V. Riccardo, T.C. Hender, P.J. Lomas, T. Bolzonella, P. de Vries, G.P. Maddisonand JET EFDA contributors

EFDA–JET–PR(03)62

Analysis of JET Halo Currents

.

Analysis of JET Halo Currents

V. Riccardo, T.C. Hender, P.J. Lomas, T. Bolzonella1, P. de Vries, G.P. Maddisonand JET-EFDA contributors*

EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK1Consorzio RFX, Associazione ENEA-EURATOM, I-35127 Padova, Italy

* See annex of J. Pamela et al, “Overview of Recent JET Results and Future Perspectives”,Fusion Energy 2000 (Proc. 18th Int. Conf. Sorrento, 2000), IAEA, Vienna (2001).

Preprint of Paper to be submitted for publication inPlasma Physics and Controlled Fusion

“This document is intended for publication in the open literature. It is made available on theunderstanding that it may not be further circulated and extracts or references may not be publishedprior to publication of the original when applicable, or without the consent of the Publications Officer,EFDA, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK.”

“Enquiries about Copyright and reproduction should be addressed to the Publications Officer, EFDA,Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK.”

1

ABSTRACT

The halo current detection system in JET was refurbished in 2001. The collected data confirm

previous results, obtained with a smaller number of sensors, and are consistent with the ITER

assumptions. Analysis of recent disruptions shows that local halo current density in JET is linked to

the average plasma current quench rate (the slower the disruption, the larger the local halo load),

rather than the plasma current. The largest local halo current densities are more likely to occur

when the equilibrium boundary safety factor is low and when it decreases to a critical value, close

to 1, during the disruption. The largest halo current fractions are found for the most vertically

unstable configurations (i.e. low ratio of resistive vessel time to vertical displacement growth time).

The information from the new pick-up coils and Rogowski coils and the only surviving old sensor

(a pick-up coil located outboard of the new system) provides an estimate of the size, and an improved

picture of the movement, of the halo/wall interaction region during disruptions.

1. INTRODUCTION

Plasma disruptions are sudden events, which lead to the complete loss of thermal and magnetic

energy [1]. Elongated plasma configurations can lose vertical stability leading to Vertical

Displacement Events (VDEs), and the plasma can contact the wall; when this happens part of the

plasma current (known as a halo current) can flow into the wall.

Disruptions, which give rise to the largest forces experienced by the vessel and the in-vessel

components, cannot be definitely avoided in the operation of tokamaks. Therefore an assessment of

expected worst-case disruption forces is essential in the design of a new tokamak [2]. The vessel

support system and the in-vessel components must be designed to a realistic estimate of the highest

stress expected, which typically occurs at disruptions. Electromagnetic loads arise from both toroidal

and poloidal currents flowing in the structure and interacting with magnetic fields. Toroidal currents

are typically induced in passive structure by plasma motion and plasma current decay during the

post-disruption current quench. Poloidal currents in the structures are largely due to halo currents.

In fact, while in the plasma part of its path, due to the low plasma pressure, the halo current is

almost parallel to the magnetic field lines, once in the conductive structures it is free to choose the

path with lowest impedance. Halo current is driven by the toroidal voltage induced by the core

current decay and by the poloidal voltage due to the change in enclosed toroidal field, and it is also

fed by plasma motion convecting core current into the halo. Many experiments have studied halo

currents [3, 4, 5 and 6]. How the JET data fit with data from other tokamaks, and how the JET data

are measured and processed is explained in section 2. The dependence on pre-disruption and

disruption quantities of the JET halo current is discussed in section 3. Section 4 analyses the halo-

wall interaction observed in JET.

2. OBSERVATION OF JET HALO CURRENT

Halo currents give rise to global vessel forces and local loads on in-vessel components. The average

poloidal halo current contributes to the axisymmetric vertical force on the vessel. The toroidal

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peaking factor, TPF, is indicative of the presence of an asymmetric load on the vessel (force long a

horizontal axis and/or torque about a horizontal axis), which in JET can be comparable to the vertical

load. The local halo current density is a determinant in the design of in-vessel components. The design

local halo current density can be determined from the product of the toroidal peaking factor and the halo

fraction, f, which is the ratio of the toroidally averaged poloidal halo current and the pre-disruption

plasma current. The TPF represents the degree of asymmetry of the halo current and it is defined as the

ratio of the maximum to the average poloidal halo current. The halo fraction and TPF are the quantities

typically used to determine design parameters for new machines, in particular for the vessel support

system and for in-vessel components. The design value of the product TPF times halo fraction, TPF•f,

for ITER-FDR [2] is normally 0.5 and 0.75 in extreme disruptions. The design value for ITER-FEAT [7]

is instead 0.58. These values have been extrapolated from empirical data, with trends not described well

by individual machine data [3-6] or by underlying theory. Therefore, studies in conditions (device size,

plasma shape, current and field) as close to those in ITER as possible are very important.

A good understanding of halo current requires reliable measurements. The technique employed

in JET is to estimate the poloidal halo current from the variation of toroidal field within the halo

current path outside the plasma. Originally JET had two toroidal field pick-up coils at the top and

two at the bottom of the vessel in locations set 1800 apart, and several local halo current density

probes in the outboard region of the vessel [8]. During the 2001 shutdown three Rogowski coils

and three toroidal field pick-up coils were installed at the inner upper part of the JET vessel [9],

together with the Improved Upper Inner Wall Protection (IUIWP) tiles. The present status of the

JET halo current sensors is summarised in Fig. 1.

The 2001 refurbishment allows more reliable measurements of the poloidal halo current in a

larger number of toroidal locations and therefore a better estimate of the halo fraction and toroidal

peaking factor. While with the two original sets of probes at 1800 the TPF for a n=1 mode could be

underestimated by 50%, with three probes at 900 it can only be underestimated only by 25%. The

phase where the saturated kink mode locks during disruptions is not fixed in JET [10], therefore the

worst TPF should be captured over a large number of events. Figure 2 shows that the TPF measured

by the IUIWP toroidal field pick-up coils in recent disruptions (labelled “2002+”) is not larger than

it used to be with only two probes (labelled “2001-“). While the old discharges were selected from

high current only events, the new discharges come from predominantly low current discharges. In

comparison with the older discharges, the recent ones have similar elongation and generally higher

triangularity. Figure 2 also contains the ITER reference design data for halo current [2] and some

JT-60U data [6]. The JET data are characterised by lower TPF values than most other machines,

even than JT-60U, where the TPF•f product is kept low because the halo fraction is low. The

uncertainty on the value of TPF for an n=1 asymmetry, due to the limited number of probes cannot

take the maximum value for JET at the level observed in other machines. In addition, the poloidal halo

current measured by all the toroidal field pick-up coils is always of the same sign. Therefore the asymmetry

has to be more localised than an n=1 and the error due to having a small number of probes is larger.

3

About 120 events are in the new database; these have been chosen because they have all the probes

working (since installation one has worked intermittently and one has recently failed). Figure 2 shows

that only one of these events has the product TPF•f higher than the present ITER design value; in

this case a low boundary safety factor and highly shaped plasma was made deliberately vertically

unstable. The next section clarifies how this extreme event is compatible with JET general halo

current trends.

3. HALO CURRENT AND (PRE-)DISRUPTION QUANTITIES

Analysis of links between pre-disruption quantities and the severity of the halo current in the

following disruption can help identifying regions of the operational space prone to the highest

electromechanical loads.

The plasma current quench rate has a strong influence on the amount and asymmetry of the

poloidal halo current, represented by the product TPF◊f. This is shown in Fig. 3, where the largest

TPF•f products occur when the plasma current quench rate is slow (<50 s-1). The plasma current

decay rate used in Fig. 3 is that measured for a 60% current decay, between 95% and 35% of the

pre-disruption plasma current, as suggested in [2]. Figure 3 also shows that preferentially at low

plasma current decay rate the minimum value of the cylindrical approximation of the boundary

safety factor [11] during the disruption decreases to values less than 1.5, and indeed all the events

with TPF•f larger than 0.2 have a qmin<1.5. The worst halo loads (large halo fraction and TPF) are

seen for the smallest values of the minimum boundary safety factor at the disruption. A similar,

although less strong, trend is seen also with respect to the pre-disruption boundary safety factor

[12], q95. Fig. 4 shows how the upper limit for the product of halo fraction and TPF decreases

as the pre-disruption q95 increases. Another pre-disruption parameter to have a strong influence

on the development of the vertical displacement event (if any) is βp=2µ0<p>/Bθ2, proportional to

the thermal energy content of the plasma. When the energy content is high (and so is βp), the

current quench rate tends to be fast [13], most likely due to stronger impurity influxes. The fast

plasma termination limits the extent of the vertical displacement and even more strongly the drop

in the boundary safety factor, often preventing asymmetries to be generated [3]. However, fast

terminations are more likely to lead to the generation of runaway electrons.

The Ip/q95 scaling proposed for the poloidal halo current in COMPASS [14] and supported by

Alcator C-mode data [15, 4], Ih,polmax ≤ ξξ/(1-ξ)/(1-λ) Ip0/q95, (where ξ=τp/τhalo is the ratio of the

effective L/R resistive time of the plasma and the halo respectively) is compatible with the JET

halo current data too, as shown in Fig. 5. The geometry coefficient that fits the JET data best is 1.2,

consistent with having a small (~1/6) fraction, l, of the total poloidal perimeter, where the halo

current flows in the conducting wall rather than on the open magnetic surfaces [14]. This scaling

suggests that amelioration techniques aimed at cooling the halo region would decrease the peak

halo current and therefore the electromechanical loads on the torus and the in-vessel components.

The vertical growth rate can be difficult to determine due to the complexity of the event. In the

following a simplified version of analytical vertical displacement growth rate, based on pre-disruption

4

quantities, will be discussed [16, 17]. The approximate formula used for the vertical growth time,

τz, and its inverse, the vertical growth rate, γz, is the following-

( )

( )

−

−

+== 1

1

112

3

a

dk

k

shell

shellz

z τγ

τ

,

where τshell is the shell penetration time (5 ms for JET), dshell is a characteristic shell dimension

(sum of the torus minor axes, 3.64 m for JET) and a and k are respectively the plasma minor radius

and elongation. In a number of controlled experiments the simplified analytical approximation of

the vertical growth rate has been found in good agreement with the measurements, especially for

growth rates higher than 150 s-1, as Fig. 7 shows. From this experimental comparison, the error

bars used in Fig. 7 have been derived. The large horizontal spread is due to the variety of disruptive

plasmas included in the database (high and low elongation, large and small plasma minor radius).

Figure 7 shows an upper limit to the halo fraction, which drops as the normalised vertical growth

time increases. This is consistent with the observed proportionality between disruption vertical

force measured at the vessel supports and initial plasma displacement vertical growth rate, since

the poloidal halo current is one of the main contributors to the force applied to the JET vacuum

vessel.

4. HALO-WALL INTERACTION

The set of halo sensors installed at the IUIWP tiles represents a first attempt at measuring local halo

current using Rogowski coils in JET. This type of sensor will be extensively used in future enhancements

[18]. The scope of the halo current sensor enhancements is to provide more detailed information on the

dynamics of the halo-wall interaction in the upper part of the vessel, away from the divertor, complementary

to refined measurement systems installed in other tokamaks’ divertors [5, 6, 19].

In the present diagnostic set-up, each Rogowski coil fitted behind a pair of IUIWP tiles measures

the halo current collected by these two tiles. Since the poloidal width of these tiles is much larger

than as the poloidal extent of the halo footprint (e.g. as estimated in [20]), only the minimum halo

current density along the field line can be determined. Instead the enhanced diagnostic set-up will

include 4 arrays (each at a fixed toroidal angle and located at 900) with up to 8 Rogowski coils.

Each coil is fitted at the back of a tile of the dump plate. The exposed area of the dump plate tiles

varies between 1/6 and 1/4 of the area of each of the IUIWP tiles, and the poloidal extent of these

tiles is comparable or smaller that the size of the halo footprint. Therefore the enhanced diagnostic

sensor will be able to provide a poloidal map of the perpendicular halo current density. This will

shade light on the size and movement of the halo footprint on a smooth and open target, besides

giving a direct measure of the perpendicular halo current density, which is the basic input to the

determination of halo current loads on in-vessel components.

The poloidal halo current is estimated from the current measured by the Rogowski coils assuming

that each pair of tiles collects ~1/48 of both the poloidal and the toroidal halo current. Often the

5

whole halo footprint is contained on the IUIWP tiles, due to the relative poloidal extent. In addition,

the toroidal component of the halo current, which enters the IUIWP subassembly form the exposed

side of this discrete protection, is roughly equal to the poloidal component times the cylindrical

approximation [11] boundary safety factor (qb). Therefore, to obtain the poloidal halo current, the

average measure of the current collected by the instrumented pairs of IUIWP tiles is multiplied by

the number of the IUIWP supports and divided by (1+qb), since the IUIWP tiles collect current on

surfaces facing the poloidal and the toroidal directions.

The traces of poloidal halo current estimated from the current collected by pairs of IUIWP tiles

and poloidal halo current as measured at the IUIWP pick-up coils and at one of the old dump plate

pick-up coil are shown in Fig. 8. The poloidal halo current estimated from the IUIWP-collected

current peaks earlier than the current measured by the toroidal field pick-up coils. A plausible

explanation for the different timing of the peaks is that the plasma moves along the vessel inner

wall. This is also consistent with the plasma axis displacement (inwards and upwards) during the

disruption. Initially, Fig. 9a, the IUIWP tiles collect halo current, but this current does not go around

the pick-up coil, as it has to go to the wall through the support located below the pick-up coil. When

the plasma is higher, Fig. 9b, the halo current needs to go around the pick-up coil to close its

poloidal path. At this stage, the current collected by the IUIWP tiles is less; as the outboard footprint

moves to the dump plate and later the inboard footprint approached the bottom of the IUIWP. The

movement of the interaction area also helps explaining why the dump plate pick-up coil systematically

measures less current than the IUIWP pick-up coils. In fact, also in the later stages of the disruption, the

part of the current that goes around the IUIWP coils does not encircle the coil behind the dump plate.

According to the combined observations of the IUIWP Rogowski and pick-coils and the dump

plate pick-up coil it seems that the plasma first moves inboard without touching the upper dump

plate and then it slides upwards. Initially the main current path is from the IUIWP tiles down to the

inner wall guard limiter. Later the halo current source (for the vessel) moves to the dump plate and

the current sink (return to the plasma) moves up, possibly past the IUIWP tiles.

CONCLUSIONS.

The JET poloidal halo current measured with the old and the new sensors is typically less than 40%

of the pre-disruption plasma current, with the TPF smaller than 2. This is in line with the ITER

design assumptions and consistent with less demanding halo current design criteria arising from

large machines, like JT-60U [6] and JET.

In JET large poloidal halo currents only occur in relatively slow disruptions. In addition, strongly

asymmetric events are observed only when the cylindrical approximation of the boundary safety

factor decreases below a critical value, close to 1, during the disruption. However, not only the

safety factor during the disruption, but also the pre-disruption q95 is closely linked to the amount

and asymmetry of the halo current: the highest values of the product of halo current fraction and

toroidal peaking factor are found only at the lowest pre-disruption q95. Among the contributors to

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a faster plasma current decay, and hence less demanding halo current loads, is a high pre-disruption

plasma thermal energy content. Apparently high βp plasmas interact more strongly with the wall at

the beginning of the disruption, maybe as a consequence of a large inboard displacement, and are

subjected to a larger influx of impurities, which makes the plasma current decay fast, preventing

any substantial plasma vertical displacement.

The poloidal halo current is one of the main contributors to the force acting on the torus during

JET disruptions. As the worst event vertical force is nearly proportional to the initial vertical growth

rate, it is natural to find that the halo current fraction has an upper limit scaling with the normalised

vertical instability growth time. The inverse dependence of the halo fraction on the normalised

vertical growth time suggests that a closely fitting conductive shell, or a passive plate, is very

important to be able to cope with highly shaped plasmas.

The ITER design guideline on halo current has been validated in very relevant experimental

conditions in terms of size, plasma shape and plasma/wall match. Trends in dimensionless pre-disruption

parameters (boundary safety factor and normalised vertical growth time) confirm the halo current

design assumption used for ITER.

ACKNOWLEDGEMENTS

Work performed under the European Fusion Development Agreement (EFDA) and partly funded

by EURATOM and the UK Engineering and Physical Sciences Research Council. The lead author

thanks Dr Sugihara for discussions on the VDE growth rate.

REFERENCES

[1]. S. Putvinski et al., Plasma Physics and Controlled Fusion 39 (1997) B157

[2]. ITER Physics Basis 1999 Nucl. Fusion 39 Chapter 3 Section 4

[3]. D. Kellman et al., in Fusion Energy 1996 (Proc. 16th Int. Conf. Montreal, 1996), Vol.1, Vienna

(1997) 739

[4]. R. Granetz, Disruption halo currents with C-Mod’s new divertor, APS-DPP, Orlando (2002)

[5]. G. Pautasso et al., 28th EPS Conf. on Plasma Physics and Controlled Fusion, Madeira (2001)

P-1.005

[6]. Y. Neyetani, Characteristics of halo currents in JT-60U, Nucl. Fusion 39 (1999) 559

[7]. ITER Technical Basis, GA0 FDR 1 01-07-13 R1.0 (July 2001) Chapter 2.2

[8]. P. Andrew et al., Proc. 17th IEEE/NPSS Symposium on Fusion Engineering (1997) 108

[9]. V. Riccardo et al., Refurbishment of the JET halo current diagnostics, Fusion Engineering and

Design 66-68 (2003) 817

[10]. V. Riccardo, Asymmetric Vertical Displacement Events in JET, PhD thesis, Imperial College,

London (1998)

[11]. J.P. Christiansen et al., Journal of Computational Physics 73 (1987) 85-106

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[12]. D.P. O’Brien et al., Nuclear Fusion 32 (1992) 1351-1360

[13]. V. Riccardo, Fusion Science and Technology 43 (2003) 493

[14]. P. Knight et al., Nuclear Fusion 40 (2000) 325-337

[15]. R. Granetz et al., Nuclear Fusion 36 (1996) 545

[16]. J.A. Wesson, Tokamaks, 2nd edition, page 320, Oxford, Clarendon Press, 1997

[17]. P.J. Lomas, private communication, May 2001

[18]. N. Pomaro et al., Review of Scientific Instruments 74 (2003) 1567

[19]. T. Evans et al., J. Nucl. Mater. 241–243 (1997) 606

[20]. P. Andrew et al., Proc. 16th Symposium on Fusion Engineering, Champaign (1995) 770

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Figure 1: Poloidal cross section of the JET machineshowing the status of the old and the new halo currentmeasurement devices (those crossed have failed).

Figure 2: The halo current data base used for the ITERPhysics Basis [ref. 2, fig. 64, chapter 3] overlapped withthe recent JET and JT-60U [6] data.

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Figure 3: In spontaneous JET disruptions, the largest halocurrent densities (proportional to the product of halofraction and TPF) are found in slow events.

Figure 4: The product of halo fraction and toroidalpeaking factor plotted versus the pre-disruption boundarysafety factor; the darker dots represent dischargesdeliberate VDEs.

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ax /

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Figure 5: The maximum of the toroidally averaged halocurrent plotted versus the ratio between pre-disruptionplasma current and boundary safety factor; the darkerdots represent discharges deliberate VDEs.

Figure 6: Measured and approximate vertical growth ratein controlled experiments.

Figure 7: The halo fraction plotted versus the normalisedanalytical vertical growth time (i.e. the ratio of the verticalgrowth time and the vessel resistive time), which isdisplayed with its estimated accuracy; the darker dotsrepresent discharges deliberate VDEs.

Figure 8: Plasma vertical position (zp3 and zp7) in twoopposite toroidal locations (oct. 3 and 7) for pulse 56817plotted together with the poloidal halo current estimatedfrom the current collected by a pair of IUIWP tiles and thepoloidal halo current measured by the toroidal field pick-up coil behind the IUIWP (Ih3, Ih5 and Ih7 at oct. 3, 5 and 7respectively) and behind the dump plate (Io3 at oct. 3)

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Figure 9: Sketch of the confined plasma interacting with the inner and upper wall in theearly (a) and late (b) stages an upward VDE.

(a) (b)

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