be practical to ramp-up plasma current solely byvertical field though the vertical field provides a significantfraction (∼40%) of the needed flux for current ramp-up [15].

Recently, JT-60U demonstrated the solenoid-free start-upby utilizing only the outer PF coils which produced 150 kAof plasma current [16]. Strong megawatt level ECH pre-ionization was used to help initiate the plasma even withoutcreating a field null. Similarly on TST-2, with about 100 kWof ECH, it was possible to initiate a plasma of up to 10 kA [17].Interestingly, with strong ECH heating, both JT-60U and TST-2experiments could start the plasma current with relatively largenegative (radially unstable) vertical field which is an intriguingresult.

2. The basic concept of the out-board Ohmicinduction utilizing outer PF coil system

A fundamental challenge for using only the outer PF coilsfor start-up purposes is the difficulty of creating a sufficientlyhigh quality field null region and at the same time retainingsignificant poloidal flux � needed for subsequent currentramp-up. With limited PF coil sets, improving the qualityof the field null region without reducing the available � isusually difficult. However, a carefully chosen proper set of PFcoils can offer the possibility. This was done by performingstatic vacuum field numerical modelling to seek the optimalPF coil position and the currents for producing the field null ata desired location described below.

A basic schematic of the solenoid-free concept utilizing aset of PF coils placed in the out-board region of the plasma [18]is shown in figure 2. As will be shown, the ST geometry offersconfigurational flexibility for the PF coil placement to producea good quality field null while retaining a significant PF flux inthe in-board of the major radius. This is important as it providesthe means for driving the loop voltage at the field null. Thepresent out-board Ohmic induction coil system tries to mimicthe solenoidal Ohmic induction property for a limited volumeas indicated in figure 2(b) as the initial plasma start-up region.In this volume, the transverse stray magnetic field can be madea small value, which will be shown in the model calculation inthe following section. The present out-board Ohmic inductioncoil consists of three basic types of PF coils labelled #1, #2and #3 although one can make further improvements usingmore coils. In this exercise, we assume the coils to be up anddown symmetric with respect to the mid-plane; thus the radialfield component is zero at the mid-plane by symmetry. Theshaded region for each coil, as shown in figure 2(b), representsa general area of placement for the coil.

Here, we first give a qualitative description of how onecan produce such a quality ‘multi-pole’ field null using onlythree basic types of out-board PF coils labelled #1, #2 and #3.The small-radius coil #1 placed near the major axis producesa vertical field BZ at the mid-plane that peaks at the majoraxis and decreases toward larger R. The large diameter coil

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Solenoid-free toroidal plasma start-up concepts

(a)

(b)φ

R

Z

Plasma

#1

#2

Null field regionInitial plasma

R

Z

a

Plasma

Mid-planeRa

Plasma

#1

#2

#3

Major Axis

#3

Figure 2. (a) A schematic of the out-board Ohmic induction coilsystem. (b) Out-board Ohmic induction null formation and plasmainitiation.

#2 produces a nearly uniform Helmholtz-type BZ at the mid-plane. The vertical field BZ produced by coil #3 placed nearthe outer mid-plane actually increases with R near the coil. Byproperly combining these three types of BZ , it is possible tocreate a high quality field null in the shaded region shown infigure 3(a). If the fields produced by coils #1 and #3 are added,the resulting BZ is peaked at the major axis which decreaseswith R; but the field gradient can be made to be small nearthe null region since the field gradients for coils #1 and #3 areopposite as shown in figure 3(a). With negative current in coil#2 with respect to those of the other coils, it is then possible toposition coil #2 to produce an appropriate gradient to cancelthe small gradient produced by the combined fields of coils #1and #3 (figure 3(b)). The position and BZ of coil #2 can beadjusted to create a good quality field null (zero net BZ) regionwhich also has zero field gradients (at least zero values for∂BZ/∂R and ∂2BZ/∂R2) as shown in figure 3(c). It is possibleto make the higher order gradient zero by a careful choice ofcoil positions and currents as shown in the numerical modelbelow. By using more ‘trim’ coils, one can further increasethe quality of the null if needed. The magnetic induction flux�, integrated from the major axis, available for the currentramp-up is the amount of vertical field flux going through thearea encircled by the plasma minor axis of fully developedplasma as depicted in figure 3(c). Since the coil #2 generates

Figure 3. (a) Vertical field (BZ) profiles generated by coils #1, #2and #3, as labelled. (b) Vertical field generated by a combination ofcoils #1 and #3 and coil #2. (c) Net BZ and the part contributing tothe available magnetic flux at the expected plasma axis.

generally a uniform field, there is a significant net flux leftover in the inner region due primarily to the peaked profileproduced by coil #1. Once the plasma initiates at the null fieldregion, the plasma current can be ramped up by utilizing theavailable poloidal flux � (i.e. volt-seconds) by ramping downthe PF coil currents. As the plasma current ramps up and theplasma size increases, the plasma position can be graduallyshifted towards the final position by a feedback control.

3. Configuration optimization

In order to give an accurate picture of how this out-board Ohmicinduction coil system actually works, numerical modellingwas performed for the Next Step Spherical Torus (NSST) [19]geometry. In this exercise, we restricted the coil placement tooutside the NSST vacuum vessel as shown in figure 4. Thenumerical code used for the static vacuum field modellingseeks the optimal PF coil currents for producing a field nullat a given location. The condition to be met for null formationis that the first, second and third derivatives of poloidal flux� with respect to the major radial coordinate R vanish, i.e.∂�/∂R = 0, ∂2�/∂R2 = 0, ∂3�/∂R3 = 0, at the givenlocation in the case of the total of five PF coils involved. IfR = R∗ is the desired location of the field null, the total � canbe written as �(R∗) = ∑5

i=1

∑Ni

j=1 wij IiG(R∗, Rij ) where G

is the Green’s function, Ii is the current of the ith coil, Ni is thenumber of segments in the ith coil, wij is the number of turnsin the j th segment of the ith coil and Rij is the major radiusof the coil segment. Then, the equations to be solved become

∑i

∑j

wij Ii

∂G

∂R

∣∣∣∣R=R∗

= 0,

∑i

∑j

wij Ii

∂2G

∂R2

∣∣∣∣R=R∗

= 0,

∑i

∑j

wij Ii

∂3G

∂R3

∣∣∣∣R=R∗

= 0,

(1)

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Figure 4. An example of simulation set-up using the NSSTconfiguration. The shaded region inside the vacuum vesselrepresents a fully developed plasma for indicating its relativelocation from the coils.

which can be expressed, after a straightforward arrangement,in the form

I3

I4

I5

= −(A−1 · B)

(I1

I2

), (2)

where A and B are 3 × 3 and 3 × 2 matrices, respectively,consisting of the derivatives of the Green’s function.Therefore, once the two coil currents (I1 and I2) are prescribedit is possible to find the currents for the other three coils (I3, I4

and I5) that satisfy the constraints. For the case of four PF coils,only one current is required to satisfy the constraints. Thatof course assumes that equation (1) describes three linearlyindependent equations. The basic reason for the coils tobe of sufficiently different types is to make these equationssufficiently linearly independent to yield interesting solutions.One should also note that a careful choice of the coil locationis also quite important since the coil position can affect thehigher order gradients. In the numerical code, an algorithmwas utilized to scan the coil position such as coil #2 to searchfor an optimized condition.

The plasma axis of NSST at the full plasma parameters isnear R = 1.75 m. The shaded region in figure 4 represents afully developed plasma, indicating its relative location withrespect to the coils and vacuum vessel. A nominal out-board mid-plane vacuum vessel location is at R = 3.0 m.In this exercise, the plasma null formation is chosen to startat R = 2.5 m which allows sufficient separation from thevacuum chamber located at 3.0 m. In figure 5(a), the BZ

profile generated at the mid-plane by each coil set is plottedas labelled. Coil #1 is located at R = 2.0 m and Z = ±3.1 mwith 16.0 MA-turn coil current. The mid-plane BZ generatedby this coil set peaks at R = 0.0 m (at the major axis) anddecreases towards large R. Coil #2 is located at R = 3.8 mand Z = ±1.4 m with −6.3 MA-turn. Coil #2 is essentially

a Helmholtz-type coil set that generates a relatively flat fieldprofile as shown in the figure. The trim coil set #3 is locatedat R = 3.2 m and Z = ±0.5 m with about 2 MA-turn. TheR = 3.2 m location is chosen to be outside the vacuum vesseland the vertical separation between the up and down coil #3of about 1 m allows the NBI access. Coil #3 is still nearly0.7 m radially outward from the field null plasma initiationpoint. It is instructive to add the field generated by coils #1and #3 as shown in figure 5(b). The combination of coils #1and #3 generates BZ that has a reduced gradient region aroundR = 2.5 m. The field generated by coil #2 is also shown. Asis seen in figure 5(b), BZ generated by coils #1 + #3 and #2,respectively, matches very well in the null field region. Theresulting net BZ is plotted in figure 5(c), where one can seethat the vertical field as well as the gradient values go to zeronear R = 2.5 m.

Figures 5(d) and (e) depict the resulting two-dimensionalflux contours and |B| (mod B) contours. As can be seen infigure 5(d), the null field created is a relatively high qualityfield null with high multiple (eight-fold) poles consideredto be desirable for the start-up. This multi-pole fieldnull configuration helps to initiate relatively stable plasmasalthough some degree of feedback control is likely to beneeded as the plasma current ramps up for plasma positioncontrol. The corresponding mod B contours are shown infigure 5(e) where the field null region of less than 20 G of 20 cmdiameter is created. The net BZ in the inner plasma radius(R � 1.75 m) contributes to the magnetic flux � available forthe current ramp-up. As seen from figure 5(f ), about 3.3 Wb(at R = 1.75 m) is available for the current ramp-up for thisparticular set of coil currents.

The loop voltage for plasma breakdown and current ramp-up can be induced by ramping down the currents in coils #1to #3 simultaneously at an appropriate rate. It is shown infigure 5(c) that the net BZ at R > 2.8 m is negative whichis radially stabilizing. This is due to coil #2 in which thecurrent flows in the direction opposite to the expected plasmacurrent, which indicates that coil #2 provides part of the verticalfield needed for the plasma current radial position stabilization.This may suggest that the ramp-down rate for the coil #2 currentcould be slower than those of coils #1 and #3 to generate anappropriate net stabilizing vertical field. Including the effectof additional flux from the equilibrium field coils, the availableflux � of about 5 Wb for the NSST case should be sufficientto ramp up the plasma current of a few MA range in NSST.The dynamic calculation results with wall eddy currents willbe briefly discussed below although detailed results will bereported in the future.

In the following, we shall give examples from several caseswhere different combination of coil locations were attemptedusing the same principle for accommodating various devicerequirements such as sufficient NBI and/or blanket access orhigher flux attainment. For all cases, we assumed the samecoil #1 current of 16.0 MA-turn as a reference. Figure 6summarizes the description of the PF coil positions and thecalculated flux contours. Case II demonstrates the case inwhich the separation between up–down coil #1 is reducedtowards the mid-plane compared with Case I for producingmore �. The vacuum vessel shape was changed to conformbetter to the plasma shape which would also allow the new

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(a) (b) (c)

(d) (e) (f)

z z z

Figure 5. Case I: vertical field (BZ) profiles and available flux (�) on the mid-plane generated by coils #1, #2 and #3, as labelled. (a) BZ

generated by the individual coil. (b) BZ generated by a combination of coils #1 and #3 compared with that of coil #2. The coil #2 current ismultiplied by (−1) for easy comparison. (c) The net BZ profile from all three coil sets. (d) Two-dimensional flux contours. (e) Mod Bcontours of the field null region. The region of less than 20 G of 20 cm diameter is created around R = 2.5 m. (f ) The available flux � as afunction of R.

coil location. Simply lowering coil #1 by 0.5 m resulted in asignificant flux increase from 3.25 to 5.20 Wb at R = 1.75 mand Z = 0 m with similar � and mod B contours.

While the 1.0 m separation between the up–down coil #3would allow the NBI port access, an attempt was made to placecoil #3 on the mid-plane with the other coils unchanged hopingto utilize the space between coils #2 and #3 (Case III). Similarquality field null and flux value were also obtained. In thisconfiguration, coil #3 consists of two independent coils #3 1and #3 2 with opposite current polarity, i.e. the direction ofcoil #3 1 current is opposite to that of coil #3 2 in such a waythat the sum of the fields cancels the net field generated bycoils #1 and #2. The sum of BZ by coils #3 1 and #3 2 locatedon the mid-plane was qualitatively very similar to Case II witha pair of up–down coil #3.

Case IV in figure 6 shows the configuration in whichthe vertical separation between the upper and lower coil #2was increased by 1.0 m compared with Case III to provideadditional horizontal access such as for the blanket module.In this case, the available flux � was only slightly reduced

compared with Case III while the field geometry remainedsimilar.

The space around the out-board-side mid-plane is valuablefor hosting various diagnostics, NBI and/or blanket access,and the placement of coils at the mid-plane can be avoidedby a further variation from Case IV. Instead of using two coils#3 1 and #3 2 on the mid-plane, another possible configurationutilizing two pairs of coils #3 1 and #3 2 that are located awayfrom the mid-plane is described as Case V in figure 6 whichcan generate a similar field profile. Although the detailedBZ profile produced by the individual coils #3 1 and #3 2 isdifferent, the sum of the fields by coils #3 1 and #3 2 showssimilarity. The available poloidal flux � and field null qualityare also similar. Since this configuration can still providea significant amount of flux of 4.5 Wb and offers excellentout-board mid-plane access of about 1.8 m vertical spacing,this configuration seems to be particularly suitable for theinterchangeable blanket modules for a compact ST-based CTF.

Cases I–V discussed above demonstrate the flexibility ofthe solenoid-free out-board PF coil-only induction concept.

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Figure 6. Position of the PF coils for five different cases considered. In Case II, coil #1 is lowered to offer more flux. The vacuum vessel iscontoured accordingly. Coil #3 is located on the mid-plane in Case III for the capability of accommodating blankets. In addition, separationbetween up and down coil #2 increased further in Case IV to provide additional space for the blanket access. On the other hand, fieldgeometry similar to Case III could also be obtained by using two pairs of up–down coils #3 1 and #3 2 as shown in Case V. The poloidalflux at the expected plasma centre (at R = 1.75 m, Z = 0.0 m) is 3.25 Wb, 5.20 Wb, 5.97 Wb, 4.60 Wb and 4.50 Wb for Cases I to V,respectively. For all cases, the coil #1 current was fixed at 16.0 MA-turn as a reference.

Various combinations of coil locations with proper alignmentof transverse fields allow the generation of a high quality fieldnull at a desired position with a few webers of flux, which willbe sufficient for ramping the plasma current up to multi-MAlevel.

4. Demonstration of break-down condition withdynamic numerical code

In order to guarantee a successful initial plasma start-up, fieldnull should be maintained for a sufficient period of time orbreakdown time, which is often defined as the time taken toreach 50% ionization of the initially pre-filled gas [20]. Inmany earlier experiments, it corresponds to the time at whichthe D-alpha emission reached maximum and is typically a fewmilliseconds in most of the large-size toroidal devices. Thesustainment of the field null for the breakdown period requiresa time-dependent calculation because the transverse stray fieldis generated not only by the currents flowing in active coilsbut also by the eddy currents induced in various conductingobjects such as the vacuum vessel, passive stabilizer and other

structural materials due to the rapidly changing coil currentsduring the period. The wall eddy currents generally slowdown flux changes and reduce the generated peak loop voltage.The field null creation can also be significantly affected.However, it is relatively straightforward to account for themby numerical means by solving coupled circuit equations withthe conducting structures considered as hundreds of dividedring elements. Through the dynamic calculation, a properwaveform of each coil can be obtained which sustains the fieldnull for a sufficient time with a significant amount of poloidalflux required for subsequent plasma current ramp-up. Thetime-dependent numerical code used for the modelling solvesthe coupled circuit equations including the terms of vacuumvessel eddy currents

L · �̇I + R · �I = �Vc + �Vst, (3)

where L is a square matrix composed of self and mutualinductance between elements and R represents a resistancematrix. The row vector �I consists of currents flowing inconducting elements, and �̇I denotes their time derivatives.

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Solenoid-free toroidal plasma start-up concepts

Coil #1

Coil #3_2

Eddy (X10)

Coil #3-1Coil #2

0.98 0.99 1.00 1.01 1.02-6-4-202468

101214

Cur

rent

(M

A-t

urn)

Time (s)

0.98 0.99 1.00 1.01 1.024

5

6

7

8

9

Loop

Vol

tage

(V

)

Time (s)

0.98 0.99 1.00 1.01 1.024.0

4.2

4.4

4.6

4.8

5.0

Flu

x (W

b)

Time (s)

(a) (b)

(c) (d)

Figure 7. An example of the time-dependent vacuum field calculation for Case V with vessel eddy currents considered. (a) Currentwaveform of the individual coil and the total eddy current, (b) the corresponding loop voltage and (c) the poloidal flux � at R = 2.5 m. Theeddy current was multiplied by 10 for comparison. (d) Contours of ET · BT/B⊥ in V m−1 at 1 s. The shape of the contours remains almostunchanged for more than 10 ms. Force balance or equilibrium of the initial plasma was not considered in the calculation.

�Vc and �Vs represent the piecewise linear bias voltage.Equation (3) was solved by the eigenmode expansion method[21]. The waveform of the optimized coils was soughtthrough an optimization procedure in which optimization wasperformed by χ2 minimization [22]. During the optimizationprocedure of the solutions, several constraints (magnitudes ofloop voltage and � and radial derivatives of BZ) were satisfiedfor the field null generation at the desired location. In addition,current, voltage and temperature limit of the PF coils were alsoconsidered in finding the optimized solution set 1.

Figure 7 illustrates an example of dynamic vacuum fieldmodelling. Coil currents with the waveforms shown infigure 7(a) produce the field null by the combined effectsof currents in the PF coils and the induced currents in themachine structures from 1.0 s for more than 10 ms. Onecan actually take advantage of the wall eddy currents bytransferring magnetic energy from the coils to the vacuumvessel, which is much closer to the plasma. In principle, onecan design the vacuum vessel and other conducting structuresto actually aid the plasma start-up. As shown in the figure,it is possible to create a reasonable quality field null regionwith �20 G for over 0.3 m diameter region while retaining asufficient loop voltage of ∼7 V for plasma initiation and �

of more than 4 Wb needed for the subsequent current ramp-up towards multi-MA level current. The condition for highlyreliable Ohmic induction breakdown can be expressed as

1 A similar calculation for NSTX is found in Kim J., Choe W. and Ono M.2004 Plasma Phys. Control. Fusion 46 1647.

ET ·BT/B⊥ >∼ 103 V m−1,which is a typical condition for anOhmic start-up without strong pre-ionization, where ET is theinduced toroidal electric field, BT is the toroidal magnetic fieldand B⊥ is the average poloidal (i.e. transverse) stray magneticfield [20]. However, an application of suitable pre-ionizationrf waves can relax this condition. For example, on DIII-D,operating at BT = 2 T, with high power (∼800 kW) ECHpre-ionization, a successful plasma initiation was achieved atET = 0.3 V m−1 with B⊥ > 50 G over most of the vesselcross-section [20]. This represents a value of ET · BT/B⊥ ≈120 V m−1. Also in the experiment, the high power ECH pre-ionization was able to shorten the breakdown time to about2 ms even with low loop voltage of a few volts. In figure 7(d),we show the contour of ET · BT/B⊥ ≈ 120 V m−1 where thediameter of the 120 V m−1 contour at 1 s was about 0.5 m whichis similar to the DIII-D plasma minor radius. The shape ofthe ET · BT/B⊥ ≈ 120 V m−1 contour remained essentiallyconstant for over 10 ms, which should be long enough for theplasma avalanche process to occur. It is interesting to note thatsince DIII-D and NSST have similar toroidal field (TF) (∼2 T)and major radius (∼2 m), the plasma start-up condition inNSST can be made remarkably similar to that of DIII-D, givingsome level of confidence in the present start-up method. OnJT-60 with strong ECH pre-ionization, a successful solenoid-free start-up was achieved with even lower Lloyd parameterof ∼20 V m−1 [16]. It is then possible to relax the field nullcondition, which should yield even more flux available for theplasma current ramp-up.

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Centre-post

Vessel

(a)

(c)

Net flux

Loopvoltage

Net flux (CP)

Plasmainitiation

(d)

(b)

-10 -5 0 5 10

-100

0

100

200

300

400

Cur

rent

(kA

/turn

)

Time (s)

PF1 PF2 PF3-1 PF3-2 Vessel (*1/3) Centre-post

10.0 10.5 11.0 11.5 12.0 12.5-100

0

100

200

300

400

500

Cur

rent

(kA

/turn

)

Time (s)

PF1 PF2 PF3-1 PF3-2 Vessel (1/3) Centre-post

-10 -5 0 5 10

0

20

40

60

80

Pol

oida

l flu

x (W

b)

Time (s)

PF1 PF2 PF3-1 PF3-2 Vessel Centre-post

10.5 11.0 11.5 12.0 12.5

0

5

10

15

0

5

10

15

Loop

vol

tage

(V

)

Pol

oida

l flu

x (W

b)

Time (s)

PF1 PF2 PF3-1 PF3-2 Vessel Centre-post

Figure 8. Numerical simulation results of the centre-post start-up scheme. (a) Waveform of coil currents and temporal evolution ofinduced currents. (b) Expanded scale during the time of interest. (c) Temporal evolution of poloidal flux � (at R = 2.5 m, Z = 0.0 m).(d) Expanded scale during the time of interest. After 10.550 s, the net poloidal flux is mostly due to the centre-post.

5. Concept of centre-post start-up

Here, we present a variant of the induction concept, whichtakes advantage of the single-turn copper TF coil inner legenvisioned for the ST-reactors [4, 23]. For an ST device witha solid copper centre-post such as the case envisioned for theCTF and power plant, one can store significant poloidal flux inthe centre-post to further aid the breakdown and current ramp-up. The poloidal flux trapped in the centre-post inherently hasa small stray field (like an Ohmic solenoid); so the additionalflux provided in this manner should provide greater flexibilityto the solenoid-free start-up. The present concept can also beextended to tokamak reactors by placing a metal ‘cylinder’ inthe central region. The cylinder could also be a part of thevacuum vessel, shields and/or the support structure. The basicidea is to use the outer PF coils to charge up the centre-postor the centrally placed metal cylinder. Using a set of outerPF coils energized in the same polarity, one can charge thecentre-post to a significant poloidal magnetic field value. Forexample, if the applied magnetic field can be 8 T, a centre-post with 0.5 m radius as in the case of NSST or the CTF-likedevice can store nearly 6 Wb of magnetic flux. This type offlux is sufficient to generate multi-MA of plasma current. If thecentre-post is 1 m radius like ARIES-ST, the stored flux canbe 24 Wb. These flux values represent a significant fractionof the flux needed to ramp up the current in both CTF andARIES-ST reactors. It should also be noted that the presentconcept can be extended to the higher aspect-ratio tokamak

reactors. For example, if a conducting flux storage shell whichcan be a part of the vacuum vessel, neutron shielding and/orsupport structure of mean radius of 3.5 m is installed in aR = 6 m advanced tokamak reactor, even a modest field ofsay 3 T can store over 100 Wb in this structure. This levelof poloidal flux should be sufficient to start a 10 MA leveladvanced tokamak reactor. Once the centre-post is charged up,one can program the PF coil currents to create an appropriatenull field region needed for the plasma initiation. Becausethe centre-post is very conducting, the flux is trapped insidethe centre-post for a much longer time compared with a moreresistive vacuum vessel and support structures. Since the fluxis trapped primarily in the centre-post after other wall eddycurrents die away, one is left with a situation very similarto a conventional Ohmic solenoid with very small fringingstray field which can be easily cancelled by applying a smallamount of vertical field. This is a favourable time to initiate thedischarge. The poloidal flux in the centre-post would decaywith the natural resistive time tr or exp(−t/tr). The inducedloop voltage also decays with a similar waveform. This typeof waveform is compatible with a typical inductive (Ohmic)start-up waveform since it takes more voltage to break downand ramp the current up in the more resistive (colder) initialplasma. In the case of a conducting central storage cylinder, itis possible to choose the wall material and thickness to controlthe effective resistive time to suit the specific needs of a reactor.The application of supplemental plasma heating and/or current

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drive would give an additional knob for the plasma initiationand current ramp-up.

A numerical simulation of this concept was conductedwith four sets of outer PF coils the same as in Case V infigure 6 with a 0.6 m radius copper centre-post for the NSST-like device configuration. It should be noted, however, that thepresent concept should work essentially with any number of PFcoils of various sizes placed at various locations. Figures 8(a)and (b) show waveforms of the driving PF coil currents andthe currents induced in the vacuum vessel and the centre-post.As depicted, the decay time of the centre-post induced currentis much longer than that of the vessel eddy current since thecopper centre-post is much less resistive. If one uses the highloop voltage generated by the large flux change due to thevessel eddy current for plasma initiation, it is indeed possibleto take advantage of the large (about 3–4 Wb) poloidal fluxprovided by the centre-post for further plasma current ramp-up (figure 8(d)). It is noted that the net flux is mainly due tothe centre-post after 10.550 s because the vessel wall currentmostly decayed away.

The radial profile of the poloidal flux and vertical fieldshown in figures 9(a) and (b) at t = 10.540 s illustrates goodsimilarities between those due to the centre-post and a typicalOhmic solenoid. As can be seen in figure 9(b), the centre-post retains a large vertical field and a significant poloidal flux

even after the field outside the centre-post decays to nearlyzero. This behaviour is very similar to that of a typical Ohmicsolenoid. The radial profile of the resulting loop voltage is alsosimilar, being constant with R when compared with linearlyincreasing with R for the PF coil-only start-up scheme. Shownin figure 9(c) is a two-dimensional plot of flux contours. Thecentre of the field null is located at R = 2.5 m and Z = 0.0 mfor this case.

In figure 10, the calculated breakdown contours (ET ·BT/B⊥ in V m−1) are depicted. As shown in the figure, the100 V m−1 contour takes a very large space (nearly ∼3 m2)inside the vacuum vessel and sustains for about 30 ms. Thisnull duration should be sufficiently long for the breakdown andinitial start-up.

6. Discussions and conclusions

In this paper, we presented two complementary inductively-based concepts to aid solenoid-free start-up for future ST andtokamak reactors. The ST configuration with a combinationof three types of out-board PF coils placed outside the vacuumvessel is shown to create a good quality field null region whileretaining a significant volt-second capability for current ramp-up. For NSST, a high quality multi-pole field null can becreated near R = 2.5 m while the nearest coil #3 is placed at

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R = 3.2 m with adequate NBI/diagnostic access. Sufficientpoloidal flux � as large as about 4–5 Wb is available forramping up the plasma current to a few MAs for the nextgeneration ST devices such as NSST without using an Ohmicsolenoid. The concept should scale well to larger devices sincethe amount of flux tends to go up as the square of the majorradius (� ∝ R2) and linear with the toroidal magnetic field.

Once high plasma current is established (�1 MA) to providesufficient plasma confinement it should be possible to use othermeans of non-inductive current drive such as the bootstrapover-drive and/or NBI/rf current drive to further ramp up tofull plasma current and maintain the current thus generated.

The PF coil system is relatively attractive from theengineering point of view. It consists of relatively simple

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circular coils placed outside the vacuum vessel so that the coilsystem can be made accessible. In addition, the maximummagnetic field at the coil is reasonable (∼15 T for coil #1) forthe NSST case generating about 5 Wb. Coil #1 is the higheststressed coil, and therefore it must be designed accordingly.Coil #2 should be compatible with the capability needed forthe vertical field required for the plasma equilibrium. Thetrim coil #3 is likely to be operated in feedback mode for fineradjustments. The concept provides sufficient flexibility in thecoil positions to accommodate the special needs of particulardevice configurations as several possible cases were shown.For a compact device such as CTF, one might consider theCase V configuration with about 1.8 m of vertical clearanceat the mid-plane to accommodate blanket modules. For amuch larger ST power plant (e.g. ARIES-ST), the access islikely to be adequate for all cases considered. The numberof coil sets can be increased to further improve the field nullconfiguration. The inherent limit of the flux value (volt-s)is likely to be imposed by the magnetic coil engineeringlimits and available power supplies. Since the present out-board Ohmic coils are inherently pulsed for a relatively shortduration, the coils are likely to be built with normal copperconductors perhaps cryogenically (nitrogen) cooled to reducethe power requirements. Through careful engineering design,it should be possible to further optimize the PF coil system tomatch the start-up requirements of a particular device.

The other concept utilizes the in-board-side conductingmaterial to store the magnetic flux which is initially chargedup by the out-board-side outer PF coils with currents in thesame polarity. For an ST, it is conceivable to utilize the centralTF conducting post for flux storage. The NSST (CTF) sizedevice can provide an additional 2–4 Wb with this method. TheARIES-ST like device would provide about 10–15 Wb. Largeraspect-ratio tokamak reactors can store larger (∼100 Wb)magnetic flux. The induced loop voltage is determined bythe flux decay rate which can be controlled to some extent bythe choice of material and conducting wall thickness whichdetermine the effective resistivity. Like the Ohmic solenoid,the stray field generated by the centre-post flux is relativelysmall which would make it suitable for solenoid-free plasmastart-up.

In these solenoid-free start-up concepts proposed, theactual available flux strongly depends on the tolerance tothe initial stray field. As shown in JT-60U and TST-2with strong ECH heating, if some level of stray fields canbe allowed, the available flux for these concepts can becorrespondingly increased. In addition to ECH, which hasbeen proved to be effective but somewhat expensive, it isworth investigating other means of pre-ionization includingplasma and/or ‘toroid’ injection to minimize the requiredLloyd parameter values. The plasma stability in the presenceof the eddy currents is an issue that will require furtherinvestigation. An accurate equilibrium calculation willgive the required amount of vertical and radial fields for

proper force balance. The presence of the nearby passivestabilizers should aid the vertical stability, and additional smallPF feedback coils can be used if necessary.

Acknowledgments

The authors would like to thank Drs. R. Goldston,R. Hawryluk, J. Menard and M. Peng for their valuablecomments and discussions. Thanks are also due to Drs.S. Jardin and C. Kessel for their valuable suggestions onnumerical techniques. This work was supported by KAISTand DoE Contract No. DE-AC02-76-CH0-3073.

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